common core state standards alignment - college...

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Common Core State Standards AlignmentAdvanced Placement®

By Beth Hart, Elaine Carman, Danielle Luisier and Natasha Vasavada

REsEaRCH REpoRt 2011-8

ConneCFor further information, visit www.collegeboard.org/research

Beth Hart is the director of English language arts curriculum and standards at the College Board.

Elaine Carman is the director of mathematics curriculum and standards at the College Board.

Danielle Luisier is the director of standards and curriculum alignment services at the College Board.

Natasha Vasavada is the executive director of standards and curriculum alignment services at the College Board.

About the College Board

The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the College Board was created to expand access to higher education. Today, the membership association is made up of more than 5,900 of the world’s leading educational institutions and is dedicated to promoting excellence and equity in education. Each year, the College Board helps more than seven million students prepare for a successful transition to college through programs and services in college readiness and college success — including the SAT® and the Advanced Placement Program®. The organization also serves the education community through research and advocacy on behalf of students, educators and schools.

© 2011 The College Board. College Board, Advanced Placement Program, AP, SAT and the acorn logo are registered trademarks of the College Board. College Board Standards for College Success, inspiring minds and ReadiStep are trademarks owned by the College Board. PSAT/NMSQT is a registered trademark of the College Board and National Merit Scholarship Corporation. All other products and services may be trademarks of their respective owners. Printed in the United States of America.

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ContentsIntroduction.............................................................................................................. 2

Content.for.Comparison........................................................................................... 3

Methodology............................................................................................................. 4

Summary.of.the.Alignment.Between.the.Common.Core.State.Standards..and.AP.English.and.Mathematics.Courses........................................................... 7

Demonstration.of.Alignment.Methodology.Table................................................. 9

References............................................................................................................... 13

Appendixes

Appendix.A:.AP.English.—.Common.Core.State.Standards.Side-by-Side.Alignment.Table............................................................................................. 15

Appendix.B:.AP.Calculus,.AP.Statistics,.and.AP.Computer.Science.A.—.Common.Core.State.Standards.Side-by-Side.Alignment.Table................ 41

2 College Board Research Reports

Common Core State Standards Alignment

How the Common Core State Standards Prepare Students to Engage in AP® CoursesIntroduction

The College Board has been a strong advocate for and played an active role in the development of the Common Core State Standards. As part of this collaboration, the College Board helped draft the standards and helped shape the initiative by providing executive guidance on the Common Core Advisory Committee. The goal of the Common Core State Standards — to establish a common set of rigorous expectations to prepare students for college and career readiness — strongly reflects the guiding mission and values of the College Board, as well as our programs and services.

Prior to the development of these Common Core State Standards, the College Board established blue ribbon panels in English language arts, mathematics and statistics, and science to define the skills and knowledge students must develop and master to succeed in college and the workforce in the 21st century. This effort resulted in the development of the College Board Standards for College Success™. These standards for English Language Arts, Mathematics and Statistics, and Science were based on empirical research conducted by the University of Oregon’s Center for Educational Policy Research in collaboration with the Association of American Universities. The standards are benchmarked against the Advanced Placement Program® (AP®) as well as national and international frameworks, including NAEP, TIMSS, and PISA (Wiley, Wyatt, & Camara, 2010). These standards were an important resource in the development of the Common Core State Standards because they were based and benchmarked on empirical evidence related to college success.

The College Board recognizes that defining clear, consistent, and rigorous standards is just the start of ensuring educational improvement. The College Board actively works with states and districts as they build their Common Core implementation plans, and we continue to provide guidance and technical assistance in the areas of:

• comprehensive alignment services;

• benchmarking standards, assessments, and performance level indicators against college outcomes;

• Common Core implementation plan development; and

• professional development.

In support of near-term goals, the College Board has developed this alignment study to document the existing correspondence between the Common Core State Standards and selected AP courses.

This report describes how the Common Core State Standards can prepare students to engage in the following courses: AP English Literature and Composition, AP English Language and Composition, AP Calculus AB, AP Calculus BC, AP Statistics, and AP Computer Science A. As new curricula and assessments emerge and existing curricula and assessments are enhanced, the College Board will conduct additional studies to understand the alignment of other forms of curricula and assessments that may be administered in support of the Common Core State Standards.

3College Board Research Reports


Content for ComparisonCommon.Core.State.Standards

The Common Core State Standards articulate the knowledge and skills students need to be ready to succeed in college and careers. They were designed to be (1) anchored in research and evidence; (2) aligned to college and workplace expectations; (3) rigorous, clear, and consistent; and (4) reflective of best practices in international frameworks. The standards span kindergarten through 12th grade.

The.Advanced.Placement.Program®

AP is a rigorous academic program built on the commitment, passion, and hard work of students and educators from both secondary schools and higher education. With more than 30 courses in a wide variety of subject areas, AP provides willing and academically prepared high school students with the opportunity to study and learn at the college level.

Each AP course is modeled upon a comparable college course, and college and university faculty play a vital role in ensuring that AP courses align with college-level standards. For example, through the AP Course Audit, AP teachers submit their syllabi for review and approval by college faculty. Only courses using syllabi that meet or exceed the college-level curricular and resource requirements for each AP course are authorized to carry the “AP” label.

AP courses culminate in a suite of college-level assessments developed and scored by college and university faculty members as well as experienced AP teachers. AP Exams are an essential part of the AP experience, enabling students to demonstrate their mastery of college-level course work. Strong performance on AP Exams is rewarded by colleges and universities worldwide. More than 90 percent of four-year colleges and universities in the United States grant students credit, placement, or both on the basis of successful AP Exam scores.

Although the Common Core State Standards create a strong foundation for many AP courses, College Board content teams focused this study within the English language arts and mathematics disciplines. The following AP courses were considered within the scope of this study:

AP.English.Literature.and.CompositionAn AP English Literature and Composition course engages students in the careful reading and critical analysis of imaginative literature. As they read, students consider a work’s structure, style, and themes, as well as specific elements such as the use of figurative language, imagery, symbolism, and tone. Such reading should be accompanied by thoughtful discussion and writing about those books in the company of one’s fellow students.

AP.English.Language.and.CompositionAn AP course in English Language and Composition engages students in becoming

AP.provides.willing.

and.academically.

prepared.high.school.

students.with.the.

opportunity.to.study.

and.learn.at.the.

college.level.



skilled readers of prose written in a variety of rhetorical contexts, and in becoming skilled writers who compose for a variety of purposes. Both their writing and their reading should make students aware of the interactions among a writer’s purposes, audience expectations, and subjects, as well as the way genre conventions and the resources of language contribute to effectiveness in writing.

AP.Calculus.AB.and.AP.Calculus.BCAP Calculus AB and AP Calculus BC are primarily concerned with developing the students’ understanding of the concepts of calculus and providing experience with its methods and applications. The courses emphasize a multi-representational approach to calculus, with concepts, results, and problems expressed graphically, numerically, analytically, and verbally. Calculus BC is a full-year course in the calculus of functions of a single variable. It includes all topics taught in Calculus AB plus additional topics, but both courses are intended to be challenging and demanding; they require a similar depth of understanding of common topics.

AP.StatisticsAn AP course in Statistics introduces students to the major tools and concepts for collecting, representing, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, sampling and experimentation, anticipating patterns, and statistical inference.

AP.Computer.Science.AAn AP course in Computer Science A emphasizes object-oriented programming methodology with a concentration on problem solving and algorithm development. It includes the study of data structures, design, and abstraction. A large part of the course is built around the development of computer programs that correctly solve a given problem, while developing the use of logic and formal methods of programming.

MethodologyResearchers and organizations have developed different methodologies and approaches to align standards (Brown & Conley, 2007; Rothman, 2003; Webb, 1997, 1999; Porter, 2002; Achieve, 2007, 2010; College Board, 2008, 2010; Blank, 2007), and the alignment approaches vary in terms of rigor and accuracy. The College Board employs rigorous alignment methodologies as it compares standards, curricula, and assessment frameworks and consistently adheres to the following alignment principles, which are recognized as best practices by thought leaders in the field:

• Deep and careful consideration must be given to the full intent and scope of each standards statement, with attention to both the content and skill components of the standard.

• Alignments must be made to the most specific component or grain size of the standard.

• The course materials utilized in the alignment study must clearly and explicitly outline the course objectives and expected student performances.

• Consideration and attention must be given to both content and cognitive demand (rigor) when developing alignments between standards and course materials.

These alignment principles are apparent in the alignment methodologies developed by



Norman Webb and Andrew Porter, as well as in the nationally recognized work from organizations such as Achieve, WestEd, the Education Policy Improvement Center (EPIC), the Center for Assessment, and the Surveys of Enacted Curriculum (SEC) Project led by the Council of Chief State School Officers in partnership with the University of Wisconsin.

For this study, the College Board applied these alignment principles to compare the Common Core State Standards to selected AP courses. The comparison is nuanced in that the Common Core State Standards are designed to articulate the knowledge and skills students need to be ready to succeed in college and careers, and AP courses and exams are designed to represent the level of a first-year college course. In light of this distinction, alignments between the Common Core State Standards and AP courses should not be interpreted as linkages of content or skills at the same level of rigor or challenge, but as areas where there is an identifiable bridge from one framework to another — a link from the Common Core State Standards to a specific AP course. Similarly, “gaps” should not be interpreted as Common Core State Standards that do not prepare students for AP, but as valuable, general content that contributes to a student’s preparedness as a whole.

The purpose of this alignment study is to identify the Common Core State Standards that prepare students to engage in selected AP courses. Correlations between the Common Core State Standards and the AP courses are indicated in the alignment tables (appendixes A and B) by an “X” next to the Common Core State Standard under the appropriate course column.

In order for a Common Core State Standard to be considered aligned to an AP course, evidence of the extension of that Common Core State Standard must be cited from at least one document from the collection of AP course materials. Evidence of the extension of a Common Core State Standard for English Language Arts will appear in the AP English courses as content and skills similar to those of the Common Core State Standards but in the differing context of first-year college-level coursework. The relationship between a Common Core State Standard for Mathematics and the evidence of the extension in the AP Calculus courses, AP Statistics, and AP Computer Science A will appear as more of a traditional prerequisite relationship between the Common Core State Standards and the AP courses.

For further explanation of the relationship between an aligned Common Core State Standard and an AP course, see the Demonstration of Alignment Methodology table.

The.comparison.

is.nuanced.in.that.

the.Common.Core.

State.Standards.are.

designed.to.articulate.

the.knowledge.and.

skills.students.need.to.

be.ready.to.succeed.

in.college.and.careers,.

and.AP.courses.and.

exams.are.designed.

to.represent.the.level.

of.a.first-year.college.

course.



AP.Course.MaterialsThe following AP course materials informed this study:

• AP Course Descriptions–Detailed descriptions of the AP courses and exams.

• AP Curricular Requirements–The set of curricular and resource expectations that college faculty nationwide have established for college-level courses.

• AP Teacher’s Guides–Additional information on the AP course, exam, curricular requirements, available resources, and sample lessons and syllabi.

• AP Syllabus Development Guides–Subject-specific documents that contain multiple samples of evidence for each requirement, illustrating the variety of ways curricular requirements can be met in a syllabus.

• AP Released Exams–Documents that include an AP Exam that was once administered as a live exam and supporting information such as answer keys and statistical information about student performance when the exam was administered.

• AP Exam Specifications–Statistical and content-based blueprints for the design of AP Exams.

This collection of resources presents a detailed view of the content knowledge and skills students should master upon completion of an AP course.

The College Board aligned the AP English courses, the AP Calculus courses, AP Statistics, and AP Computer Science A to the following Common Core State Standards grade levels and strands:

AP.English.Literature.and.AP.English.Language:Both AP English Literature and AP English Language were aligned to the Common Core State Standards for English Language Arts grade bands 9–10 and 11–12, as well as to the College and Career Readiness Anchor Standards1 (Anchor Standards).

All strands of the Common Core State Standards for English Language Arts were considered for this alignment study (i.e., all Anchor Standards, Reading Standards for Literature, Reading Standards for Informational Text, Writing Standards, Speaking and Listening Standards, and Language Standards/Progressive Skills)2.

AP.Calculus,.AP.Statistics,.and.AP.Computer.Science.A:AP Calculus AB, AP Calculus BC, AP Statistics, and AP Computer Science A were aligned to the Common Core State Standards for Mathematics grade 6 through high school, as well as to the Standards for Mathematical Practice. Middle school mathematics standards were included in this alignment study because content within the Common Core State Standards at the middle school grade levels had been traditionally identified within high school-level coursework in most state standards. In addition, in order to accurately demonstrate the body of prerequisite knowledge and skills required to be prepared for an AP mathematics courses, it was necessary to include the full middle school and high school Common Core State Standards.

1. The College and Career Readiness Anchor Standards define general literacy expectations and are meant to be considered in tandem with the Common Core State Standards high school grade bands.

2. The Standards for Literacy in History/Social Studies, Science, and Technical Subjects were not included within the scope of this alignment study. These literacy standards are designed to inform literacy instruction across the disciplines and so would not be appropriate for an alignment to the AP English courses.



It is important to note that the intent of the Common Core State Standards is to provide focused standards that all students should meet in order to be college and career ready. Additional mathematics content that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by a (+) within the Common Core State Standards for Mathematics and the alignment table.

Summary of the Alignment Between the Common Core State Standards and AP English and Mathematics CoursesGiven the nature of the alignment between the Common Core State Standards and AP courses, it is more appropriate to discuss the degrees of alignment in terms of concentration instead of strength of coverage. As expected, the highest concentration of alignment between the Common Core State Standards and AP courses occurs within the strand most specific to the AP course (e.g., the highest concentration of alignment between the Common Core State Standards and AP English Language occurs within the Reading Standards for Informational Text). Overall, the alignment indicates that a student following a curriculum based on the Common Core State Standards would be well prepared for a number of AP courses.

AP.English.Literature.and.CompositionThere is a high concentration of alignment between the Common Core State Standards for English Language Arts and AP English Literature, specifically in the areas of the Reading Anchor Standards, the Reading Standards for Literature at grade bands 9–10 and 11–12, the Writing Anchor Standards, the Writing Standards at grade bands 9–10 and 11–12, the Language Anchor Standards, and the Language Standards and Progressive Skills at grade bands 9–10 and 11–12. The few Common Core State Standards in these strands that do not align to AP English Literature should not be considered superfluous. Some standards, such as those that reference comparing artistic media, will enhance a student’s preparation for AP but are not directly evidenced in the AP materials.

The scarcity of alignment between the Reading Standards for Informational Text and AP English Literature is to be expected. While informational text may be useful for students conducting a critical analysis of fiction, the focus of AP English Literature is decidedly imaginative literature. Similarly, there is less frequent alignment between AP English Literature and the groups of Common Core State Standards in Writing and Language that address the more specific elements of research and the use of reference materials. There is also a lower concentration of alignment between the Speaking and Listening Standards and AP English Literature. This limited alignment should not be interpreted to mean that these standards do not contribute to a student’s preparation for AP. Speaking and listening

Overall,.the.alignment.

indicates.that.a.

student.following.a.

curriculum.based.on.

the.Common.Core.

State.Standards.would.

be.well.prepared.for.a.

number.of.AP.courses.



skills, such as those addressed in the Common Core State Standards, are expected to be mastered by students prior to their entering an AP course and so are not emphasized in the AP English Course Description. In addition, these skills, typically evaluated through classroom observation, are unlikely to appear in materials related to assessment.

AP.English.Language.and.CompositionThe most concentrated alignment between the Common Core State Standards for English Language Arts and AP English Language occurs in the areas of the Reading Anchor Standards and the Reading Standards for Informational Text at grade bands 9–10 and 11–12. In addition, there is a high concentration of alignment in the areas of the Writing Anchor Standards, the Writing Standards at grade bands 9–10 and 11–12, the Language Anchor Standards, and the Language Standards and Progressive Skills at grade bands 9–10 and 11–12. Because the AP English Course Description notes that fiction and poetry can have a place in the AP English Language course, there is also significant alignment between the Reading Standards for Literature and AP English Language.

There is limited alignment between the Speaking and Listening Standards and AP English Language. Much like the relationship between the Speaking and Listening Standards and AP English Literature, speaking and listening skills are valuable to a student entering AP English Language; however, these skills are considered prerequisite and best measured through classroom observation. For these reasons, speaking and listening skills are not emphasized as part of the AP English Course Description or exam materials, but they are evident within AP classroom practice.

AP.Calculus.AB.and.AP.Calculus.BCThe Common Core State Standards for Mathematics contain additional standards, identified by a (+), to indicate concepts linked to more advanced work in mathematics, work that may lead to a course such as AP Calculus. A majority of these “+” standards were linked to AP Calculus AB and AP Calculus BC as prerequisite skills, which illustrates how AP Calculus is part of a logical progression in an advanced mathematics course plan.

There is a high concentration of alignment between the Common Core State Standards for Mathematics at the grade 6 through high school level within the Standards for Mathematical Practice as well as in the conceptual categories of Number and Quantity, Algebra, Functions, and Geometry. As anticipated, a less concentrated alignment to the Common Core State Standards at the grade 6 through high school level occurs in the conceptual category of Statistics and Probability. Standards that align to AP Calculus BC but not to AP Calculus AB are those standards that provide support for the study of content unique to AP Calculus BC such as polar and vector functions.

AP.StatisticsAP Statistics should also be viewed as part of a logical progression in an advanced mathematics course plan based upon the Common Core State Standards. There is a high concentration of alignment between the Common Core State Standards for Mathematics at the grade 6 through high school level and AP Statistics within the Standards for Mathematical Practice as well as in the conceptual categories of Statistics and Probability, Number and Quantity, Algebra, and Functions. While the alignment to the Common Core State Standards at the grade 6 through high school level is less concentrated in the conceptual category of Geometry, it is important to understand that the AP Statistics course is considered an option for any secondary school student who has successfully completed a second course in algebra. Teachers and curriculum developers should not interpret a less concentrated alignment in conceptual categories to mean that there is no benefit to mastering those



uncorrelated standards prior to taking an AP Statistics course. Those skills will enhance the student’s mathematical abilities and afford the student a more rounded opportunity for success in AP Statistics.

AP.Computer.Science.AAP Computer Science A aligns to the Common Core State Standards for Mathematics in a less concentrated manner. As stated within the AP Computer Science A documents, the prerequisite skills needed to be successful in an AP Computer Science A course include knowledge of basic algebra and functions as well as problem-solving skills. Concentration of alignment to the Common Core State Standards for Mathematics at the grade 6 through high school level occurs primarily within the Standards for Mathematical Practice and within the conceptual categories of Algebra and Number and Quantity. A less concentrated alignment to the Common Core State Standards is evident within the conceptual categories of Functions and Geometry.

Despite the lower concentration of alignment in some conceptual categories, it can be concluded that the Common Core State Standards for Mathematics effectively prepare students to participate in AP Computer Science A. Students learning the mathematics of the Common Core State Standards will have experienced mathematical content and skills that go beyond the minimum requirements of the mathematics skills needed to be prepared to take the AP Computer Science A course. Teachers and curriculum developers should not interpret a lack of correlation to mean that there is no benefit to mastering the uncorrelated standards prior to taking an AP Computer Science A course. Those skills will enhance the student’s mathematical abilities and afford the student a more rounded opportunity for success in AP Computer Science A.

Demonstration of Alignment Methodology TableThis table illustrates the methodology used in the alignment study by highlighting examples of the relationship between the Common Core State Standards and AP courses. In order for a Common Core State Standard to be considered aligned to an AP course, evidence of the extension of that Common Core State Standard must be cited from least one of the documents from the collection of AP course materials. The full alignment tables (appendixes A and B) demonstrate a macroscopic view of this methodology.

AP Course Common Core State Standard Evidence of Extension into APAP English Literature

Demonstrate.knowledge.of.eighteenth-,.nineteenth-.and.early.twentieth-century.foundational.works.of.American.literature,.including.how.two.or.more.texts.from.the.same.period.treat.similar.themes.or.topics..(RL.11-12.9)

By.the.time.the.student.completes.AP.English.Literature.and.Composition,.she.or.he.will.have.studied.during.high.school.literature.from.both.British.and.American.writers,.as.well.as.works.written.in.several.genres.from.the.sixteenth.century.to.contemporary.times..The.works.selected.for.the.course.should.require.careful,.deliberate.reading.that.yields.multiple.meanings..(AP.English.Literature.and.Composition:.Curricular.Requirements)

Write.arguments.to.support.claims.in.an.analysis.of.substantive.topics.or.texts.using.valid.reasoning.and.relevant.and.sufficient.evidence..(W.CCR.1)

Writing.is.an.integral.part.of.the.AP.English.Literature.and.Composition.course.and.exam..Writing.assignments.focus.on.the.critical.analysis.of.literature.and.include.expository,.analytical.and.argumentative.essays..(AP.English.Course.Description)



AP Course Common Core State Standard Evidence of Extension into APAP English Language

Gather.relevant.information.from.multiple.print.and.digital.sources,.assess.the.credibility.and.accuracy.of.each.source,.and.integrate.the.information.while.avoiding.plagiarism..(W.CCR.8)

The.course.teaches.research.skills,.and.in.particular,.the.ability.to.evaluate,.use.and.cite.primary.and.secondary.sources..The.course.assigns.projects.such.as.the.researched.argument.paper,.which.goes.beyond.the.parameters.of.a.traditional.research.paper.by.asking.students.to.present.an.argument.of.their.own.that.includes.the.analysis.and.synthesis.of.ideas.from.an.array.of.sources..(AP.English.Language.and.Composition:.Curricular.Requirements)

Demonstrate.command.of.the.conventions.of.standard.English.grammar.and.usage.when.writing.or.speaking..(L.CCR.1)

The.intense.concentration.on.language.use.in.the.course.enhances.students’.ability.to.use.grammatical.conventions.appropriately.and.to.develop.stylistic.maturity.in.their.prose..(AP.English.Course.Description)

AP Calculus AB

Understand the relationship between zeros and factors of polynomials.Identify.zeros.of.polynomials.when.suitable.factorizations.are.available,.and.use.the.zeros.to.construct.a.rough.graph.of.the.function.defined.by.the.polynomial..(A-APR.3)

Students.enrolled.in.an.AP.Calculus.AB.course.will.study.limits.of.functions.and.will.develop.an.intuitive.understanding.of.the.limiting.process,.the.ability.to.calculate.limits.using.algebra,.and.estimate.limits.from.graphs.or.tables.of.data..(AP.Calculus.Course.Description)

AP Calculus BC

Represent and model with vector quantities.Solve.problems.involving.velocity.and.other.quantities.that.can.be.represented.by.vectors..(N-VM.3)

Students.enrolled.in.an.AP.Calculus.BC.course.will.study.the.applications.of.derivatives..Students.will.analyze.planar.curves.given.in.parametric.form,.polar.form.and.vector.form,.including.velocity.and.acceleration..(AP.Calculus.Course.Description)

AP Calculus AB & AP Calculus BC

Use appropriate tools strategically.Mathematically.proficient.students.consider.the.available.tools.when.solving.a.mathematical.problem..These.tools.might.include.….a.calculator,.a.spreadsheet,.a.computer.algebra.system,.a.statistical.package,.or.dynamic.geometry.software..Proficient.students.….make.sound.decisions.about.when.each.of.these.tools.might.be.helpful,.recognizing.both.the.insight.to.be.gained.and.their.limitations..….They.are.able.to.use.technological.tools.to.explore.and.deepen.their.understanding.of.concepts..(MP.5)

Students.enrolled.in.an.AP.Calculus.course.will.study.the.analysis.of.graphs..With.the.aid.of.technology,.graphs.of.functions.are.often.easy.to.produce..The.emphasis.is.on.the.interplay.between.the.geometric.and.analytic.information.and.on.the.use.of.calculus.both.to.predict.and.to.explain.the.observed.local.and.global.behavior.of.a.function..(AP.Calculus.Course.Description)

AP Statistics Make inferences and justify conclusions from sample surveys, experiments, and observational studies.Use.data.from.a.sample.survey.to.estimate.a.population.mean.or.proportion;.develop.a.margin.of.error.through.the.use.of.simulation.models.for.random.sampling..(S-IC.4)

Students.enrolled.in.an.AP.statistics.course.will.study.four.major.themes,.one.of.which.is.exploring.data..Exploratory.analysis.of.data.makes.use.of.graphical.and.numerical.techniques.to.study.patterns.and.departures.from.patterns..Emphasis.is.placed.on.interpreting.information.from.graphical.and.numerical.displays.and.summaries..This.includes.constructing.and.interpreting.graphical.displays.of.distributions.of.univariate.data.(dot.plot,.stem.plot,.histogram,.cumulative.frequency.plot)..Students.will.study.center.and.spread,.clusters.and.gaps,.outliers.and.other.unusual.features,.and.shape..(AP.Statistics.Course.Description)



AP Course Common Core State Standard Evidence of Extension into APAP Statistics Construct viable arguments and critique the

reasoning of others.Mathematically.proficient.students.understand.and.use.stated.assumptions,.definitions,.and.previously.established.results.in.constructing.arguments..They.make.conjectures.and.build.a.logical.progression.of.statements.to.explore.the.truth.of.their.conjectures..….They.reason.inductively.about.data,.making.plausible.arguments.that.take.into.account.the.context.from.which.the.data.arose..Mathematically.proficient.students.are.also.able.to.compare.the.effectiveness.of.two.plausible.arguments,.distinguish.correct.logic.or.reasoning.from.that.which.is.flawed,.and.—.if.there.is.a.flaw.in.an.argument.—.explain.what.it.is..….Students.learn.to.determine.domains.to.which.an.argument.applies..Students.at.all.grades.can.listen.or.read.the.arguments.of.others,.decide.whether.they.make.sense,.and.ask.useful.questions.to.clarify.or.improve.the.arguments..(MP.3)

Students.enrolled.in.an.AP.statistics.course.will.study.four.major.themes,.one.of.which.is.statistical.inference..Statistical.inference.guides.the.selection.of.appropriate.models..Models.and.data.interact.in.statistical.work:.models.are.used.to.draw.conclusions.from.data,.while.the.data.are.allowed.to.criticize.and.even.falsify.the.model.through.inferential.and.diagnostic.methods..Inference.from.data.can.be.thought.of.as.the.process.of.selecting.a.reasonable.model,.including.a.statement.in.probability.language.of.how.confident.one.can.be.about.the.selection..(AP.Statistics.Course.Description)

AP Computer Science A

Understand the concept of a function and use function notation.Understand.that.a.function.from.one.set.(called.the.domain).to.another.set.(called.the.range).assigns.to.each.element.of.the.domain.exactly.one.element.of.the.range..If.f.is.a.function.and.x.is.an.element.of.its.domain,.then.f(x).denotes.the.output.of.f.corresponding.to.the.input.x..The.graph.of.f.is.the.graph.of.the.equation y = f(x)..(F-IF.1)

A.student.in.the.AP.Computer.Science.A.course.should.be.comfortable.with.functions.and.the.concepts.found.in.the.uses.of.functional.notation,.such.as.f(x) = x + 2.and.f(x) = g(h(x))..(AP.Computer.Science.A.Course.Description)

Reason abstractly and quantitatively.Mathematically.proficient.students.make.sense.of.quantities.and.their.relationships.in.problem.situations..They.bring.two.complementary.abilities.to.bear.on.problems.involving.quantitative.relationships:.the.ability.to.decontextualize.—.to.abstract.a.given.situation.and.represent.it.symbolically.….—.and.the.ability.to.contextualize,.to.pause.as.needed.during.the.manipulation.process.in.order.to.probe.into.the.referents.for.the.symbols.involved..Quantitative.reasoning.entails.habits.of.creating.a.coherent.representation.of.the.problem.at.hand;.considering.the.units.involved;.attending.to.the.meaning.of.quantities,.not.just.how.to.compute.them;.and.knowing.and.flexibly.using.different.properties.of.operations.and.objects..(MP.2)

By.the.time.students.complete.the.AP.Computer.Science.course,.they.should.be.able.to.design.and.implement.solutions.to.problems.by.writing,.running.and.debugging.computer.programs..To.do.this,.they.should.be.able.to.develop.and.select.appropriate.algorithms.and.data.structures.to.solve.problems..(AP.Computer.Science.A.Course.Description)



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Achieve. (2010). A comparison of the Common Core State Standards for mathematics to the American Diploma Project Benchmarks for mathematics. Washington, DC: Author.

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Brown, R. S., & Conley, D. T. (2007). Comparing state high school assessments to standards for success in entry-level university courses. Educational Assessment, 12(2), 137–160.

Carter, D. C. (2007). AP Computer Science Teacher’s Guide. Retrieved from the College Board website: http://apcentral.collegeboard.com/apc/members/repository/ap07_compsci_teachersguide.pdf

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Wiley, A., Wyatt, J., & Camara, W. J. (2010). The development of a multidimensional college readiness index. (College Board Research Report 2010-3). Retrieved from College Board website: http://professionals.collegeboard.com/profdownload/pdf/10b_3110_CollegeReadiness_RR_WEB_110315.pdf


Appendixes

Appendix.AAP English — Common Core State Standards Side-by-Side Alignment Table


Appendixes

AP.

Eng

lish.

—.C

omm

on.C

ore.

Stat

e.St

anda

rds.

Side

-by-

Side

.Alig

nm

ent.

Tab

le

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eC

CR

Rea

din

gK

ey.Id

eas.

and.

Det

ails

Rea

d.cl

osel

y.to

.det

erm

ine.

wha

t.th

e.te

xt.s

ays.

expl

icit

ly.a

nd.t

o.m

ake.

log

ical

.infe

renc

es.fr

om.it

;.ci

te.s

peci

fic.t

extu

al.e

vide

nce.

whe

n.w

riti

ng.o

r.sp

eaki

ng.t

o.su

ppor

t.co

nclu

sion

s.d

raw

n.fr

om.t

he.

text

.

R.C

CR

.1X

X

Det

erm

ine.

cent

ral.i

deas

.or.

them

es.o

f.a.t

ext.

and.

anal

yze.

thei

r.de

velo

pmen

t;.su

mm

ariz

e.th

e.ke

y.su

ppor

ting

.det

ails

.and

.idea

s.

R.C

CR

.2X

X

Ana

lyze

.how

.and

.why

.ind

ivid

uals

,.eve

nts,

.and

.id

eas.

deve

lop.

and.

inte

ract

.ove

r.th

e.co

urs

e.of

.a.

text

.

R.C

CR

.3X

X

Cra

ft.a

nd.

Stru

ctu

reIn

terp

ret.

wor

ds.a

nd.p

hra

ses.

as.t

hey.

are.

used

.in

.a.t

ext,

.incl

udin

g.de

term

inin

g.te

chn

ical

,.co

nno

tati

ve,.a

nd.fi

gu

rati

ve.m

ean

ings

,.and

.an

alyz

e.ho

w.s

peci

fic.w

ord.

choi

ces.

shap

e.m

ean

ing.

or.t

one.

R.C

CR

.4X

X

Ana

lyze

.the

.str

uctu

re.o

f.tex

ts,.i

nclu

din

g.ho

w.

spec

ific

.sen

tenc

es,.p

arag

raph

s,.a

nd.la

rger

.po

rtio

ns.

of.t

he.t

ext.

(e.g

.,.a.

sect

ion,

.cha

pter

,.sc

ene,

.or.

stan

za).r

elat

e.to

.eac

h.ot

her.

and.

the.

who

le.

R.C

CR

.5X

X

Ass

ess.

how

.poi

nt.o

f.vie

w.o

r.pu

rpos

e.sh

apes

.the

.co

nten

t.an

d.st

yle.

of.a

.tex

t.R

.CC

R.6

XX

Inte

gra

tion

.of.

Kno

wle

dge.

and.

Idea

s

Inte

gra

te.a

nd.e

valu

ate.

cont

ent.

pres

ente

d.in

.d

iver

se.fo

rmat

s.an

d.m

edia

,.inc

lud

ing.

visu

ally

.an

d.q

uant

itat

ivel

y,.a

s.w

ell.a

s.in

.wor

ds.*

R.C

CR

.7X

Del

inea

te.a

nd.e

valu

ate.

the.

arg

um

ent.

and.

spec

ific

.cla

ims.

in.a

.tex

t,.in

clud

ing.

the.

valid

ity.

of.t

he.r

easo

nin

g.as

.wel

l.as.

the.

rele

vanc

e.an

d.su

ffic

ienc

y.of

.the

.evi

denc

e.

R.C

CR

.8X

X

Ana

lyze

.how

.tw

o.or

.mor

e.te

xts.

add

ress

.sim

ilar.

them

es.o

r.to

pics

.in.o

rder

.to.

build

.kno

wle

dge.

or.

to.c

ompa

re.t

he.a

ppro

ache

s.th

e.au

thor

s.ta

ke.

R.C

CR

.9X

X

Ran

ge.o

f.R

ead

ing.

and.

Leve

l.of.T

ext.

Com

plex

ity

Rea

d.an

d.co

mpr

ehen

d.co

mpl

ex.li

tera

ry.

and.

info

rmat

iona

l.tex

ts.in

depe

nden

tly.

and.

prof

icie

ntly

.

R.C

CR

.10

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

e9-

10R

ead

ing.

Stan

dard

s.fo

r.L

iter

atu

re

Key

.Idea

s.an

d.D

etai

lsC

ite.

stro

ng.a

nd.t

horo

ugh.

text

ual.e

vide

nce.

to.

supp

ort.

anal

ysis

.of.w

hat.

the.

text

.say

s.ex

plic

itly

.as

.wel

l.as.

infe

renc

es.d

raw

n.fr

om.t

he.t

ext.

RL

.9-1

0.1

XX

Det

erm

ine.

a.th

eme.

or.c

entr

al.id

ea.o

f.a.t

ext.

and.

anal

yze.

in.d

etai

l.its

.dev

elop

men

t.ov

er.t

he.c

ours

e.of

.the

.tex

t,.in

clud

ing.

how

.it.e

mer

ges.

and.

is.

shap

ed.a

nd.r

efin

ed.b

y.sp

ecif

ic.d

etai

ls;.p

rovi

de.

an.o

bjec

tive

.su

mm

ary.

of.t

he.t

ext.

RL

.9-1

0.2

X

Ana

lyze

.how

.com

plex

.cha

ract

ers.

(e.g

.,.th

ose.

wit

h.m

ulti

ple.

or.c

onfli

ctin

g.m

otiv

atio

ns)

.dev

elop

.ov

er.t

he.c

ours

e.of

.a.t

ext,

.inte

ract

.wit

h.ot

her.

char

acte

rs,.a

nd.a

dvan

ce.t

he.p

lot.

or.d

evel

op.t

he.

them

e.

RL

.9-1

0.3

X

Cra

ft.a

nd.

Stru

ctu

reD

eter

min

e.th

e.m

ean

ing.

of.w

ords

.and

.ph

rase

s.as

.the

y.ar

e.us

ed.in

.the

.tex

t,.in

clud

ing.

figu

rati

ve.

and.

con

nota

tive

.mea

nin

gs;.a

naly

ze.t

he.

cum

ula

tive

.impa

ct.o

f.spe

cific

.wor

d.ch

oice

s.on

.m

ean

ing.

and.

tone

.(e.g

.,.ho

w.t

he.la

ngua

ge.e

voke

s.a.

sen

se.o

f.tim

e.an

d.pl

ace;

.how

.it.s

ets.

a.fo

rmal

.or.

info

rmal

.ton

e).

RL

.9-1

0.4

XX

Ana

lyze

.how

.an.

auth

or’s

.cho

ices

.con

cern

ing.

how

.to

.str

uctu

re.a

.tex

t,.o

rder

.eve

nts.

wit

hin

.it.(e

.g.,.

para

llel.p

lots

),.an

d.m

anip

ula

te.t

ime.

(e.g

.,.pa

cing

,.fla

shba

cks)

.cre

ate.

such

.effe

cts.

as.m

yste

ry,.

ten

sion

,.or.

surp

rise

.

RL

.9-1

0.5

XX

Ana

lyze

.a.p

arti

cula

r.po

int.

of.v

iew

.or.

cultu

ral.

expe

rien

ce.r

efle

cted

.in.a

.wor

k.of

.lite

ratu

re.fr

om.

outs

ide.

the.

Un

ited

.Sta

tes,

.dra

win

g.on

.a.w

ide.

read

ing.

of.w

orld

.lite

ratu

re.

RL

.9-1

0.6

X

Inte

gra

tion

.of.

Kno

wle

dge.

and.

Idea

s

Ana

lyze

.the

.rep

rese

ntat

ion.

of.a

.su

bjec

t.or

.a.

key.

scen

e.in

.tw

o.d

iffe

rent

.art

isti

c.m

ediu

ms,

.in

clud

ing.

wha

t.is

.em

phas

ized

.or.

abse

nt.in

.eac

h.tr

eatm

ent.

(e.g

.,.A

uden

’s.“

Mus

ée.d

es.B

eau

x.A

rts”

.an

d.B

reug

hel’s

.Lan

dsca

pe w

ith

the

Fall

of Ic

arus

).

RL

.9-1

0.7

(Not

.app

licab

le.t

o.lit

erat

ure

)R

L.9

-10.

8

Ana

lyze

.how

.an.

auth

or.d

raw

s.on

.and

.tra

nsf

orm

s.so

urc

e.m

ater

ial.i

n.a.

spec

ific

.wor

k.(e

.g.,.

how

.Sh

akes

pear

e.tr

eats

.a.t

hem

e.or

.top

ic.fr

om.O

vid.

or.

the.

Bib

le.o

r.ho

w.a

.late

r.au

thor

.dra

ws.

on.a

.pla

y.by

.Sh

akes

pear

e).

RL

.9-1

0.9

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eR

ange

.of.

Rea

din

g.an

d.Le

vel.o

f.Tex

t.C

ompl

exit

y

By.

the.

end.

of.g

rade

.9,.r

ead.

and.

com

preh

end.

liter

atu

re,.i

nclu

din

g.st

orie

s,.d

ram

as,.a

nd.

poem

s,.in

.the

.gra

des.

9–10

.tex

t.co

mpl

exit

y.ba

nd.p

rofic

ient

ly,.w

ith.

scaf

fold

ing.

as.n

eede

d.at

.th

e.h

igh.

end.

of.t

he.r

ange

..By.

the.

end.

of.g

rade

.10

,.rea

d.an

d.co

mpr

ehen

d.lit

erat

ure

,.inc

lud

ing.

stor

ies,

.dra

mas

,.and

.poe

ms,

.at.

the.

hig

h.en

d.of

.the

.gra

des.

9–10

.tex

t.co

mpl

exit

y.ba

nd.

inde

pend

entl

y.an

d.pr

ofic

ient

ly.

RL

.9-1

0.10

XX

11-1

2R

ead

ing.

Stan

dard

s.fo

r.L

iter

atu

re

Key

.Idea

s.an

d.D

etai

lsC

ite.

stro

ng.a

nd.t

horo

ugh.

text

ual.e

vide

nce.

to.

supp

ort.

anal

ysis

.of.w

hat.

the.

text

.say

s.ex

plic

itly

.as

.wel

l.as.

infe

renc

es.d

raw

n.fr

om.t

he.t

ext,

.in

clud

ing.

dete

rmin

ing.

whe

re.t

he.t

ext.

leav

es.

mat

ters

.unc

erta

in.

RL

.11-

12.1

XX

Det

erm

ine.

two.

or.m

ore.

them

es.o

r.ce

ntra

l.ide

as.

of.a

.tex

t.an

d.an

alyz

e.th

eir.

deve

lopm

ent.

over

.the

.co

urse

.of.t

he.t

ext,

.incl

udin

g.ho

w.t

hey.

inte

ract

.an

d.bu

ild.o

n.on

e.an

othe

r.to

.pro

duce

.a.c

ompl

ex.

acco

unt;.

prov

ide.

an.o

bjec

tive

.sum

mar

y.of

.the

.te

xt.

RL

.11-

12.2

X

Ana

lyze

.the

.impa

ct.o

f.the

.aut

hor’s

.cho

ices

.re

gard

ing.

how

.to.

deve

lop.

and.

rela

te.e

lem

ents

.of.

a.st

ory.

or.d

ram

a.(e

.g.,.

whe

re.a

.sto

ry.is

.set

,.how

.th

e.ac

tion

.is.o

rder

ed,.h

ow.t

he.c

hara

cter

s.ar

e.in

trod

uced

.and

.dev

elop

ed).

RL

.11-

12.3

X

Cra

ft.a

nd.

Stru

ctu

reD

eter

min

e.th

e.m

ean

ing.

of.w

ords

.and

.ph

rase

s.as

.the

y.ar

e.us

ed.in

.the

.tex

t,.in

clud

ing.

figu

rati

ve.

and.

con

nota

tive

.mea

nin

gs;.a

naly

ze.t

he.im

pact

.of

.spe

cific

.wor

d.ch

oice

s.on

.mea

nin

g.an

d.to

ne,.

incl

udin

g.w

ords

.wit

h.m

ulti

ple.

mea

nin

gs.o

r.la

ngua

ge.t

hat.

is.p

arti

cula

rly.fr

esh,

.eng

agin

g,.o

r.be

auti

ful..

(Inc

lude

.Sha

kesp

eare

.as.

wel

l.as.

othe

r.au

thor

s.)

RL

.11-

12.4

XX

Ana

lyze

.how

.an.

auth

or’s

.cho

ices

.con

cern

ing.

how

.to.

stru

ctu

re.s

peci

fic.p

arts

.of.a

.tex

t.(e

.g.,.

the.

choi

ce.o

f.whe

re.t

o.be

gin

.or.

end.

a.st

ory,

.the

.ch

oice

.to.

prov

ide.

a.co

med

ic.o

r.tr

agic

.res

olut

ion)

.co

ntri

bute

.to.

its.

over

all.s

truc

ture

.and

.mea

nin

g.as

.wel

l.as.

its.

aest

heti

c.im

pact

.

RL

.11-

12.5

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eA

naly

ze.a

.cas

e.in

.wh

ich.

gra

spin

g.po

int.

of.v

iew

.re

qu

ires

.dis

ting

uis

hin

g.w

hat.

is.d

irec

tly.

stat

ed.

in.a

.tex

t.fr

om.w

hat.

is.r

eally

.mea

nt.(e

.g.,.

sati

re,.

sarc

asm

,.iro

ny,.o

r.u

nder

stat

emen

t).

RL

.11-

12.6

XX

Inte

gra

tion

.of.

Kno

wle

dge.

and.

Idea

s

Ana

lyze

.mu

ltipl

e.in

terp

reta

tion

s.of

.a.s

tory

,.d

ram

a,.o

r.po

em.(e

.g.,.

reco

rded

.or.

live.

prod

ucti

on.

of.a

.pla

y.or

.rec

orde

d.no

vel.o

r.po

etry

),.ev

alua

ting

.ho

w.e

ach.

vers

ion.

inte

rpre

ts.t

he.s

ourc

e.te

xt..

(Inc

lude

.at.

leas

t.on

e.pl

ay.b

y.Sh

akes

pear

e.an

d.on

e.pl

ay.b

y.an

.Am

eric

an.d

ram

atis

t.)

RL

.11-

12.7

(Not

.app

licab

le.t

o.lit

erat

ure

)R

L.1

1-12

.8

Dem

onst

rate

.kno

wle

dge.

of.e

ight

eent

h-,.

nin

etee

nth-

.and

.ear

ly-t

wen

tiet

h-ce

ntu

ry.

fou

ndat

iona

l.wor

ks.o

f.Am

eric

an.li

tera

ture

,.in

clud

ing.

how

.tw

o.or

.mor

e.te

xts.

from

.the

.sam

e.pe

riod

.tre

at.s

imila

r.th

emes

.or.

topi

cs.

RL

.11-

12.9

X

Ran

ge.o

f.R

ead

ing.

and.

Leve

l.of.T

ext.

Com

plex

ity

By.

the.

end.

of.g

rade

.11,

.rea

d.an

d.co

mpr

ehen

d.lit

erat

ure

,.inc

lud

ing.

stor

ies,

.dra

mas

,.and

.poe

ms,

.in

.the

.gra

des.

11–C

CR

.tex

t.co

mpl

exit

y.ba

nd.

prof

icie

ntly

,.wit

h.sc

affo

ldin

g.as

.nee

ded.

at.t

he.

hig

h.en

d.of

.the

.ran

ge..B

y.th

e.en

d.of

.gra

de.1

2,.

read

.and

.com

preh

end.

liter

atu

re,.i

nclu

din

g.st

orie

s,.d

ram

as,.a

nd.p

oem

s,.a

t.th

e.h

igh.

end.

of.t

he.g

rade

s.11

–CC

R.t

ext.

com

plex

ity.

band

.in

depe

nden

tly.

and.

prof

icie

ntly

.

RL

.11-

12.1

0X

X

9-10

Read

ing.

Stan

dard

s.fo

r.In

form

atio

nal.

Text

Key

.Idea

s.an

d.D

etai

lsC

ite.

stro

ng.a

nd.t

horo

ugh.

text

ual.e

vide

nce.

to.

supp

ort.

anal

ysis

.of.w

hat.

the.

text

.say

s.ex

plic

itly

.as

.wel

l.as.

infe

renc

es.d

raw

n.fr

om.t

he.t

ext.

RI.9

-10.

1X

Det

erm

ine.

a.ce

ntra

l.ide

a.of

.a.t

ext.

and.

anal

yze.

its.

deve

lopm

ent.

over

.the

.cou

rse.

of.t

he.t

ext,

.in

clud

ing.

how

.it.e

mer

ges.

and.

is.s

hape

d.an

d.re

fine

d.by

.spe

cific

.det

ails

;.pro

vide

.an.

obje

ctiv

e.su

mm

ary.

of.t

he.t

ext.

RI.9

-10.

2X

Ana

lyze

.how

.the

.aut

hor.

un

fold

s.an

.ana

lysi

s.or

.se

ries

.of.i

deas

.or.

even

ts,.i

nclu

din

g.th

e.or

der.

in.w

hic

h.th

e.po

ints

.are

.mad

e,.h

ow.t

hey.

are.

intr

oduc

ed.a

nd.d

evel

oped

,.and

.the

.con

nect

ion

s.th

at.a

re.d

raw

n.be

twee

n.th

em.

RI.9

-10.

3X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eC

raft

.and

.St

ruct

ure

Det

erm

ine.

the.

mea

nin

g.of

.wor

ds.a

nd.p

hra

ses.

as.t

hey.

are.

used

.in.a

.tex

t,.in

clud

ing.

figu

rati

ve,.

con

nota

tive

,.and

.tec

hn

ical

.mea

nin

gs;.a

naly

ze.

the.

cum

ula

tive

.impa

ct.o

f.spe

cific

.wor

d.ch

oice

s.on

.mea

nin

g.an

d.to

ne.(e

.g.,.

how

.the

.lang

uage

.of.a

.co

urt

.opi

nio

n.d

iffe

rs.fr

om.t

hat.

of.a

.new

spap

er).

RI.9

-10.

4X

Ana

lyze

.in.d

etai

l.how

.an.

auth

or’s

.idea

s.or

.cl

aim

s.ar

e.de

velo

ped.

and.

refi

ned.

by.p

arti

cula

r.se

nten

ces,

.par

agra

phs,

.or.

larg

er.p

orti

ons.

of.a

.tex

t.(e

.g.,.

a.se

ctio

n.or

.cha

pter

).

RI.9

-10.

5X

Det

erm

ine.

an.a

utho

r’s.p

oint

.of.v

iew

.or.

purp

ose.

in.a

.tex

t.an

d.an

alyz

e.ho

w.a

n.au

thor

.use

s.rh

etor

ic.

to.a

dvan

ce.t

hat.

poin

t.of

.vie

w.o

r.pu

rpos

e.

RI.9

-10.

6X

Inte

gra

tion

.of.

Kno

wle

dge.

and.

Idea

s

Ana

lyze

.var

ious

.acc

ount

s.of

.a.s

ubj

ect.

told

.in.

dif

fere

nt.m

ediu

ms.

(e.g

.,.a.

pers

on’s

.life

.sto

ry.in

.bo

th.p

rint

.and

.mu

ltim

edia

),.de

term

inin

g.w

hic

h.de

tails

.are

.em

phas

ized

.in.e

ach.

acco

unt

.

RI.9

-10.

7X

Del

inea

te.a

nd.e

valu

ate.

the.

arg

um

ent.

and.

spec

ific

.cla

ims.

in.a

.tex

t,.a

sses

sing

.whe

ther

.the

.re

ason

ing.

is.v

alid

.and

.the

.evi

denc

e.is

.rel

evan

t.an

d.su

ffic

ient

;.ide

ntif

y.fa

lse.

stat

emen

ts.a

nd.

falla

ciou

s.re

ason

ing.

RI.9

-10.

8X

Ana

lyze

.sem

inal

.U.S

..doc

um

ents

.of.h

isto

rica

l.an

d.lit

erar

y.si

gn

ific

ance

.(e.g

.,.W

ash

ing

ton’

s.Fa

rew

ell.A

ddre

ss,.t

he.G

etty

sbu

rg.A

ddre

ss,.

Roo

seve

lt’s.

Fou

r.F

reed

oms.

spee

ch,.K

ing’

s.“L

ette

r.fr

om.B

irm

ingh

am.J

ail”

),.in

clud

ing.

how

.the

y.ad

dre

ss.r

elat

ed.t

hem

es.a

nd.c

once

pts.

RI.9

-10.

9X

Ran

ge.o

f.R

ead

ing.

and.

Leve

l.of.T

ext.

Com

plex

ity

By.

the.

end.

of.g

rade

.9,.r

ead.

and.

com

preh

end.

liter

ary.

non

ficti

on.in

.the

.gra

des.

9–10

.tex

t.co

mpl

exit

y.ba

nd.p

rofic

ient

ly,.w

ith.

scaf

fold

ing.

as.n

eede

d.at

.the

.hig

h.en

d.of

.the

.ran

ge..B

y.th

e.en

d.of

.gra

de.1

0,.r

ead.

and.

com

preh

end.

liter

ary.

non

ficti

on.a

t.th

e.h

igh.

end.

of.t

he.g

rade

s.9–

10.t

ext.

com

plex

ity.

band

.inde

pend

entl

y.an

d.pr

ofic

ient

ly.

RI.9

-10.

10X

11-1

2R

ead

ing.

Stan

dard

s.fo

r.In

form

atio

nal.

Tex

t

Key

.Idea

s.an

d.D

etai

lsC

ite.

stro

ng.a

nd.t

horo

ugh.

text

ual.e

vide

nce.

to.

supp

ort.

anal

ysis

.of.w

hat.

the.

text

.say

s.ex

plic

itly

.as

.wel

l.as.

infe

renc

es.d

raw

n.fr

om.t

he.t

ext,

.in

clud

ing.

dete

rmin

ing.

whe

re.t

he.t

ext.

leav

es.

mat

ters

.unc

erta

in.

RI.1

1-12

.1X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eD

eter

min

e.tw

o.or

.mor

e.ce

ntra

l.ide

as.o

f.a.t

ext.

and.

anal

yze.

thei

r.de

velo

pmen

t.ov

er.t

he.c

ours

e.of

.th

e.te

xt,.i

nclu

din

g.ho

w.t

hey.

inte

ract

.and

.bu

ild.

on.o

ne.a

noth

er.t

o.pr

ovid

e.a.

com

plex

.ana

lysi

s;.

prov

ide.

an.o

bjec

tive

.su

mm

ary.

of.t

he.t

ext.

RI.1

1-12

.2X

Ana

lyze

.a.c

ompl

ex.s

et.o

f.ide

as.o

r.se

que

nce.

of.

even

ts.a

nd.e

xpla

in.h

ow.s

peci

fic.in

div

idua

ls,.

idea

s,.o

r.ev

ents

.inte

ract

.and

.dev

elop

.ove

r.th

e.co

urs

e.of

.the

.tex

t.

RI.1

1-12

.3X

Cra

ft.a

nd.

Stru

ctu

reD

eter

min

e.th

e.m

ean

ing.

of.w

ords

.and

.ph

rase

s.as

.the

y.ar

e.us

ed.in

.a.t

ext,

.incl

udin

g.fig

ura

tive

,.co

nno

tati

ve,.a

nd.t

ech

nic

al.m

ean

ings

;.ana

lyze

.ho

w.a

n.au

thor

.use

s.an

d.re

fine

s.th

e.m

ean

ing.

of.a

.ke

y.te

rm.o

r.te

rms.

over

.the

.cou

rse.

of.a

.tex

t.(e

.g.,.

how

.Mad

ison

.def

ines

.fact

ion

in.F

eder

alis

t N

o.

10).

RI.1

1-12

.4X

Ana

lyze

.and

.eva

luat

e.th

e.ef

fect

iven

ess.

of.t

he.

stru

ctu

re.a

n.au

thor

.use

s.in

.his

.or.

her.

expo

siti

on.

or.a

rgu

men

t,.in

clud

ing.

whe

ther

.the

.str

uctu

re.

mak

es.p

oint

s.cl

ear,.

conv

inci

ng,.a

nd.e

ngag

ing.

RI.1

1-12

.5X

Det

erm

ine.

an.a

utho

r’s.p

oint

.of.v

iew

.or.

purp

ose.

in.a

.tex

t.in

.wh

ich.

the.

rhet

oric

.is.p

arti

cula

rly.

effe

ctiv

e,.a

naly

zing

.how

.sty

le.a

nd.c

onte

nt.

cont

ribu

te.t

o.th

e.po

wer

,.per

suas

iven

ess,

.or.

beau

ty.o

f.the

.tex

t.

RI.1

1-12

.6X

Inte

gra

tion

.of.

Kno

wle

dge.

and.

Idea

s

Inte

gra

te.a

nd.e

valu

ate.

mu

ltipl

e.so

urc

es.o

f.in

form

atio

n.pr

esen

ted.

in.d

iffe

rent

.med

ia.o

r.fo

rmat

s.(e

.g.,.

visu

ally

,.qua

ntit

ativ

ely)

.as.

wel

l.as.

in.w

ords

.in.o

rder

.to.

add

ress

.a.q

uest

ion.

or.s

olve

.a.

prob

lem

.

RI.1

1-12

.7X

Del

inea

te.a

nd.e

valu

ate.

the.

reas

onin

g.in

.se

min

al.U

.S..t

exts

,.inc

lud

ing.

the.

appl

icat

ion.

of.c

onst

itut

iona

l.pri

ncip

les.

and.

use.

of.le

gal.

reas

onin

g.(e

.g.,.

in.U

.S..S

upre

me.

Cou

rt.m

ajor

ity.

opin

ion

s.an

d.d

isse

nts)

.and

.the

.pre

mis

es,.

purp

oses

,.and

.arg

um

ents

.in.w

orks

.of.p

ubl

ic.

advo

cacy

.(e.g

.,.T

he F

eder

alis

t,.pr

esid

enti

al.

add

ress

es).

RI.1

1-12

.8X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eA

naly

ze.s

even

teen

th-,.

eigh

teen

th-,.

and.

nin

etee

nth-

cent

ury

.fou

ndat

iona

l.U.S

..doc

um

ents

.of

.his

tori

cal.a

nd.li

tera

ry.s

ign

ific

ance

.(inc

lud

ing.

The

.Dec

lara

tion

.of.I

ndep

ende

nce,

.the

.Pre

ambl

e.to

.the

.Con

stit

utio

n,.t

he.B

ill.o

f.Rig

hts,

.and

.L

inco

ln’s

.Sec

ond.

Inau

gu

ral.A

ddre

ss).f

or.t

heir

.th

emes

,.pu

rpos

es,.a

nd.r

heto

rica

l.fea

ture

s.

RI.1

1-12

.9X

Ran

ge.o

f.R

ead

ing.

and.

Leve

l.of.T

ext.

Com

plex

ity

By.

the.

end.

of.g

rade

.11,

.rea

d.an

d.co

mpr

ehen

d.lit

erar

y.no

nfic

tion

.in.t

he.g

rade

s.11

–CC

R.t

ext.

com

plex

ity.

band

.pro

ficie

ntly

,.wit

h.sc

affo

ldin

g.as

.nee

ded.

at.t

he.h

igh.

end.

of.t

he.r

ange

..By.

the.

end.

of.g

rade

.12,

.rea

d.an

d.co

mpr

ehen

d.lit

erar

y.no

nfic

tion

.at.

the.

hig

h.en

d.of

.the

.gra

des.

11–

CC

R.t

ext.

com

plex

ity.

band

.inde

pend

entl

y.an

d.pr

ofic

ient

ly.

RI.1

1-12

.10

X

CC

RW

riti

ngT

ext.

Type

s.an

d.P

urp

oses

*

Wri

te.a

rgu

men

ts.t

o.su

ppor

t.cl

aim

s.in

.an.

anal

ysis

.of

.su

bsta

ntiv

e.to

pics

.or.

text

s,.u

sing

.val

id.

reas

onin

g.an

d.re

leva

nt.a

nd.s

uff

icie

nt.e

vide

nce.

W.C

CR

.1X

X

Wri

te.in

form

ativ

e/ex

plan

ator

y.te

xts.

to.e

xam

ine.

and.

conv

ey.c

ompl

ex.id

eas.

and.

info

rmat

ion.

clea

rly.a

nd.a

ccu

rate

ly.t

hro

ugh.

the.

effe

ctiv

e.se

lect

ion,

.org

aniz

atio

n,.a

nd.a

naly

sis.

of.c

onte

nt.

W.C

CR

.2X

X

Wri

te.n

arra

tive

s.to

.dev

elop

.rea

l.or.

imag

ined

.ex

peri

ence

s.or

.eve

nts.

usin

g.ef

fect

ive.

tech

niq

ue,.

wel

l-cho

sen.

deta

ils,.a

nd.w

ell-s

truc

ture

d.ev

ent.

seq

uenc

es.

W.C

CR

.3X

X

Pro

duct

ion.

and.

Dis

trib

utio

n.of

.Wri

ting

Pro

duce

.cle

ar.a

nd.c

oher

ent.

wri

ting

.in.w

hic

h.th

e.de

velo

pmen

t,.o

rgan

izat

ion,

.and

.sty

le.a

re.

appr

opri

ate.

to.t

ask,

.pu

rpos

e,.a

nd.a

udie

nce.

W.C

CR

.4X

X

Dev

elop

.and

.str

eng

then

.wri

ting

.as.

need

ed.b

y.pl

ann

ing,

.rev

isin

g,.e

dit

ing,

.rew

riti

ng,.o

r.tr

ying

.a.

new

.app

roac

h.

W.C

CR

.5X

X

Use

.tec

hno

log

y,.in

clud

ing.

the.

Inte

rnet

,.to.

prod

uce.

and.

publ

ish.

wri

ting

.and

.to.

inte

ract

.and

.co

llabo

rate

.wit

h.ot

hers

.

W.C

CR

.6


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eR

esea

rch.

to.B

uild

.an

d.P

rese

nt.

Kno

wle

dge

Con

duct

.sho

rt.a

s.w

ell.a

s.m

ore.

sust

aine

d.re

sear

ch.p

roje

cts.

base

d.on

.focu

sed.

que

stio

ns,

.de

mon

stra

ting

.und

erst

and

ing.

of.t

he.s

ubj

ect.

und

er.in

vest

igat

ion.

W.C

CR

.7X

X

Gat

her.

rele

vant

.info

rmat

ion.

from

.mu

ltipl

e.pr

int.

and.

dig

ital

.sou

rces

,.ass

ess.

the.

cred

ibili

ty.a

nd.

accu

racy

.of.e

ach.

sou

rce,

.and

.inte

gra

te.t

he.

info

rmat

ion.

wh

ile.a

void

ing.

plag

iari

sm.

W.C

CR

.8X

Dra

w.e

vide

nce.

from

.lite

rary

.or.

info

rmat

iona

l.te

xts.

to.s

uppo

rt.a

naly

sis,

.ref

lect

ion,

.and

.re

sear

ch.

W.C

CR

.9X

X

Ran

ge.o

f.W

riti

ngW

rite

.rou

tine

ly.o

ver.

exte

nded

.tim

e.fr

ames

.(tim

e.fo

r.re

sear

ch,.r

efle

ctio

n,.a

nd.r

evis

ion)

.and

.sho

rter

.ti

me.

fram

es.(a

.sin

gle.

sitt

ing.

or.a

.day

.or.

two)

.for.

a.ra

nge.

of.t

asks

,.pu

rpos

es,.a

nd.a

udie

nces

.

W.C

CR

.10

XX

9-10

Wri

ting

Tex

t.Ty

pes.

and.

Pu

rpos

esW

rite

.arg

um

ents

.to.

supp

ort.

clai

ms.

in.a

n.an

alys

is.

of.s

ubs

tant

ive.

topi

cs.o

r.te

xts,

.usi

ng.v

alid

.re

ason

ing.

and.

rele

vant

.and

.su

ffic

ient

.evi

denc

e.

Intr

oduc

e.pr

ecis

e.cl

aim

(s),.

dis

ting

uis

h.th

e.cl

aim

(s).f

rom

.alte

rnat

e.or

.opp

osin

g.cl

aim

s,.a

nd.

crea

te.a

n.or

gan

izat

ion.

that

.est

ablis

hes.

clea

r.re

lati

onsh

ips.

amon

g.cl

aim

(s),.

cou

nter

clai

ms,

.re

ason

s,.a

nd.e

vide

nce.

W.9

-10.

1aX

X

Dev

elop

.cla

im(s

).and

.cou

nter

clai

ms.

fair

ly,.

supp

lyin

g.ev

iden

ce.fo

r.ea

ch.w

hile

.poi

ntin

g.ou

t.th

e.st

reng

ths.

and.

limit

atio

ns.

of.b

oth.

in.a

.man

ner.

that

.ant

icip

ates

.the

.aud

ienc

e’s.

know

ledg

e.le

vel.

and.

conc

ern

s.

W.9

-10.

1bX

X

Use

.wor

ds,.p

hra

ses,

.and

.cla

uses

.to.

link.

the.

maj

or.

sect

ion

s.of

.the

.tex

t,.c

reat

e.co

hesi

on,.a

nd.c

lari

fy.

the.

rela

tion

ship

s.be

twee

n.cl

aim

(s).a

nd.r

easo

ns,

.be

twee

n.re

ason

s.an

d.ev

iden

ce,.a

nd.b

etw

een.

clai

m(s

).and

.cou

nter

clai

ms.

W.9

-10.

1cX

X

Est

ablis

h.an

d.m

aint

ain.

a.fo

rmal

.sty

le.a

nd.

obje

ctiv

e.to

ne.w

hile

.att

end

ing.

to.t

he.n

orm

s.an

d.co

nven

tion

s.of

.the

.dis

cipl

ine.

in.w

hic

h.th

ey.a

re.

wri

ting

.

W.9

-10.

1dX

X

Pro

vide

.a.c

oncl

udin

g.st

atem

ent.

or.s

ecti

on.

that

.follo

ws.

from

.and

.sup

port

s.th

e.ar

gu

men

t.pr

esen

ted.

W.9

-10.

1eX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eW

rite

.info

rmat

ive/

expl

anat

ory.

text

s.to

.exa

min

e.an

d.co

nvey

.com

plex

.idea

s,.c

once

pts,

.and

.in

form

atio

n.cl

early

.and

.acc

ura

tely

.th

roug

h.th

e.ef

fect

ive.

sele

ctio

n,.o

rgan

izat

ion,

.and

.ana

lysi

s.of

.co

nten

t.

Intr

oduc

e.a.

topi

c;.o

rgan

ize.

com

plex

.idea

s,.

conc

epts

,.and

.info

rmat

ion.

to.m

ake.

impo

rtan

t.co

nne

ctio

ns.

and.

dis

tinc

tion

s;.in

clud

e.fo

rmat

ting

.(e

.g.,.

head

ings

),.g

raph

ics.

(e.g

.,.fig

ure

s,.t

able

s),.

and.

mu

ltim

edia

.whe

n.us

efu

l.to.

aid

ing.

com

preh

ensi

on.

W.9

-10.

2aX

X

Dev

elop

.the

.top

ic.w

ith.

wel

l-cho

sen,

.rel

evan

t,.

and.

suff

icie

nt.fa

cts,

.ext

ende

d.de

fin

itio

ns,

.co

ncre

te.d

etai

ls,.q

uota

tion

s,.o

r.ot

her.

info

rmat

ion.

and.

exam

ples

.app

ropr

iate

.to.

the.

aud

ienc

e’s.

know

ledg

e.of

.the

.top

ic.

W.9

-10.

2bX

X

Use

.app

ropr

iate

.and

.var

ied.

tran

siti

ons.

to.li

nk.

the.

maj

or.s

ecti

ons.

of.t

he.t

ext,

.cre

ate.

cohe

sion

,.and

.cl

arif

y.th

e.re

lati

onsh

ips.

amon

g.co

mpl

ex.id

eas.

and.

conc

epts

.

W.9

-10.

2cX

X

Use

.pre

cise

.lang

uage

.and

.dom

ain-

spec

ific

.vo

cabu

lary

.to.

man

age.

the.

com

plex

ity.

of.t

he.

topi

c.

W.9

-10.

2dX

X

Est

ablis

h.an

d.m

aint

ain.

a.fo

rmal

.sty

le.a

nd.

obje

ctiv

e.to

ne.w

hile

.att

end

ing.

to.t

he.n

orm

s.an

d.co

nven

tion

s.of

.the

.dis

cipl

ine.

in.w

hic

h.th

ey.a

re.

wri

ting

.

W.9

-10.

2eX

X

Pro

vide

.a.c

oncl

udin

g.st

atem

ent.

or.s

ecti

on.

that

.follo

ws.

from

.and

.sup

port

s.th

e.in

form

atio

n.or

.exp

lana

tion

.pre

sent

ed.(e

.g.,.

arti

cula

ting

.im

plic

atio

ns.

or.t

he.s

ign

ific

ance

.of.t

he.t

opic

).

W.9

-10.

2fX

Wri

te.n

arra

tive

s.to

.dev

elop

.rea

l.or.

imag

ined

.ex

peri

ence

s.or

.eve

nts.

usin

g.ef

fect

ive.

tech

niq

ue,.

wel

l-cho

sen.

deta

ils,.a

nd.w

ell-s

truc

ture

d.ev

ent.

seq

uenc

es.

Eng

age.

and.

orie

nt.t

he.r

eade

r.by

.set

ting

.out

.a.

prob

lem

,.sit

uati

on,.o

r.ob

serv

atio

n,.e

stab

lish

ing.

one.

or.m

ulti

ple.

poin

t(s)

.of.v

iew

,.and

.intr

oduc

ing.

a.na

rrat

or.a

nd/o

r.ch

arac

ters

;.cre

ate.

a.sm

ooth

.pr

ogre

ssio

n.of

.exp

erie

nces

.or.

even

ts.

W.9

-10.

3aX

X

Use

.nar

rati

ve.t

ech

niq

ues,

.suc

h.as

.dia

log

ue,.

paci

ng,.d

escr

ipti

on,.r

efle

ctio

n,.a

nd.m

ulti

ple.

plot

.lin

es,.t

o.de

velo

p.ex

peri

ence

s,.e

vent

s,.a

nd/o

r.ch

arac

ters

.

W.9

-10.

3bX

X

Use

.a.v

arie

ty.o

f.tec

hn

ique

s.to

.seq

uenc

e.ev

ents

.so

.tha

t.th

ey.b

uild

.on.

one.

anot

her.

to.c

reat

e.a.

cohe

rent

.who

le.

W.9

-10.

3cX

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eU

se.p

reci

se.w

ords

.and

.phr

ases

,.tel

ling.

deta

ils,.a

nd.

sens

ory.

lang

uage

.to.

conv

ey.a

.viv

id.p

ictu

re.o

f.the

.ex

peri

ence

s,.e

vent

s,.s

etti

ng,.a

nd/o

r.cha

ract

ers.

W.9

-10.

3dX

X

Pro

vide

.a.c

oncl

usio

n.th

at.fo

llow

s.fr

om.a

nd.

refle

cts.

on.w

hat.

is.e

xper

ienc

ed,.o

bser

ved,

.or.

reso

lved

.ove

r.th

e.co

urs

e.of

.the

.nar

rati

ve.

W.9

-10.

3e

Pro

duct

ion.

and.

Dis

trib

utio

n.of

.Wri

ting

Pro

duce

.cle

ar.a

nd.c

oher

ent.

wri

ting

.in.w

hic

h.th

e.de

velo

pmen

t,.o

rgan

izat

ion,

.and

.sty

le.a

re.

appr

opri

ate.

to.t

ask,

.pu

rpos

e,.a

nd.a

udie

nce.

.(G

rade

-spe

cific

.exp

ecta

tion

s.fo

r.w

riti

ng.t

ypes

.ar

e.de

fine

d.in

.sta

ndar

ds.1

–3.a

bove

.)

W.9

-10.

4X

X

Dev

elop

.and

.str

eng

then

.wri

ting

.as.

need

ed.

by.p

lan

nin

g,.r

evis

ing,

.ed

itin

g,.r

ewri

ting

,.or.

tryi

ng.a

.new

.app

roac

h,.fo

cusi

ng.o

n.ad

dre

ssin

g.w

hat.

is.m

ost.

sig

nif

ican

t.fo

r.a.

spec

ific

.pu

rpos

e.an

d.au

die

nce.

.(Ed

itin

g.fo

r.co

nven

tion

s.sh

ould

.de

mon

stra

te.c

omm

and.

of.L

ang

uage

.sta

ndar

ds.

1–3.

up.t

o.an

d.in

clud

ing.

gra

des.

9–10

.on.

page

.54.

)

W.9

-10.

5X

X

Use

.tec

hno

log

y,.in

clud

ing.

the.

Inte

rnet

,.to.

prod

uce,

.pu

blis

h,.a

nd.u

pdat

e.in

div

idua

l.or.

shar

ed.w

riti

ng.p

rodu

cts,

.tak

ing.

adva

ntag

e.of

.te

chno

log

y’s.

capa

city

.to.

link.

to.o

ther

.info

rmat

ion.

and.

to.d

ispl

ay.in

form

atio

n.fle

xibl

y.an

d.dy

nam

ical

ly.

W.9

-10.

6

Res

earc

h.to

.Bu

ild.

and.

Pre

sent

.K

now

ledg

e

Con

duct

.sho

rt.a

s.w

ell.a

s.m

ore.

sust

aine

d.re

sear

ch.p

roje

cts.

to.a

nsw

er.a

.que

stio

n.(in

clud

ing.

a.se

lf-ge

nera

ted.

que

stio

n).o

r.so

lve.

a.pr

oble

m;.

narr

ow.o

r.br

oade

n.th

e.in

qu

iry.

whe

n.ap

prop

riat

e;.

synt

hesi

ze.m

ulti

ple.

sou

rces

.on.

the.

subj

ect,

.de

mon

stra

ting

.und

erst

and

ing.

of.t

he.s

ubj

ect.

und

er.in

vest

igat

ion.

W.9

-10.

7X

X

Gat

her.

rele

vant

.info

rmat

ion.

from

.mu

ltipl

e.au

thor

itat

ive.

prin

t.an

d.d

igit

al.s

ourc

es,.u

sing

.ad

vanc

ed.s

earc

hes.

effe

ctiv

ely;

.ass

ess.

the.

usef

uln

ess.

of.e

ach.

sou

rce.

in.a

nsw

erin

g.th

e.re

sear

ch.q

uest

ion;

.inte

gra

te.in

form

atio

n.in

to.t

he.

text

.sel

ecti

vely

.to.

mai

ntai

n.th

e.flo

w.o

f.ide

as,.

avoi

din

g.pl

agia

rism

.and

.follo

win

g.a.

stan

dard

.fo

rmat

.for.

cita

tion

.

W.9

-10.

8X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eD

raw

.evi

denc

e.fr

om.li

tera

ry.o

r.in

form

atio

nal.

text

s.to

.sup

port

.ana

lysi

s,.r

efle

ctio

n,.a

nd.

rese

arch

.

App

ly.g

rade

s 9–

10 R

ead

ing

stan

dard

s.to

.lit

erat

ure

.(e.g

.,.“A

naly

ze.h

ow.a

n.au

thor

.dra

ws.

on.a

nd.t

ran

sfor

ms.

sou

rce.

mat

eria

l.in.

a.sp

ecif

ic.

wor

k.[e

.g.,.

how

.Sha

kesp

eare

.tre

ats.

a.th

eme.

or.

topi

c.fr

om.O

vid.

or.t

he.B

ible

.or.

how

.a.la

ter.

auth

or.

dra

ws.

on.a

.pla

y.by

.Sha

kesp

eare

]”).

W.9

-10.

9aX

X

App

ly.g

rade

s 9–

10 R

ead

ing

stan

dard

s.to

.lit

erar

y.no

nfic

tion

.(e.g

.,.“D

elin

eate

.and

.eva

luat

e.th

e.ar

gu

men

t.an

d.sp

ecif

ic.c

laim

s.in

.a.t

ext,

.as

sess

ing.

whe

ther

.the

.rea

son

ing.

is.v

alid

.and

.the

.ev

iden

ce.is

.rel

evan

t.an

d.su

ffic

ient

;.ide

ntif

y.fa

lse.

stat

emen

ts.a

nd.fa

llaci

ous.

reas

onin

g”).

W.9

-10.

9bX

Ran

ge.o

f.W

riti

ngW

rite

.rou

tine

ly.o

ver.

exte

nded

.tim

e.fr

ames

.(tim

e.fo

r.re

sear

ch,.r

efle

ctio

n,.a

nd.r

evis

ion)

.and

.sho

rter

.ti

me.

fram

es.(a

.sin

gle.

sitt

ing.

or.a

.day

.or.

two)

.for.

a.ra

nge.

of.t

asks

,.pu

rpos

es,.a

nd.a

udie

nces

.

W.9

-10.

10X

X

11-1

2W

riti

ngT

ext.

Type

s.an

d.P

urp

oses

Wri

te.a

rgu

men

ts.t

o.su

ppor

t.cl

aim

s.in

.an.

anal

ysis

.of

.su

bsta

ntiv

e.to

pics

.or.

text

s,.u

sing

.val

id.

reas

onin

g.an

d.re

leva

nt.a

nd.s

uff

icie

nt.e

vide

nce.

Intr

oduc

e.pr

ecis

e,.k

now

ledg

eabl

e.cl

aim

(s),.

esta

blis

h.th

e.si

gn

ific

ance

.of.t

he.c

laim

(s),.

dis

ting

uis

h.th

e.cl

aim

(s).f

rom

.alte

rnat

e.or

.op

posi

ng.c

laim

s,.a

nd.c

reat

e.an

.org

aniz

atio

n.th

at.lo

gic

ally

.seq

uenc

es.c

laim

(s),.

cou

nter

clai

ms,

.re

ason

s,.a

nd.e

vide

nce.

W.1

1-12

.1a

XX

"Dev

elop

.cla

im(s

).and

.cou

nter

clai

ms.

fair

ly.a

nd.

thor

ough

ly,.s

uppl

ying

.the

.mos

t.re

leva

nt.e

vide

nce.

for.

each

.wh

ile.p

oint

ing.

out.

the.

stre

ngth

s.an

d.lim

itat

ion

s.of

.bot

h.in

.a.m

anne

r.th

at.a

ntic

ipat

es.

the.

aud

ienc

e’s.

know

ledg

e.le

vel,.

conc

ern

s,.v

alue

s,.

and.

poss

ible

.bia

ses.

W.1

1-12

.1b

XX

Use

.wor

ds,.p

hra

ses,

.and

.cla

uses

.as.

wel

l.as.

vari

ed.s

ynta

x.to

.lin

k.th

e.m

ajor

.sec

tion

s.of

.th

e.te

xt,.c

reat

e.co

hesi

on,.a

nd.c

lari

fy.t

he.

rela

tion

ship

s.be

twee

n.cl

aim

(s).a

nd.r

easo

ns,

.be

twee

n.re

ason

s.an

d.ev

iden

ce,.a

nd.b

etw

een.

clai

m(s

).and

.cou

nter

clai

ms.

W.1

1-12

.1c

XX

Est

ablis

h.an

d.m

aint

ain.

a.fo

rmal

.sty

le.a

nd.

obje

ctiv

e.to

ne.w

hile

.att

end

ing.

to.t

he.n

orm

s.an

d.co

nven

tion

s.of

.the

.dis

cipl

ine.

in.w

hic

h.th

ey.a

re.

wri

ting

.

W.1

1-12

.1d

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eP

rovi

de.a

.con

clud

ing.

stat

emen

t.or

.sec

tion

.th

at.fo

llow

s.fr

om.a

nd.s

uppo

rts.

the.

arg

um

ent.

pres

ente

d.

W.1

1-12

.1e

Wri

te.in

form

ativ

e/ex

plan

ator

y.te

xts.

to.e

xam

ine.

and.

conv

ey.c

ompl

ex.id

eas,

.con

cept

s,.a

nd.

info

rmat

ion.

clea

rly.a

nd.a

ccu

rate

ly.t

hro

ugh.

the.

effe

ctiv

e.se

lect

ion,

.org

aniz

atio

n,.a

nd.a

naly

sis.

of.

cont

ent.

Intr

oduc

e.a.

topi

c;.o

rgan

ize.

com

plex

.idea

s,.

conc

epts

,.and

.info

rmat

ion.

so.t

hat.

each

.new

.el

emen

t.bu

ilds.

on.t

hat.

wh

ich.

prec

edes

.it.t

o.cr

eate

.a.u

nif

ied.

who

le;.i

nclu

de.fo

rmat

ting

.(e

.g.,.

head

ings

),.g

raph

ics.

(e.g

.,.fig

ure

s,.t

able

s),.

and.

mu

ltim

edia

.whe

n.us

efu

l.to.

aid

ing.

com

preh

ensi

on.

W.1

1-12

.2a

XX

Dev

elop

.the

.top

ic.t

horo

ugh

ly.b

y.se

lect

ing.

the.

mos

t.si

gn

ific

ant.

and.

rele

vant

.fact

s,.e

xten

ded.

defi

nit

ion

s,.c

oncr

ete.

deta

ils,.q

uota

tion

s,.o

r.ot

her.

info

rmat

ion.

and.

exam

ples

.app

ropr

iate

.to.

the.

aud

ienc

e’s.

know

ledg

e.of

.the

.top

ic.

W.1

1-12

.2b

XX

Use

.app

ropr

iate

.and

.var

ied.

tran

siti

ons.

and.

synt

ax.t

o.lin

k.th

e.m

ajor

.sec

tion

s.of

.the

.tex

t,.

crea

te.c

ohes

ion,

.and

.cla

rify

.the

.rel

atio

nsh

ips.

amon

g.co

mpl

ex.id

eas.

and.

conc

epts

.

W.1

1-12

.2c

XX

Use

.pre

cise

.lang

uage

,.dom

ain-

spec

ific

.vo

cabu

lary

,.and

.tec

hn

ique

s.su

ch.a

s.m

etap

hor,.

sim

ile,.a

nd.a

nalo

gy.

to.m

anag

e.th

e.co

mpl

exit

y.of

.th

e.to

pic.

W.1

1-12

.2d

XX

Est

ablis

h.an

d.m

aint

ain.

a.fo

rmal

.sty

le.a

nd.

obje

ctiv

e.to

ne.w

hile

.att

end

ing.

to.t

he.n

orm

s.an

d.co

nven

tion

s.of

.the

.dis

cipl

ine.

in.w

hic

h.th

ey.a

re.

wri

ting

.

W.1

1-12

.2e

XX

Pro

vide

.a.c

oncl

udin

g.st

atem

ent.

or.s

ecti

on.

that

.follo

ws.

from

.and

.sup

port

s.th

e.in

form

atio

n.or

.exp

lana

tion

.pre

sent

ed.(e

.g.,.

arti

cula

ting

.im

plic

atio

ns.

or.t

he.s

ign

ific

ance

.of.t

he.t

opic

).

W.1

1-12

.2f

Wri

te.n

arra

tive

s.to

.dev

elop

.rea

l.or.

imag

ined

.ex

peri

ence

s.or

.eve

nts.

usin

g.ef

fect

ive.

tech

niq

ue,.

wel

l-cho

sen.

deta

ils,.a

nd.w

ell-s

truc

ture

d.ev

ent.

seq

uenc

es.

Eng

age.

and.

orie

nt.t

he.r

eade

r.by

.set

ting

.out

.a.

prob

lem

,.sit

uati

on,.o

r.ob

serv

atio

n.an

d.it

s.si

gn

ific

ance

,.est

ablis

hin

g.on

e.or

.mu

ltipl

e.po

int(

s).o

f.vie

w,.a

nd.in

trod

ucin

g.a.

narr

ator

.and

/or

.cha

ract

ers;

.cre

ate.

a.sm

ooth

.pro

gre

ssio

n.of

.ex

peri

ence

s.or

.eve

nts.

W.1

1-12

.3a

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eU

se.n

arra

tive

.tec

hn

ique

s,.s

uch.

as.d

ialo

gue

,.pa

cing

,.des

crip

tion

,.ref

lect

ion,

.and

.mu

ltipl

e.pl

ot.

lines

,.to.

deve

lop.

expe

rien

ces,

.eve

nts,

.and

/or.

char

acte

rs.

W.1

1-12

.3b

XX

Use

.a.v

arie

ty.o

f.tec

hn

ique

s.to

.seq

uenc

e.ev

ents

.so

.tha

t.th

ey.b

uild

.on.

one.

anot

her.

to.c

reat

e.a.

cohe

rent

.who

le.a

nd.b

uild

.tow

ard.

a.pa

rtic

ula

r.to

ne.a

nd.o

utco

me.

(e.g

.,.a.

sen

se.o

f.mys

tery

,.su

spen

se,.g

row

th,.o

r.re

solu

tion

).

W.1

1-12

.3c

XX

Use

.pre

cise

.wor

ds.a

nd.p

hra

ses,

.tel

ling.

deta

ils,.

and.

sen

sory

.lang

uage

.to.

conv

ey.a

.viv

id.p

ictu

re.

of.t

he.e

xper

ienc

es,.e

vent

s,.s

etti

ng,.a

nd/o

r.ch

arac

ters

.

W.1

1-12

.3d

XX

Pro

vide

.a.c

oncl

usio

n.th

at.fo

llow

s.fr

om.a

nd.

refle

cts.

on.w

hat.

is.e

xper

ienc

ed,.o

bser

ved,

.or.

reso

lved

.ove

r.th

e.co

urs

e.of

.the

.nar

rati

ve.

W.1

1-12

.3e

Pro

duct

ion.

and.

Dis

trib

utio

n.of

.Wri

ting

Pro

duce

.cle

ar.a

nd.c

oher

ent.

wri

ting

.in.w

hic

h.th

e.de

velo

pmen

t,.o

rgan

izat

ion,

.and

.sty

le.a

re.

appr

opri

ate.

to.t

ask,

.pu

rpos

e,.a

nd.a

udie

nce.

.(G

rade

-spe

cific

.exp

ecta

tion

s.fo

r.w

riti

ng.t

ypes

.ar

e.de

fine

d.in

.sta

ndar

ds.1

–3.a

bove

.)

W.1

1-12

.4X

X

Dev

elop

.and

.str

eng

then

.wri

ting

.as.

need

ed.

by.p

lan

nin

g,.r

evis

ing,

.ed

itin

g,.r

ewri

ting

,.or.

tryi

ng.a

.new

.app

roac

h,.fo

cusi

ng.o

n.ad

dre

ssin

g.w

hat.

is.m

ost.

sig

nif

ican

t.fo

r.a.

spec

ific

.pu

rpos

e.an

d.au

die

nce.

.(Ed

itin

g.fo

r.co

nven

tion

s.sh

ould

.de

mon

stra

te.c

omm

and.

of.L

ang

uage

.sta

ndar

ds.

1–3.

up.t

o.an

d.in

clud

ing.

gra

des.

11–1

2.on

.pag

e.54

.)

W.1

1-12

.5X

X

Use

.tec

hno

log

y,.in

clud

ing.

the.

Inte

rnet

,.to.

prod

uce,

.pu

blis

h,.a

nd.u

pdat

e.in

div

idua

l.or

.sha

red.

wri

ting

.pro

duct

s.in

.res

pon

se.t

o.on

goin

g.fe

edba

ck,.i

nclu

din

g.ne

w.a

rgu

men

ts.o

r.in

form

atio

n.

W.1

1-12

.6


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eR

esea

rch.

to.B

uild

.an

d.P

rese

nt.

Kno

wle

dge

Con

duct

.sho

rt.a

s.w

ell.a

s.m

ore.

sust

aine

d.re

sear

ch.p

roje

cts.

to.a

nsw

er.a

.que

stio

n.(in

clud

ing.

a.se

lf-ge

nera

ted.

que

stio

n).o

r.so

lve.

a.pr

oble

m;.

narr

ow.o

r.br

oade

n.th

e.in

qu

iry.

whe

n.ap

prop

riat

e;.

synt

hesi

ze.m

ulti

ple.

sou

rces

.on.

the.

subj

ect,

.de

mon

stra

ting

.und

erst

and

ing.

of.t

he.s

ubj

ect.

und

er.in

vest

igat

ion.

W.1

1-12

.7X

X

Gat

her.

rele

vant

.info

rmat

ion.

from

.mu

ltipl

e.au

thor

itat

ive.

prin

t.an

d.d

igit

al.s

ourc

es,.u

sing

.ad

vanc

ed.s

earc

hes.

effe

ctiv

ely;

.ass

ess.

the.

stre

ngth

s.an

d.lim

itat

ion

s.of

.eac

h.so

urc

e.in

.ter

ms.

of.t

he.t

ask,

.pu

rpos

e,.a

nd.a

udie

nce;

.inte

gra

te.

info

rmat

ion.

into

.the

.tex

t.se

lect

ivel

y.to

.mai

ntai

n.th

e.flo

w.o

f.ide

as,.a

void

ing.

plag

iari

sm.a

nd.

over

relia

nce.

on.a

ny.o

ne.s

ourc

e.an

d.fo

llow

ing.

a.st

anda

rd.fo

rmat

.for.

cita

tion

.

W.1

1-12

.8X

Dra

w.e

vide

nce.

from

.lite

rary

.or.

info

rmat

iona

l.te

xts.

to.s

uppo

rt.a

naly

sis,

.ref

lect

ion,

.and

.re

sear

ch.

App

ly.g

rade

s 11

–12

Rea

din

g st

anda

rds.

to.

liter

atu

re.(e

.g.,.

“Dem

onst

rate

.kno

wle

dge.

of.

eigh

teen

th-,.

nin

etee

nth-

.and

.ear

ly-t

wen

tiet

h-ce

ntu

ry.fo

und

atio

nal.w

orks

.of.A

mer

ican

.lit

erat

ure

,.inc

lud

ing.

how

.tw

o.or

.mor

e.te

xts.

from

.th

e.sa

me.

peri

od.t

reat

.sim

ilar.

them

es.o

r.to

pics

”).

W.1

1-12

.9a

XX

App

ly.g

rade

s 11

–12

Rea

din

g st

anda

rds.

to.li

tera

ry.

non

ficti

on.(e

.g.,.

“Del

inea

te.a

nd.e

valu

ate.

the.

reas

onin

g.in

.sem

inal

.U.S

..tex

ts,.i

nclu

din

g.th

e.ap

plic

atio

n.of

.con

stit

utio

nal.p

rinc

iple

s.an

d.us

e.of

.lega

l.rea

son

ing.

[e.g

.,.in

.U.S

..Sup

rem

e.C

ourt

.C

ase.

maj

orit

y.op

inio

ns.

and.

dis

sent

s].a

nd.t

he.

prem

ises

,.pu

rpos

es,.a

nd.a

rgu

men

ts.in

.wor

ks.o

f.pu

blic

.adv

ocac

y.[e

.g.,

The

Fed

eral

ist,.

pres

iden

tial

.ad

dre

sses

]”).

W.1

1-12

.9b

X

Ran

ge.o

f.W

riti

ngW

rite

.rou

tine

ly.o

ver.

exte

nded

.tim

e.fr

ames

.(tim

e.fo

r.re

sear

ch,.r

efle

ctio

n,.a

nd.r

evis

ion)

.and

.sho

rter

.ti

me.

fram

es.(a

.sin

gle.

sitt

ing.

or.a

.day

.or.

two)

.for.

a.ra

nge.

of.t

asks

,.pu

rpos

es,.a

nd.a

udie

nces

.

W.1

1-12

.10

XX

CC

RSp

eaki

ng.a

nd.

Lis

ten

ing

Com

preh

ensi

on.

and.

.C

olla

bora

tion

Pre

pare

.for.

and.

part

icip

ate.

effe

ctiv

ely.

in.a

.ra

nge.

of.c

onve

rsat

ion

s.an

d.co

llabo

rati

ons.

wit

h.d

iver

se.p

artn

ers,

.bu

ildin

g.on

.oth

ers’

.idea

s.an

d.ex

pres

sing

.the

ir.o

wn.

clea

rly.a

nd.p

ersu

asiv

ely.

SL.C

CR

.1X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eIn

teg

rate

.and

.eva

luat

e.in

form

atio

n.pr

esen

ted.

in.

div

erse

.med

ia.a

nd.fo

rmat

s,.in

clud

ing.

visu

ally

,.q

uant

itat

ivel

y,.a

nd.o

rally

.

SL.C

CR

.2

Eva

luat

e.a.

spea

ker’s

.poi

nt.o

f.vie

w,.r

easo

nin

g,.

and.

use.

of.e

vide

nce.

and.

rhet

oric

.SL

.CC

R.3

Pre

sent

atio

n.of

.Kno

wle

dge.

and.

Idea

s

Pre

sent

.info

rmat

ion,

.find

ings

,.and

.sup

port

ing.

evid

ence

.suc

h.th

at.li

sten

ers.

can.

follo

w.t

he.li

ne.

of.r

easo

nin

g.an

d.th

e.or

gan

izat

ion,

.dev

elop

men

t,.

and.

styl

e.ar

e.ap

prop

riat

e.to

.tas

k,.p

urp

ose,

.and

.au

die

nce.

SL.C

CR

.4

Mak

e.st

rate

gic

.use

.of.d

igit

al.m

edia

.and

.vis

ual.

dis

play

s.of

.dat

a.to

.exp

ress

.info

rmat

ion.

and.

enha

nce.

und

erst

and

ing.

of.p

rese

ntat

ion

s.

SL.C

CR

.5

Ada

pt.s

peec

h.to

.a.v

arie

ty.o

f.con

text

s.an

d.co

mm

un

icat

ive.

task

s,.d

emon

stra

ting

.com

man

d.of

.form

al.E

nglis

h.w

hen.

ind

icat

ed.o

r.ap

prop

riat

e.

SL.C

CR

.6

9-10

Spea

king

.and

.L

iste

nin

g.St

anda

rds

Com

preh

ensi

on.

and.

.C

olla

bora

tion

Init

iate

.and

.par

tici

pate

.effe

ctiv

ely.

in.a

.ran

ge.o

f.co

llabo

rati

ve.d

iscu

ssio

ns.

(one

-on-

one,

.in.g

roup

s,.

and.

teac

her-

led)

.wit

h.d

iver

se.p

artn

ers.

on.g

rade

s 9–

10 t

opic

s, t

exts

, and

issu

es,.b

uild

ing.

on.o

ther

s’.

idea

s.an

d.ex

pres

sing

.the

ir.o

wn.

clea

rly.a

nd.

pers

uasi

vely

.

Com

e.to

.dis

cuss

ion

s.pr

epar

ed,.h

avin

g.re

ad.a

nd.

rese

arch

ed.m

ater

ial.u

nder

.stu

dy;.e

xplic

itly

.dra

w.

on.t

hat.

prep

arat

ion.

by.r

efer

ring

.to.

evid

ence

.from

.te

xts.

and.

othe

r.re

sear

ch.o

n.th

e.to

pic.

or.is

sue.

to.

stim

ula

te.a

.tho

ught

ful,.

wel

l-rea

sone

d.ex

chan

ge.

of.id

eas.

SL.9

-10.

1aX

Wor

k.w

ith.

peer

s.to

.set

.ru

les.

for.

colle

gia

l.d

iscu

ssio

ns.

and.

deci

sion

-mak

ing.

(e.g

.,.in

form

al.

con

sen

sus,

.tak

ing.

vote

s.on

.key

.issu

es,.

pres

enta

tion

.of.a

ltern

ate.

view

s),.c

lear

.goa

ls.a

nd.

dead

lines

,.and

.ind

ivid

ual.r

oles

.as.

need

ed.

SL.9

-10.

1b

Pro

pel.c

onve

rsat

ion

s.by

.pos

ing.

and.

resp

ond

ing.

to.q

uest

ion

s.th

at.r

elat

e.th

e.cu

rren

t.d

iscu

ssio

n.to

.bro

ader

.the

mes

.or.

larg

er.id

eas;

.act

ivel

y.in

corp

orat

e.ot

hers

.into

.the

.dis

cuss

ion;

.and

.cl

arif

y,.v

erif

y,.o

r.ch

alle

nge.

idea

s.an

d.co

nclu

sion

s.

SL.9

-10.

1c

Res

pond

.tho

ught

fully

.to.

div

erse

.per

spec

tive

s,.

sum

mar

ize.

poin

ts.o

f.ag

reem

ent.

and.

dis

agre

emen

t,.a

nd,.w

hen.

war

rant

ed,.q

ualif

y.or

.ju

stif

y.th

eir.

own.

view

s.an

d.u

nder

stan

din

g.an

d.m

ake.

new

.con

nect

ion

s.in

.ligh

t.of

.the

.evi

denc

e.an

d.re

ason

ing.

pres

ente

d.

SL.9

-10.

1d


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eIn

teg

rate

.mu

ltipl

e.so

urc

es.o

f.in

form

atio

n.pr

esen

ted.

in.d

iver

se.m

edia

.or.

form

ats.

(e.g

.,.vi

sual

ly,.q

uant

itat

ivel

y,.o

rally

).eva

luat

ing.

the.

cred

ibili

ty.a

nd.a

ccu

racy

.of.e

ach.

sou

rce.

SL.9

-10.

2

Eva

luat

e.a.

spea

ker’s

.poi

nt.o

f.vie

w,.r

easo

nin

g,.

and.

use.

of.e

vide

nce.

and.

rhet

oric

,.ide

ntif

ying

.any

.fa

llaci

ous.

reas

onin

g.or

.exa

gger

ated

.or.

dis

tort

ed.

evid

ence

.

SL.9

-10.

3

Pre

sent

atio

n.of

.Kno

wle

dge.

and.

Idea

s

Pre

sent

.info

rmat

ion,

.find

ings

,.and

.sup

port

ing.

evid

ence

.cle

arly

,.con

cise

ly,.a

nd.lo

gic

ally

.suc

h.th

at.li

sten

ers.

can.

follo

w.t

he.li

ne.o

f.rea

son

ing.

and.

the.

orga

niz

atio

n,.d

evel

opm

ent,

.su

bsta

nce,

.and

.st

yle.

are.

appr

opri

ate.

to.p

urp

ose,

.aud

ienc

e,.a

nd.

task

.

SL.9

-10.

4

Mak

e.st

rate

gic

.use

.of.d

igit

al.m

edia

.(e.g

.,.te

xtua

l,.g

raph

ical

,.aud

io,.v

isua

l,.an

d.in

tera

ctiv

e.el

emen

ts).i

n.pr

esen

tati

ons.

to.e

nha

nce.

und

erst

and

ing.

of.fi

ndin

gs,.r

easo

nin

g,.a

nd.

evid

ence

.and

.to.

add.

inte

rest

.

SL.9

-10.

5

Ada

pt.s

peec

h.to

.a.v

arie

ty.o

f.con

text

s.an

d.ta

sks,

.de

mon

stra

ting

.com

man

d.of

.form

al.E

nglis

h.w

hen.

ind

icat

ed.o

r.ap

prop

riat

e..(S

ee.g

rade

s.9–

10.

Lan

gua

ge.s

tand

ards

.1.a

nd.3

.on.

page

s.54

.for.

spec

ific

.exp

ecta

tion

s.)

SL.9

-10.

6

11-1

2Sp

eaki

ng.a

nd.

Lis

ten

ing.

Stan

dard

s

Com

preh

ensi

on.

and.

.C

olla

bora

tion

Init

iate

.and

.par

tici

pate

.effe

ctiv

ely.

in.a

.ran

ge.o

f.co

llabo

rati

ve.d

iscu

ssio

ns.

(one

-on-

one,

.in.g

roup

s,.

and.

teac

her-

led)

.wit

h.d

iver

se.p

artn

ers.

on.g

rade

s 11

–12

topi

cs, t

exts

, and

issu

es,.b

uild

ing.

on.

othe

rs’.i

deas

.and

.exp

ress

ing.

thei

r.ow

n.cl

early

.an

d.pe

rsua

sive

ly.

Com

e.to

.dis

cuss

ion

s.pr

epar

ed,.h

avin

g.re

ad.a

nd.

rese

arch

ed.m

ater

ial.u

nder

.stu

dy;.e

xplic

itly

.dra

w.

on.t

hat.

prep

arat

ion.

by.r

efer

ring

.to.

evid

ence

.from

.te

xts.

and.

othe

r.re

sear

ch.o

n.th

e.to

pic.

or.is

sue.

to.

stim

ula

te.a

.tho

ught

ful,.

wel

l-rea

sone

d.ex

chan

ge.

of.id

eas.

SL.1

1-12

.1a

X

Wor

k.w

ith.

peer

s.to

.pro

mot

e.ci

vil,.

dem

ocra

tic.

dis

cuss

ion

s.an

d.de

cisi

on-m

akin

g,.s

et.c

lear

.goa

ls.

and.

dead

lines

,.and

.est

ablis

h.in

div

idua

l.rol

es.a

s.ne

eded

.

SL.1

1-12

.1b

Pro

pel.c

onve

rsat

ion

s.by

.pos

ing.

and.

resp

ond

ing.

to.q

uest

ion

s.th

at.p

robe

.rea

son

ing.

and.

evid

ence

;.en

sure

.a.h

eari

ng.fo

r.a.

full.

rang

e.of

.pos

itio

ns.

on.

a.to

pic.

or.is

sue;

.cla

rify

,.ver

ify,

.or.

chal

leng

e.id

eas.

and.

conc

lusi

ons;

.and

.pro

mot

e.d

iver

gent

.and

.cr

eati

ve.p

ersp

ecti

ves.

SL.1

1-12

.1c


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eR

espo

nd.t

houg

htfu

lly.t

o.di

vers

e.pe

rspe

ctiv

es;.

synt

hesi

ze.c

omm

ents

,.cla

ims,

.and

.evi

denc

e.m

ade.

on.a

ll.si

des.

of.a

n.is

sue;

.reso

lve.

cont

radi

ctio

ns.

whe

n.po

ssib

le;.a

nd.d

eter

min

e.w

hat.

addi

tion

al.

info

rmat

ion.

or.re

sear

ch.is

.requ

ired

.to.

deep

en.t

he.

inve

stig

atio

n.or

.com

plet

e.th

e.ta

sk.

SL.1

1-12

.1d

Inte

grat

e.m

ulti

ple.

sour

ces.

of.in

form

atio

n.pr

esen

ted.

in.d

iver

se.fo

rmat

s.an

d.m

edia

.(e.g

.,.vi

sual

ly,.q

uant

itat

ivel

y,.o

rally

).in.

orde

r.to

.mak

e.in

form

ed.d

ecis

ions

.and

.sol

ve.p

robl

ems,

.eva

luat

ing.

the.

cred

ibili

ty.a

nd.a

ccur

acy.

of.e

ach.

sour

ce.a

nd.

noti

ng.a

ny.d

iscr

epan

cies

.am

ong.

the.

data

.

SL.1

1-12

.2

Eva

luat

e.a.

spea

ker’s

.poi

nt.o

f.vie

w,.r

easo

nin

g,.

and.

use.

of.e

vide

nce.

and.

rhet

oric

,.ass

essi

ng.

the.

stan

ce,.p

rem

ises

,.lin

ks.a

mon

g.id

eas,

.wor

d.ch

oice

,.poi

nts.

of.e

mph

asis

,.and

.ton

e.us

ed.

SL.1

1-12

.3

Pre

sent

atio

n.of

.Kno

wle

dge.

and.

Idea

s

Pre

sent

.info

rmat

ion,

.find

ings

,.and

.sup

port

ing.

evid

ence

,.con

veyi

ng.a

.cle

ar.a

nd.d

isti

nct.

pers

pect

ive,

.suc

h.th

at.li

sten

ers.

can.

follo

w.

the.

line.

of.r

easo

nin

g,.a

ltern

ativ

e.or

.opp

osin

g.pe

rspe

ctiv

es.a

re.a

ddre

ssed

,.and

.the

.or

gan

izat

ion,

.dev

elop

men

t,.s

ubs

tanc

e,.a

nd.s

tyle

.ar

e.ap

prop

riat

e.to

.pu

rpos

e,.a

udie

nce,

.and

.a.

rang

e.of

.form

al.a

nd.in

form

al.t

asks

.

SL.1

1-12

.4

Mak

e.st

rate

gic

.use

.of.d

igit

al.m

edia

.(e.g

.,.te

xtua

l,.g

raph

ical

,.aud

io,.v

isua

l,.an

d.in

tera

ctiv

e.el

emen

ts).i

n.pr

esen

tati

ons.

to.e

nha

nce.

und

erst

and

ing.

of.fi

ndin

gs,.r

easo

nin

g,.a

nd.

evid

ence

.and

.to.

add.

inte

rest

.

SL.1

1-12

.5

Ada

pt.s

peec

h.to

.a.v

arie

ty.o

f.con

text

s.an

d.ta

sks,

.de

mon

stra

ting

.a.c

omm

and.

of.fo

rmal

.Eng

lish.

whe

n.in

dic

ated

.or.

appr

opri

ate.

.(See

.gra

des.

11–1

2.L

ang

uage

.sta

ndar

ds.1

.and

.3.o

n.pa

ge.5

4.fo

r.sp

ecif

ic.e

xpec

tati

ons.

)

SL.1

1-12

.6

CC

RL

ang

uage

Con

vent

ion

s.of

.Sta

ndar

d.E

nglis

h

Dem

onst

rate

.com

man

d.of

.the

.con

vent

ion

s.of

.st

anda

rd.E

nglis

h.g

ram

mar

.and

.usa

ge.w

hen.

wri

ting

.or.

spea

king

.

L.C

CR

.1X

X

Dem

onst

rate

.com

man

d.of

.the

.con

vent

ion

s.of

.st

anda

rd.E

nglis

h.ca

pita

lizat

ion,

.pu

nctu

atio

n,.a

nd.

spel

ling.

whe

n.w

riti

ng.

L.C

CR

.2X

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eK

now

ledg

e.of

.L

ang

uage

App

ly.k

now

ledg

e.of

.lang

uage

.to.

und

erst

and.

how

.lang

uage

.func

tion

s.in

.dif

fere

nt.c

onte

xts,

.to

.mak

e.ef

fect

ive.

choi

ces.

for.

mea

nin

g.or

.sty

le,.

and.

to.c

ompr

ehen

d.m

ore.

fully

.whe

n.re

adin

g.or

.lis

ten

ing.

L.C

CR

.3X

X

Voc

abu

lary

.A

cqu

isit

ion.

and.

Use

Det

erm

ine.

or.c

lari

fy.t

he.m

ean

ing.

of.u

nkn

own.

and.

mu

ltipl

e-m

ean

ing.

wor

ds.a

nd.p

hra

ses.

by.

usin

g.co

ntex

t.cl

ues,

.ana

lyzi

ng.m

ean

ing

ful.w

ord.

part

s,.a

nd.c

onsu

lting

.gen

eral

.and

.spe

cial

ized

.re

fere

nce.

mat

eria

ls,.a

s.ap

prop

riat

e.

L.C

CR

.4X

X

Dem

onst

rate

.und

erst

and

ing.

of.fi

gu

rati

ve.

lang

uage

,.wor

d.re

lati

onsh

ips,

.and

.nua

nces

.in.

wor

d.m

ean

ings

.

L.C

CR

.5X

X

Acq

uir

e.an

d.us

e.ac

cura

tely

.a.r

ange

.of.g

ener

al.

acad

emic

.and

.dom

ain-

spec

ific

.wor

ds.a

nd.

phra

ses.

suff

icie

nt.fo

r.re

adin

g,.w

riti

ng,.s

peak

ing,

.an

d.lis

ten

ing.

at.t

he.c

olle

ge.a

nd.c

aree

r.re

adin

ess.

leve

l;.de

mon

stra

te.in

depe

nden

ce.in

.gat

heri

ng.

voca

bula

ry.k

now

ledg

e.w

hen.

con

side

ring

.a.

wor

d.or

.ph

rase

.impo

rtan

t.to

.com

preh

ensi

on.o

r.ex

pres

sion

.

L.C

CR

.6X

X

9-10

Lan

gua

geC

onve

ntio

ns.

of.S

tand

ard.

Eng

lish

Dem

onst

rate

.com

man

d.of

.the

.con

vent

ion

s.of

.st

anda

rd.E

nglis

h.g

ram

mar

.and

.usa

ge.w

hen.

wri

ting

.or.

spea

king

.

Use

.par

alle

l.str

uctu

re.*

L.9

-10.

1aX

X

Use

.var

ious

.typ

es.o

f.ph

rase

s.(n

oun,

.ver

b,.

adje

ctiv

al,.a

dver

bial

,.par

tici

pial

,.pre

posi

tion

al,.

abso

lute

).and

.cla

uses

.(ind

epen

dent

,.dep

ende

nt;.

nou

n,.r

elat

ive,

.adv

erbi

al).t

o.co

nvey

.spe

cific

.m

ean

ings

.and

.add

.var

iety

.and

.inte

rest

.to.

wri

ting

.or

.pre

sent

atio

ns.

L.9

-10.

1bX

X

En

sure

.su

bjec

t-ve

rb.a

nd.p

rono

un-

ante

cede

nt.

agre

emen

t.L

.3.1

fX

X

Pro

duce

.com

plet

e.se

nten

ces,

.rec

ogn

izin

g.an

d.co

rrec

ting

.inap

prop

riat

e.fr

agm

ents

.and

.ru

n-on

s.L

.4.1

fX

X

Cor

rect

ly.u

se.fr

eque

ntly

.con

fuse

d.w

ord

s.(e

.g.,.

to/

too/

two;

the

re/t

heir

).L

.4.1

gX

X

Rec

ogn

ize.

and.

corr

ect.

inap

prop

riat

e.sh

ifts

.in.

verb

.ten

se.

L.5

.1d

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eR

ecog

niz

e.an

d.co

rrec

t.in

appr

opri

ate.

shif

ts.in

.pr

onou

n.nu

mbe

r.an

d.pe

rson

.L

.6.1

cX

X

Rec

ogn

ize.

and.

corr

ect.

vag

ue.p

rono

un

s.(i.

e.,.o

nes.

wit

h.u

ncle

ar.o

r.am

big

uous

.ant

eced

ents

).L

.6.1

dX

X

"Rec

ogn

ize.

vari

atio

ns.

from

.sta

ndar

d.E

nglis

h.in

.th

eir.

own.

and.

othe

rs’.w

riti

ng.a

nd.s

peak

ing,

.and

.id

enti

fy.a

nd.u

se.s

trat

egie

s.to

.impr

ove.

expr

essi

on.

in.c

onve

ntio

nal.l

ang

uage

.

L.6

.1e

XX

Plac

e.ph

rase

s.an

d.cl

ause

s.w

ith

in.a

.sen

tenc

e,.

reco

gn

izin

g.an

d.co

rrec

ting

.mis

plac

ed.a

nd.

dang

ling.

mod

ifie

rs.

L.7

.1c

XX

Rec

ogn

ize.

and.

corr

ect.

inap

prop

riat

e.sh

ifts

.in.

verb

.voi

ce.a

nd.m

ood.

L.8

.1d

XX

Dem

onst

rate

.com

man

d.of

.the

.con

vent

ion

s.of

.st

anda

rd.E

nglis

h.ca

pita

lizat

ion,

.pu

nctu

atio

n,.a

nd.

spel

ling.

whe

n.w

riti

ng.

Use

.a.s

emic

olon

.(and

.per

haps

.a.c

onju

ncti

ve.

adve

rb).t

o.lin

k.tw

o.or

.mor

e.cl

osel

y.re

late

d.in

depe

nden

t.cl

ause

s.

L.9

-10.

2aX

X

Use

.a.c

olon

.to.

intr

oduc

e.a.

list.

or.q

uota

tion

.L

.9-1

0.2b

XX

Spel

l.cor

rect

ly.

L.9

-10.

2cX

X

Use

.pu

nctu

atio

n.(c

omm

as,.p

aren

thes

es,.d

ashe

s).

to.s

et.o

ff.no

nre

stri

ctiv

e/pa

rent

heti

cal.e

lem

ents

.L

.6.2

aX

X

Kno

wle

dge.

of.

Lan

gua

geA

pply

.kno

wle

dge.

of.la

ngua

ge.t

o.u

nder

stan

d.ho

w.la

ngua

ge.fu

ncti

ons.

in.d

iffe

rent

.con

text

s,.

to.m

ake.

effe

ctiv

e.ch

oice

s.fo

r.m

ean

ing.

or.s

tyle

,.an

d.to

.com

preh

end.

mor

e.fu

lly.w

hen.

read

ing.

or.

liste

nin

g.

Wri

te.a

nd.e

dit

.wor

k.so

.tha

t.it

.con

form

s.to

.th

e.g

uid

elin

es.in

.a.s

tyle

.man

ual.(

e.g.

,.ML

A

Han

dbo

ok,.T

ura

bian

’s.M

anua

l for

Wri

ters

).ap

prop

riat

e.fo

r.th

e.d

isci

plin

e.an

d.w

riti

ng.t

ype.

L.9

-10.

3aX

Cho

ose.

wor

ds.a

nd.p

hra

ses.

for.

effe

ct.

L.3

.3a

XX

Cho

ose.

punc

tuat

ion.

for.

effe

ct.

L.4

.3b

XX

Var

y.se

nten

ce.p

atte

rns.

for.

mea

nin

g,.r

eade

r/lis

tene

r.in

tere

st,.a

nd.s

tyle

.‡L

.6.3

aX

X

Mai

ntai

n.co

nsi

sten

cy.in

.sty

le.a

nd.t

one.

L.6

.3b

XX

Cho

ose.

lang

uage

.tha

t.ex

pres

ses.

idea

s.pr

ecis

ely.

and.

conc

isel

y,.r

ecog

niz

ing.

and.

elim

inat

ing.

wor

din

ess.

and.

redu

ndan

cy.

L.7

.3a

XX

Voc

abu

lary

.A

cqu

isit

ion.

and.

Use

Det

erm

ine.

or.c

lari

fy.t

he.m

ean

ing.

of.u

nkn

own.

and.

mu

ltipl

e-m

ean

ing.

wor

ds.a

nd.p

hra

ses.

base

d.on

.gra

des.

9–10

.rea

din

g.an

d.co

nten

t,.c

hoos

ing.

flexi

bly.

from

.a.r

ange

.of.s

trat

egie

s.

Use

.con

text

.(e.g

.,.th

e.ov

eral

l.mea

nin

g.of

.a.

sent

ence

,.par

agra

ph,.o

r.te

xt;.a

.wor

d’s.

posi

tion

.or.

func

tion

.in.a

.sen

tenc

e).a

s.a.

clue

.to.

the.

mea

nin

g.of

.a.w

ord.

or.p

hra

se.

L.9

-10.

4aX

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eId

enti

fy.a

nd.c

orre

ctly

.use

.pat

tern

s.of

.wor

d.ch

ange

s.th

at.in

dic

ate.

dif

fere

nt.m

ean

ings

.or.

part

s.of

.spe

ech.

(e.g

.,.an

alyz

e,.a

naly

sis,

.ana

lyti

cal;.

advo

cate

,.adv

ocac

y).

L.9

-10.

4b

Con

sult.

gene

ral.a

nd.s

peci

aliz

ed.r

efer

ence

.m

ater

ials

.(e.g

.,.d

icti

onar

ies,

.glo

ssar

ies,

.th

esau

ruse

s),.b

oth.

prin

t.an

d.d

igit

al,.t

o.fi

nd.t

he.

pron

unc

iati

on.o

f.a.w

ord.

or.d

eter

min

e.or

.cla

rify

.it

s.pr

ecis

e.m

ean

ing,

.its.

part

.of.s

peec

h,.o

r.it

s.et

ymol

ogy.

L.9

-10.

4c

Ver

ify.

the.

prel

imin

ary.

dete

rmin

atio

n.of

.the

.m

ean

ing.

of.a

.wor

d.or

.ph

rase

.(e.g

.,.by

.che

ckin

g.th

e.in

ferr

ed.m

ean

ing.

in.c

onte

xt.o

r.in

.a.

dic

tion

ary)

.

L.9

-10.

4dX

X

Dem

onst

rate

.und

erst

and

ing.

of.fi

gu

rati

ve.

lang

uage

,.wor

d.re

lati

onsh

ips,

.and

.nua

nces

.in.

wor

d.m

ean

ings

.

Inte

rpre

t.fig

ure

s.of

.spe

ech.

(e.g

.,.eu

phem

ism

,.ox

ymor

on).i

n.co

ntex

t.an

d.an

alyz

e.th

eir.

role

.in.

the.

text

.

L.9

-10.

5aX

X

Ana

lyze

.nua

nces

.in.t

he.m

ean

ing.

of.w

ord

s.w

ith.

sim

ilar.

deno

tati

ons.

L.9

-10.

5bX

X

Acq

uir

e.an

d.us

e.ac

cura

tely

.gen

eral

.aca

dem

ic.

and.

dom

ain-

spec

ific

.wor

ds.a

nd.p

hra

ses,

.su

ffic

ient

.for.

read

ing,

.wri

ting

,.spe

akin

g,.a

nd.

liste

nin

g.at

.the

.col

lege

.and

.car

eer.

read

ines

s.le

vel;.

dem

onst

rate

.inde

pend

ence

.in.g

athe

ring

.vo

cabu

lary

.kno

wle

dge.

whe

n.co

nsi

deri

ng.a

.w

ord.

or.p

hra

se.im

port

ant.

to.c

ompr

ehen

sion

.or.

expr

essi

on.

L.9

-10.

6X

X

11-1

2L

ang

uage

Con

vent

ion

s.of

.Sta

ndar

d.E

nglis

h

Dem

onst

rate

.com

man

d.of

.the

.con

vent

ion

s.of

.st

anda

rd.E

nglis

h.g

ram

mar

.and

.usa

ge.w

hen.

wri

ting

.or.

spea

king

.

App

ly.t

he.u

nder

stan

din

g.th

at.u

sage

.is.a

.mat

ter.

of.c

onve

ntio

n,.c

an.c

hang

e.ov

er.t

ime,

.and

.is.

som

etim

es.c

onte

sted

.

L.1

1-12

.1a

X

Res

olve

.issu

es.o

f.com

plex

.or.

cont

este

d.us

age,

.co

nsu

lting

.ref

eren

ces.

(e.g

.,.M

erri

am-W

ebst

er’s

D

icti

onar

y of

Eng

lish

Usa

ge, G

arne

r’s M

oder

n A

mer

ican

Usa

ge).a

s.ne

eded

.

L.1

1-12

.1b

En

sure

.su

bjec

t-ve

rb.a

nd.p

rono

un-

ante

cede

nt.

agre

emen

t.L

.3.1

fX

X

Pro

duce

.com

plet

e.se

nten

ces,

.rec

ogn

izin

g.an

d.co

rrec

ting

.inap

prop

riat

e.fr

agm

ents

.and

.ru

n-on

s.L

.4.1

fX

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eC

orre

ctly

.use

.freq

uent

ly.c

onfu

sed.

wor

ds.

(e.g

.,.to

/to

o/tw

o; t

here

/the

ir).

L.4

.1g

XX

Rec

ogn

ize.

and.

corr

ect.

inap

prop

riat

e.sh

ifts

.in.

verb

.ten

se.

L.5

.1d

XX

Rec

ogn

ize.

and.

corr

ect.

inap

prop

riat

e.sh

ifts

.in.

pron

oun.

num

ber.

and.

pers

on.

L.6

.1c

XX

Rec

ogn

ize.

and.

corr

ect.

vag

ue.p

rono

un

s.(i.

e.,.o

nes.

wit

h.u

ncle

ar.o

r.am

big

uous

.ant

eced

ents

).L

.6.1

dX

X

Rec

ogn

ize.

vari

atio

ns.

from

.sta

ndar

d.E

nglis

h.in

.th

eir.

own.

and.

othe

rs’.w

riti

ng.a

nd.s

peak

ing,

.and

.id

enti

fy.a

nd.u

se.s

trat

egie

s.to

.impr

ove.

expr

essi

on.

in.c

onve

ntio

nal.l

ang

uage

.

L.6

.1e

XX

Plac

e.ph

rase

s.an

d.cl

ause

s.w

ith

in.a

.sen

tenc

e,.

reco

gn

izin

g.an

d.co

rrec

ting

.mis

plac

ed.a

nd.

dang

ling.

mod

ifie

rs.

L.7

.1c

XX

Rec

ogn

ize.

and.

corr

ect.

inap

prop

riat

e.sh

ifts

.in.

verb

.voi

ce.a

nd.m

ood.

L.8

.1d

XX

Use

.par

alle

l.str

uctu

re.

L.9

-10.

1aX

X

Dem

onst

rate

.com

man

d.of

.the

.con

vent

ion

s.of

.st

anda

rd.E

nglis

h.ca

pita

lizat

ion,

.pu

nctu

atio

n,.a

nd.

spel

ling.

whe

n.w

riti

ng.

Obs

erve

.hyp

hena

tion

.con

vent

ion

s.L

.11-

12.2

aX

X

Spel

l.cor

rect

ly.

L.1

1-12

.2b

XX

Use

.pu

nctu

atio

n.(c

omm

as,.p

aren

thes

es,.d

ashe

s).

to.s

et.o

ff.no

nre

stri

ctiv

e/pa

rent

heti

cal.e

lem

ents

.L

.6.2

aX

X

Kno

wle

dge.

of.

Lan

gua

geA

pply

.kno

wle

dge.

of.la

ngua

ge.t

o.u

nder

stan

d.ho

w.la

ngua

ge.fu

ncti

ons.

in.d

iffe

rent

.con

text

s,.

to.m

ake.

effe

ctiv

e.ch

oice

s.fo

r.m

ean

ing.

or.s

tyle

,.an

d.to

.com

preh

end.

mor

e.fu

lly.w

hen.

read

ing.

or.

liste

nin

g.

Var

y.sy

ntax

.for.

effe

ct,.c

onsu

lting

.ref

eren

ces.

(e.g

.,.Tu

fte’

s.A

rtfu

l Sen

tenc

es).f

or.g

uid

ance

.as.

need

ed;.

appl

y.an

.und

erst

and

ing.

of.s

ynta

x.to

.the

.stu

dy.o

f.co

mpl

ex.t

exts

.whe

n.re

adin

g.

L.1

1-12

.3a

XX

Cho

ose.

wor

ds.a

nd.p

hra

ses.

for.

effe

ct.

L.3

.3a

XX

Cho

ose.

punc

tuat

ion.

for.

effe

ct.

L.4

.3b

XX

Mai

ntai

n.co

nsi

sten

cy.in

.sty

le.a

nd.t

one.

L.6

.3b

XX

Cho

ose.

lang

uage

.tha

t.ex

pres

ses.

idea

s.pr

ecis

ely.

and.

conc

isel

y,.r

ecog

niz

ing.

and.

elim

inat

ing.

wor

din

ess.

and.

redu

ndan

cy.

L.7

.3a

XX


Appendixes

Eng

lish.

Lang

uage

.Art

s.Si

de-b

y-Si

de.A

lign

men

t.T

able

:.AP®

—C

omm

on.C

ore.

Stat

e.St

anda

rds

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Str

and

Ban

dS

tan

dar

dS

kil

lC

CS

S

IDA

P

Lit

erat

ure

AP

L

ang

uag

eV

ocab

ula

ry.

Acq

uis

itio

n.an

d.U

se

Det

erm

ine.

or.c

lari

fy.t

he.m

ean

ing.

of.u

nkn

own.

and.

mu

ltipl

e-m

ean

ing.

wor

ds.a

nd.p

hra

ses.

base

d.on

.gra

des

11–1

2 re

adin

g an

d co

nten

t,.ch

oosi

ng.

flexi

bly.

from

.a.r

ange

.of.s

trat

egie

s.

Use

.con

text

.(e.g

.,.th

e.ov

eral

l.mea

nin

g.of

.a.

sent

ence

,.par

agra

ph,.o

r.te

xt;.a

.wor

d’s.

posi

tion

.or.

func

tion

.in.a

.sen

tenc

e).a

s.a.

clue

.to.

the.

mea

nin

g.of

.a.w

ord.

or.p

hra

se.

L.1

1-12

.4a

XX

Iden

tify

.and

.cor

rect

ly.u

se.p

atte

rns.

of.w

ord.

chan

ges.

that

.ind

icat

e.d

iffe

rent

.mea

nin

gs.o

r.pa

rts.

of.s

peec

h.(e

.g.,.

conc

eive

, con

cept

ion,

co

ncei

vabl

e).

L.1

1-12

.4b

Con

sult.

gene

ral.a

nd.s

peci

aliz

ed.r

efer

ence

.m

ater

ials

.(e.g

.,.d

icti

onar

ies,

.glo

ssar

ies,

.th

esau

ruse

s),.b

oth.

prin

t.an

d.d

igit

al,.t

o.fi

nd.t

he.

pron

unc

iati

on.o

f.a.w

ord.

or.d

eter

min

e.or

.cla

rify

.it

s.pr

ecis

e.m

ean

ing,

.its.

part

.of.s

peec

h,.it

s.et

ymol

ogy,

.or.

its.

stan

dard

.usa

ge.

L.1

1-12

.4c

Ver

ify.

the.

prel

imin

ary.

dete

rmin

atio

n.of

.the

.m

ean

ing.

of.a

.wor

d.or

.ph

rase

.(e.g

.,.by

.che

ckin

g.th

e.in

ferr

ed.m

ean

ing.

in.c

onte

xt.o

r.in

.a.

dic

tion

ary)

.

L.1

1-12

.4d

XX

Dem

onst

rate

.und

erst

and

ing.

of.fi

gu

rati

ve.

lang

uage

,.wor

d.re

lati

onsh

ips,

.and

.nua

nces

.in.

wor

d.m

ean

ings

.

Inte

rpre

t.fig

ure

s.of

.spe

ech.

(e.g

.,.hy

perb

ole,

.pa

rado

x).in

.con

text

.and

.ana

lyze

.the

ir.r

ole.

in.t

he.

text

.

L.1

1-12

.5a

XX

Ana

lyze

.nua

nces

.in.t

he.m

ean

ing.

of.w

ord

s.w

ith.

sim

ilar.

deno

tati

ons.

L.1

1-12

.5b

XX

Acq

uir

e.an

d.us

e.ac

cura

tely

.gen

eral

.aca

dem

ic.

and.

dom

ain-

spec

ific

.wor

ds.a

nd.p

hra

ses,

.su

ffic

ient

.for.

read

ing,

.wri

ting

,.spe

akin

g,.a

nd.

liste

nin

g.at

.the

.col

lege

.and

.car

eer.

read

ines

s.le

vel;.

dem

onst

rate

.inde

pend

ence

.in.g

athe

ring

.vo

cabu

lary

.kno

wle

dge.

whe

n.co

nsi

deri

ng.a

.w

ord.

or.p

hra

se.im

port

ant.

to.c

ompr

ehen

sion

.or.

expr

essi

on.

L.1

1-12

.6X

X


Appendixes

Appendix.BAP Calculus, AP Statistics, and AP Computer Science A — Common Core State Standards Side-by-Side Alignment Table


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

6R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Und

erst

and.

rati

o.co

ncep

ts.a

nd.u

se.

rati

o.re

ason

ing.

to.

solv

e.pr

oble

ms.

Und

erst

and.

the.

conc

ept.

of.a

.rat

io.a

nd.

use.

rati

o.la

ngua

ge.t

o.de

scri

be.a

.rat

io.

rela

tion

ship

.bet

wee

n.tw

o.q

uant

itie

s.

6.R

P.1

XX

XX

6R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Und

erst

and.

rati

o.co

ncep

ts.a

nd.u

se.

rati

o.re

ason

ing.

to.

solv

e.pr

oble

ms.

Und

erst

and.

the.

conc

ept.

of.a

.un

it.r

ate.

a/b.

asso

ciat

ed.w

ith.

a.ra

tio.

a:b.

wit

h b

≠.0,

.and

.use

.rat

e.la

ngua

ge.in

.the

.co

ntex

t.of

.a.r

atio

.rel

atio

nsh

ip.

6.R

P.2

XX

XX

6R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Und

erst

and.

rati

o.co

ncep

ts.a

nd.u

se.

rati

o.re

ason

ing.

to.

solv

e.pr

oble

ms.

Use

.rat

io.a

nd.r

ate.

reas

onin

g.to

.sol

ve.

real

-wor

ld.a

nd.m

athe

mat

ical

.pro

blem

s,.

e.g.

,.by.

reas

onin

g.ab

out.

tabl

es.o

f.eq

uiv

alen

t.ra

tios

,.tap

e.d

iag

ram

s,.

dou

ble.

num

ber.

line.

dia

gra

ms,

.or.

equa

tion

s.

Mak

e.ta

bles

.of.e

qu

ival

ent.

rati

os.r

elat

ing.

qua

ntit

ies.

wit

h.w

hole

-nu

mbe

r.m

easu

rem

ents

,.fin

d.m

issi

ng.v

alue

s.in

.the

.ta

bles

,.and

.plo

t.th

e.pa

irs.

of.v

alue

s.on

.the

.co

ord

inat

e.pl

ane.

.Use

.ta

bles

.to.

com

pare

.rat

ios.

6.R

P.3a

XX

XX

6R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Und

erst

and.

rati

o.co

ncep

ts.a

nd.u

se.

rati

o.re

ason

ing.

to.

solv

e.pr

oble

ms.

Use

.rat

io.a

nd.r

ate.

reas

onin

g.to

.sol

ve.

real

-wor

ld.a

nd.m

athe

mat

ical

.pro

blem

s,.

e.g.

,.by.

reas

onin

g.ab

out.

tabl

es.o

f.eq

uiv

alen

t.ra

tios

,.tap

e.d

iag

ram

s,.

dou

ble.

num

ber.

line.

dia

gra

ms,

.or.

equa

tion

s.

Solv

e.u

nit

.rat

e.pr

oble

ms.

incl

udin

g.th

ose.

invo

lvin

g.u

nit

.pri

cing

.and

.con

stan

t.sp

eed.

6.R

P.3b

XX

XX

6R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Und

erst

and.

rati

o.co

ncep

ts.a

nd.u

se.

rati

o.re

ason

ing.

to.

solv

e.pr

oble

ms.

Use

.rat

io.a

nd.r

ate.

reas

onin

g.to

.sol

ve.

real

-wor

ld.a

nd.m

athe

mat

ical

.pro

blem

s,.

e.g.

,.by.

reas

onin

g.ab

out.

tabl

es.o

f.eq

uiv

alen

t.ra

tios

,.tap

e.d

iag

ram

s,.

dou

ble.

num

ber.

line.

dia

gra

ms,

.or.

equa

tion

s.

Fin

d.a.

perc

ent.

of.a

.q

uant

ity.

as.a

.rat

e.pe

r.10

0.(e

.g.,.

30%

.of.a

.qua

ntit

y.m

ean

s.30

/100

.tim

es.t

he.

qua

ntit

y);.s

olve

.pro

blem

s.in

volv

ing.

find

ing.

the.

who

le,.g

iven

.a.p

art.

and.

the.

perc

ent.

6.R

P.3c

XX

XX

6R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Und

erst

and.

rati

o.co

ncep

ts.a

nd.u

se.

rati

o.re

ason

ing.

to.

solv

e.pr

oble

ms.

Use

.rat

io.a

nd.r

ate.

reas

onin

g.to

.sol

ve.

real

-wor

ld.a

nd.m

athe

mat

ical

.pro

blem

s,.

e.g.

,.by.

reas

onin

g.ab

out.

tabl

es.o

f.eq

uiv

alen

t.ra

tios

,.tap

e.d

iag

ram

s,.

dou

ble.

num

ber.

line.

dia

gra

ms,

.or.

equa

tion

s.

Use

.rat

io.r

easo

nin

g.to

.co

nver

t.m

easu

rem

ent.

un

its;

.man

ipu

late

..an

d.tr

ansf

orm

.un

its.

appr

opri

atel

y.w

hen.

mu

ltipl

ying

.or.

div

idin

g.q

uant

itie

s.

6.R

P.3d

XX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

6T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.m

ulti

plic

atio

n.an

d.d

ivis

ion.

to.

div

ide.

frac

tion

s.by

.frac

tion

s.

Inte

rpre

t.an

d.co

mpu

te.q

uoti

ents

.of.

frac

tion

s,.a

nd.s

olve

.wor

d.pr

oble

ms.

invo

lvin

g.d

ivis

ion.

of.fr

acti

ons.

by.

frac

tion

s,.e

.g.,.

by.u

sing

.vis

ual.f

ract

ion.

mod

els.

and.

equa

tion

s.to

.rep

rese

nt.t

he.

prob

lem

.

6.N

S.1

XX

XX

6T

he.N

um

ber.

Syst

emC

ompu

te.f

luen

tly.

wit

h.m

ulti

-dig

it.

num

bers

.and

.find

.co

mm

on.fa

ctor

s.an

d.m

ulti

ples

.

Flu

entl

y.d

ivid

e.m

ulti

-dig

it.n

um

bers

.us

ing.

the.

stan

dard

.alg

orit

hm

.6.

NS.

2X

XX

X

6T

he.N

um

ber.

Syst

emC

ompu

te.f

luen

tly.

wit

h.m

ulti

-dig

it.

num

bers

.and

.find

.co

mm

on.fa

ctor

s.an

d.m

ulti

ples

.

Flu

entl

y.ad

d,.s

ubt

ract

,.mu

ltipl

y,.a

nd.

div

ide.

mu

lti-d

igit

.dec

imal

s.us

ing.

the.

stan

dard

.alg

orit

hm

.for.

each

.ope

rati

on.

6.N

S.3

XX

XX

6T

he.N

um

ber.

Syst

emC

ompu

te.f

luen

tly.

wit

h.m

ulti

-dig

it.

num

bers

.and

.find

.co

mm

on.fa

ctor

s.an

d.m

ulti

ples

.

Fin

d.th

e.g

reat

est.

com

mon

.fact

or.o

f.tw

o.w

hole

.nu

mbe

rs.le

ss.t

han.

or.e

qua

l.to.

100.

and.

the.

leas

t.co

mm

on.m

ulti

ple.

of.

two.

who

le.n

um

bers

.less

.tha

n.or

.eq

ual.

to.1

2..U

se.t

he.d

istr

ibut

ive.

prop

erty

.to.

expr

ess.

a.su

m.o

f.tw

o.w

hole

.nu

mbe

rs.

1–10

0.w

ith.

a.co

mm

on.fa

ctor

.as.

a.m

ulti

ple.

of.a

.su

m.o

f.tw

o.w

hole

.nu

mbe

rs.

wit

h.no

.com

mon

.fact

or.

6.N

S.4

XX

X

6T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.n

um

bers

.to.

the.

syst

em.o

f.rat

iona

l.nu

mbe

rs.

Und

erst

and.

that

.pos

itiv

e.an

d.ne

gati

ve.

num

bers

.are

.use

d.to

geth

er.t

o.de

scri

be.

qua

ntit

ies.

havi

ng.o

ppos

ite.

dir

ecti

ons.

or.

valu

es.(e

.g.,.

tem

pera

ture

.abo

ve/b

elow

.ze

ro,.e

leva

tion

.abo

ve/b

elow

.sea

.leve

l,.cr

edit

s/de

bits

,.pos

itiv

e/ne

gati

ve.e

lect

ric.

char

ge);.

use.

posi

tive

.and

.neg

ativ

e.nu

mbe

rs.t

o.re

pres

ent.

qua

ntit

ies.

in.r

eal-

wor

ld.c

onte

xts,

.exp

lain

ing.

the.

mea

nin

g.of

.0.in

.eac

h.si

tuat

ion.

6.N

S.5

XX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

6T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.n

um

bers

.to.

the.

syst

em.o

f.rat

iona

l.nu

mbe

rs.

Und

erst

and.

a.ra

tion

al.n

um

ber.

as.a

.po

int.

on.t

he.n

um

ber.

line.

.Ext

end.

num

ber.

line.

dia

gra

ms.

and.

coor

din

ate.

axes

.fam

iliar

.from

.pre

viou

s.g

rade

s.to

.rep

rese

nt.p

oint

s.on

.the

.line

.and

.in

.the

.pla

ne.w

ith.

nega

tive

.nu

mbe

r.co

ord

inat

es.

Rec

ogn

ize.

oppo

site

.sig

ns.

of.n

um

bers

.as.

ind

icat

ing.

loca

tion

s.on

.opp

osit

e.si

des.

of.0

.on.

the.

num

ber.

line;

.rec

ogn

ize.

that

.the

.op

posi

te.o

f.the

.opp

osit

e.of

.a.

num

ber.

is.t

he.n

um

ber.

itse

lf,.e

.g.,.

–(–3

).=.3

,.and

.th

at.0

.is.it

s.ow

n.op

posi

te.

6.N

S.6a

XX

XX

6T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.n

um

bers

.to.

the.

syst

em.o

f.rat

iona

l.nu

mbe

rs.

Und

erst

and.

a.ra

tion

al.n

um

ber.

as.a

.po

int.

on.t

he.n

um

ber.

line.

.Ext

end.

num

ber.

line.

dia

gra

ms.

and.

coor

din

ate.

axes

.fam

iliar

.from

.pre

viou

s.g

rade

s.to

.rep

rese

nt.p

oint

s.on

.the

.line

.and

.in

.the

.pla

ne.w

ith.

nega

tive

.nu

mbe

r.co

ord

inat

es.

Und

erst

and.

sig

ns.

of.

num

bers

.in.o

rder

ed.

pair

s.as

.ind

icat

ing.

loca

tion

s.in

.qua

dra

nts.

of.t

he.c

oord

inat

e.pl

ane;

.re

cog

niz

e.th

at.w

hen.

two.

orde

red.

pair

s.d

iffe

r.on

ly.

by.s

ign

s,.t

he.lo

cati

ons.

of.

the.

poin

ts.a

re.r

elat

ed.b

y.re

flect

ion

s.ac

ross

.one

.or.

both

.axe

s.

6.N

S.6b

XX

XX

6T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.n

um

bers

.to.

the.

syst

em.o

f.rat

iona

l.nu

mbe

rs.

Und

erst

and.

a.ra

tion

al.n

um

ber.

as.a

.po

int.

on.t

he.n

um

ber.

line.

.Ext

end.

num

ber.

line.

dia

gra

ms.

and.

coor

din

ate.

axes

.fam

iliar

.from

.pre

viou

s.g

rade

s.to

.rep

rese

nt.p

oint

s.on

.the

.line

.and

.in

.the

.pla

ne.w

ith.

nega

tive

.nu

mbe

r.co

ord

inat

es.

Fin

d.an

d.po

siti

on.in

tege

rs.

and.

othe

r.ra

tion

al.

num

bers

.on.

a.ho

rizo

ntal

.or

.ver

tica

l.nu

mbe

r.lin

e.d

iag

ram

;.fin

d.an

d.po

siti

on.

pair

s.of

.inte

gers

.and

.oth

er.

rati

onal

.nu

mbe

rs.o

n.a.

coor

din

ate.

plan

e.

6.N

S.6c

XX

XX

6T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.n

um

bers

.to.

the.

syst

em.o

f.rat

iona

l.nu

mbe

rs.

Und

erst

and.

orde

ring

.and

.abs

olut

e.va

lue.

of.r

atio

nal.n

um

bers

.In

terp

ret.

stat

emen

ts.o

f.in

equa

lity.

as.s

tate

men

ts.

abou

t.th

e.re

lati

ve.p

osit

ion.

of.t

wo.

num

bers

.on.

a.nu

mbe

r.lin

e.d

iag

ram

.

6.N

S.7a

XX

.X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

6T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.n

um

bers

.to.

the.

syst

em.o

f.rat

iona

l.nu

mbe

rs.

Und

erst

and.

orde

ring

.and

.abs

olut

e.va

lue.

of.r

atio

nal.n

um

bers

.W

rite

,.int

erpr

et,.a

nd.

expl

ain.

stat

emen

ts.o

f.or

der.

for.

rati

onal

.nu

mbe

rs.

in.r

eal-w

orld

.con

text

s.

6.N

S.7b

XX

XX

6T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.n

um

bers

.to.

the.

syst

em.o

f.rat

iona

l.nu

mbe

rs.

Und

erst

and.

orde

ring

.and

.abs

olut

e.va

lue.

of.r

atio

nal.n

um

bers

.U

nder

stan

d.th

e.ab

solu

te.

valu

e.of

.a.r

atio

nal.n

um

ber.

as.it

s.d

ista

nce.

from

.0.

on.t

he.n

um

ber.

line;

.in

terp

ret.

abso

lute

.val

ue.a

s.m

agn

itud

e.fo

r.a.

posi

tive

.or

.neg

ativ

e.q

uant

ity.

in.a

.re

al-w

orld

.sit

uati

on.

6.N

S.7c

XX

XX

6T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.n

um

bers

.to.

the.

syst

em.o

f.rat

iona

l.nu

mbe

rs.

Und

erst

and.

orde

ring

.and

.abs

olut

e.va

lue.

of.r

atio

nal.n

um

bers

.D

isti

ngu

ish.

com

pari

son

s.of

.abs

olut

e.va

lue.

from

.st

atem

ents

.abo

ut.o

rder

.

6.N

S.7d

XX

.

6T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.n

um

bers

.to.

the.

syst

em.o

f.rat

iona

l.nu

mbe

rs.

Solv

e.re

al-w

orld

.and

.mat

hem

atic

al.

prob

lem

s.by

.gra

phin

g.po

ints

.in.a

ll.fo

ur.

qua

dra

nts.

of.t

he.c

oord

inat

e.pl

ane.

.In

clud

e.us

e.of

.coo

rdin

ates

.and

.abs

olut

e.va

lue.

to.fi

nd.d

ista

nces

.bet

wee

n.po

ints

.w

ith.

the.

sam

e.fi

rst.

coor

din

ate.

or.t

he.

sam

e.se

cond

.coo

rdin

ate.

6.N

S.8

XX

XX

6E

xpre

ssio

ns.

and.

Eq

uati

ons

App

ly.a

nd.

exte

nd.p

revi

ous.

und

erst

and

ings

.of

.ari

thm

etic

.to

.alg

ebra

ic.

expr

essi

ons.

Wri

te.a

nd.e

valu

ate.

num

eric

al.

expr

essi

ons.

invo

lvin

g.w

hole

-nu

mbe

r.ex

pone

nts.

6.E

E.1

XX

XX

6E

xpre

ssio

ns.

and.

Eq

uati

ons

App

ly.a

nd.

exte

nd.p

revi

ous.

und

erst

and

ings

.of

.ari

thm

etic

.to

.alg

ebra

ic.

expr

essi

ons.

Wri

te,.r

ead,

.and

.eva

luat

e.ex

pres

sion

s.in

.w

hic

h.le

tter

s.st

and.

for.

num

bers

.W

rite

.exp

ress

ion

s.th

at.

reco

rd.o

pera

tion

s.w

ith.

num

bers

.and

.wit

h.le

tter

s.st

and

ing.

for.

num

bers

.

6.E

E.2

aX

XX

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

6E

xpre

ssio

ns.

and.

Eq

uati

ons

App

ly.a

nd.

exte

nd.p

revi

ous.

und

erst

and

ings

.of

.ari

thm

etic

.to

.alg

ebra

ic.

expr

essi

ons.

Wri

te,.r

ead,

.and

.eva

luat

e.ex

pres

sion

s.in

.w

hic

h.le

tter

s.st

and.

for.

num

bers

.Id

enti

fy.p

arts

.of.a

n.ex

pres

sion

.usi

ng.

mat

hem

atic

al.t

erm

s.(s

um

,.te

rm,.p

rodu

ct,.f

acto

r,.q

uoti

ent,

.coe

ffic

ient

);.vi

ew.o

ne.o

r.m

ore.

part

s.of

.an

.exp

ress

ion.

as.a

.sin

gle.

enti

ty.

6.E

E.2

bX

XX

X

6E

xpre

ssio

ns.

and.

Eq

uati

ons

App

ly.a

nd.

exte

nd.p

revi

ous.

und

erst

and

ings

.of

.ari

thm

etic

.to

.alg

ebra

ic.

expr

essi

ons.

Wri

te,.r

ead,

.and

.eva

luat

e.ex

pres

sion

s.in

.w

hic

h.le

tter

s.st

and.

for.

num

bers

.E

valu

ate.

expr

essi

ons.

at.s

peci

fic.v

alue

s.of

.th

eir.

vari

able

s..In

clud

e.ex

pres

sion

s.th

at.a

rise

.fr

om.fo

rmu

las.

used

.in.re

al-

wor

ld.p

robl

ems.

.Per

form

.ar

ith

met

ic.o

pera

tion

s,.

incl

udin

g.th

ose.

invo

lvin

g.w

hole

-nu

mbe

r.ex

pone

nts,

.in

.the

.con

vent

iona

l.or

der.

whe

n.th

ere.

are.

no.

pare

nthe

ses.

to.s

peci

fy.a

.pa

rtic

ula

r.or

der.

(Ord

er.o

f.O

pera

tion

s).

6.E

E.2

cX

XX

X

6E

xpre

ssio

ns.

and.

Eq

uati

ons

App

ly.a

nd.

exte

nd.p

revi

ous.

und

erst

and

ings

.of

.ari

thm

etic

.to

.alg

ebra

ic.

expr

essi

ons.

App

ly.t

he.p

rope

rtie

s.of

.ope

rati

ons.

to.

gene

rate

.eq

uiv

alen

t.ex

pres

sion

s.6.

EE

.3X

XX

X

6E

xpre

ssio

ns.

and.

Eq

uati

ons

App

ly.a

nd.

exte

nd.p

revi

ous.

und

erst

and

ings

.of

.ari

thm

etic

.to

.alg

ebra

ic.

expr

essi

ons.

Iden

tify

.whe

n.tw

o.ex

pres

sion

s.ar

e.eq

uiv

alen

t.(i.

e.,.w

hen.

the.

two.

expr

essi

ons.

nam

e.th

e.sa

me.

num

ber.

rega

rdle

ss.o

f.wh

ich.

valu

e.is

.su

bsti

tute

d.in

to.t

hem

).

6.E

E.4

XX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

6E

xpre

ssio

ns.

and.

Eq

uati

ons

Rea

son.

abou

t.an

d.so

lve.

one-

vari

able

.eq

uati

ons.

and.

ineq

ualit

ies.

Und

erst

and.

solv

ing.

an.e

qua

tion

.or.

ineq

ualit

y.as

.a.p

roce

ss.o

f.an

swer

ing.

a.q

uest

ion:

.wh

ich.

valu

es.fr

om.a

.sp

ecif

ied.

set,

.if.a

ny,.m

ake.

the.

equa

tion

.or

.ineq

ualit

y.tr

ue?.

Use

.su

bsti

tuti

on.t

o.de

term

ine.

whe

ther

.a.g

iven

.nu

mbe

r.in

.a.

spec

ifie

d.se

t.m

akes

.an.

equa

tion

.or.

ineq

ualit

y.tr

ue.

6.E

E.5

XX

XX

6E

xpre

ssio

ns.

and.

Eq

uati

ons

Rea

son.

abou

t.an

d.so

lve.

one-

vari

able

.eq

uati

ons.

and.

ineq

ualit

ies.

Use

.var

iabl

es.t

o.re

pres

ent.

num

bers

.an

d.w

rite

.exp

ress

ion

s.w

hen.

solv

ing.

a.re

al-w

orld

.or.

mat

hem

atic

al.p

robl

em;.

und

erst

and.

that

.a.v

aria

ble.

can.

repr

esen

t.an

.un

know

n.nu

mbe

r,.or

,.de

pend

ing.

on.t

he.p

urp

ose.

at.h

and,

.any

.nu

mbe

r.in

.a.s

peci

fied.

set.

6.E

E.6

XX

XX

6E

xpre

ssio

ns.

and.

Eq

uati

ons

Rea

son.

abou

t.an

d.so

lve.

one-

vari

able

.eq

uati

ons.

and.

ineq

ualit

ies.

Solv

e.re

al-w

orld

.and

.mat

hem

atic

al.

prob

lem

s.by

.wri

ting

.and

.sol

ving

.eq

uati

ons.

of.t

he.fo

rm.x

.+.p

.=.q

.and

.px

= q

.for.

case

s.in

.wh

ich.

p,.q

.and

.x.a

re.

all.n

onne

gati

ve.r

atio

nal.n

um

bers

.

6.E

E.7

XX

XX

6E

xpre

ssio

ns.

and.

Eq

uati

ons

Rea

son.

abou

t.an

d.so

lve.

one-

vari

able

.eq

uati

ons.

and.

ineq

ualit

ies.

Wri

te.a

n.in

equa

lity.

of.t

he.fo

rm.

x.>

.c.o

r.x.

<.c

.to.

repr

esen

t.a.

con

stra

int.

or.c

ond

itio

n.in

.a.r

eal-w

orld

.or.

mat

hem

atic

al.p

robl

em..R

ecog

niz

e.th

at.in

equa

litie

s.of

.the

.form

.x.>

.c.o

r.x.

<.c

.hav

e.in

fin

itel

y.m

any.

solu

tion

s;.

repr

esen

t.so

luti

ons.

of.s

uch.

ineq

ualit

ies.

on.n

um

ber.

line.

dia

gra

ms.

6.E

E.8

XX

XX

6E

xpre

ssio

ns.

and.

Eq

uati

ons

Rep

rese

nt.

and.

anal

yze.

qua

ntit

ativ

e.re

lati

onsh

ips.

betw

een.

depe

nden

t.an

d.in

depe

nden

t.va

riab

les.

Use

.var

iabl

es.t

o.re

pres

ent.

two.

qua

ntit

ies.

in.a

.rea

l-wor

ld.p

robl

em.t

hat.

chan

ge.in

.rel

atio

nsh

ip.t

o.on

e.an

othe

r;.

wri

te.a

n.eq

uati

on.t

o.ex

pres

s.on

e.q

uant

ity,

.tho

ught

.of.a

s.th

e.de

pend

ent.

vari

able

,.in.

term

s.of

.the

.oth

er.q

uant

ity,

.th

ough

t.of

.as.

the.

inde

pend

ent.

vari

able

..A

naly

ze.t

he.r

elat

ion

ship

.bet

wee

n.th

e.de

pend

ent.

and.

inde

pend

ent.

vari

able

s.us

ing.

gra

phs.

and.

tabl

es,.a

nd.r

elat

e.th

ese.

to.t

he.e

qua

tion

.

6.E

E.9

XX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

6G

eom

etry

Solv

e.re

al-w

orld

.an

d.m

athe

mat

ical

.pr

oble

ms.

invo

lvin

g.ar

ea,.

surf

ace.

area

,.and

.vo

lum

e.

Fin

d.th

e.ar

ea.o

f.rig

ht.t

rian

gles

,.oth

er.

tria

ngle

s,.s

peci

al.q

uad

rila

tera

ls,.a

nd.

poly

gon

s.by

.com

posi

ng.in

to.r

ecta

ngle

s.or

.dec

ompo

sing

.into

.tri

angl

es.a

nd.

othe

r.sh

apes

;.app

ly.t

hese

.tec

hn

ique

s.in

.the

.con

text

.of.s

olvi

ng.r

eal-w

orld

.and

.m

athe

mat

ical

.pro

blem

s.

6.G

.1X

XX

6G

eom

etry

Solv

e.re

al-w

orld

.an

d.m

athe

mat

ical

.pr

oble

ms.

invo

lvin

g.ar

ea,.

surf

ace.

area

,.and

.vo

lum

e.

Fin

d.th

e.vo

lum

e.of

.a.r

ight

.rec

tang

ula

r.pr

ism

.wit

h.fr

acti

onal

.edg

e.le

ngth

s.by

.pac

king

.it.w

ith.

un

it.c

ube

s.of

.the

.ap

prop

riat

e.u

nit

.frac

tion

.edg

e.le

ngth

s,.

and.

show

.tha

t.th

e.vo

lum

e.is

.the

.sam

e.as

.wou

ld.b

e.fo

und

.by.

mu

ltipl

ying

.th

e.ed

ge.le

ngth

s.of

.the

.pri

sm..A

pply

.th

e.fo

rmu

las.

V.=

.l.w

h.a

nd.V

.= b

h.

to.fi

nd.v

olu

mes

.of.r

ight

.rec

tang

ula

r.pr

ism

s.w

ith.

frac

tion

al.e

dge.

leng

ths.

in.

the.

cont

ext.

of.s

olvi

ng.r

eal-w

orld

.and

.m

athe

mat

ical

.pro

blem

s.

6.G

.2X

X

6G

eom

etry

Solv

e.re

al-w

orld

.an

d.m

athe

mat

ical

.pr

oble

ms.

invo

lvin

g.ar

ea,.

surf

ace.

area

,.and

.vo

lum

e.

Dra

w.p

olyg

ons.

in.t

he.c

oord

inat

e.pl

ane.

giv

en.c

oord

inat

es.fo

r.th

e.ve

rtic

es;.

use.

coor

din

ates

.to.

find

.the

.leng

th.o

f.a.

side

.join

ing.

poin

ts.w

ith.

the.

sam

e.fi

rst.

coor

din

ate.

or.t

he.s

ame.

seco

nd.

coor

din

ate.

.App

ly.t

hese

.tec

hn

ique

s.in

.th

e.co

ntex

t.of

.sol

ving

.rea

l-wor

ld.a

nd.

mat

hem

atic

al.p

robl

ems.

6.G

.3X

X

6G

eom

etry

Solv

e.re

al-

wor

ld.a

nd.

mat

hem

atic

al.

prob

lem

s.in

volv

ing.

area

,.su

rfac

e.ar

ea,.a

nd.

volu

me.

Rep

rese

nt.t

hre

e-d

imen

sion

al.fi

gu

res.

usin

g.ne

ts.m

ade.

up.o

f.rec

tang

les.

and.

tria

ngle

s,.a

nd.u

se.t

he.n

ets.

to.fi

nd.t

he.

surf

ace.

area

.of.t

hese

.fig

ure

s..A

pply

.th

ese.

tech

niq

ues.

in.t

he.c

onte

xt.o

f.so

lvin

g.re

al-w

orld

.and

.mat

hem

atic

al.

prob

lem

s.

6.G

.4

6St

atis

tics

.and

.P

roba

bilit

yD

evel

op.

und

erst

and

ing.

of.s

tati

stic

al.

vari

abili

ty.

Rec

ogn

ize.

a.st

atis

tica

l.que

stio

n.as

.one

.th

at.a

ntic

ipat

es.v

aria

bilit

y.in

.the

.dat

a.re

late

d.to

.the

.que

stio

n.an

d.ac

cou

nts.

for.

it.in

.the

.an

swer

s.

6.SP

.1X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

6St

atis

tics

.and

.P

roba

bilit

yD

evel

op.

und

erst

and

ing.

of.s

tati

stic

al.

vari

abili

ty.

Und

erst

and.

that

.a.s

et.o

f.dat

a.co

llect

ed.

to.a

nsw

er.a

.sta

tist

ical

.que

stio

n.ha

s.a.

dis

trib

utio

n.w

hic

h.ca

n.be

.des

crib

ed.b

y.it

s.ce

nter

,.spr

ead,

.and

.ove

rall.

shap

e.

6.SP

.2X

6St

atis

tics

.and

.P

roba

bilit

yD

evel

op.

und

erst

and

ing.

of.s

tati

stic

al.

vari

abili

ty.

Rec

ogn

ize.

that

.a.m

easu

re.o

f.cen

ter.

for.

a.nu

mer

ical

.dat

a.se

t.su

mm

ariz

es.a

ll.of

.it

s.va

lues

.wit

h.a.

sing

le.n

um

ber,.

wh

ile.a

.m

easu

re.o

f.var

iati

on.d

escr

ibes

.how

.its.

valu

es.v

ary.

wit

h.a.

sing

le.n

um

ber.

6.SP

.3X

6St

atis

tics

.and

.P

roba

bilit

ySu

mm

ariz

e.an

d.de

scri

be.

dis

trib

utio

ns.

Dis

play

.nu

mer

ical

.dat

a.in

.plo

ts.o

n.a.

num

ber.

line,

.incl

udin

g.do

t.pl

ots,

.h

isto

gra

ms,

.and

.box

.plo

ts.

6.SP

.4X

6St

atis

tics

.and

.P

roba

bilit

ySu

mm

ariz

e.an

d.de

scri

be.

dis

trib

utio

ns.

Sum

mar

ize.

num

eric

al.d

ata.

sets

.in.

rela

tion

.to.

thei

r.co

ntex

t,.s

uch.

as.b

y:R

epor

ting

.the

.nu

mbe

r.of

.ob

serv

atio

ns.

6.SP

.5a

X

6St

atis

tics

.and

.P

roba

bilit

ySu

mm

ariz

e.an

d.de

scri

be.

dis

trib

utio

ns.

Sum

mar

ize.

num

eric

al.d

ata.

sets

.in.

rela

tion

.to.

thei

r.co

ntex

t,.s

uch.

as.b

y:D

escr

ibin

g.th

e.na

ture

.of

.the

.att

ribu

te.u

nder

.in

vest

igat

ion,

.incl

udin

g.ho

w.it

.was

.mea

sure

d.an

d.it

s.u

nit

s.of

.mea

sure

men

t.

6.SP

.5b

X

6St

atis

tics

.and

.P

roba

bilit

ySu

mm

ariz

e.an

d.de

scri

be.

dis

trib

utio

ns.

Sum

mar

ize.

num

eric

al.d

ata.

sets

.in.

rela

tion

.to.

thei

r.co

ntex

t,.s

uch.

as.b

y:G

ivin

g.q

uant

itat

ive.

mea

sure

s.of

.cen

ter.

(med

ian.

and

/or.

mea

n).a

nd.

vari

abili

ty.(i

nter

qua

rtile

.ra

nge.

and

/or.

mea

n.ab

solu

te.d

evia

tion

),.as

.w

ell.a

s.de

scri

bing

.any

.ov

eral

l.pat

tern

.and

.any

.st

riki

ng.d

evia

tion

s.fr

om.

the.

over

all.p

atte

rn.w

ith.

refe

renc

e.to

.the

.con

text

.in

.wh

ich.

the.

data

.wer

e.ga

ther

ed.

6.SP

.5c

X

6St

atis

tics

.and

.P

roba

bilit

ySu

mm

ariz

e.an

d.de

scri

be.

dis

trib

utio

ns.

Sum

mar

ize.

num

eric

al.d

ata.

sets

.in.

rela

tion

.to.

thei

r.co

ntex

t,.s

uch.

as.b

y:R

elat

ing.

the.

choi

ce.o

f.m

easu

res.

of.c

ente

r.an

d.va

riab

ility

.to.

the.

shap

e.of

.th

e.da

ta.d

istr

ibut

ion.

and.

the.

cont

ext.

in.w

hic

h.th

e.da

ta.w

ere.

gath

ered

.

6.SP

.5d

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

7R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Ana

lyze

.pr

opor

tion

al.

rela

tion

ship

s.an

d.us

e.th

em.t

o.so

lve.

real

-wor

ld.a

nd.

mat

hem

atic

al.

prob

lem

s.

Com

pute

.un

it.r

ates

.ass

ocia

ted.

wit

h.ra

tios

.of.f

ract

ion

s,.in

clud

ing.

rati

os.o

f.le

ngth

s,.a

reas

.and

.oth

er.q

uant

itie

s.m

easu

red.

in.li

ke.o

r.d

iffe

rent

.un

its.

7.R

P.1

XX

7R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Ana

lyze

.pr

opor

tion

al.

rela

tion

ship

s.an

d.us

e.th

em.t

o.so

lve.

real

-wor

ld.a

nd.

mat

hem

atic

al.

prob

lem

s.

Rec

ogn

ize.

and.

repr

esen

t.pr

opor

tion

al.

rela

tion

ship

s.be

twee

n.q

uant

itie

s.D

ecid

e.w

heth

er.t

wo.

qua

ntit

ies.

are.

in.a

.pr

opor

tion

al.r

elat

ion

ship

,.e.

g.,.b

y.te

stin

g.fo

r.eq

uiv

alen

t.ra

tios

.in.a

.ta

ble.

or.g

raph

ing.

on.a

.co

ord

inat

e.pl

ane.

and.

obse

rvin

g.w

heth

er.t

he.

gra

ph.is

.a.s

trai

ght.

line.

thro

ugh.

the.

orig

in.

7.R

P.2a

XX

X

7R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Ana

lyze

.pr

opor

tion

al.

rela

tion

ship

s.an

d.us

e.th

em.t

o.so

lve.

real

-wor

ld.a

nd.

mat

hem

atic

al.

prob

lem

s.

Rec

ogn

ize.

and.

repr

esen

t.pr

opor

tion

al.

rela

tion

ship

s.be

twee

n.q

uant

itie

s.Id

enti

fy.t

he.c

onst

ant.

of.p

ropo

rtio

nalit

y.(u

nit

.ra

te).i

n.ta

bles

,.gra

phs,

.eq

uati

ons,

.dia

gra

ms,

.and

.ve

rbal

.des

crip

tion

s.of

.pr

opor

tion

al.r

elat

ion

ship

s.

7.R

P.2b

XX

X

7R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Ana

lyze

.pr

opor

tion

al.

rela

tion

ship

s.an

d.us

e.th

em.t

o.so

lve.

real

-wor

ld.a

nd.

mat

hem

atic

al.

prob

lem

s.

Rec

ogn

ize.

and.

repr

esen

t.pr

opor

tion

al.

rela

tion

ship

s.be

twee

n.q

uant

itie

s.R

epre

sent

.pro

port

iona

l.re

lati

onsh

ips.

by.

equa

tion

s.

7.R

P.2c

XX

X

7R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Ana

lyze

.pr

opor

tion

al.

rela

tion

ship

s.an

d.us

e.th

em.t

o.so

lve.

real

-wor

ld.a

nd.

mat

hem

atic

al.

prob

lem

s.

Rec

ogn

ize.

and.

repr

esen

t.pr

opor

tion

al.

rela

tion

ship

s.be

twee

n.q

uant

itie

s.E

xpla

in.w

hat.

a.po

int.

(x, y

).on.

the.

gra

ph.o

f.a.

prop

orti

onal

.rel

atio

nsh

ip.

mea

ns.

in.t

erm

s.of

.the

.si

tuat

ion,

.wit

h.sp

ecia

l.at

tent

ion.

to.t

he.p

oint

s.(0

, 0).a

nd.(1

, r).w

here

.r.is

.th

e.u

nit

.rat

e.

7.R

P.2d

XX

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

7R

atio

s.an

d.P

ropo

rtio

nal.

Rel

atio

nsh

ips

Ana

lyze

.pr

opor

tion

al.

rela

tion

ship

s.an

d.us

e.th

em.t

o.so

lve.

real

-wor

ld.a

nd.

mat

hem

atic

al.

prob

lem

s.

Use

.pro

port

iona

l.rel

atio

nsh

ips.

to.s

olve

.m

ulti

step

.rat

io.a

nd.p

erce

nt.p

robl

ems.

7.R

P.3

XX

X

7T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.o

pera

tion

s.w

ith.

frac

tion

s.to

.add

,.su

btra

ct,.

mu

ltipl

y,.a

nd.

div

ide.

rati

onal

.nu

mbe

rs.

App

ly.a

nd.e

xten

d.pr

evio

us.

und

erst

and

ings

.of.a

ddit

ion.

and.

subt

ract

ion.

to.a

dd.a

nd.s

ubt

ract

.rat

iona

l.nu

mbe

rs;.r

epre

sent

.add

itio

n.an

d.su

btra

ctio

n.on

.a.h

oriz

onta

l.or.

vert

ical

.nu

mbe

r.lin

e.d

iag

ram

.

Des

crib

e.si

tuat

ion

s.in

.w

hic

h.op

posi

te.q

uant

itie

s.co

mbi

ne.t

o.m

ake.

0.

7.N

S.1a

XX

.X

7T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.o

pera

tion

s.w

ith.

frac

tion

s.to

.add

,.su

btra

ct,.

mu

ltipl

y,.a

nd.

div

ide.

rati

onal

.nu

mbe

rs.

App

ly.a

nd.e

xten

d.pr

evio

us.

und

erst

and

ings

.of.a

ddit

ion.

and.

subt

ract

ion.

to.a

dd.a

nd.s

ubt

ract

.rat

iona

l.nu

mbe

rs;.r

epre

sent

.add

itio

n.an

d.su

btra

ctio

n.on

.a.h

oriz

onta

l.or.

vert

ical

.nu

mbe

r.lin

e.d

iag

ram

.

Und

erst

and.

p.+

.q.a

s.th

e.nu

mbe

r.lo

cate

d.a.

dis

tanc

e.|q

|.fro

m.p

,.in.

the.

posi

tive

.or.

nega

tive

.d

irec

tion

.dep

end

ing.

on.

whe

ther

.q.is

.pos

itiv

e.or

.neg

ativ

e..S

how

.th

at.a

.nu

mbe

r.an

d.it

s.op

posi

te.h

ave.

a.su

m.o

f.0.

(are

.add

itiv

e.in

vers

es)..

Inte

rpre

t.su

ms.

of.r

atio

nal.

num

bers

.by.

desc

ribi

ng.

real

-wor

ld.c

onte

xts.

7.N

S.1b

XX

X.X

7T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.o

pera

tion

s.w

ith.

frac

tion

s.to

.add

,.su

btra

ct,.

mu

ltipl

y,.a

nd.

div

ide.

rati

onal

.nu

mbe

rs.

App

ly.a

nd.e

xten

d.pr

evio

us.

und

erst

and

ings

.of.a

ddit

ion.

and.

subt

ract

ion.

to.a

dd.a

nd.s

ubt

ract

.rat

iona

l.nu

mbe

rs;.r

epre

sent

.add

itio

n.an

d.su

btra

ctio

n.on

.a.h

oriz

onta

l.or.

vert

ical

.nu

mbe

r.lin

e.d

iag

ram

.

Und

erst

and.

subt

ract

ion.

of.r

atio

nal.n

um

bers

.as.

add

ing.

the.

add

itiv

e.in

vers

e,.p

.–.q

.=.p

.+.(–

q)..

Show

.tha

t.th

e.d

ista

nce.

betw

een.

two.

rati

onal

.nu

mbe

rs.o

n.th

e.nu

mbe

r.lin

e.is

.the

.abs

olut

e.va

lue.

of.t

heir

.dif

fere

nce,

.and

.ap

ply.

this

.pri

ncip

le.in

.re

al-w

orld

.con

text

s.

7.N

S.1c

XX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

7T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.o

pera

tion

s.w

ith.

frac

tion

s.to

.add

,.su

btra

ct,.

mu

ltipl

y,.a

nd.

div

ide.

rati

onal

.nu

mbe

rs.

App

ly.a

nd.e

xten

d.pr

evio

us.

und

erst

and

ings

.of.a

ddit

ion.

and.

subt

ract

ion.

to.a

dd.a

nd.s

ubt

ract

.rat

iona

l.nu

mbe

rs;.r

epre

sent

.add

itio

n.an

d.su

btra

ctio

n.on

.a.h

oriz

onta

l.or.

vert

ical

.nu

mbe

r.lin

e.d

iag

ram

.

App

ly.p

rope

rtie

s.of

.op

erat

ion

s.as

.str

ateg

ies.

to.

add.

and.

subt

ract

.rat

iona

l.nu

mbe

rs.

7.N

S.1d

XX

XX

7T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.m

ulti

plic

atio

n.an

d.d

ivis

ion.

and.

of.fr

acti

ons.

to.m

ulti

ply.

and.

div

ide.

rati

onal

.nu

mbe

rs.

App

ly.a

nd.e

xten

d.pr

evio

us.

und

erst

and

ings

.of.m

ulti

plic

atio

n.an

d.d

ivis

ion.

and.

of.fr

acti

ons.

to.m

ulti

ply.

and.

div

ide.

rati

onal

.nu

mbe

rs.

Und

erst

and.

that

.m

ulti

plic

atio

n.is

.ext

ende

d.fr

om.fr

acti

ons.

to.r

atio

nal.

num

bers

.by.

req

uir

ing.

that

.ope

rati

ons.

cont

inue

.to

.sat

isfy

.the

.pro

pert

ies.

of.o

pera

tion

s,.p

arti

cula

rly.

the.

dis

trib

utiv

e.pr

oper

ty,.

lead

ing.

to.p

rodu

cts.

such

.as

.(–1)

(–1)

.=.1

.and

.the

.ru

les.

for.

mu

ltipl

ying

.si

gne

d.nu

mbe

rs..I

nter

pret

.pr

oduc

ts.o

f.rat

iona

l.nu

mbe

rs.b

y.de

scri

bing

.re

al-w

orld

.con

text

s.

7.N

S.2a

XX

XX

7T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.m

ulti

plic

atio

n.an

d.d

ivis

ion.

and.

of.fr

acti

ons.

to.m

ulti

ply.

and.

div

ide.

rati

onal

.nu

mbe

rs.

App

ly.a

nd.e

xten

d.pr

evio

us.

und

erst

and

ings

.of.m

ulti

plic

atio

n.an

d.d

ivis

ion.

and.

of.fr

acti

ons.

to.m

ulti

ply.

and.

div

ide.

rati

onal

.nu

mbe

rs.

Und

erst

and.

that

.inte

gers

.ca

n.be

.div

ided

,.pro

vide

d.th

at.t

he.d

ivis

or.is

.not

.ze

ro,.a

nd.e

very

.quo

tien

t.of

.inte

gers

.(wit

h.no

n-ze

ro.d

ivis

or).i

s.a.

rati

onal

.nu

mbe

r..If

.p.a

nd.q

.are

.in

tege

rs,.t

hen.

–(p/

q).=

.(–

p)/q

.=.p

/(–q)

..Int

erpr

et.

quo

tien

ts.o

f.rat

iona

l.nu

mbe

rs.b

y.de

scri

bing

.re

al-w

orld

.con

text

s.

7.N

S.2b

XX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

7T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.m

ulti

plic

atio

n.an

d.d

ivis

ion.

and.

of.fr

acti

ons.

to.m

ulti

ply.

and.

div

ide.

rati

onal

.nu

mbe

rs.

App

ly.a

nd.e

xten

d.pr

evio

us.

und

erst

and

ings

.of.m

ulti

plic

atio

n.an

d.d

ivis

ion.

and.

of.fr

acti

ons.

to.m

ulti

ply.

and.

div

ide.

rati

onal

.nu

mbe

rs.

App

ly.p

rope

rtie

s.of

.op

erat

ion

s.as

.str

ateg

ies.

to.m

ulti

ply.

and.

div

ide.

rati

onal

.nu

mbe

rs.

7.N

S.2c

XX

XX

7T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.m

ulti

plic

atio

n.an

d.d

ivis

ion.

and.

of.fr

acti

ons.

to.m

ulti

ply.

and.

div

ide.

rati

onal

.nu

mbe

rs.

App

ly.a

nd.e

xten

d.pr

evio

us.

und

erst

and

ings

.of.m

ulti

plic

atio

n.an

d.d

ivis

ion.

and.

of.fr

acti

ons.

to.m

ulti

ply.

and.

div

ide.

rati

onal

.nu

mbe

rs.

Con

vert

.a.r

atio

nal.n

um

ber.

to.a

.dec

imal

.usi

ng.lo

ng.

div

isio

n;.k

now

.tha

t.th

e.de

cim

al.fo

rm.o

f.a.r

atio

nal.

num

ber.

term

inat

es.in

.0s.

or.e

vent

ually

.rep

eats

.

7.N

S.2d

XX

XX

7T

he.N

um

ber.

Syst

emA

pply

.and

.ex

tend

.pre

viou

s.u

nder

stan

din

gs.

of.m

ulti

plic

atio

n.an

d.d

ivis

ion.

and.

of.fr

acti

ons.

to.m

ulti

ply.

and.

div

ide.

rati

onal

.nu

mbe

rs.

Solv

e.re

al-w

orld

.and

.mat

hem

atic

al.

prob

lem

s.in

volv

ing.

the.

fou

r.op

erat

ion

s.w

ith.

rati

onal

.nu

mbe

rs.

7.N

S.3

XX

XX

7E

xpre

ssio

ns.

and.

Eq

uati

ons

Use

.pro

pert

ies.

of.o

pera

tion

s.to

.gen

erat

e.eq

uiv

alen

t.ex

pres

sion

s.

App

ly.p

rope

rtie

s.of

.ope

rati

ons.

as.

stra

teg

ies.

to.a

dd,.s

ubt

ract

,.fac

tor,.

and.

expa

nd.li

near

.exp

ress

ion

s.w

ith.

rati

onal

.co

effic

ient

s.

7.E

E.1

XX

XX

7E

xpre

ssio

ns.

and.

Eq

uati

ons

Use

.pro

pert

ies.

of.o

pera

tion

s.to

.gen

erat

e.eq

uiv

alen

t.ex

pres

sion

s.

Und

erst

and.

that

.rew

riti

ng.a

n.ex

pres

sion

.in.d

iffe

rent

.form

s.in

.a.

prob

lem

.con

text

.can

.she

d.lig

ht.o

n.th

e.pr

oble

m.a

nd.h

ow.t

he.q

uant

itie

s.in

.it.

are.

rela

ted.

7.E

E.2

XX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

7E

xpre

ssio

ns.

and.

Eq

uati

ons

Solv

e.re

al-li

fe.a

nd.

mat

hem

atic

al.

prob

lem

s.us

ing.

num

eric

al.

and.

alge

brai

c.ex

pres

sion

s.an

d.eq

uati

ons.

Solv

e.m

ulti

-ste

p.re

al-li

fe.a

nd.

mat

hem

atic

al.p

robl

ems.

pose

d.w

ith.

posi

tive

.and

.neg

ativ

e.ra

tion

al.n

um

bers

.in

.any

.form

.(who

le.n

um

bers

,.fra

ctio

ns,

.an

d.de

cim

als)

,.usi

ng.t

ools

.str

ateg

ical

ly..

App

ly.p

rope

rtie

s.of

.ope

rati

ons.

to.

calc

ula

te.w

ith.

num

bers

.in.a

ny.fo

rm;.

conv

ert.

betw

een.

form

s.as

.app

ropr

iate

;.an

d.as

sess

.the

.rea

sona

blen

ess.

of.

answ

ers.

usin

g.m

enta

l.com

puta

tion

.and

.es

tim

atio

n.st

rate

gie

s.

7.E

E.3

XX

XX

7E

xpre

ssio

ns.

and.

Eq

uati

ons

Solv

e.re

al-li

fe.a

nd.

mat

hem

atic

al.

prob

lem

s.us

ing.

num

eric

al.

and.

alge

brai

c.ex

pres

sion

s.an

d.eq

uati

ons.

Use

.var

iabl

es.t

o.re

pres

ent.

qua

ntit

ies.

in.

a.re

al-w

orld

.or.

mat

hem

atic

al.p

robl

em,.

and.

con

stru

ct.s

impl

e.eq

uati

ons.

and.

ineq

ualit

ies.

to.s

olve

.pro

blem

s.by

.re

ason

ing.

abou

t.th

e.q

uant

itie

s.

Solv

e.w

ord.

prob

lem

s.le

adin

g.to

.eq

uati

ons.

of.

the.

form

.px.

+.q

.=.r

.and

.p(

x.+

.q).=

.r,.w

here

.p,.q

,.an

d.r.

are.

spec

ific

.rat

iona

l.nu

mbe

rs..S

olve

.eq

uati

ons.

of.t

hese

.form

s.flu

entl

y..

Com

pare

.an.

alge

brai

c.so

luti

on.t

o.an

.ari

thm

etic

.so

luti

on,.i

dent

ifyi

ng.

the.

seq

uenc

e.of

.the

.op

erat

ion

s.us

ed.in

.eac

h.ap

proa

ch.

7.E

E.4

aX

XX

X

7E

xpre

ssio

ns.

and.

Eq

uati

ons

Solv

e.re

al-li

fe.a

nd.

mat

hem

atic

al.

prob

lem

s.us

ing.

num

eric

al.

and.

alge

brai

c.ex

pres

sion

s.an

d.eq

uati

ons.

Use

.var

iabl

es.t

o.re

pres

ent.

qua

ntit

ies.

in.

a.re

al-w

orld

.or.

mat

hem

atic

al.p

robl

em,.

and.

con

stru

ct.s

impl

e.eq

uati

ons.

and.

ineq

ualit

ies.

to.s

olve

.pro

blem

s.by

.re

ason

ing.

abou

t.th

e.q

uant

itie

s.

Solv

e.w

ord.

prob

lem

s.le

adin

g.to

.ineq

ualit

ies.

of.

the.

form

.px.

+.q

.>.r

.or.

px +

.q.

<.r,

.whe

re.p

,.q,.a

nd.r

.are

.sp

ecif

ic.r

atio

nal.n

um

bers

..G

raph

.the

.sol

utio

n.se

t.of

.the

.ineq

ualit

y.an

d.in

terp

ret.

it.in

.the

.con

text

.of

.the

.pro

blem

.

7.E

E.4

bX

XX

X

7G

eom

etry

Dra

w,.c

onst

ruct

,.an

d.de

scri

be.

geom

etri

cal.

figu

res.

and.

desc

ribe

.the

.re

lati

onsh

ips.

betw

een.

them

.

Solv

e.pr

oble

ms.

invo

lvin

g.sc

ale.

dra

win

gs.o

f.geo

met

ric.

figu

res,

.in

clud

ing.

com

puti

ng.a

ctua

l.len

gth

s.an

d.ar

eas.

from

.a.s

cale

.dra

win

g.an

d.re

prod

ucin

g.a.

scal

e.d

raw

ing.

at.a

.d

iffe

rent

.sca

le.

7.G

.1X

X.


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

7G

eom

etry

Dra

w,.c

onst

ruct

,.an

d.de

scri

be.

geom

etri

cal.

figu

res.

and.

desc

ribe

.the

.re

lati

onsh

ips.

betw

een.

them

.

Dra

w.(f

reeh

and,

.wit

h.ru

ler.

and.

prot

ract

or,.a

nd.w

ith.

tech

nolo

gy)

.ge

omet

ric.

shap

es.w

ith.

giv

en.

cond

itio

ns.

.Foc

us.o

n.co

nst

ruct

ing.

tria

ngle

s.fr

om.t

hre

e.m

easu

res.

of.a

ngle

s.or

.sid

es,.n

otic

ing.

whe

n.th

e.co

ndit

ion

s.de

term

ine.

a.u

niq

ue.t

rian

gle,

.mor

e.th

an.

one.

tria

ngle

,.or.

no.t

rian

gle.

7.G

.2X

X

7G

eom

etry

Dra

w,.c

onst

ruct

,.an

d.de

scri

be.

geom

etri

cal.

figu

res.

and.

desc

ribe

.the

.re

lati

onsh

ips.

betw

een.

them

.

Des

crib

e.th

e.tw

o-d

imen

sion

al.

figu

res.

that

.res

ult.

from

.slic

ing.

thre

e-d

imen

sion

al.fi

gu

res,

.as.

in.p

lane

.se

ctio

ns.

of.r

ight

.rec

tang

ula

r.pr

ism

s.an

d.ri

ght.

rect

ang

ula

r.py

ram

ids.

7.G

.3X

X

7G

eom

etry

Solv

e.re

al-li

fe.a

nd.

mat

hem

atic

al.

prob

lem

s.in

volv

ing.

angl

e.m

easu

re,.a

rea,

.su

rfac

e.ar

ea,.a

nd.

volu

me.

Kno

w.t

he.fo

rmu

las.

for.

the.

area

.and

.ci

rcu

mfe

renc

e.of

.a.c

ircl

e.an

d.us

e.th

em.

to.s

olve

.pro

blem

s;.g

ive.

an.in

form

al.

deri

vati

on.o

f.the

.rel

atio

nsh

ip.b

etw

een.

the.

circ

um

fere

nce.

and.

area

.of.a

.cir

cle.

7.G

.4X

X

7G

eom

etry

Solv

e.re

al-li

fe.a

nd.

mat

hem

atic

al.

prob

lem

s.in

volv

ing.

angl

e.m

easu

re,.a

rea,

.su

rfac

e.ar

ea,.a

nd.

volu

me.

Use

.fact

s.ab

out.

supp

lem

enta

ry,.

com

plem

enta

ry,.v

erti

cal,.

and.

adja

cent

.an

gles

.in.a

.mu

lti-s

tep.

prob

lem

.to.

wri

te.

and.

solv

e.si

mpl

e.eq

uati

ons.

for.

an.

un

know

n.an

gle.

in.a

.fig

ure

.

7.G

.5X

X

7G

eom

etry

Solv

e.re

al-li

fe.a

nd.

mat

hem

atic

al.

prob

lem

s.in

volv

ing.

angl

e.m

easu

re,.a

rea,

.su

rfac

e.ar

ea,.a

nd.

volu

me.

Solv

e.re

al-w

orld

.and

.mat

hem

atic

al.

prob

lem

s.in

volv

ing.

area

,.vol

um

e.an

d.su

rfac

e.ar

ea.o

f.tw

o-.a

nd.t

hre

e-d

imen

sion

al.o

bjec

ts.c

ompo

sed.

of.

tria

ngle

s,.q

uad

rila

tera

ls,.p

olyg

ons,

.cu

bes,

.and

.rig

ht.p

rism

s.

7.G

.6X

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

7St

atis

tics

.and

.P

roba

bilit

yU

se.r

ando

m.

sam

plin

g.to

.dra

w.

infe

renc

es.a

bout

.a.

popu

lati

on.

Und

erst

and.

that

.sta

tist

ics.

can.

be.

used

.to.

gain

.info

rmat

ion.

abou

t.a.

popu

lati

on.b

y.ex

amin

ing.

a.sa

mpl

e.of

.th

e.po

pula

tion

;.gen

eral

izat

ion

s.ab

out.

a.po

pula

tion

.from

.a.s

ampl

e.ar

e.va

lid.

only

.if.t

he.s

ampl

e.is

.rep

rese

ntat

ive.

of.t

hat.

popu

lati

on..U

nder

stan

d.th

at.

rand

om.s

ampl

ing.

tend

s.to

.pro

duce

.re

pres

enta

tive

.sam

ples

.and

.sup

port

.va

lid.in

fere

nces

.

7.SP

.1X

7St

atis

tics

.and

.P

roba

bilit

yU

se.r

ando

m.

sam

plin

g.to

.dra

w.

infe

renc

es.a

bout

.a.

popu

lati

on.

Use

.dat

a.fr

om.a

.ran

dom

.sam

ple.

to.

dra

w.in

fere

nces

.abo

ut.a

.pop

ula

tion

.w

ith.

an.u

nkn

own.

char

acte

rist

ic.o

f.in

tere

st..G

ener

ate.

mu

ltipl

e.sa

mpl

es.(o

r.si

mu

late

d.sa

mpl

es).o

f.the

.sam

e.si

ze.

to.g

auge

.the

.var

iati

on.in

.est

imat

es.o

r.pr

edic

tion

s.

7.SP

.2X

7St

atis

tics

.and

.P

roba

bilit

yD

raw

.info

rmal

.co

mpa

rati

ve.

infe

renc

es.a

bout

.tw

o.po

pula

tion

s.

Info

rmal

ly.a

sses

s.th

e.de

gre

e.of

.vi

sual

.ove

rlap.

of.t

wo.

num

eric

al.d

ata.

dis

trib

utio

ns.

wit

h.si

mila

r.va

riab

iliti

es,.

mea

suri

ng.t

he.d

iffe

renc

e.be

twee

n.th

e.ce

nter

s.by

.exp

ress

ing.

it.a

s.a.

mu

ltipl

e.of

.a.

mea

sure

.of.v

aria

bilit

y.

7.SP

.3X

7St

atis

tics

.and

.P

roba

bilit

yD

raw

.info

rmal

.co

mpa

rati

ve.

infe

renc

es.a

bout

.tw

o.po

pula

tion

s.

Use

.mea

sure

s.of

.cen

ter.

and.

mea

sure

s.of

.var

iabi

lity.

for.

num

eric

al.d

ata.

from

.ra

ndom

.sam

ples

.to.

dra

w.in

form

al.

com

para

tive

.infe

renc

es.a

bout

.tw

o.po

pula

tion

s.

7.SP

.4X

7St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.ch

ance

.pro

cess

es.

and.

deve

lop,

.use

,.an

d.ev

alua

te.

prob

abili

ty.

mod

els.

Und

erst

and.

that

.the

.pro

babi

lity.

of.a

.ch

ance

.eve

nt.is

.a.n

um

ber.

betw

een.

0.an

d.1.

that

.exp

ress

es.t

he.li

kelih

ood.

of.t

he.e

vent

.occ

urr

ing.

.Lar

ger.

num

bers

.ind

icat

e.g

reat

er.li

kelih

ood.

.A

.pro

babi

lity.

near

.0.in

dic

ates

.an.

un

likel

y.ev

ent,

.a.p

roba

bilit

y.ar

ound

.1/

2.in

dic

ates

.an.

even

t.th

at.is

.nei

ther

.u

nlik

ely.

nor.

likel

y,.a

nd.a

.pro

babi

lity.

near

.1.in

dic

ates

.a.li

kely

.eve

nt.

7.SP

.5X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

7St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.ch

ance

.pro

cess

es.

and.

deve

lop,

.use

,.an

d.ev

alua

te.

prob

abili

ty.

mod

els.

App

roxi

mat

e.th

e.pr

obab

ility

.of.a

.ch

ance

.eve

nt.b

y.co

llect

ing.

data

.on.

the.

chan

ce.p

roce

ss.t

hat.

prod

uces

.it.

and.

obse

rvin

g.it

s.lo

ng-r

un.

rela

tive

.fr

eque

ncy,

.and

.pre

dic

t.th

e.ap

prox

imat

e.re

lati

ve.fr

eque

ncy.

giv

en.t

he.p

roba

bilit

y.

7.SP

.6X

7St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.ch

ance

.pro

cess

es.

and.

deve

lop,

.use

,.an

d.ev

alua

te.

prob

abili

ty.

mod

els.

Dev

elop

.a.p

roba

bilit

y.m

odel

.and

.use

.it.

to.fi

nd.p

roba

bilit

ies.

of.e

vent

s..C

ompa

re.

prob

abili

ties

.from

.a.m

odel

.to.

obse

rved

.fr

eque

ncie

s;.if

.the

.ag

reem

ent.

is.n

ot.

good

,.exp

lain

.pos

sibl

e.so

urc

es.o

f.the

.d

iscr

epan

cy.

Dev

elop

.a.u

nifo

rm.

prob

abili

ty.m

odel

.by

.ass

ign

ing.

equa

l.pr

obab

ility

.to.

all.

outc

omes

,.and

.use

.the

.m

odel

.to.

dete

rmin

e.pr

obab

iliti

es.o

f.eve

nts.

7.SP

.7a

X

7St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.ch

ance

.pro

cess

es.

and.

deve

lop,

.use

,.an

d.ev

alua

te.

prob

abili

ty.

mod

els.

Dev

elop

.a.p

roba

bilit

y.m

odel

.and

.use

.it.

to.fi

nd.p

roba

bilit

ies.

of.e

vent

s..C

ompa

re.

prob

abili

ties

.from

.a.m

odel

.to.

obse

rved

.fr

eque

ncie

s;.if

.the

.ag

reem

ent.

is.n

ot.

good

,.exp

lain

.pos

sibl

e.so

urc

es.o

f.the

.d

iscr

epan

cy.

Dev

elop

.a.p

roba

bilit

y.m

odel

.(wh

ich.

may

.not

.be.

un

iform

).by.

obse

rvin

g.fr

eque

ncie

s.in

.dat

a.ge

nera

ted.

from

.a.c

hanc

e.pr

oces

s.

7.SP

.7b

X

7St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.ch

ance

.pro

cess

es.

and.

deve

lop,

.use

,.an

d.ev

alua

te.

prob

abili

ty.

mod

els.

Fin

d.pr

obab

iliti

es.o

f.com

pou

nd.e

vent

s.us

ing.

orga

niz

ed.li

sts,

.tab

les,

.tre

e.d

iag

ram

s,.a

nd.s

imu

lati

on.

Und

erst

and.

that

,.jus

t.as

.w

ith.

sim

ple.

even

ts,.t

he.

prob

abili

ty.o

f.a.c

ompo

und

.ev

ent.

is.t

he.fr

acti

on.o

f.ou

tcom

es.in

.the

.sam

ple.

spac

e.fo

r.w

hic

h.th

e.co

mpo

und

.eve

nt.o

ccu

rs.

7.SP

.8a

X

7St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.ch

ance

.pro

cess

es.

and.

deve

lop,

.use

,.an

d.ev

alua

te.

prob

abili

ty.

mod

els.

Fin

d.pr

obab

iliti

es.o

f.com

pou

nd.e

vent

s.us

ing.

orga

niz

ed.li

sts,

.tab

les,

.tre

e.d

iag

ram

s,.a

nd.s

imu

lati

on.

Rep

rese

nt.s

ampl

e.sp

aces

.fo

r.co

mpo

und

.eve

nts.

usin

g.m

etho

ds.s

uch.

as.

orga

niz

ed.li

sts,

.tab

les.

and.

tree

.dia

gra

ms.

.For

.an

.eve

nt.d

escr

ibed

.in.

ever

yday

.lang

uage

.(e.g

.,.“r

ollin

g.do

ubl

e.si

xes”

),.id

enti

fy.t

he.o

utco

mes

.in.

the.

sam

ple.

spac

e.w

hic

h.co

mpo

se.t

he.e

vent

.

7.SP

.8b

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

7St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.ch

ance

.pro

cess

es.

and.

deve

lop,

.use

,.an

d.ev

alua

te.

prob

abili

ty.

mod

els.

Fin

d.pr

obab

iliti

es.o

f.com

pou

nd.e

vent

s.us

ing.

orga

niz

ed.li

sts,

.tab

les,

.tre

e.d

iag

ram

s,.a

nd.s

imu

lati

on.

Des

ign.

and.

use.

a.si

mu

lati

on.t

o.ge

nera

te.

freq

uenc

ies.

for.

com

pou

nd.

even

ts.

7.SP

.8c

X

8T

he.N

um

ber.

Syst

emK

now

.tha

t.th

ere.

are.

num

bers

.tha

t.ar

e.no

t.ra

tion

al,.

and.

appr

oxim

ate.

them

.by.

rati

onal

.nu

mbe

rs.

Und

erst

and.

info

rmal

ly.t

hat.

ever

y.nu

mbe

r.ha

s.a.

deci

mal

.exp

ansi

on;.

the.

rati

onal

.nu

mbe

rs.a

re.t

hose

.wit

h.de

cim

al.e

xpan

sion

s.th

at.t

erm

inat

e.in

.0s.

or.e

vent

ually

.rep

eat.

..Kno

w.t

hat.

othe

r.nu

mbe

rs.a

re.c

alle

d.ir

rati

onal

.

8.N

S.1

XX

XX

8T

he.N

um

ber.

Syst

emK

now

.tha

t.th

ere.

are.

num

bers

.tha

t.ar

e.no

t.ra

tion

al,.

and.

appr

oxim

ate.

them

.by.

rati

onal

.nu

mbe

rs.

Use

.rat

iona

l.app

roxi

mat

ion

s.of

.ir

rati

onal

.nu

mbe

rs.t

o.co

mpa

re.t

he.

size

.of.i

rrat

iona

l.nu

mbe

rs,.l

ocat

e.th

em.a

ppro

xim

atel

y.on

.a.n

um

ber.

line.

dia

gra

m,.a

nd.e

stim

ate.

the.

valu

e.of

.ex

pres

sion

s.(e

.g.,.

π2 ).

8.N

S.2

XX

X

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Wor

k.w

ith.

rad

ical

s.an

d.in

tege

r.ex

pone

nts.

Kno

w.a

nd.a

pply

.the

.pro

pert

ies.

of.in

tege

r.ex

pone

nts.

to.g

ener

ate.

equ

ival

ent.

num

eric

al.e

xpre

ssio

ns.

8.E

E.1

XX

XX

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Wor

k.w

ith.

rad

ical

s.an

d.in

tege

r.ex

pone

nts.

Use

.sq

uare

.roo

t.an

d.cu

be.r

oot.

sym

bols

.to

.rep

rese

nt.s

olut

ion

s.to

.eq

uati

ons.

of.

the.

form

.x2 .=

.p.a

nd.x

3 .=.p

,.whe

re.p

.is.

a.po

siti

ve.r

atio

nal.n

um

ber..

Eva

luat

e.sq

uare

.roo

ts.o

f.sm

all.p

erfe

ct.s

qua

res.

and.

cube

.roo

ts.o

f.sm

all.p

erfe

ct.c

ube

s..

Kno

w.t

hat.

√2 .is.

irra

tion

al.

8.E

E.2

XX

XX

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Wor

k.w

ith.

rad

ical

s.an

d.in

tege

r.ex

pone

nts.

Use

.nu

mbe

rs.e

xpre

ssed

.in.t

he.fo

rm.o

f.a.

sing

le.d

igit

.tim

es.a

n.in

tege

r.po

wer

.of.

10.t

o.es

tim

ate.

very

.larg

e.or

.ver

y.sm

all.

qua

ntit

ies,

.and

.to.

expr

ess.

how

.man

y.ti

mes

.as.

muc

h.on

e.is

.tha

n.th

e.ot

her.

8.E

E.3

XX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Wor

k.w

ith.

rad

ical

s.an

d.in

tege

r.ex

pone

nts.

Perf

orm

.ope

rati

ons.

wit

h.nu

mbe

rs.

expr

esse

d.in

.sci

enti

fic.n

otat

ion,

.in

clud

ing.

prob

lem

s.w

here

.bot

h.de

cim

al.

and.

scie

ntif

ic.n

otat

ion.

are.

used

..Use

.sc

ient

ific

.not

atio

n.an

d.ch

oose

.un

its.

of.

appr

opri

ate.

size

.for.

mea

sure

men

ts.o

f.ve

ry.la

rge.

or.v

ery.

smal

l.qua

ntit

ies.

(e.g

.,.us

e.m

illim

eter

s.pe

r.ye

ar.fo

r.se

aflo

or.

spre

adin

g)..I

nter

pret

.sci

enti

fic.n

otat

ion.

that

.has

.bee

n.ge

nera

ted.

by.t

ech

nolo

gy.

8.E

E.4

XX

X

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Und

erst

and.

the.

con

nect

ion

s.be

twee

n.pr

opor

tion

al.

rela

tion

ship

s,.

lines

,.and

.line

ar.

equa

tion

s.

Gra

ph.p

ropo

rtio

nal.r

elat

ion

ship

s,.

inte

rpre

ting

.the

.un

it.r

ate.

as.t

he.s

lope

.of

.the

.gra

ph..C

ompa

re.t

wo.

dif

fere

nt.

prop

orti

onal

.rel

atio

nsh

ips.

repr

esen

ted.

in.d

iffe

rent

.way

s.

8.E

E.5

XX

X

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Und

erst

and.

the.

con

nect

ion

s.be

twee

n.pr

opor

tion

al.

rela

tion

ship

s,.

lines

,.and

.line

ar.

equa

tion

s.

Use

.sim

ilar.

tria

ngle

s.to

.exp

lain

.why

.th

e.sl

ope.

m.is

.the

.sam

e.be

twee

n.an

y.tw

o.d

isti

nct.

poin

ts.o

n.a.

non-

vert

ical

.lin

e.in

.the

.coo

rdin

ate.

plan

e;.d

eriv

e.th

e.eq

uati

on y

= m

x fo

r.a.

line.

thro

ugh.

the.

orig

in.a

nd.t

he.e

qua

tion

y =

mx

+ b

for.

a.lin

e.in

terc

epti

ng.t

he.v

erti

cal.a

xis.

at.b

.

8.E

E.6

XX

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Ana

lyze

.and

.so

lve.

linea

r.eq

uati

ons.

and.

pair

s.of

.si

mu

ltane

ous.

linea

r.eq

uati

ons.

Solv

e.lin

ear.

equa

tion

s.in

.one

.var

iabl

e.G

ive.

exam

ples

.of.

linea

r.eq

uati

ons.

in.

one.

vari

able

.wit

h.on

e.so

luti

on,.i

nfi

nit

ely.

man

y.so

luti

ons,

.or.

no.s

olut

ion

s..

Show

.wh

ich.

of.t

hese

.po

ssib

iliti

es.is

.the

.cas

e.by

.su

cces

sive

ly.t

ran

sfor

min

g.th

e.g

iven

.eq

uati

on.in

to.

sim

pler

.form

s,.u

ntil.

an.

equ

ival

ent.

equa

tion

.of.t

he.

form

.x.=

.a,.a

.=.a

,.or.

a.=

b

resu

lts.(w

here

.a.a

nd b

are

.d

iffe

rent

.nu

mbe

rs).

8.E

E.7

aX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Ana

lyze

.and

.so

lve.

linea

r.eq

uati

ons.

and.

pair

s.of

.si

mu

ltane

ous.

linea

r.eq

uati

ons.

Solv

e.lin

ear.

equa

tion

s.in

.one

.var

iabl

e.So

lve.

linea

r.eq

uati

ons.

wit

h.ra

tion

al.n

um

ber.

coef

ficie

nts,

.incl

udin

g.eq

uati

ons.

who

se.s

olut

ion

s.re

qu

ire.

expa

ndin

g.ex

pres

sion

s.us

ing.

the.

dis

trib

utiv

e.pr

oper

ty.a

nd.

colle

ctin

g.lik

e.te

rms.

8.E

E.7

bX

XX

X

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Ana

lyze

.and

.so

lve.

linea

r.eq

uati

ons.

and.

pair

s.of

.si

mu

ltane

ous.

linea

r.eq

uati

ons.

Ana

lyze

.and

.sol

ve.p

airs

.of.

sim

ulta

neou

s.lin

ear.

equa

tion

s.U

nder

stan

d.th

at.s

olut

ion

s.to

.a.s

yste

m.o

f.tw

o.lin

ear.

equa

tion

s.in

.tw

o.va

riab

les.

corr

espo

nd.t

o.po

ints

.of

.inte

rsec

tion

.of.t

heir

.g

raph

s,.b

ecau

se.p

oint

s.of

.in

ters

ecti

on.s

atis

fy.b

oth.

equa

tion

s.si

mu

ltane

ousl

y.

8.E

E.a

XX

X

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Ana

lyze

.and

.so

lve.

linea

r.eq

uati

ons.

and.

pair

s.of

.si

mu

ltane

ous.

linea

r.eq

uati

ons.

Ana

lyze

.and

.sol

ve.p

airs

.of.

sim

ulta

neou

s.lin

ear.

equa

tion

s.So

lve.

syst

ems.

of.t

wo.

linea

r.eq

uati

ons.

in.t

wo.

vari

able

s.al

gebr

aica

lly,.

and.

esti

mat

e.so

luti

ons.

by.

gra

phin

g.th

e.eq

uati

ons.

.So

lve.

sim

ple.

case

s.by

.in

spec

tion

.

8.E

E.b

XX

X

8E

xpre

ssio

ns.

and.

Eq

uati

ons

Ana

lyze

.and

.so

lve.

linea

r.eq

uati

ons.

and.

pair

s.of

.si

mu

ltane

ous.

linea

r.eq

uati

ons.

Ana

lyze

.and

.sol

ve.p

airs

.of.

sim

ulta

neou

s.lin

ear.

equa

tion

s.So

lve.

real

-wor

ld.a

nd.

mat

hem

atic

al.p

robl

ems.

lead

ing.

to.t

wo.

linea

r.eq

uati

ons.

in.t

wo.

vari

able

s.

8.E

E.c

XX

X

8F

unc

tion

sD

efin

e,.e

valu

ate,

.an

d.co

mpa

re.

func

tion

s.

Und

erst

and.

that

.a.fu

ncti

on.is

.a.r

ule

.th

at.a

ssig

ns.

to.e

ach.

inpu

t.ex

actl

y.on

e.ou

tput

..The

.gra

ph.o

f.a.fu

ncti

on.is

.the

.se

t.of

.ord

ered

.pai

rs.c

onsi

stin

g.of

.an.

inpu

t.an

d.th

e.co

rres

pond

ing.

outp

ut.

8.F.

1X

XX

X

8F

unc

tion

sD

efin

e,.e

valu

ate,

.an

d.co

mpa

re.

func

tion

s.

Com

pare

.pro

pert

ies.

of.t

wo.

func

tion

s.ea

ch.r

epre

sent

ed.in

.a.d

iffe

rent

.way

.(a

lgeb

raic

ally

,.gra

phic

ally

,.nu

mer

ical

ly.

in.t

able

s,.o

r.by

.ver

bal.d

escr

ipti

ons)

.

8.F.

2X

XX

.


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

8F

unc

tion

sD

efin

e,.e

valu

ate,

.an

d.co

mpa

re.

func

tion

s.

Inte

rpre

t.th

e.eq

uati

on y

= m

x +

b a

s.de

fin

ing.

a.lin

ear.

func

tion

,.who

se.g

raph

.is

.a.s

trai

ght.

line;

.giv

e.ex

ampl

es.o

f.fu

ncti

ons.

that

.are

.not

.line

ar.

8.F.

3X

XX

X

8F

unc

tion

sU

se.fu

ncti

ons.

to.m

odel

.re

lati

onsh

ips.

betw

een.

qua

ntit

ies.

Con

stru

ct.a

.func

tion

.to.

mod

el.a

.line

ar.

rela

tion

ship

.bet

wee

n.tw

o.q

uant

itie

s..

Det

erm

ine.

the.

rate

.of.c

hang

e.an

d.in

itia

l.val

ue.o

f.the

.func

tion

.from

.a.

desc

ript

ion.

of.a

.rel

atio

nsh

ip.o

r.fr

om.t

wo.

(x, y

).val

ues,

.incl

udin

g.re

adin

g.th

ese.

from

.a.t

able

.or.

from

.a.g

raph

..Int

erpr

et.

the.

rate

.of.c

hang

e.an

d.in

itia

l.val

ue.o

f.a.

linea

r.fu

ncti

on.in

.ter

ms.

of.t

he.s

itua

tion

.it

.mod

els,

.and

.in.t

erm

s.of

.its.

gra

ph.o

r.a.

tabl

e.of

.val

ues.

8.F.

4X

XX

X

8F

unc

tion

sU

se.fu

ncti

ons.

to.m

odel

.re

lati

onsh

ips.

betw

een.

qua

ntit

ies.

Des

crib

e.q

ualit

ativ

ely.

the.

func

tion

al.

rela

tion

ship

.bet

wee

n.tw

o.q

uant

itie

s.by

.ana

lyzi

ng.a

.gra

ph.(e

.g.,.

whe

re.t

he.

func

tion

.is.in

crea

sing

.or.

decr

easi

ng,.

linea

r.or

.non

linea

r)..S

ketc

h.a.

gra

ph.

that

.exh

ibit

s.th

e.q

ualit

ativ

e.fe

atu

res.

of.a

.func

tion

.tha

t.ha

s.be

en.d

escr

ibed

.ve

rbal

ly.

8.F.

5X

XX

.

8G

eom

etry

Und

erst

and.

cong

ruen

ce.a

nd.

sim

ilari

ty.u

sing

.ph

ysic

al.m

odel

s,.

tran

spar

enci

es,.

or.g

eom

etry

.so

ftw

are.

Ver

ify.

expe

rim

enta

lly.t

he.p

rope

rtie

s.of

.ro

tati

ons,

.ref

lect

ion

s,.a

nd.t

ran

slat

ion

s:L

ines

.are

.tak

en.t

o.lin

es,.

and.

line.

seg

men

ts.t

o.lin

e.se

gm

ents

.of.t

he.s

ame.

leng

th.

8.G

.1a

XX

8G

eom

etry

Und

erst

and.

cong

ruen

ce.a

nd.

sim

ilari

ty.u

sing

.ph

ysic

al.m

odel

s,.

tran

spar

enci

es,.

or.g

eom

etry

.so

ftw

are.

Ver

ify.

expe

rim

enta

lly.t

he.p

rope

rtie

s.of

.ro

tati

ons,

.ref

lect

ion

s,.a

nd.t

ran

slat

ion

s:A

ngle

s.ar

e.ta

ken.

to.a

ngle

s.of

.the

.sam

e.m

easu

re.

8.G

.1b

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

8G

eom

etry

Und

erst

and.

cong

ruen

ce.a

nd.

sim

ilari

ty.u

sing

.ph

ysic

al.m

odel

s,.

tran

spar

enci

es,.

or.g

eom

etry

.so

ftw

are.

Ver

ify.

expe

rim

enta

lly.t

he.p

rope

rtie

s.of

.ro

tati

ons,

.ref

lect

ion

s,.a

nd.t

ran

slat

ion

s:Pa

ralle

l.lin

es.a

re.t

aken

.to.

para

llel.l

ines

.8.

G.1

cX

X

8G

eom

etry

Und

erst

and.

cong

ruen

ce.a

nd.

sim

ilari

ty.u

sing

.ph

ysic

al.m

odel

s,.

tran

spar

enci

es,.

or.g

eom

etry

.so

ftw

are.

Und

erst

and.

that

.a.t

wo-

dim

ensi

onal

.fig

ure

.is.c

ong

ruen

t.to

.ano

ther

.if.t

he.

seco

nd.c

an.b

e.ob

tain

ed.fr

om.t

he.fi

rst.

by.a

.seq

uenc

e.of

.rot

atio

ns,

.ref

lect

ion

s,.

and.

tran

slat

ion

s;.g

iven

.tw

o.co

ngru

ent.

figu

res,

.des

crib

e.a.

seq

uenc

e.th

at.

exh

ibit

s.th

e.co

ngru

ence

.bet

wee

n.th

em.

8.G

.2X

X

8G

eom

etry

Und

erst

and.

cong

ruen

ce.a

nd.

sim

ilari

ty.u

sing

.ph

ysic

al.m

odel

s,.

tran

spar

enci

es,.

or.g

eom

etry

.so

ftw

are.

Des

crib

e.th

e.ef

fect

.of.d

ilati

ons,

.tr

ansl

atio

ns,

.rot

atio

ns,

.and

.ref

lect

ion

s.on

.tw

o-d

imen

sion

al.fi

gu

res.

usin

g.co

ord

inat

es.

8.G

.3X

X

8G

eom

etry

Und

erst

and.

cong

ruen

ce.a

nd.

sim

ilari

ty.u

sing

.ph

ysic

al.m

odel

s,.

tran

spar

enci

es,.

or.g

eom

etry

.so

ftw

are.

Und

erst

and.

that

.a.t

wo-

dim

ensi

onal

.fig

ure

.is.s

imila

r.to

.ano

ther

.if.t

he.

seco

nd.c

an.b

e.ob

tain

ed.fr

om.t

he.fi

rst.

by.a

.seq

uenc

e.of

.rot

atio

ns,

.ref

lect

ion

s,.

tran

slat

ion

s,.a

nd.d

ilati

ons;

.giv

en.

two.

sim

ilar.

two-

dim

ensi

onal

.fig

ure

s,.

desc

ribe

.a.s

eque

nce.

that

.exh

ibit

s.th

e.si

mila

rity

.bet

wee

n.th

em.

8.G

.4X

X

8G

eom

etry

Und

erst

and.

cong

ruen

ce.a

nd.

sim

ilari

ty.u

sing

.ph

ysic

al.m

odel

s,.

tran

spar

enci

es,.

or.g

eom

etry

.so

ftw

are.

Use

.info

rmal

.arg

um

ents

.to.

esta

blis

h.fa

cts.

abou

t.th

e.an

gle.

sum

.and

.ext

erio

r.an

gle.

of.t

rian

gles

,.abo

ut.t

he.a

ngle

s.cr

eate

d.w

hen.

para

llel.l

ines

.are

.cut

.by

.a.t

ran

sver

sal,.

and.

the.

angl

e-an

gle.

crit

erio

n.fo

r.si

mila

rity

.of.t

rian

gles

.

8.G

.5X

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

8G

eom

etry

Und

erst

and.

and.

appl

y.th

e.P

ytha

gore

an.

The

orem

.

Exp

lain

.a.p

roof

.of.t

he.P

ytha

gore

an.

The

orem

.and

.its.

conv

erse

.8.

G.6

XX

8G

eom

etry

Und

erst

and.

and.

appl

y.th

e.P

ytha

gore

an.

The

orem

.

App

ly.t

he.P

ytha

gore

an.T

heor

em.t

o.de

term

ine.

un

know

n.si

de.le

ngth

s.in

.rig

ht.t

rian

gles

.in.r

eal-w

orld

.and

.m

athe

mat

ical

.pro

blem

s.in

.tw

o.an

d.th

ree.

dim

ensi

ons.

8.G

.7X

X

8G

eom

etry

Und

erst

and.

and.

appl

y.th

e.P

ytha

gore

an.

The

orem

.

App

ly.t

he.P

ytha

gore

an.T

heor

em.t

o.fi

nd.

the.

dis

tanc

e.be

twee

n.tw

o.po

ints

.in.a

.co

ord

inat

e.sy

stem

.

8.G

.8X

X

8G

eom

etry

Solv

e.re

al-

wor

ld.a

nd.

mat

hem

atic

al.

prob

lem

s.in

volv

ing.

volu

me.

of.c

ylin

ders

,.co

nes,

.and

.sp

here

s.

Kno

w.t

he.fo

rmu

las.

for.

the.

volu

mes

.of

.con

es,.c

ylin

ders

,.and

.sph

eres

.and

.us

e.th

em.t

o.so

lve.

real

-wor

ld.a

nd.

mat

hem

atic

al.p

robl

ems.

8.G

.9X

X

8St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.pa

tter

ns.

of.

asso

ciat

ion.

in.

biva

riat

e.da

ta.

Con

stru

ct.a

nd.in

terp

ret.

scat

ter.

plot

s.fo

r.bi

vari

ate.

mea

sure

men

t.da

ta.t

o.in

vest

igat

e.pa

tter

ns.

of.a

ssoc

iati

on.

betw

een.

two.

qua

ntit

ies.

.Des

crib

e.pa

tter

ns.

such

.as.

clus

teri

ng,.o

utlie

rs,.

posi

tive

.or.

nega

tive

.ass

ocia

tion

,.lin

ear.

asso

ciat

ion,

.and

.non

linea

r.as

soci

atio

n.

8.SP

.1X

8St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.pa

tter

ns.

of.

asso

ciat

ion.

in.

biva

riat

e.da

ta.

Kno

w.t

hat.

stra

ight

.line

s.ar

e.w

idel

y.us

ed.t

o.m

odel

.rel

atio

nsh

ips.

betw

een.

two.

qua

ntit

ativ

e.va

riab

les.

.For

.sca

tter

.pl

ots.

that

.sug

gest

.a.li

near

.ass

ocia

tion

,.in

form

ally

.fit.

a.st

raig

ht.li

ne,.a

nd.

info

rmal

ly.a

sses

s.th

e.m

odel

.fit.

by.

judg

ing.

the.

clos

enes

s.of

.the

.dat

a.po

ints

.to

.the

.line

.

8.SP

.2X

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

8St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.pa

tter

ns.

of.

asso

ciat

ion.

in.

biva

riat

e.da

ta.

Use

.the

.eq

uati

on.o

f.a.li

near

.mod

el.

to.s

olve

.pro

blem

s.in

.the

.con

text

.of

.biv

aria

te.m

easu

rem

ent.

data

,.in

terp

reti

ng.t

he.s

lope

.and

.inte

rcep

t.

8.SP

.3X

XX

8St

atis

tics

.and

.P

roba

bilit

yIn

vest

igat

e.pa

tter

ns.

of.

asso

ciat

ion.

in.

biva

riat

e.da

ta.

Und

erst

and.

that

.pat

tern

s.of

.ass

ocia

tion

.ca

n.al

so.b

e.se

en.in

.biv

aria

te.

cate

gori

cal.d

ata.

by.d

ispl

ayin

g.fr

eque

ncie

s.an

d.re

lati

ve.fr

eque

ncie

s.in

.a.t

wo-

way

.tab

le..C

onst

ruct

.and

.in

terp

ret.

a.tw

o-w

ay.t

able

.su

mm

ariz

ing.

data

.on.

two.

cate

gori

cal.v

aria

bles

.co

llect

ed.fr

om.t

he.s

ame.

subj

ects

..Use

.re

lati

ve.fr

eque

ncie

s.ca

lcu

late

d.fo

r.ro

ws.

or.c

olu

mn

s.to

.des

crib

e.po

ssib

le.

asso

ciat

ion.

betw

een.

the.

two.

vari

able

s.

8.SP

.4X

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Rea

l.N

um

ber.

Syst

em

Ext

end.

the.

prop

erti

es.o

f.ex

pone

nts.

to.r

atio

nal.

expo

nent

s.

Exp

lain

.how

.the

.def

init

ion.

of.t

he.

mea

nin

g.of

.rat

iona

l.exp

onen

ts.fo

llow

s.fr

om.e

xten

din

g.th

e.pr

oper

ties

.of.i

nteg

er.

expo

nent

s.to

.tho

se.v

alue

s,.a

llow

ing.

for.

a.no

tati

on.fo

r.ra

dic

als.

in.t

erm

s.of

.ra

tion

al.e

xpon

ents

.

N-R

N.1

XX

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Rea

l.N

um

ber.

Syst

em

Ext

end.

the.

prop

erti

es.o

f.ex

pone

nts.

to.r

atio

nal.

expo

nent

s.

Rew

rite

.exp

ress

ion

s.in

volv

ing.

rad

ical

s.an

d.ra

tion

al.e

xpon

ents

.usi

ng.t

he.

prop

erti

es.o

f.exp

onen

ts.

N-R

N.2

XX

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Rea

l.N

um

ber.

Syst

em

Use

.pro

pert

ies.

of.r

atio

nal.

and.

irra

tion

al.

num

bers

.

Exp

lain

.why

.the

.su

m.o

r.pr

oduc

t.of

.tw

o.ra

tion

al.n

um

bers

.is.r

atio

nal;.

that

.th

e.su

m.o

f.a.r

atio

nal.n

um

ber.

and.

an.

irra

tion

al.n

um

ber.

is.ir

rati

onal

;.and

.th

at.t

he.p

rodu

ct.o

f.a.n

onze

ro.r

atio

nal.

num

ber.

and.

an.ir

rati

onal

.nu

mbe

r.is

.ir

rati

onal

.

N-R

N.3

XX

..

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Qua

ntit

ies

Rea

son.

qua

ntit

ativ

ely.

and.

use.

un

its.

to.

solv

e.pr

oble

ms.

Use

.un

its.

as.a

.way

.to.

und

erst

and.

prob

lem

s.an

d.to

.gu

ide.

the.

solu

tion

.of

.mu

lti-s

tep.

prob

lem

s;.c

hoos

e.an

d.in

terp

ret.

un

its.

con

sist

ently

.in.fo

rmu

las;

.ch

oose

.and

.inte

rpre

t.th

e.sc

ale.

and.

the.

orig

in.in

.gra

phs.

and.

data

.dis

play

s.

N-Q

.1X

XX

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Qua

ntit

ies

Rea

son.

qua

ntit

ativ

ely.

and.

use.

un

its.

to.

solv

e.pr

oble

ms.

Def

ine.

appr

opri

ate.

qua

ntit

ies.

for.

the.

purp

ose.

of.d

escr

ipti

ve.m

odel

ing.

N-Q

.2X

XX

.

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Qua

ntit

ies

Rea

son.

qua

ntit

ativ

ely.

and.

use.

un

its.

to.

solv

e.pr

oble

ms.

Cho

ose.

a.le

vel.o

f.acc

ura

cy.a

ppro

pria

te.

to.li

mit

atio

ns.

on.m

easu

rem

ent.

whe

n.re

port

ing.

qua

ntit

ies.

N-Q

.3X

XX

X

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Com

plex

.N

um

ber.

Syst

em

Perf

orm

.ar

ith

met

ic.

oper

atio

ns.

wit

h.co

mpl

ex.

num

bers

.

Kno

w.t

here

.is.a

.com

plex

.nu

mbe

r.i.s

uch.

that

.i2 .=.–

1,.a

nd.e

very

.com

plex

.nu

mbe

r.ha

s.th

e.fo

rm.a

.+.b

i.wit

h.a.

and

b re

al.

N-C

N.1

XX

.

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Com

plex

.N

um

ber.

Syst

em

Perf

orm

.ar

ith

met

ic.

oper

atio

ns.

wit

h.co

mpl

ex.

num

bers

.

Use

.the

.rel

atio

n.i2 .=

.–1.

and.

the.

com

mut

ativ

e,.a

ssoc

iati

ve,.a

nd.

dis

trib

utiv

e.pr

oper

ties

.to.

add,

.su

btra

ct,.

and.

mu

ltipl

y.co

mpl

ex.n

um

bers

.

N-C

N.2

XX

.

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Com

plex

.N

um

ber.

Syst

em

Perf

orm

.ar

ith

met

ic.

oper

atio

ns.

wit

h.co

mpl

ex.

num

bers

.

(+).F

ind.

the.

conj

ugat

e.of

.a.c

ompl

ex.

num

ber;.

use.

conj

ugat

es.t

o.fi

nd.m

odu

li.an

d.q

uoti

ents

.of.c

ompl

ex.n

um

bers

.

N-C

N.3

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Com

plex

.N

um

ber.

Syst

em

Rep

rese

nt.

com

plex

.nu

mbe

rs.

and.

thei

r.op

erat

ion

s.on

.the

.co

mpl

ex.p

lane

.

(+).R

epre

sent

.com

plex

.nu

mbe

rs.o

n.th

e.co

mpl

ex.p

lane

.in.r

ecta

ngu

lar.

and.

pola

r.fo

rm.(i

nclu

din

g.re

al.a

nd.im

agin

ary.

num

bers

),.an

d.ex

plai

n.w

hy.t

he.

rect

ang

ula

r.an

d.po

lar.

form

s.of

.a.g

iven

.co

mpl

ex.n

um

ber.

repr

esen

t.th

e.sa

me.

num

ber.

N-C

N.4

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Com

plex

.N

um

ber.

Syst

em

Rep

rese

nt.

com

plex

.nu

mbe

rs.

and.

thei

r.op

erat

ion

s.on

.the

.co

mpl

ex.p

lane

.

(+).R

epre

sent

.add

itio

n,.s

ubt

ract

ion,

.m

ulti

plic

atio

n,.a

nd.c

onju

gati

on.o

f.co

mpl

ex.n

um

bers

.geo

met

rica

lly.o

n.th

e.co

mpl

ex.p

lane

;.use

.pro

pert

ies.

of.t

his

.re

pres

enta

tion

.for.

com

puta

tion

.

N-C

N.5

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Com

plex

.N

um

ber.

Syst

em

Rep

rese

nt.

com

plex

.nu

mbe

rs.

and.

thei

r.op

erat

ion

s.on

.the

.co

mpl

ex.p

lane

.

(+).C

alcu

late

.the

.dis

tanc

e.be

twee

n.nu

mbe

rs.in

.the

.com

plex

.pla

ne.a

s.th

e.m

odu

lus.

of.t

he.d

iffe

renc

e,.a

nd.t

he.

mid

poin

t.of

.a.s

egm

ent.

as.t

he.a

vera

ge.o

f.th

e.nu

mbe

rs.a

t.it

s.en

dpoi

nts.

N-C

N.6

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Com

plex

.N

um

ber.

Syst

em

Use

.com

plex

.nu

mbe

rs.in

.po

lyno

mia

l.id

enti

ties

.and

.eq

uati

ons.

Solv

e.q

uad

rati

c.eq

uati

ons.

wit

h.re

al.c

oeff

icie

nts.

that

.hav

e.co

mpl

ex.

solu

tion

s.

N-C

N.7

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Com

plex

.N

um

ber.

Syst

em

Use

.com

plex

.nu

mbe

rs.in

.po

lyno

mia

l.id

enti

ties

.and

.eq

uati

ons.

(+).E

xten

d.po

lyno

mia

l.ide

ntit

ies.

to.t

he.

com

plex

.nu

mbe

rs.

N-C

N.8

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

The

.Com

plex

.N

um

ber.

Syst

em

Use

.com

plex

.nu

mbe

rs.in

.po

lyno

mia

l.id

enti

ties

.and

.eq

uati

ons.

(+).K

now

.the

.Fu

ndam

enta

l.The

orem

.of

.Alg

ebra

;.sho

w.t

hat.

it.is

.tru

e.fo

r.q

uad

rati

c.po

lyno

mia

ls.

N-C

N.9

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Rep

rese

nt.a

nd.

mod

el.w

ith.

vect

or.q

uant

itie

s.

(+).R

ecog

niz

e.ve

ctor

.qua

ntit

ies.

as.

havi

ng.b

oth.

mag

nit

ude.

and.

dir

ecti

on..

Rep

rese

nt.v

ecto

r.q

uant

itie

s.by

.dir

ecte

d.lin

e.se

gm

ents

,.and

.use

.app

ropr

iate

.sy

mbo

ls.fo

r.ve

ctor

s.an

d.th

eir.

mag

nit

udes

.(e.g

.,.v,

.|v|,.

||v||,

.v).

N-V

M.1

.X

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Rep

rese

nt.a

nd.

mod

el.w

ith.

vect

or.q

uant

itie

s.

(+).F

ind.

the.

com

pone

nts.

of.a

.vec

tor.

by.

subt

ract

ing.

the.

coor

din

ates

.of.a

n.in

itia

l.po

int.

from

.the

.coo

rdin

ates

.of.a

.ter

min

al.

poin

t.

N-V

M.2

.X

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Rep

rese

nt.a

nd.

mod

el.w

ith.

vect

or.q

uant

itie

s.

(+).S

olve

.pro

blem

s.in

volv

ing.

velo

city

.an

d.ot

her.

qua

ntit

ies.

that

.can

.be.

repr

esen

ted.

by.v

ecto

rs.

N-V

M.3

.X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.ve

ctor

s.

(+).A

dd.a

nd.s

ubt

ract

.vec

tors

.A

dd.v

ecto

rs.e

nd-t

o-en

d,.

com

pone

nt-w

ise,

.and

.by.

the.

para

llelo

gra

m.r

ule

..U

nder

stan

d.th

at.t

he.

mag

nit

ude.

of.a

.su

m.o

f.tw

o.ve

ctor

s.is

.typ

ical

ly.

not.

the.

sum

.of.t

he.

mag

nit

udes

.

N-V

M.4

a.

X

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.ve

ctor

s.

(+).A

dd.a

nd.s

ubt

ract

.vec

tors

.G

iven

.tw

o.ve

ctor

s.in

.m

agn

itud

e.an

d.d

irec

tion

.fo

rm,.d

eter

min

e.th

e.m

agn

itud

e.an

d.d

irec

tion

.of

.the

ir.s

um

.

N-V

M.4

b.

X

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.ve

ctor

s.

(+).A

dd.a

nd.s

ubt

ract

.vec

tors

.U

nder

stan

d.ve

ctor

.su

btra

ctio

n.v.

–.w

.as.v.

+.(–w

),.w

here

.–w

.is.t

he.

addi

tive

.inve

rse.

of.w

,.w

ith.

the.

sam

e.m

agni

tude

.as

.w.a

nd.p

oint

ing.

in.

the.

oppo

site

.dir

ecti

on..

Rep

rese

nt.v

ecto

r.su

btra

ctio

n.g

raph

ical

ly.

by.c

onne

ctin

g.th

e.ti

ps.in

.th

e.ap

prop

riat

e.or

der,.

and.

perf

orm

.vec

tor.

subt

ract

ion.

com

pone

nt-w

ise.

N-V

M.4

c.

X

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.ve

ctor

s.

(+).M

ulti

ply.

a.ve

ctor

.by.

a.sc

alar

.R

epre

sent

.sca

lar.

mu

ltipl

icat

ion.

gra

phic

ally

.by

.sca

ling.

vect

ors.

and.

poss

ibly

.rev

ersi

ng.t

heir

.d

irec

tion

;.per

form

.sca

lar.

mu

ltipl

icat

ion.

com

pone

nt-

wis

e,.e

.g.,.

as.c

(vx ,.

vy ).=

.(c

vx ,.cv

y ).

N-V

M.5

a.

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.ve

ctor

s.

(+).M

ulti

ply.

a.ve

ctor

.by.

a.sc

alar

.C

ompu

te.t

he.m

agn

itud

e.of

.a.s

cala

r.m

ulti

ple.

cv.u

sing

.||cv

||.=

.|c|v

..C

ompu

te.t

he.d

irec

tion

.of.

cv.k

now

ing.

that

.whe

n.|c

|v.

≠.0,

.the

.dir

ecti

on.o

f.cv.

is.

eith

er.a

long

.v.(f

or.c

.>.0

).or.

agai

nst

.v.(f

or.c

.<.0

).

N-V

M.5

b.

X

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.m

atri

ces.

and.

use.

mat

rice

s.in

.ap

plic

atio

ns.

(+).U

se.m

atri

ces.

to.r

epre

sent

.and

.m

anip

ula

te.d

ata,

.e.g

.,.to

.rep

rese

nt.

payo

ffs.

or.in

cide

nce.

rela

tion

ship

s.in

.a.

netw

ork.

N-V

M.6

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.m

atri

ces.

and.

use.

mat

rice

s.in

.ap

plic

atio

ns.

(+).M

ulti

ply.

mat

rice

s.by

.sca

lars

.to.

prod

uce.

new

.mat

rice

s,.e

.g.,.

as.w

hen.

all.

of.t

he.p

ayof

fs.in

.a.g

ame.

are.

dou

bled

.

N-V

M.7

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.m

atri

ces.

and.

use.

mat

rice

s.in

.ap

plic

atio

ns.

(+).A

dd,.s

ubt

ract

,.and

.mu

ltipl

y.m

atri

ces.

of.a

ppro

pria

te.d

imen

sion

s.N

-VM

.8X

X

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.m

atri

ces.

and.

use.

mat

rice

s.in

.ap

plic

atio

ns.

(+).U

nder

stan

d.th

at,.u

nlik

e.m

ulti

plic

atio

n.of

.nu

mbe

rs,.m

atri

x.m

ulti

plic

atio

n.fo

r.sq

uare

.mat

rice

s.is

.not

.a.c

omm

utat

ive.

oper

atio

n,.b

ut.

still

.sat

isfie

s.th

e.as

soci

ativ

e.an

d.d

istr

ibut

ive.

prop

erti

es.

N-V

M.9

XX

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.m

atri

ces.

and.

use.

mat

rice

s.in

.ap

plic

atio

ns.

(+).U

nder

stan

d.th

at.t

he.z

ero.

and.

iden

tity

.mat

rice

s.pl

ay.a

.rol

e.in

.mat

rix.

add

itio

n.an

d.m

ulti

plic

atio

n.si

mila

r.to

.th

e.ro

le.o

f.0.a

nd.1

.in.t

he.r

eal.n

um

bers

..T

he.d

eter

min

ant.

of.a

.sq

uare

.mat

rix.

is.

nonz

ero.

if.an

d.on

ly.if

.the

.mat

rix.

has.

a.m

ulti

plic

ativ

e.in

vers

e.

N-V

M.1

0X

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.m

atri

ces.

and.

use.

mat

rice

s.in

.ap

plic

atio

ns.

(+).M

ulti

ply.

a.ve

ctor

.(reg

arde

d.as

.a.

mat

rix.

wit

h.on

e.co

lum

n).b

y.a.

mat

rix.

of.s

uit

able

.dim

ensi

ons.

to.p

rodu

ce.

anot

her.

vect

or..W

ork.

wit

h.m

atri

ces.

as.

tran

sfor

mat

ion

s.of

.vec

tors

.

N-V

M.1

1X

X

Hig

h.Sc

hool

-N

um

ber.

and.

Qua

ntit

y

Vec

tor.

and.

Mat

rix.

Qua

ntit

ies

Perf

orm

.op

erat

ion

s.on

.m

atri

ces.

and.

use.

mat

rice

s.in

.ap

plic

atio

ns.

(+).W

ork.

wit

h.2.

×.2

.mat

rice

s.as

.tr

ansf

orm

atio

ns.

of.t

he.p

lane

,.and

.in

terp

ret.

the.

abso

lute

.val

ue.o

f.the

.de

term

inan

t.in

.ter

ms.

of.a

rea.

N-V

M.1

2X

X

Hig

h.Sc

hool

-A

lgeb

ra

Seei

ng.

Stru

ctu

re.in

.E

xpre

ssio

ns

Inte

rpre

t.th

e.st

ruct

ure

.of.

expr

essi

ons

Inte

rpre

t.ex

pres

sion

s.th

at.r

epre

sent

.a.

qua

ntit

y.in

.ter

ms.

of.it

s.co

ntex

t.In

terp

ret.

part

s.of

.an.

expr

essi

on,.s

uch.

as.t

erm

s,.

fact

ors,

.and

.coe

ffic

ient

s.

A-S

SE.1

aX

XX

X

Hig

h.Sc

hool

-A

lgeb

ra

Seei

ng.

Stru

ctu

re.in

.E

xpre

ssio

ns

Inte

rpre

t.th

e.st

ruct

ure

.of.

expr

essi

ons

Inte

rpre

t.ex

pres

sion

s.th

at.r

epre

sent

.a.

qua

ntit

y.in

.ter

ms.

of.it

s.co

ntex

t.In

terp

ret.

com

plic

ated

.ex

pres

sion

s.by

.vie

win

g.on

e.or

.mor

e.of

.the

ir.p

arts

.as

.a.s

ingl

e.en

tity

.

A-S

SE.1

bX

XX

X

Hig

h.Sc

hool

-A

lgeb

ra

Seei

ng.

Stru

ctu

re.in

.E

xpre

ssio

ns

Inte

rpre

t.th

e.st

ruct

ure

.of.

expr

essi

ons

Use

.the

.str

uctu

re.o

f.an.

expr

essi

on.t

o.id

enti

fy.w

ays.

to.r

ewri

te.it

.A

-SSE

.2X

XX

X

Hig

h.Sc

hool

-A

lgeb

ra

Seei

ng.

Stru

ctu

re.in

.E

xpre

ssio

ns

Wri

te.e

xpre

ssio

ns.

in.e

qu

ival

ent.

form

s.to

.sol

ve.

prob

lem

s

Cho

ose.

and.

prod

uce.

an.e

qu

ival

ent.

form

.of

.an.

expr

essi

on.t

o.re

veal

.and

.exp

lain

.pr

oper

ties

.of.t

he.q

uant

ity.

repr

esen

ted.

by.t

he.e

xpre

ssio

n.

Fact

or.a

.qua

dra

tic.

expr

essi

on.t

o.re

veal

.the

.ze

ros.

of.t

he.fu

ncti

on.it

.de

fine

s.

A-S

SE.3

aX

X

Hig

h.Sc

hool

-A

lgeb

ra

Seei

ng.

Stru

ctu

re.in

.E

xpre

ssio

ns

Wri

te.e

xpre

ssio

ns.

in.e

qu

ival

ent.

form

s.to

.sol

ve.

prob

lem

s

Cho

ose.

and.

prod

uce.

an.e

qu

ival

ent.

form

.of

.an.

expr

essi

on.t

o.re

veal

.and

.exp

lain

.pr

oper

ties

.of.t

he.q

uant

ity.

repr

esen

ted.

by.t

he.e

xpre

ssio

n.

Com

plet

e.th

e.sq

uare

.in.

a.q

uad

rati

c.ex

pres

sion

.to

.rev

eal.t

he.m

axim

um

.or

.min

imu

m.v

alue

.of.t

he.

func

tion

.it.d

efin

es.

A-S

SE.3

bX

X

Hig

h.Sc

hool

-A

lgeb

ra

Seei

ng.

Stru

ctu

re.in

.E

xpre

ssio

ns

Wri

te.e

xpre

ssio

ns.

in.e

qu

ival

ent.

form

s.to

.sol

ve.

prob

lem

s

Cho

ose.

and.

prod

uce.

an.e

qu

ival

ent.

form

.of

.an.

expr

essi

on.t

o.re

veal

.and

.exp

lain

.pr

oper

ties

.of.t

he.q

uant

ity.

repr

esen

ted.

by.t

he.e

xpre

ssio

n.

Use

.the

.pro

pert

ies.

of.

expo

nent

s.to

.tra

nsf

orm

.ex

pres

sion

s.fo

r.ex

pone

ntia

l.fu

ncti

ons.

A-S

SE.3

cX

XX

X

Hig

h.Sc

hool

-A

lgeb

ra

Seei

ng.

Stru

ctu

re.in

.E

xpre

ssio

ns

Wri

te.e

xpre

ssio

ns.

in.e

qu

ival

ent.

form

s.to

.sol

ve.

prob

lem

s

Der

ive.

the.

form

ula

.for.

the.

sum

.of.a

.fi

nit

e.ge

omet

ric.

seri

es.(w

hen.

the.

com

mon

.rat

io.is

.not

.1),.

and.

use.

the.

form

ula

.to.

solv

e.pr

oble

ms.

A-S

SE.4

XX

.


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-A

lgeb

ra

Ari

thm

etic

.wit

h.Po

lyno

mia

ls.

and.

Rat

iona

l.E

xpre

ssio

ns

Perf

orm

.ar

ith

met

ic.

oper

atio

ns.

on.

poly

nom

ials

Und

erst

and.

that

.pol

ynom

ials

.form

.a.

syst

em.a

nalo

gous

.to.

the.

inte

gers

,.na

mel

y,.t

hey.

are.

clos

ed.u

nder

.the

.op

erat

ion

s.of

.add

itio

n,.s

ubt

ract

ion,

.an

d.m

ulti

plic

atio

n;.a

dd,.s

ubt

ract

,.and

.m

ulti

ply.

poly

nom

ials

.

A-A

PR.1

XX

Hig

h.Sc

hool

-A

lgeb

ra

Ari

thm

etic

.wit

h.Po

lyno

mia

ls.

and.

Rat

iona

l.E

xpre

ssio

ns

Und

erst

and.

the.

rela

tion

ship

.be

twee

n.ze

ros.

and.

fact

ors.

of.

poly

nom

ials

Kno

w.a

nd.a

pply

.the

.Rem

aind

er.

The

orem

:.For

.a.p

olyn

omia

l.p(x

).and

.a.

num

ber.

a,.t

he.r

emai

nder

.on.

div

isio

n.by

.x.–

.a.is

.p(a

),.so

.p(a

).=.0

.if.a

nd.o

nly

.if.

(x.–

.a).i

s.a.

fact

or.o

f.p(x

).

A-A

PR.2

XX

Hig

h.Sc

hool

-A

lgeb

ra

Ari

thm

etic

.wit

h.Po

lyno

mia

ls.

and.

Rat

iona

l.E

xpre

ssio

ns

Und

erst

and.

the.

rela

tion

ship

.be

twee

n.ze

ros.

and.

fact

ors.

of.

poly

nom

ials

Iden

tify

.zer

os.o

f.pol

ynom

ials

.whe

n.su

itab

le.fa

ctor

izat

ion

s.ar

e.av

aila

ble,

.an

d.us

e.th

e.ze

ros.

to.c

onst

ruct

.a.r

ough

.g

raph

.of.t

he.fu

ncti

on.d

efin

ed.b

y.th

e.po

lyno

mia

l.

A-A

PR.3

XX

Hig

h.Sc

hool

-A

lgeb

ra

Ari

thm

etic

.wit

h.Po

lyno

mia

ls.

and.

Rat

iona

l.E

xpre

ssio

ns

Use

.pol

ynom

ial.

iden

titi

es.t

o.so

lve.

prob

lem

s

Pro

ve.p

olyn

omia

l.ide

ntit

ies.

and.

use.

them

.to.

desc

ribe

.nu

mer

ical

.re

lati

onsh

ips.

A-A

PR.4

XX

Hig

h.Sc

hool

-A

lgeb

ra

Ari

thm

etic

.wit

h.Po

lyno

mia

ls.

and.

Rat

iona

l.E

xpre

ssio

ns

Use

.pol

ynom

ial.

iden

titi

es.t

o.so

lve.

prob

lem

s

(+).K

now

.and

.app

ly.t

he.B

inom

ial.

The

orem

.for.

the.

expa

nsio

n.of

.(x.+

.y)n .

in.

pow

ers.

of.x

.and

y fo

r.a.

posi

tive

.inte

ger.

n,.w

here

.x.a

nd y

are

.any

.num

bers

,.wit

h.co

effic

ient

s.de

term

ined

.for.

exam

ple.

by.

Pasc

al’s

.Tri

angl

e.

A-A

PR.5

XX

X

Hig

h.Sc

hool

-A

lgeb

ra

Ari

thm

etic

.wit

h.Po

lyno

mia

ls.

and.

Rat

iona

l.E

xpre

ssio

ns

Rew

rite

.rat

iona

l.ex

pres

sion

sR

ewri

te.s

impl

e.ra

tion

al.e

xpre

ssio

ns.

in.

dif

fere

nt.fo

rms;

.wri

te.a

(x)/

b(x)

.in.t

he.

form

.q(x

).+.r

(x)/

b(x)

,.whe

re.a

(x),.

b(x)

,.q

(x),.

and.

r(x)

.are

.pol

ynom

ials

.wit

h.th

e.de

gre

e.of

.r(x

).les

s.th

an.t

he.d

egre

e.of

.b(

x),.u

sing

.insp

ecti

on,.l

ong.

div

isio

n,.o

r,.fo

r.th

e.m

ore.

com

plic

ated

.exa

mpl

es,.a

.co

mpu

ter.

alge

bra.

syst

em.

A-A

PR.6

XX

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-A

lgeb

ra

Ari

thm

etic

.wit

h.Po

lyno

mia

ls.

and.

Rat

iona

l.E

xpre

ssio

ns

Rew

rite

.rat

iona

l.ex

pres

sion

s(+

).Und

erst

and.

that

.rat

iona

l.exp

ress

ion

s.fo

rm.a

.sys

tem

.ana

logo

us.t

o.th

e.ra

tion

al.

num

bers

,.clo

sed.

und

er.a

ddit

ion,

.su

btra

ctio

n,.m

ulti

plic

atio

n,.a

nd.d

ivis

ion.

by.a

.non

zero

.rat

iona

l.exp

ress

ion;

.add

,.su

btra

ct,.m

ulti

ply,

.and

.div

ide.

rati

onal

.ex

pres

sion

s.

A-A

PR.7

XX

.X

Hig

h.Sc

hool

-A

lgeb

ra

Cre

atin

g.E

qua

tion

sC

reat

e.eq

uati

ons.

that

.des

crib

e.nu

mbe

rs.o

r.re

lati

onsh

ips

Cre

ate.

equa

tion

s.an

d.in

equa

litie

s.in

.on

e.va

riab

le.a

nd.u

se.t

hem

.to.

solv

e.pr

oble

ms.

.Incl

ude.

equa

tion

s.ar

isin

g.fr

om.li

near

.and

.qua

dra

tic.

func

tion

s,.

and.

sim

ple.

rati

onal

.and

.exp

onen

tial

.fu

ncti

ons.

A-C

ED

.1X

XX

X

Hig

h.Sc

hool

-A

lgeb

ra

Cre

atin

g.E

qua

tion

sC

reat

e.eq

uati

ons.

that

.des

crib

e.nu

mbe

rs.o

r.re

lati

onsh

ips

Cre

ate.

equa

tion

s.in

.tw

o.or

.mor

e.va

riab

les.

to.r

epre

sent

.rel

atio

nsh

ips.

betw

een.

qua

ntit

ies;

.gra

ph.e

qua

tion

s.on

.co

ord

inat

e.ax

es.w

ith.

labe

ls.a

nd.s

cale

s.

A-C

ED

.2X

XX

X

Hig

h.Sc

hool

-A

lgeb

ra

Cre

atin

g.E

qua

tion

sC

reat

e.eq

uati

ons.

that

.des

crib

e.nu

mbe

rs.o

r.re

lati

onsh

ips

Rep

rese

nt.c

onst

rain

ts.b

y.eq

uati

ons.

or.in

equa

litie

s,.a

nd.b

y.sy

stem

s.of

.eq

uati

ons.

and

/or.

ineq

ualit

ies,

.an

d.in

terp

ret.

solu

tion

s.as

.via

ble.

or.n

onvi

able

.opt

ion

s.in

.a.m

odel

ing.

cont

ext.

A-C

ED

.3X

XX

X

Hig

h.Sc

hool

-A

lgeb

ra

Cre

atin

g.E

qua

tion

sC

reat

e.eq

uati

ons.

that

.des

crib

e.nu

mbe

rs.o

r.re

lati

onsh

ips

Rea

rran

ge.fo

rmu

las.

to.h

igh

light

.a.

qua

ntit

y.of

.inte

rest

,.usi

ng.t

he.s

ame.

reas

onin

g.as

.in.s

olvi

ng.e

qua

tion

s.

A-C

ED

.4X

XX

X

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Und

erst

and.

solv

ing.

equa

tion

s.as

.a.p

roce

ss.o

f.re

ason

ing.

and.

expl

ain.

the.

reas

onin

g

Exp

lain

.eac

h.st

ep.in

.sol

ving

.a.s

impl

e.eq

uati

on.a

s.fo

llow

ing.

from

.the

.eq

ualit

y.of

.nu

mbe

rs.a

sser

ted.

at.t

he.p

revi

ous.

step

,.sta

rtin

g.fr

om.t

he.a

ssu

mpt

ion.

that

.th

e.or

igin

al.e

qua

tion

.has

.a.s

olut

ion.

.C

onst

ruct

.a.v

iabl

e.ar

gu

men

t.to

.just

ify.

a.so

luti

on.m

etho

d.

A-R

EI.1

XX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Und

erst

and.

solv

ing.

equa

tion

s.as

.a.p

roce

ss.o

f.re

ason

ing.

and.

expl

ain.

the.

reas

onin

g

Solv

e.si

mpl

e.ra

tion

al.a

nd.r

adic

al.

equa

tion

s.in

.one

.var

iabl

e,.a

nd.g

ive.

exam

ples

.sho

win

g.ho

w.e

xtra

neou

s.so

luti

ons.

may

.ari

se.

A-R

EI.2

XX

XX

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Solv

e.eq

uati

ons.

and.

ineq

ualit

ies.

in.o

ne.v

aria

ble

Solv

e.lin

ear.

equa

tion

s.an

d.in

equa

litie

s.in

.one

.var

iabl

e,.in

clud

ing.

equa

tion

s.w

ith.

coef

ficie

nts.

repr

esen

ted.

by.le

tter

s.

A-R

EI.3

XX

XX

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Solv

e.eq

uati

ons.

and.

ineq

ualit

ies.

in.o

ne.v

aria

ble

Solv

e.q

uad

rati

c.eq

uati

ons.

in.o

ne.

vari

able

.U

se.t

he.m

etho

d.of

.co

mpl

etin

g.th

e.sq

uare

.to.

tran

sfor

m.a

ny.q

uad

rati

c.eq

uati

on.in

.x.in

to.a

n.eq

uati

on.o

f.the

.form

.(x

.–.p

)2 .=.q

.tha

t.ha

s.th

e.sa

me.

solu

tion

s..D

eriv

e.th

e.q

uad

rati

c.fo

rmu

la.fr

om.

this

.form

.

A-R

EI.4

aX

X

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Solv

e.eq

uati

ons.

and.

ineq

ualit

ies.

in.o

ne.v

aria

ble

Solv

e.q

uad

rati

c.eq

uati

ons.

in.o

ne.

vari

able

.So

lve.

qua

dra

tic.

equa

tion

s.by

.insp

ecti

on.(e

.g.,.

for.

x2 .=

.49)

,.tak

ing.

squa

re.r

oots

,.co

mpl

etin

g.th

e.sq

uare

,.th

e.q

uad

rati

c.fo

rmu

la.a

nd.

fact

orin

g,.a

s.ap

prop

riat

e.to

.the

.init

ial.f

orm

.of.t

he.

equa

tion

..Rec

ogn

ize.

whe

n.th

e.q

uad

rati

c.fo

rmu

la.

giv

es.c

ompl

ex.s

olut

ion

s.an

d.w

rite

.the

m.a

s.a.

±.b

i.fo

r.re

al.n

um

bers

.a.a

nd.b

.

A-R

EI.4

bX

X

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Solv

e.sy

stem

s.of

.eq

uati

ons

Pro

ve.t

hat,

.giv

en.a

.sys

tem

.of.t

wo.

equa

tion

s.in

.tw

o.va

riab

les,

.rep

laci

ng.

one.

equa

tion

.by.

the.

sum

.of.t

hat.

equa

tion

.and

.a.m

ulti

ple.

of.t

he.o

ther

.pr

oduc

es.a

.sys

tem

.wit

h.th

e.sa

me.

solu

tion

s.

A-R

EI.5

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Solv

e.sy

stem

s.of

.eq

uati

ons

Solv

e.sy

stem

s.of

.line

ar.e

qua

tion

s.ex

actl

y.an

d.ap

prox

imat

ely.

(e.g

.,.w

ith.

gra

phs)

,.foc

usin

g.on

.pai

rs.o

f.lin

ear.

equa

tion

s.in

.tw

o.va

riab

les.

A-R

EI.6

XX

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Solv

e.sy

stem

s.of

.eq

uati

ons

Solv

e.a.

sim

ple.

syst

em.c

onsi

stin

g.of

.a.

linea

r.eq

uati

on.a

nd.a

.qua

dra

tic.

equa

tion

.in.t

wo.

vari

able

s.al

gebr

aica

lly.

and.

gra

phic

ally

.

A-R

EI.7

XX

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Solv

e.sy

stem

s.of

.eq

uati

ons

(+).R

epre

sent

.a.s

yste

m.o

f.lin

ear.

equa

tion

s.as

.a.s

ingl

e.m

atri

x.eq

uati

on.

in.a

.vec

tor.

vari

able

.

A-R

EI.8

XX

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Solv

e.sy

stem

s.of

.eq

uati

ons

(+).F

ind.

the.

inve

rse.

of.a

.mat

rix.

if.it

.ex

ists

.and

.use

.it.t

o.so

lve.

syst

ems.

of.

linea

r.eq

uati

ons.

(usi

ng.t

ech

nolo

gy.

for.

mat

rice

s.of

.dim

ensi

on.3

.×.3

.or.

gre

ater

).

A-R

EI.9

XX

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Rep

rese

nt.a

nd.

solv

e.eq

uati

ons.

and.

ineq

ualit

ies.

gra

phic

ally

Und

erst

and.

that

.the

.gra

ph.o

f.an.

equa

tion

.in.t

wo.

vari

able

s.is

.the

.se

t.of

.all.

its.

solu

tion

s.pl

otte

d.in

.the

.co

ord

inat

e.pl

ane,

.oft

en.fo

rmin

g.a.

curv

e.(w

hic

h.co

uld

.be.

a.lin

e).

A-R

EI.1

0X

XX

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Rep

rese

nt.a

nd.

solv

e.eq

uati

ons.

and.

ineq

ualit

ies.

gra

phic

ally

Exp

lain

.why

.the

.x-c

oord

inat

es.

of.t

he.p

oint

s.w

here

.the

.gra

phs.

of.

the.

equa

tion

s y

=.f

(x).a

nd y

=.g

(x).

inte

rsec

t.ar

e.th

e.so

luti

ons.

of.t

he.

equa

tion

.f(x

).=.g

(x);.

find

.the

.sol

utio

ns.

appr

oxim

atel

y,.e

.g.,.

usin

g.te

chno

log

y.to

.gra

ph.t

he.fu

ncti

ons,

.mak

e.ta

bles

.of.v

alue

s,.o

r.fi

nd.s

ucce

ssiv

e.ap

prox

imat

ion

s..In

clud

e.ca

ses.

whe

re.

f(x)

.and

/or.

g(x

).are

.line

ar,.p

olyn

omia

l,.ra

tion

al,.a

bsol

ute.

valu

e,.e

xpon

enti

al,.

and.

loga

rith

mic

.func

tion

s.

A-R

EI.1

1X

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-A

lgeb

ra

Rea

son

ing.

wit

h.E

qua

tion

s.an

d.In

equa

litie

s

Rep

rese

nt.a

nd.

solv

e.eq

uati

ons.

and.

ineq

ualit

ies.

gra

phic

ally

Gra

ph.t

he.s

olut

ion

s.to

.a.li

near

.in

equa

lity.

in.t

wo.

vari

able

s.as

.a.h

alf-

plan

e.(e

xclu

din

g.th

e.bo

und

ary.

in.t

he.

case

.of.a

.str

ict.

ineq

ualit

y),.a

nd.g

raph

.th

e.so

luti

on.s

et.t

o.a.

syst

em.o

f.lin

ear.

ineq

ualit

ies.

in.t

wo.

vari

able

s.as

.the

.in

ters

ecti

on.o

f.the

.cor

resp

ond

ing.

half-

plan

es.

A-R

EI.1

2X

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sU

nder

stan

d.th

e.co

ncep

t.of

.a.

func

tion

.and

.use

.fu

ncti

on.n

otat

ion

Und

erst

and.

that

.a.fu

ncti

on.fr

om.o

ne.

set.

(cal

led.

the.

dom

ain)

.to.

anot

her.

set.

(cal

led.

the.

rang

e).a

ssig

ns.

to.e

ach.

elem

ent.

of.t

he.d

omai

n.ex

actl

y.on

e.el

emen

t.of

.the

.ran

ge..I

f.f.is

.a.fu

ncti

on.

and.

x.is

.an.

elem

ent.

of.it

s.do

mai

n,.

then

.f(x

).den

otes

.the

.out

put.

of.f.

corr

espo

ndin

g.to

.the

.inpu

t.x.

.The

.gra

ph.

of.f.

is.t

he.g

raph

.of.t

he.e

qua

tion

y =

.f(x

).

F-IF

.1X

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sU

nder

stan

d.th

e.co

ncep

t.of

.a.

func

tion

.and

.use

.fu

ncti

on.n

otat

ion

Use

.func

tion

.not

atio

n,.e

valu

ate.

func

tion

s.fo

r.in

puts

.in.t

heir

.dom

ain

s,.

and.

inte

rpre

t.st

atem

ents

.tha

t.us

e.fu

ncti

on.n

otat

ion.

in.t

erm

s.of

.a.c

onte

xt.

F-IF

.2X

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sU

nder

stan

d.th

e.co

ncep

t.of

.a.

func

tion

.and

.use

.fu

ncti

on.n

otat

ion

Rec

ogn

ize.

that

.seq

uenc

es.a

re.

func

tion

s,.s

omet

imes

.def

ined

.re

curs

ivel

y,.w

hose

.dom

ain.

is.a

.su

bset

.of

.the

.inte

gers

.

F-IF

.3X

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sIn

terp

ret.

func

tion

s.th

at.a

rise

.in.

appl

icat

ion

s.in

.ter

ms.

of.t

he.

cont

ext

For.

a.fu

ncti

on.t

hat.

mod

els.

a.re

lati

onsh

ip.b

etw

een.

two.

qua

ntit

ies,

.in

terp

ret.

key.

feat

ure

s.of

.gra

phs.

and.

tabl

es.in

.ter

ms.

of.t

he.q

uant

itie

s,.a

nd.

sket

ch.g

raph

s.sh

owin

g.ke

y.fe

atu

res.

giv

en.a

.ver

bal.d

escr

ipti

on.o

f.the

.re

lati

onsh

ip..K

ey.fe

atu

res.

incl

ude:

.in

terc

epts

;.int

erva

ls.w

here

.the

.func

tion

.is

.incr

easi

ng,.d

ecre

asin

g,.p

osit

ive,

.or

.neg

ativ

e;.r

elat

ive.

max

imu

ms.

and.

min

imu

ms;

.sym

met

ries

;.end

.beh

avio

r;.

and.

peri

odic

ity.

F-IF

.4X

XX

.


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sIn

terp

ret.

func

tion

s.th

at.a

rise

.in.

appl

icat

ion

s.in

.ter

ms.

of.t

he.

cont

ext

Rel

ate.

the.

dom

ain.

of.a

.func

tion

.to.

its.

gra

ph.a

nd,.w

here

.app

licab

le,.t

o.th

e.q

uant

itat

ive.

rela

tion

ship

.it.d

escr

ibes

.

F-IF

.5X

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sIn

terp

ret.

func

tion

s.th

at.a

rise

.in.

appl

icat

ion

s.in

.ter

ms.

of.t

he.

cont

ext

Cal

cula

te.a

nd.in

terp

ret.

the.

aver

age.

rate

.of.c

hang

e.of

.a.fu

ncti

on.(p

rese

nted

.sy

mbo

lical

ly.o

r.as

.a.t

able

).ove

r.a.

spec

ifie

d.in

terv

al..E

stim

ate.

the.

rate

.of.

chan

ge.fr

om.a

.gra

ph.

F-IF

.6X

XX

.

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sA

naly

ze.

func

tion

s.us

ing.

dif

fere

nt.

repr

esen

tati

ons

Gra

ph.fu

ncti

ons.

expr

esse

d.sy

mbo

lical

ly.

and.

show

.key

.feat

ure

s.of

.the

.gra

ph,.

by.h

and.

in.s

impl

e.ca

ses.

and.

usin

g.te

chno

log

y.fo

r.m

ore.

com

plic

ated

.cas

es.

Gra

ph.li

near

.and

.q

uad

rati

c.fu

ncti

ons.

and.

show

.inte

rcep

ts,.m

axim

a,.

and.

min

ima.

F-IF

.7a

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sA

naly

ze.

func

tion

s.us

ing.

dif

fere

nt.

repr

esen

tati

ons

Gra

ph.fu

ncti

ons.

expr

esse

d.sy

mbo

lical

ly.

and.

show

.key

.feat

ure

s.of

.the

.gra

ph,.

by.h

and.

in.s

impl

e.ca

ses.

and.

usin

g.te

chno

log

y.fo

r.m

ore.

com

plic

ated

.cas

es.

Gra

ph.s

qua

re.r

oot,

.cu

be.

root

,.and

.pie

cew

ise-

defi

ned.

func

tion

s,.

incl

udin

g.st

ep.fu

ncti

ons.

and.

abso

lute

.val

ue.

func

tion

s.

F-IF

.7b

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sA

naly

ze.

func

tion

s.us

ing.

dif

fere

nt.

repr

esen

tati

ons

Gra

ph.fu

ncti

ons.

expr

esse

d.sy

mbo

lical

ly.

and.

show

.key

.feat

ure

s.of

.the

.gra

ph,.

by.h

and.

in.s

impl

e.ca

ses.

and.

usin

g.te

chno

log

y.fo

r.m

ore.

com

plic

ated

.cas

es.

Gra

ph.p

olyn

omia

l.fu

ncti

ons,

.iden

tify

ing.

zero

s.w

hen.

suit

able

.fa

ctor

izat

ion

s.ar

e.av

aila

ble,

.and

.sho

win

g.en

d.be

havi

or.

F-IF

.7c

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sA

naly

ze.

func

tion

s.us

ing.

dif

fere

nt.

repr

esen

tati

ons

Gra

ph.fu

ncti

ons.

expr

esse

d.sy

mbo

lical

ly.

and.

show

.key

.feat

ure

s.of

.the

.gra

ph,.

by.h

and.

in.s

impl

e.ca

ses.

and.

usin

g.te

chno

log

y.fo

r.m

ore.

com

plic

ated

.cas

es.

(+).G

raph

.rat

iona

l.fu

ncti

ons,

.iden

tify

ing.

zero

s.an

d.as

ympt

otes

.w

hen.

suit

able

.fa

ctor

izat

ion

s.ar

e.av

aila

ble,

.and

.sho

win

g.en

d.be

havi

or.

F-IF

.7d

XX

.


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sA

naly

ze.

func

tion

s.us

ing.

dif

fere

nt.

repr

esen

tati

ons

Gra

ph.fu

ncti

ons.

expr

esse

d.sy

mbo

lical

ly.

and.

show

.key

.feat

ure

s.of

.the

.gra

ph,.

by.h

and.

in.s

impl

e.ca

ses.

and.

usin

g.te

chno

log

y.fo

r.m

ore.

com

plic

ated

.cas

es.

Gra

ph.e

xpon

enti

al.a

nd.

loga

rith

mic

.func

tion

s,.

show

ing.

inte

rcep

ts.

and.

end.

beha

vior

,.and

.tr

igon

omet

ric.

func

tion

s,.

show

ing.

peri

od,.m

idlin

e,.

and.

ampl

itud

e.

F-IF

.7e

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sA

naly

ze.

func

tion

s.us

ing.

dif

fere

nt.

repr

esen

tati

ons

Wri

te.a

.func

tion

.def

ined

.by.

an.

expr

essi

on.in

.dif

fere

nt.b

ut.e

qu

ival

ent.

form

s.to

.rev

eal.a

nd.e

xpla

in.d

iffe

rent

.pr

oper

ties

.of.t

he.fu

ncti

on.

Use

.the

.pro

cess

.of.

fact

orin

g.an

d.co

mpl

etin

g.th

e.sq

uare

.in.a

.qua

dra

tic.

func

tion

.to.

show

.zer

os,.

extr

eme.

valu

es,.a

nd.

sym

met

ry.o

f.the

.gra

ph,.

and.

inte

rpre

t.th

ese.

in.

term

s.of

.a.c

onte

xt.

F-IF

.8a

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sA

naly

ze.

func

tion

s.us

ing.

dif

fere

nt.

repr

esen

tati

ons

Wri

te.a

.func

tion

.def

ined

.by.

an.

expr

essi

on.in

.dif

fere

nt.b

ut.e

qu

ival

ent.

form

s.to

.rev

eal.a

nd.e

xpla

in.d

iffe

rent

.pr

oper

ties

.of.t

he.fu

ncti

on.

Use

.the

.pro

pert

ies.

of.

expo

nent

s.to

.inte

rpre

t.ex

pres

sion

s.fo

r.ex

pone

ntia

l.fu

ncti

ons.

F-IF

.8b

XX

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Inte

rpre

ting

.F

unc

tion

sA

naly

ze.

func

tion

s.us

ing.

dif

fere

nt.

repr

esen

tati

ons

Com

pare

.pro

pert

ies.

of.t

wo.

func

tion

s.ea

ch.r

epre

sent

ed.in

.a.d

iffe

rent

.way

.(a

lgeb

raic

ally

,.gra

phic

ally

,.nu

mer

ical

ly.

in.t

able

s,.o

r.by

.ver

bal.d

escr

ipti

ons)

.

F-IF

.9X

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Bu

ildin

g.F

unc

tion

sB

uild

.a.fu

ncti

on.

that

.mod

els.

a.re

lati

onsh

ip.

betw

een.

two.

qua

ntit

ies

Wri

te.a

.func

tion

.tha

t.de

scri

bes.

a.re

lati

onsh

ip.b

etw

een.

two.

qua

ntit

ies.

Det

erm

ine.

an.e

xplic

it.

expr

essi

on,.a

.rec

urs

ive.

proc

ess,

.or.

step

s.fo

r.ca

lcu

lati

on.fr

om.a

.con

text

.

F-B

F.1a

XX

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Bu

ildin

g.F

unc

tion

sB

uild

.a.fu

ncti

on.

that

.mod

els.

a.re

lati

onsh

ip.

betw

een.

two.

qua

ntit

ies

Wri

te.a

.func

tion

.tha

t.de

scri

bes.

a.re

lati

onsh

ip.b

etw

een.

two.

qua

ntit

ies.

Com

bine

.sta

ndar

d.fu

ncti

on.t

ypes

.usi

ng.

arit

hm

etic

.ope

rati

ons.

F-B

F.1b

XX

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Bu

ildin

g.F

unc

tion

sB

uild

.a.fu

ncti

on.

that

.mod

els.

a.re

lati

onsh

ip.

betw

een.

two.

qua

ntit

ies

Wri

te.a

.func

tion

.tha

t.de

scri

bes.

a.re

lati

onsh

ip.b

etw

een.

two.

qua

ntit

ies.

(+).C

ompo

se.fu

ncti

ons.

F-B

F.1c

XX

..


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-Fu

ncti

ons

Bu

ildin

g.F

unc

tion

sB

uild

.a.fu

ncti

on.

that

.mod

els.

a.re

lati

onsh

ip.

betw

een.

two.

qua

ntit

ies

Wri

te.a

rith

met

ic.a

nd.g

eom

etri

c.se

que

nces

.bot

h.re

curs

ivel

y.an

d.w

ith.

an.e

xplic

it.fo

rmu

la,.u

se.t

hem

.to.

mod

el.

situ

atio

ns,

.and

.tra

nsl

ate.

betw

een.

the.

two.

form

s.

F-B

F.2

XX

.

Hig

h.Sc

hool

-Fu

ncti

ons

Bu

ildin

g.F

unc

tion

sB

uild

.new

.fu

ncti

ons.

from

.exi

stin

g.fu

ncti

ons

Iden

tify

.the

.effe

ct.o

n.th

e.g

raph

.of.

repl

acin

g.f(

x).b

y.f(

x).+

.k,.k

.f(x)

,.f(k

x),.

and.

f(x.

+.k

).for

.spe

cific

.val

ues.

of.k

.(bot

h.po

siti

ve.a

nd.n

egat

ive)

;.fin

d.th

e.va

lue.

of.k

.giv

en.t

he.g

raph

s..E

xper

imen

t.w

ith.

case

s.an

d.ill

ustr

ate.

an.e

xpla

nati

on.

of.t

he.e

ffect

s.on

.the

.gra

ph.u

sing

.te

chno

log

y..In

clud

e.re

cog

nizi

ng.e

ven.

and.

odd.

func

tion

s.fr

om.t

heir

.gra

phs.

and.

alge

brai

c.ex

pres

sion

s.fo

r.th

em.

F-B

F.3

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Bu

ildin

g.F

unc

tion

sB

uild

.new

.fu

ncti

ons.

from

.exi

stin

g.fu

ncti

ons

Fin

d.in

vers

e.fu

ncti

ons.

Solv

e.an

.eq

uati

on.o

f.the

.fo

rm.f

(x).=

.c.fo

r.a.

sim

ple.

func

tion

.f.th

at.h

as.a

n.in

vers

e.an

d.w

rite

.an.

expr

essi

on.fo

r.th

e.in

vers

e.

F-B

F.4a

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Bu

ildin

g.F

unc

tion

sB

uild

.new

.fu

ncti

ons.

from

.exi

stin

g.fu

ncti

ons

Fin

d.in

vers

e.fu

ncti

ons.

(+).V

erif

y.by

.com

posi

tion

.th

at.o

ne.fu

ncti

on.is

.the

.in

vers

e.of

.ano

ther

.

F-B

F.4b

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Bu

ildin

g.F

unc

tion

sB

uild

.new

.fu

ncti

ons.

from

.exi

stin

g.fu

ncti

ons

Fin

d.in

vers

e.fu

ncti

ons.

(+).R

ead.

valu

es.o

f.an.

inve

rse.

func

tion

.from

.a.

gra

ph.o

r.a.

tabl

e,.g

iven

.th

at.t

he.fu

ncti

on.h

as.a

n.in

vers

e.

F-B

F.4c

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Bu

ildin

g.F

unc

tion

sB

uild

.new

.fu

ncti

ons.

from

.exi

stin

g.fu

ncti

ons

Fin

d.in

vers

e.fu

ncti

ons.

(+).P

rodu

ce.a

n.in

vert

ible

.fu

ncti

on.fr

om.a

.non

-in

vert

ible

.func

tion

.by.

rest

rict

ing.

the.

dom

ain.

F-B

F.4d

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Bu

ildin

g.F

unc

tion

sB

uild

.new

.fu

ncti

ons.

from

.exi

stin

g.fu

ncti

ons

(+).U

nder

stan

d.th

e.in

vers

e.re

lati

onsh

ip.

betw

een.

expo

nent

s.an

d.lo

gari

thm

s.an

d.us

e.th

is.r

elat

ion

ship

.to.

solv

e.pr

oble

ms.

invo

lvin

g.lo

gari

thm

s.an

d.ex

pone

nts.

F-B

F.5

XX

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-Fu

ncti

ons

Lin

ear,.

Qua

dra

tic,

.and

.E

xpon

enti

al.

Mod

els

Con

stru

ct.a

nd.

com

pare

.line

ar,.

qua

dra

tic,

.and

.ex

pone

ntia

l.m

odel

s.an

d.so

lve.

prob

lem

s

Dis

ting

uis

h.be

twee

n.si

tuat

ion

s.th

at.

can.

be.m

odel

ed.w

ith.

linea

r.fu

ncti

ons.

and.

wit

h.ex

pone

ntia

l.fu

ncti

ons.

Pro

ve.t

hat.

linea

r.fu

ncti

ons.

gro

w.b

y.eq

ual.d

iffe

renc

es.

over

.eq

ual.i

nter

vals

,.and

.th

at.e

xpon

enti

al.fu

ncti

ons.

gro

w.b

y.eq

ual.f

acto

rs.o

ver.

equa

l.int

erva

ls.

F-L

E.1

aX

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Lin

ear,.

Qua

dra

tic,

.and

.E

xpon

enti

al.

Mod

els

Con

stru

ct.a

nd.

com

pare

.line

ar,.

qua

dra

tic,

.and

.ex

pone

ntia

l.m

odel

s.an

d.so

lve.

prob

lem

s

Dis

ting

uis

h.be

twee

n.si

tuat

ion

s.th

at.

can.

be.m

odel

ed.w

ith.

linea

r.fu

ncti

ons.

and.

wit

h.ex

pone

ntia

l.fu

ncti

ons.

Rec

ogn

ize.

situ

atio

ns.

in.w

hic

h.on

e.q

uant

ity.

chan

ges.

at.a

.con

stan

t.ra

te.

per.

un

it.in

terv

al.r

elat

ive.

to.

anot

her.

F-L

E.1

bX

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Lin

ear,.

Qua

dra

tic,

.and

.E

xpon

enti

al.

Mod

els

Con

stru

ct.a

nd.

com

pare

.line

ar,.

qua

dra

tic,

.and

.ex

pone

ntia

l.m

odel

s.an

d.so

lve.

prob

lem

s

Dis

ting

uis

h.be

twee

n.si

tuat

ion

s.th

at.

can.

be.m

odel

ed.w

ith.

linea

r.fu

ncti

ons.

and.

wit

h.ex

pone

ntia

l.fu

ncti

ons.

Rec

ogn

ize.

situ

atio

ns.

in.w

hic

h.a.

qua

ntit

y.g

row

s.or

.dec

ays.

by.a

.co

nst

ant.

perc

ent.

rate

.per

.u

nit

.inte

rval

.rel

ativ

e.to

.an

othe

r.

F-L

E.1

cX

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Lin

ear,.

Qua

dra

tic,

.and

.E

xpon

enti

al.

Mod

els

Con

stru

ct.a

nd.

com

pare

.line

ar,.

qua

dra

tic,

.and

.ex

pone

ntia

l.m

odel

s.an

d.so

lve.

prob

lem

s

Con

stru

ct.li

near

.and

.exp

onen

tial

.fu

ncti

ons,

.incl

udin

g.ar

ith

met

ic.a

nd.

geom

etri

c.se

que

nces

,.giv

en.a

.gra

ph,.

a.de

scri

ptio

n.of

.a.r

elat

ion

ship

,.or.

two.

inpu

t-ou

tput

.pai

rs.(i

nclu

de.r

ead

ing.

thes

e.fr

om.a

.tab

le).

F-L

E.2

XX

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Lin

ear,.

Qua

dra

tic,

.and

.E

xpon

enti

al.

Mod

els

Con

stru

ct.a

nd.

com

pare

.line

ar,.

qua

dra

tic,

.and

.ex

pone

ntia

l.m

odel

s.an

d.so

lve.

prob

lem

s

Obs

erve

.usi

ng.g

raph

s.an

d.ta

bles

.tha

t.a.

qua

ntit

y.in

crea

sing

.exp

onen

tial

ly.

even

tual

ly.e

xcee

ds.a

.qua

ntit

y.in

crea

sing

.line

arly

,.qua

dra

tica

lly,.

or.(m

ore.

gene

rally

).as.

a.po

lyno

mia

l.fu

ncti

on.

F-L

E.3

XX

X

Hig

h.Sc

hool

-Fu

ncti

ons

Lin

ear,.

Qua

dra

tic,

.and

.E

xpon

enti

al.

Mod

els

Con

stru

ct.a

nd.

com

pare

.line

ar,.

qua

dra

tic,

.and

.ex

pone

ntia

l.m

odel

s.an

d.so

lve.

prob

lem

s

For.

expo

nent

ial.m

odel

s,.e

xpre

ss.a

s.a.

loga

rith

m.t

he.s

olut

ion.

to.a

bct.=

.d.w

here

.a,

.c,.a

nd.d

.are

.nu

mbe

rs.a

nd.t

he.b

ase

b is

.2,.1

0,.o

r.e;

.eva

luat

e.th

e.lo

gari

thm

.us

ing.

tech

nolo

gy.

F-L

E.4

XX

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-Fu

ncti

ons

Lin

ear,.

Qua

dra

tic,

.and

.E

xpon

enti

al.

Mod

els*

Inte

rpre

t.ex

pres

sion

s.fo

r.fu

ncti

ons.

in.t

erm

s.of

.the

.si

tuat

ion.

they

.m

odel

Inte

rpre

t.th

e.pa

ram

eter

s.in

.a.li

near

.or

.exp

onen

tial

.func

tion

.in.t

erm

s.of

.a.

cont

ext.

F-L

E.5

XX

X.

Hig

h.Sc

hool

-Fu

ncti

ons

Tri

gono

met

ric.

Fu

ncti

ons

Ext

end.

the.

dom

ain.

of.

trig

onom

etri

c.fu

ncti

ons.

usin

g.th

e.u

nit

.cir

cle

Und

erst

and.

rad

ian.

mea

sure

.of.a

n.an

gle.

as.t

he.le

ngth

.of.t

he.a

rc.o

n.th

e.u

nit

.ci

rcle

.su

bten

ded.

by.t

he.a

ngle

.

F-T

F.1

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Tri

gono

met

ric.

Fu

ncti

ons

Ext

end.

the.

dom

ain.

of.

trig

onom

etri

c.fu

ncti

ons.

usin

g.th

e.u

nit

.cir

cle

Exp

lain

.how

.the

.un

it.c

ircl

e.in

.th

e.co

ord

inat

e.pl

ane.

enab

les.

the.

exte

nsi

on.o

f.tri

gono

met

ric.

func

tion

s.to

.all.

real

.nu

mbe

rs,.i

nter

pret

ed.a

s.ra

dia

n.m

easu

res.

of.a

ngle

s.tr

aver

sed.

cou

nter

cloc

kwis

e.ar

ound

.the

.un

it.

circ

le.

F-T

F.2

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Tri

gono

met

ric.

Fu

ncti

ons

Ext

end.

the.

dom

ain.

of.

trig

onom

etri

c.fu

ncti

ons.

usin

g.th

e.u

nit

.cir

cle

(+).U

se.s

peci

al.t

rian

gles

.to.

dete

rmin

e.ge

omet

rica

lly.t

he.v

alue

s.of

.sin

e,.c

osin

e,.

tang

ent.

for.

π/3,

.π/4

.and

.π/6

,.and

.use

.th

e.u

nit

.cir

cle.

to.e

xpre

ss.t

he.v

alue

s.of

.si

ne,.c

osin

e,.a

nd.t

ange

nt.fo

r.π–

x,.π

+x,.

and.

2π–x

.in.t

erm

s.of

.the

ir.v

alue

s.fo

r.x,

.w

here

.x.is

.any

.rea

l.nu

mbe

r.

F-T

F.3

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Tri

gono

met

ric.

Fu

ncti

ons

Ext

end.

the.

dom

ain.

of.

trig

onom

etri

c.fu

ncti

ons.

usin

g.th

e.u

nit

.cir

cle

(+).U

se.t

he.u

nit

.cir

cle.

to.e

xpla

in.

sym

met

ry.(o

dd.a

nd.e

ven)

.and

.pe

riod

icit

y.of

.tri

gono

met

ric.

func

tion

s.

F-T

F.4

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Tri

gono

met

ric.

Fu

ncti

ons

Mod

el.p

erio

dic

.ph

enom

ena.

wit

h.tr

igon

omet

ric.

func

tion

s

Cho

ose.

trig

onom

etri

c.fu

ncti

ons.

to.

mod

el.p

erio

dic

.phe

nom

ena.

wit

h.sp

ecif

ied.

ampl

itud

e,.fr

eque

ncy,

.and

.m

idlin

e.

F-T

F.5

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Tri

gono

met

ric.

Fu

ncti

ons

Mod

el.p

erio

dic

.ph

enom

ena.

wit

h.tr

igon

omet

ric.

func

tion

s

(+).U

nder

stan

d.th

at.r

estr

icti

ng.a

.tr

igon

omet

ric.

func

tion

.to.

a.do

mai

n.on

.w

hic

h.it

.is.a

lway

s.in

crea

sing

.or.

alw

ays.

decr

easi

ng.a

llow

s.it

s.in

vers

e.to

.be.

con

stru

cted

.

F-T

F.6

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-Fu

ncti

ons

Tri

gono

met

ric.

Fu

ncti

ons

Mod

el.p

erio

dic

.ph

enom

ena.

wit

h.tr

igon

omet

ric.

func

tion

s

(+).U

se.in

vers

e.fu

ncti

ons.

to.s

olve

.tr

igon

omet

ric.

equa

tion

s.th

at.a

rise

.in

.mod

elin

g.co

ntex

ts;.e

valu

ate.

the.

solu

tion

s.us

ing.

tech

nolo

gy,

.and

.in

terp

ret.

them

.in.t

erm

s.of

.the

.con

text

.

F-T

F.7

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Tri

gono

met

ric.

Fu

ncti

ons

Pro

ve.a

nd.a

pply

.tr

igon

omet

ric.

iden

titi

es

Pro

ve.t

he.P

ytha

gore

an.id

enti

ty.

sin

2 (θ).+

.cos

2 (θ).=

.1.a

nd.u

se.it

.to.

calc

ula

te.t

rigo

nom

etri

c.ra

tios

.

F-T

F.8

XX

Hig

h.Sc

hool

-Fu

ncti

ons

Tri

gono

met

ric.

Fu

ncti

ons

Pro

ve.a

nd.a

pply

.tr

igon

omet

ric.

iden

titi

es

(+).P

rove

.the

.add

itio

n.an

d.su

btra

ctio

n.fo

rmu

las.

for.

sine

,.cos

ine,

.and

.tan

gent

.an

d.us

e.th

em.t

o.so

lve.

prob

lem

s.

F-T

F.9

XX

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Exp

erim

ent.

wit

h.tr

ansf

orm

atio

ns.

in.t

he.p

lane

Kno

w.p

reci

se.d

efin

itio

ns.

of.a

ngle

,.ci

rcle

,.per

pend

icu

lar.

line,

.par

alle

l.lin

e,.a

nd.li

ne.s

egm

ent,

.bas

ed.o

n.th

e.u

ndef

ined

.not

ion

s.of

.poi

nt,.l

ine,

.d

ista

nce.

alon

g.a.

line,

.and

.dis

tanc

e.ar

ound

.a.c

ircu

lar.

arc.

G-C

O.1

XX

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Exp

erim

ent.

wit

h.tr

ansf

orm

atio

ns.

in.t

he.p

lane

Rep

rese

nt.t

ran

sfor

mat

ion

s.in

.the

.pl

ane.

usin

g,.e

.g.,.

tran

spar

enci

es.

and.

geom

etry

.sof

twar

e;.d

escr

ibe.

tran

sfor

mat

ion

s.as

.func

tion

s.th

at.

take

.poi

nts.

in.t

he.p

lane

.as.

inpu

ts.a

nd.

giv

e.ot

her.

poin

ts.a

s.ou

tput

s..C

ompa

re.

tran

sfor

mat

ion

s.th

at.p

rese

rve.

dis

tanc

e.an

d.an

gle.

to.t

hose

.tha

t.do

.not

.(e.g

.,.tr

ansl

atio

n.ve

rsus

.hor

izon

tal.s

tret

ch).

G-C

O.2

XX

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Exp

erim

ent.

wit

h.tr

ansf

orm

atio

ns.

in.t

he.p

lane

Giv

en.a

.rec

tang

le,.p

aral

lelo

gra

m,.

trap

ezoi

d,.o

r.re

gu

lar.

poly

gon,

.des

crib

e.th

e.ro

tati

ons.

and.

refle

ctio

ns.

that

.car

ry.

it.o

nto.

itse

lf.

G-C

O.3

XX

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Exp

erim

ent.

wit

h.tr

ansf

orm

atio

ns.

in.t

he.p

lane

Dev

elop

.def

init

ion

s.of

.rot

atio

ns,

.re

flect

ion

s,.a

nd.t

ran

slat

ion

s.in

.ter

ms.

of.a

ngle

s,.c

ircl

es,.p

erpe

ndic

ula

r.lin

es,.

para

llel.l

ines

,.and

.line

.seg

men

ts.

G-C

O.4

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Exp

erim

ent.

wit

h.tr

ansf

orm

atio

ns.

in.t

he.p

lane

Giv

en.a

.geo

met

ric.

figu

re.a

nd.a

.rot

atio

n,.

refle

ctio

n,.o

r.tr

ansl

atio

n,.d

raw

.the

.tr

ansf

orm

ed.fi

gu

re.u

sing

,.e.g

.,.g

raph

.pa

per,.

trac

ing.

pape

r,.or

.geo

met

ry.

soft

war

e..S

peci

fy.a

.seq

uenc

e.of

.tr

ansf

orm

atio

ns.

that

.will

.car

ry.a

.giv

en.

figu

re.o

nto.

anot

her.

G-C

O.5

XX

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Und

erst

and.

cong

ruen

ce.in

.te

rms.

of.r

igid

.m

otio

ns

Use

.geo

met

ric.

desc

ript

ion

s.of

.rig

id.

mot

ion

s.to

.tra

nsf

orm

.fig

ure

s.an

d.to

.pre

dic

t.th

e.ef

fect

.of.a

.giv

en.r

igid

.m

otio

n.on

.a.g

iven

.fig

ure

;.giv

en.

two.

figu

res,

.use

.the

.def

init

ion.

of.

cong

ruen

ce.in

.ter

ms.

of.r

igid

.mot

ion

s.to

.de

cide

.if.t

hey.

are.

cong

ruen

t.

G-C

O.6

XX

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Und

erst

and.

cong

ruen

ce.in

.te

rms.

of.r

igid

.m

otio

ns

Use

.the

.def

init

ion.

of.c

ong

ruen

ce.in

.te

rms.

of.r

igid

.mot

ion

s.to

.sho

w.t

hat.

two.

tria

ngle

s.ar

e.co

ngru

ent.

if.an

d.on

ly.if

.cor

resp

ond

ing.

pair

s.of

.sid

es.

and.

corr

espo

ndin

g.pa

irs.

of.a

ngle

s.ar

e.co

ngru

ent.

G-C

O.7

XX

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Und

erst

and.

cong

ruen

ce.in

.te

rms.

of.r

igid

.m

otio

ns

Exp

lain

.how

.the

.cri

teri

a.fo

r.tr

iang

le.

cong

ruen

ce.(A

SA,.S

AS,

.and

.SSS

).fol

low

.fr

om.t

he.d

efin

itio

n.of

.con

gru

ence

.in.

term

s.of

.rig

id.m

otio

ns.

G-C

O.8

XX

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Pro

ve.g

eom

etri

c.th

eore

ms

Pro

ve.t

heor

ems.

abou

t.lin

es.a

nd.a

ngle

s..

The

orem

s in

clud

e: v

erti

cal a

ngle

s ar

e co

ngru

ent;

whe

n a

tran

sver

sal c

ross

es

para

llel l

ines

, alte

rnat

e in

teri

or a

ngle

s ar

e co

ngru

ent

and

corr

espo

ndin

g an

gles

are

con

gru

ent;

poin

ts o

n a

perp

end

icu

lar

bise

ctor

of a

line

seg

men

t ar

e ex

actly

tho

se e

qu

idis

tant

from

the

se

gm

ent’s

end

poin

ts.

G-C

O.9

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Pro

ve.g

eom

etri

c.th

eore

ms

Pro

ve.t

heor

ems.

abou

t.tr

iang

les.

.T

heor

ems

incl

ude:

mea

sure

s of

inte

rior

an

gles

of a

tri

angl

e su

m t

o 18

0°;

base

ang

les

of is

osce

les

tria

ngle

s ar

e co

ngru

ent;

the

seg

men

t jo

inin

g m

idpo

ints

of t

wo

side

s of

a t

rian

gle

is

para

llel t

o th

e th

ird

side

and

hal

f the

le

ngth

; the

med

ians

of a

tri

angl

e m

eet

at a

poi

nt.

G-C

O.1

0X

X

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Pro

ve.g

eom

etri

c.th

eore

ms

Pro

ve.t

heor

ems.

abou

t.pa

ralle

log

ram

s..

The

orem

s in

clud

e: o

ppos

ite

side

s ar

e co

ngru

ent,

opp

osit

e an

gles

ar

e co

ngru

ent,

the

dia

gona

ls o

f a

para

llelo

gra

m b

isec

t ea

ch o

ther

, an

d co

nver

sely

, rec

tang

les

are

para

llelo

gra

ms

wit

h co

ngru

ent

dia

gona

ls.

G-C

O.1

1X

X

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Mak

e.ge

omet

ric.

con

stru

ctio

ns

Mak

e.fo

rmal

.geo

met

ric.

con

stru

ctio

ns.

wit

h.a.

vari

ety.

of.t

ools

.and

.met

hods

.(c

ompa

ss.a

nd.s

trai

ghte

dge,

.str

ing,

.re

flect

ive.

devi

ces,

.pap

er.fo

ldin

g,.

dyna

mic

.geo

met

ric.

soft

war

e,.e

tc.).

.C

opyi

ng a

seg

men

t; co

pyin

g an

ang

le;

bise

ctin

g a

seg

men

t; bi

sect

ing

an

angl

e; c

onst

ruct

ing

perp

end

icu

lar

lines

, in

clud

ing

the

perp

end

icu

lar

bise

ctor

of

a lin

e se

gm

ent;

and

cons

truc

ting

a li

ne

para

llel t

o a

giv

en li

ne t

hro

ugh

a po

int

not

on t

he li

ne.

G-C

O.1

2X

X

Hig

h.Sc

hool

-G

eom

etry

Con

gru

ence

Mak

e.ge

omet

ric.

con

stru

ctio

ns

Con

stru

ct.a

n.eq

uila

tera

l.tri

angl

e,.

a.sq

uare

,.and

.a.r

egu

lar.

hexa

gon.

insc

ribe

d.in

.a.c

ircl

e.

G-C

O.1

3X

X

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

Und

erst

and.

sim

ilari

ty.

in.t

erm

s.of

.si

mila

rity

.tr

ansf

orm

atio

ns

Ver

ify.

expe

rim

enta

lly.t

he.p

rope

rtie

s.of

.d

ilati

ons.

giv

en.b

y.a.

cent

er.a

nd.a

.sca

le.

fact

or:

A.d

ilati

on.t

akes

.a.li

ne.

not.

pass

ing.

thro

ugh.

the.

cent

er.o

f.the

.dila

tion

.to.

a.pa

ralle

l.lin

e,.a

nd.le

aves

.a.

line.

pass

ing.

thro

ugh.

the.

cent

er.u

ncha

nged

.

G-S

RT.

1aX

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

Und

erst

and.

sim

ilari

ty.

in.t

erm

s.of

.si

mila

rity

.tr

ansf

orm

atio

ns

Ver

ify.

expe

rim

enta

lly.t

he.p

rope

rtie

s.of

.d

ilati

ons.

giv

en.b

y.a.

cent

er.a

nd.a

.sca

le.

fact

or:

The

.dila

tion

.of.a

.line

.se

gm

ent.

is.lo

nger

.or.

shor

ter.

in.t

he.r

atio

.giv

en.

by.t

he.s

cale

.fact

or.

G-S

RT.

1bX

X

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

Und

erst

and.

sim

ilari

ty.

in.t

erm

s.of

.si

mila

rity

.tr

ansf

orm

atio

ns

Giv

en.t

wo.

figu

res,

.use

.the

.def

init

ion.

of.s

imila

rity

.in.t

erm

s.of

.sim

ilari

ty.

tran

sfor

mat

ion

s.to

.dec

ide.

if.th

ey.

are.

sim

ilar;.

expl

ain.

usin

g.si

mila

rity

.tr

ansf

orm

atio

ns.

the.

mea

nin

g.of

.si

mila

rity

.for.

tria

ngle

s.as

.the

.eq

ualit

y.of

.all.

corr

espo

ndin

g.pa

irs.

of.a

ngle

s.an

d.th

e.pr

opor

tion

alit

y.of

.all.

corr

espo

ndin

g.pa

irs.

of.s

ides

.

G-S

RT.

2X

X

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

Und

erst

and.

sim

ilari

ty.

in.t

erm

s.of

.si

mila

rity

.tr

ansf

orm

atio

ns

Use

.the

.pro

pert

ies.

of.s

imila

rity

.tr

ansf

orm

atio

ns.

to.e

stab

lish.

the.

AA

.cr

iter

ion.

for.

two.

tria

ngle

s.to

.be.

sim

ilar.

G-S

RT.

3X

X

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

Pro

ve.t

heor

ems.

invo

lvin

g.si

mila

rity

Pro

ve.t

heor

ems.

abou

t.tr

iang

les.

.T

heor

ems

incl

ude:

a li

ne p

aral

lel t

o on

e si

de o

f a t

rian

gle

div

ides

the

oth

er

two

prop

orti

onal

ly, a

nd c

onve

rsel

y; t

he

Pyt

hago

rean

The

orem

pro

ved

usin

g tr

iang

le s

imila

rity

.

G-S

RT.

4X

X

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

Pro

ve.t

heor

ems.

invo

lvin

g.si

mila

rity

Use

.con

gru

ence

.and

.sim

ilari

ty.c

rite

ria.

for.

tria

ngle

s.to

.sol

ve.p

robl

ems.

and.

to.p

rove

.rel

atio

nsh

ips.

in.g

eom

etri

c.fig

ure

s.

G-S

RT.

5X

X

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

Def

ine.

trig

onom

etri

c.ra

tios

.and

.so

lve.

prob

lem

s.in

volv

ing.

righ

t.tr

iang

les

Und

erst

and.

that

.by.

sim

ilari

ty,.s

ide.

rati

os.in

.rig

ht.t

rian

gles

.are

.pro

pert

ies.

of.t

he.a

ngle

s.in

.the

.tri

angl

e,.le

adin

g.to

.de

fin

itio

ns.

of.t

rigo

nom

etri

c.ra

tios

.for.

acut

e.an

gles

.

G-S

RT.

6X

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

Def

ine.

trig

onom

etri

c.ra

tios

.and

.so

lve.

prob

lem

s.in

volv

ing.

righ

t.tr

iang

les

Exp

lain

.and

.use

.the

.rel

atio

nsh

ip.

betw

een.

the.

sine

.and

.cos

ine.

of.

com

plem

enta

ry.a

ngle

s.

G-S

RT.

7X

X

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

Def

ine.

trig

onom

etri

c.ra

tios

.and

.so

lve.

prob

lem

s.in

volv

ing.

righ

t.tr

iang

les

Use

.tri

gono

met

ric.

rati

os.a

nd.t

he.

Pyt

hago

rean

.The

orem

.to.

solv

e.ri

ght.

tria

ngle

s.in

.app

lied.

prob

lem

s.

G-S

RT.

8X

X

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

App

ly.

trig

onom

etry

.to.

gene

ral.t

rian

gles

(+).D

eriv

e.th

e.fo

rmu

la.A

.=.1

/2.a

b.si

n(C

).for

.the

.are

a.of

.a.t

rian

gle.

by.

dra

win

g.an

.au

xilia

ry.li

ne.fr

om.a

.ver

tex.

perp

end

icu

lar.

to.t

he.o

ppos

ite.

side

.

G-S

RT.

9X

X

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

App

ly.

trig

onom

etry

.to.

gene

ral.t

rian

gles

(+).P

rove

.the

.Law

s.of

.Sin

es.a

nd.C

osin

es.

and.

use.

them

.to.

solv

e.pr

oble

ms.

G-S

RT.

10X

X

Hig

h.Sc

hool

-G

eom

etry

Sim

ilari

ty,.

Rig

ht.

Tri

angl

es,.a

nd.

Tri

gono

met

ry

App

ly.

trig

onom

etry

.to.

gene

ral.t

rian

gles

(+).U

nder

stan

d.an

d.ap

ply.

the.

Law

.of.

Sine

s.an

d.th

e.L

aw.o

f.Cos

ines

.to.

find

.u

nkn

own.

mea

sure

men

ts.in

.rig

ht.a

nd.

non-

righ

t.tr

iang

les.

(e.g

.,.su

rvey

ing.

prob

lem

s,.r

esu

ltant

.forc

es).

G-S

RT.

11X

X

Hig

h.Sc

hool

-G

eom

etry

Cir

cles

Und

erst

and.

and.

appl

y.th

eore

ms.

abou

t.ci

rcle

s

Pro

ve.t

hat.

all.c

ircl

es.a

re.s

imila

r.G

-C.1

XX

Hig

h.Sc

hool

-G

eom

etry

Cir

cles

Und

erst

and.

and.

appl

y.th

eore

ms.

abou

t.ci

rcle

s

Iden

tify

.and

.des

crib

e.re

lati

onsh

ips.

amon

g.in

scri

bed.

angl

es,.r

adii,

.and

.ch

ords

..Inc

lude

.the

.rel

atio

nsh

ip.

betw

een.

cent

ral,.

insc

ribe

d,.a

nd.

circ

um

scri

bed.

angl

es;.i

nsc

ribe

d.an

gles

.on

.a.d

iam

eter

.are

.rig

ht.a

ngle

s;.t

he.

rad

ius.

of.a

.cir

cle.

is.p

erpe

ndic

ula

r.to

.the

.ta

ngen

t.w

here

.the

.rad

ius.

inte

rsec

ts.t

he.

circ

le.

G-C

.2X

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-G

eom

etry

Cir

cles

Und

erst

and.

and.

appl

y.th

eore

ms.

abou

t.ci

rcle

s

Con

stru

ct.t

he.in

scri

bed.

and.

circ

um

scri

bed.

circ

les.

of.a

.tri

angl

e,.

and.

prov

e.pr

oper

ties

.of.a

ngle

s.fo

r.a.

qua

dri

late

ral.i

nsc

ribe

d.in

.a.c

ircl

e.

G-C

.3X

X

Hig

h.Sc

hool

-G

eom

etry

Cir

cles

Und

erst

and.

and.

appl

y.th

eore

ms.

abou

t.ci

rcle

s

(+).C

onst

ruct

.a.t

ange

nt.li

ne.fr

om.a

.poi

nt.

outs

ide.

a.g

iven

.cir

cle.

to.t

he.c

ircl

e.G

-C.4

XX

Hig

h.Sc

hool

-G

eom

etry

Cir

cles

Fin

d.ar

c.le

ngth

s.an

d.ar

eas.

of.

sect

ors.

of.c

ircl

es

Der

ive.

usin

g.si

mila

rity

.the

.fact

.tha

t.th

e.le

ngth

.of.t

he.a

rc.in

terc

epte

d.by

.an

.ang

le.is

.pro

port

iona

l.to.

the.

rad

ius,

.an

d.de

fine

.the

.rad

ian.

mea

sure

.of.t

he.

angl

e.as

.the

.con

stan

t.of

.pro

port

iona

lity;

.de

rive

.the

.form

ula

.for.

the.

area

.of.a

.se

ctor

.

G-C

.5X

X

Hig

h.Sc

hool

-G

eom

etry

Exp

ress

ing.

Geo

met

ric.

Pro

pert

ies.

Eq

uati

ons

Tra

nsl

ate.

betw

een.

the.

geom

etri

c.de

scri

ptio

n.an

d.th

e.eq

uati

on.fo

r.a.

con

ic.s

ecti

on

Der

ive.

the.

equa

tion

.of.a

.cir

cle.

of.

giv

en.c

ente

r.an

d.ra

diu

s.us

ing.

the.

Pyt

hago

rean

.The

orem

;.com

plet

e.th

e.sq

uare

.to.

find

.the

.cen

ter.

and.

rad

ius.

of.a

.ci

rcle

.giv

en.b

y.an

.eq

uati

on.

G-G

PE.1

XX

Hig

h.Sc

hool

-G

eom

etry

Exp

ress

ing.

Geo

met

ric.

Pro

pert

ies.

Eq

uati

ons

Tra

nsl

ate.

betw

een.

the.

geom

etri

c.de

scri

ptio

n.an

d.th

e.eq

uati

on.fo

r.a.

con

ic.s

ecti

on

Der

ive.

the.

equa

tion

.of.a

.par

abol

a.g

iven

.a.

focu

s.an

d.d

irec

trix

.G

-GPE

.2X

X

Hig

h.Sc

hool

-G

eom

etry

Exp

ress

ing.

Geo

met

ric.

Pro

pert

ies.

Eq

uati

ons

Tra

nsl

ate.

betw

een.

the.

geom

etri

c.de

scri

ptio

n.an

d.th

e.eq

uati

on.fo

r.a.

con

ic.s

ecti

on

(+).D

eriv

e.th

e.eq

uati

ons.

of.e

llips

es.a

nd.

hype

rbol

as.g

iven

.the

.foci

,.usi

ng.t

he.fa

ct.

that

.the

.su

m.o

r.d

iffe

renc

e.of

.dis

tanc

es.

from

.the

.foci

.is.c

onst

ant.

G-G

PE.3

XX

Hig

h.Sc

hool

-G

eom

etry

Exp

ress

ing.

Geo

met

ric.

Pro

pert

ies.

Eq

uati

ons

Use

.coo

rdin

ates

.to

.pro

ve.s

impl

e.ge

omet

ric.

theo

rem

s.al

gebr

aica

lly

Use

.coo

rdin

ates

.to.

prov

e.si

mpl

e.ge

omet

ric.

theo

rem

s.al

gebr

aica

lly.

G-G

PE.4

XX


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-G

eom

etry

Exp

ress

ing.

Geo

met

ric.

Pro

pert

ies.

Eq

uati

ons

Use

.coo

rdin

ates

.to

.pro

ve.s

impl

e.ge

omet

ric.

theo

rem

s.al

gebr

aica

lly

Pro

ve.t

he.s

lope

.cri

teri

a.fo

r.pa

ralle

l.an

d.pe

rpen

dic

ula

r.lin

es.a

nd.u

se.t

hem

.to

.sol

ve.g

eom

etri

c.pr

oble

ms.

(e.g

.,.fi

nd.t

he.e

qua

tion

.of.a

.line

.par

alle

l.or

.per

pend

icu

lar.

to.a

.giv

en.li

ne.t

hat.

pass

es.t

hro

ugh.

a.g

iven

.poi

nt).

G-G

PE.5

XX

Hig

h.Sc

hool

-G

eom

etry

Exp

ress

ing.

Geo

met

ric.

Pro

pert

ies.

Eq

uati

ons

Use

.coo

rdin

ates

.to

.pro

ve.s

impl

e.ge

omet

ric.

theo

rem

s.al

gebr

aica

lly

Fin

d.th

e.po

int.

on.a

.dir

ecte

d.lin

e.se

gm

ent.

betw

een.

two.

giv

en.p

oint

s.th

at.

part

itio

ns.

the.

seg

men

t.in

.a.g

iven

.rat

io.

G-G

PE.6

XX

Hig

h.Sc

hool

-G

eom

etry

Exp

ress

ing.

Geo

met

ric.

Pro

pert

ies.

Eq

uati

ons

Use

.coo

rdin

ates

.to

.pro

ve.s

impl

e.ge

omet

ric.

theo

rem

s.al

gebr

aica

lly

Use

.coo

rdin

ates

.to.

com

pute

.per

imet

ers.

of.p

olyg

ons.

and.

area

s.of

.tri

angl

es.a

nd.

rect

angl

es,.e

.g.,.

usin

g.th

e.d

ista

nce.

form

ula

.

G-G

PE.7

XX

Hig

h.Sc

hool

-G

eom

etry

Geo

met

ric.

Mea

sure

men

t.an

d.D

imen

sion

Exp

lain

.vol

um

e.fo

rmu

las.

and.

use.

them

.to.

solv

e.pr

oble

ms

Giv

e.an

.info

rmal

.arg

um

ent.

for.

the.

form

ula

s.fo

r.th

e.ci

rcu

mfe

renc

e.of

.a.

circ

le,.a

rea.

of.a

.cir

cle,

.vol

um

e.of

.a.c

ylin

der,.

pyra

mid

,.and

.con

e..

Use

dis

sect

ion

arg

um

ents

, Cav

alie

ri’s

pr

inci

ple,

and

info

rmal

lim

it ar

gu

men

ts.

G-G

MD

.1X

X

Hig

h.Sc

hool

-G

eom

etry

Geo

met

ric.

Mea

sure

men

t.an

d.D

imen

sion

Exp

lain

.vol

um

e.fo

rmu

las.

and.

use.

them

.to.

solv

e.pr

oble

ms

(+).G

ive.

an.in

form

al.a

rgu

men

t.us

ing.

Cav

alie

ri’s

.pri

ncip

le.fo

r.th

e.fo

rmu

las.

for.

the.

volu

me.

of.a

.sph

ere.

and.

othe

r.so

lid.

figu

res.

G-G

MD

.2X

X

Hig

h.Sc

hool

-G

eom

etry

Geo

met

ric.

Mea

sure

men

t.an

d.D

imen

sion

Exp

lain

.vol

um

e.fo

rmu

las.

and.

use.

them

.to.

solv

e.pr

oble

ms

Use

.vol

um

e.fo

rmu

las.

for.

cylin

ders

,.py

ram

ids,

.con

es,.a

nd.s

pher

es.t

o.so

lve.

prob

lem

s.

G-G

MD

.3X

X

Hig

h.Sc

hool

-G

eom

etry

Geo

met

ric.

Mea

sure

men

t.an

d.D

imen

sion

Vis

ualiz

e.re

lati

onsh

ips.

betw

een.

two-

dim

ensi

onal

.an

d.th

ree-

dim

ensi

onal

.ob

ject

s

Iden

tify

.the

.sha

pes.

of.t

wo-

dim

ensi

onal

.cr

oss-

sect

ion

s.of

.th

ree-

dim

ensi

onal

.ob

ject

s,.a

nd.id

enti

fy.t

hre

e-d

imen

sion

al.

obje

cts.

gene

rate

d.by

.rot

atio

ns.

of.t

wo-

dim

ensi

onal

.obj

ects

.

G-G

MD

.4X

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-G

eom

etry

Mod

elin

g.w

ith.

Geo

met

ryA

pply

.geo

met

ric.

conc

epts

.in.

mod

elin

g.si

tuat

ion

s

Use

.geo

met

ric.

shap

es,.t

heir

.mea

sure

s,.

and.

thei

r.pr

oper

ties

.to.

desc

ribe

.obj

ects

.(e

.g.,.

mod

elin

g.a.

tree

.tru

nk.

or.a

.hu

man

.to

rso.

as.a

.cyl

inde

r).

G-M

G.1

XX

Hig

h.Sc

hool

-G

eom

etry

Mod

elin

g.w

ith.

Geo

met

ryA

pply

.geo

met

ric.

conc

epts

.in.

mod

elin

g.si

tuat

ion

s

App

ly.c

once

pts.

of.d

ensi

ty.b

ased

.on.

area

.and

.vol

um

e.in

.mod

elin

g.si

tuat

ion

s.(e

.g.,.

pers

ons.

per.

squa

re.m

ile,.B

TU

s.pe

r.cu

bic.

foot

).

G-M

G.2

XX

Hig

h.Sc

hool

-G

eom

etry

Mod

elin

g.w

ith.

Geo

met

ryA

pply

.geo

met

ric.

conc

epts

.in.

mod

elin

g.si

tuat

ion

s

App

ly.g

eom

etri

c.m

etho

ds.t

o.so

lve.

desi

gn.

prob

lem

s.(e

.g.,.

desi

gn

ing.

an.

obje

ct.o

r.st

ruct

ure

.to.

sati

sfy.

phys

ical

.co

nst

rain

ts.o

r.m

inim

ize.

cost

;.wor

king

.w

ith.

typo

gra

phic

.gri

d.sy

stem

s.ba

sed.

on.r

atio

s).

G-M

G.3

XX

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Sum

mar

ize,

.re

pres

ent,

.and

.in

terp

ret.

data

.on.

a.si

ngle

.cou

nt.

or.m

easu

rem

ent.

vari

able

.

Rep

rese

nt.d

ata.

wit

h.pl

ots.

on.t

he.r

eal.

num

ber.

line.

(dot

.plo

ts,.h

isto

gra

ms,

.and

.bo

x.pl

ots)

.

S-ID

.1X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Sum

mar

ize,

.re

pres

ent,

.and

.in

terp

ret.

data

.on.

a.si

ngle

.cou

nt.

or.m

easu

rem

ent.

vari

able

.

Use

.sta

tist

ics.

appr

opri

ate.

to.t

he.s

hape

.of

.the

.dat

a.d

istr

ibut

ion.

to.c

ompa

re.

cent

er.(m

edia

n,.m

ean)

.and

.spr

ead.

(inte

rqua

rtile

.ran

ge,.s

tand

ard.

devi

atio

n).

of.t

wo.

or.m

ore.

dif

fere

nt.d

ata.

sets

.

S-ID

.2X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Sum

mar

ize,

.re

pres

ent,

.and

.in

terp

ret.

data

.on.

a.si

ngle

.cou

nt.

or.m

easu

rem

ent.

vari

able

.

Inte

rpre

t.d

iffe

renc

es.in

.sha

pe,.c

ente

r,.an

d.sp

read

.in.t

he.c

onte

xt.o

f.the

.dat

a.se

ts,.a

ccou

ntin

g.fo

r.po

ssib

le.e

ffect

s.of

.ex

trem

e.da

ta.p

oint

s.(o

utlie

rs).

S-ID

.3X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Sum

mar

ize,

.re

pres

ent,

.and

.in

terp

ret.

data

.on.

a.si

ngle

.cou

nt.

or.m

easu

rem

ent.

vari

able

.

Use

.the

.mea

n.an

d.st

anda

rd.d

evia

tion

.of

.a.d

ata.

set.

to.fi

t.it

.to.

a.no

rmal

.d

istr

ibut

ion.

and.

to.e

stim

ate.

popu

lati

on.

perc

enta

ges.

.Rec

ogn

ize.

that

.the

re.a

re.

data

.set

s.fo

r.w

hic

h.su

ch.a

.pro

cedu

re.

is.n

ot.a

ppro

pria

te..U

se.c

alcu

lato

rs,.

spre

adsh

eets

,.and

.tab

les.

to.e

stim

ate.

area

s.u

nder

.the

.nor

mal

.cu

rve.

S-ID

.4X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Sum

mar

ize,

.re

pres

ent,

.and

.in

terp

ret.

data

.on.

two.

cate

gori

cal.

and.

qua

ntit

ativ

e.va

riab

les.

Sum

mar

ize.

cate

gori

cal.d

ata.

for.

two.

cate

gori

es.in

.tw

o-w

ay.fr

eque

ncy.

tabl

es..I

nter

pret

.rel

ativ

e.fr

eque

ncie

s.in

.the

.con

text

.of.t

he.d

ata.

(incl

udin

g.jo

int,

.mar

gin

al,.a

nd.c

ond

itio

nal.r

elat

ive.

freq

uenc

ies)

..Rec

ogn

ize.

poss

ible

.as

soci

atio

ns.

and.

tren

ds.in

.the

.dat

a.

S-ID

.5X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Sum

mar

ize,

.re

pres

ent,

.and

.in

terp

ret.

data

.on.

two.

cate

gori

cal.

and.

qua

ntit

ativ

e.va

riab

les.

Rep

rese

nt.d

ata.

on.t

wo.

qua

ntit

ativ

e.va

riab

les.

on.a

.sca

tter

.plo

t,.a

nd.d

escr

ibe.

how

.the

.var

iabl

es.a

re.r

elat

ed.

Fit

.a.fu

ncti

on.t

o.th

e.da

ta;.u

se.fu

ncti

ons.

fitte

d.to

.dat

a.to

.sol

ve.

prob

lem

s.in

.the

.con

text

.of

.the

.dat

a..U

se g

iven

fu

ncti

ons

or c

hoos

e a

func

tion

sug

gest

ed b

y th

e co

ntex

t. E

mph

asiz

e lin

ear,

qua

dra

tic,

and

exp

onen

tial

m

odel

s.

S-ID

.6a

XX

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Sum

mar

ize,

.re

pres

ent,

.and

.in

terp

ret.

data

.on.

two.

cate

gori

cal.

and.

qua

ntit

ativ

e.va

riab

les.

Rep

rese

nt.d

ata.

on.t

wo.

qua

ntit

ativ

e.va

riab

les.

on.a

.sca

tter

.plo

t,.a

nd.d

escr

ibe.

how

.the

.var

iabl

es.a

re.r

elat

ed.

Info

rmal

ly.a

sses

s.th

e.fit

.of.

a.fu

ncti

on.b

y.pl

otti

ng.a

nd.

anal

yzin

g.re

sidu

als.

S-ID

.6b

XX

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Sum

mar

ize,

.re

pres

ent,

.and

.in

terp

ret.

data

.on.

two.

cate

gori

cal.

and.

qua

ntit

ativ

e.va

riab

les.

Rep

rese

nt.d

ata.

on.t

wo.

qua

ntit

ativ

e.va

riab

les.

on.a

.sca

tter

.plo

t,.a

nd.d

escr

ibe.

how

.the

.var

iabl

es.a

re.r

elat

ed.

Fit

.a.li

near

.func

tion

.for.

a.sc

atte

r.pl

ot.t

hat.

sugg

ests

.a.

linea

r.as

soci

atio

n.

S-ID

.6c

XX

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Inte

rpre

t.lin

ear.

mod

els

Inte

rpre

t.th

e.sl

ope.

(rat

e.of

.cha

nge)

.and

.th

e.in

terc

ept.

(con

stan

t.te

rm).o

f.a.li

near

.m

odel

.in.t

he.c

onte

xt.o

f.the

.dat

a.

S-ID

.7X

XX

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Inte

rpre

t.lin

ear.

mod

els

Com

pute

.(usi

ng.t

ech

nolo

gy)

.and

.in

terp

ret.

the.

corr

elat

ion.

coef

ficie

nt.o

f.a.

linea

r.fit

.

S-ID

.8X

XX

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Inte

rpre

ting

.C

ateg

oric

al.a

nd.

Qua

ntit

ativ

e.D

ata

Inte

rpre

t.lin

ear.

mod

els

Dis

ting

uis

h.be

twee

n.co

rrel

atio

n.an

d.ca

usat

ion.

S-ID

.9X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Mak

ing.

Infe

renc

es.

and.

Just

ifyi

ng.

Con

clus

ion

s

Und

erst

and.

and.

eval

uate

.ran

dom

.pr

oces

ses.

und

erly

ing.

stat

isti

cal.

expe

rim

ents

Und

erst

and.

stat

isti

cs.a

s.a.

proc

ess.

for.

mak

ing.

infe

renc

es.a

bout

.pop

ula

tion

.pa

ram

eter

s.ba

sed.

on.a

.ran

dom

.sam

ple.

from

.tha

t.po

pula

tion

.

S-IC

.1X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Mak

ing.

Infe

renc

es.

and.

Just

ifyi

ng.

Con

clus

ion

s

Und

erst

and.

and.

eval

uate

.ran

dom

.pr

oces

ses.

und

erly

ing.

stat

isti

cal.

expe

rim

ents

Dec

ide.

if.a.

spec

ifie

d.m

odel

.is.

con

sist

ent.

wit

h.re

sults

.from

.a.g

iven

.da

ta-g

ener

atin

g.pr

oces

s,.e

.g.,.

usin

g.si

mu

lati

on.

S-IC

.2X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Mak

ing.

Infe

renc

es.

and.

Just

ifyi

ng.

Con

clus

ion

s

Mak

e.in

fere

nces

.an

d.ju

stif

y.co

nclu

sion

s.fr

om.

sam

ple.

surv

eys,

.ex

peri

men

ts,.a

nd.

obse

rvat

iona

l.st

udie

s

Rec

ogn

ize.

the.

purp

oses

.of.a

nd.

dif

fere

nces

.am

ong.

sam

ple.

surv

eys,

.ex

peri

men

ts,.a

nd.o

bser

vati

onal

.stu

die

s;.

expl

ain.

how

.ran

dom

izat

ion.

rela

tes.

to.

each

.

S-IC

.3X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Mak

ing.

Infe

renc

es.

and.

Just

ifyi

ng.

Con

clus

ion

s

Mak

e.in

fere

nces

.an

d.ju

stif

y.co

nclu

sion

s.fr

om.

sam

ple.

surv

eys,

.ex

peri

men

ts,.a

nd.

obse

rvat

iona

l.st

udie

s

Use

.dat

a.fr

om.a

.sam

ple.

surv

ey.

to.e

stim

ate.

a.po

pula

tion

.mea

n.or

.pr

opor

tion

;.dev

elop

.a.m

arg

in.o

f.err

or.

thro

ugh.

the.

use.

of.s

imu

lati

on.m

odel

s.fo

r.ra

ndom

.sam

plin

g.

S-IC

.4X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Mak

ing.

Infe

renc

es.

and.

Just

ifyi

ng.

Con

clus

ion

s

Mak

e.in

fere

nces

.an

d.ju

stif

y.co

nclu

sion

s.fr

om.

sam

ple.

surv

eys,

.ex

peri

men

ts,.a

nd.

obse

rvat

iona

l.st

udie

s

Use

.dat

a.fr

om.a

.ran

dom

ized

.exp

erim

ent.

to.c

ompa

re.t

wo.

trea

tmen

ts;.u

se.

sim

ula

tion

s.to

.dec

ide.

if.d

iffe

renc

es.

betw

een.

para

met

ers.

are.

sig

nif

ican

t.

S-IC

.5X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Mak

ing.

Infe

renc

es.

and.

Just

ifyi

ng.

Con

clus

ion

s

Mak

e.in

fere

nces

.an

d.ju

stif

y.co

nclu

sion

s.fr

om.

sam

ple.

surv

eys,

.ex

peri

men

ts,.a

nd.

obse

rvat

iona

l.st

udie

s

Eva

luat

e.re

port

s.ba

sed.

on.d

ata.

S-IC

.6X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Con

dit

iona

l.P

roba

bilit

y.an

d.th

e.R

ule

s.of

.P

roba

bilit

y

Und

erst

and.

inde

pend

ence

.an

d.co

ndit

iona

l.pr

obab

ility

.and

.us

e.th

em.t

o.in

terp

ret.

data

Des

crib

e.ev

ents

.as.

subs

ets.

of.a

.sam

ple.

spac

e.(t

he.s

et.o

f.out

com

es).u

sing

.ch

arac

teri

stic

s.(o

r.ca

tego

ries

).of.t

he.

outc

omes

,.or.

as.u

nio

ns,

.inte

rsec

tion

s,.

or.c

ompl

emen

ts.o

f.oth

er.e

vent

s.(“

or,”

.“a

nd,”

.“no

t”).

S-C

P.1

X.

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Con

dit

iona

l.P

roba

bilit

y.an

d.th

e.R

ule

s.of

.P

roba

bilit

y

Und

erst

and.

inde

pend

ence

.an

d.co

ndit

iona

l.pr

obab

ility

.and

.us

e.th

em.t

o.in

terp

ret.

data

Und

erst

and.

that

.tw

o.ev

ents

.A.a

nd.

B.a

re.in

depe

nden

t.if.

the.

prob

abili

ty.

of.A

.and

.B.o

ccu

rrin

g.to

geth

er.is

.the

.pr

oduc

t.of

.the

ir.p

roba

bilit

ies,

.and

.use

.th

is.c

hara

cter

izat

ion.

to.d

eter

min

e.if

.th

ey.a

re.in

depe

nden

t.

S-C

P.2

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Con

dit

iona

l.P

roba

bilit

y.an

d.th

e.R

ule

s.of

.P

roba

bilit

y

Und

erst

and.

inde

pend

ence

.an

d.co

ndit

iona

l.pr

obab

ility

.and

.us

e.th

em.t

o.in

terp

ret.

data

Und

erst

and.

the.

cond

itio

nal.p

roba

bilit

y.of

.A.g

iven

.B.a

s.P

(A.a

nd.B

)/P

(B),.

and.

inte

rpre

t.in

depe

nden

ce.o

f.A.a

nd.B

.as.

sayi

ng.t

hat.

the.

cond

itio

nal.p

roba

bilit

y.of

.A.g

iven

.B.is

.the

.sam

e.as

.the

.pr

obab

ility

.of.A

,.and

.the

.con

dit

iona

l.pr

obab

ility

.of.B

.giv

en.A

.is.t

he.s

ame.

as.

the.

prob

abili

ty.o

f.B.

S-C

P.3

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Con

dit

iona

l.P

roba

bilit

y.an

d.th

e.R

ule

s.of

.P

roba

bilit

y

Und

erst

and.

inde

pend

ence

.an

d.co

ndit

iona

l.pr

obab

ility

.and

.us

e.th

em.t

o.in

terp

ret.

data

Con

stru

ct.a

nd.in

terp

ret.

two-

way

.fr

eque

ncy.

tabl

es.o

f.dat

a.w

hen.

two.

cate

gori

es.a

re.a

ssoc

iate

d.w

ith.

each

.ob

ject

.bei

ng.c

lass

ifie

d..U

se.t

he.t

wo-

way

.tab

le.a

s.a.

sam

ple.

spac

e.to

.dec

ide.

if.ev

ents

.are

.inde

pend

ent.

and.

to.

appr

oxim

ate.

cond

itio

nal.p

roba

bilit

ies.

S-C

P.4

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Con

dit

iona

l.P

roba

bilit

y.an

d.th

e.R

ule

s.of

.P

roba

bilit

y

Und

erst

and.

inde

pend

ence

.an

d.co

ndit

iona

l.pr

obab

ility

.and

.us

e.th

em.t

o.in

terp

ret.

data

Rec

ogn

ize.

and.

expl

ain.

the.

conc

epts

.of

.con

dit

iona

l.pro

babi

lity.

and.

inde

pend

ence

.in.e

very

day.

lang

uage

.an

d.ev

eryd

ay.s

itua

tion

s.

S-C

P.5

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Con

dit

iona

l.P

roba

bilit

y.an

d.th

e.R

ule

s.of

.P

roba

bilit

y

Use

.the

.ru

les.

of.p

roba

bilit

y.to

.com

pute

.pr

obab

iliti

es.o

f.co

mpo

und

.eve

nts.

in.a

.un

iform

.pr

obab

ility

.mod

el

Fin

d.th

e.co

ndit

iona

l.pro

babi

lity.

of.A

.g

iven

.B.a

s.th

e.fr

acti

on.o

f.B’s

.out

com

es.

that

.als

o.be

long

.to.

A,.a

nd.in

terp

ret.

the.

answ

er.in

.ter

ms.

of.t

he.m

odel

.

S-C

P.6

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Con

dit

iona

l.P

roba

bilit

y.an

d.th

e.R

ule

s.of

.P

roba

bilit

y

Use

.the

.ru

les.

of.p

roba

bilit

y.to

.com

pute

.pr

obab

iliti

es.o

f.co

mpo

und

.eve

nts.

in.a

.un

iform

.pr

obab

ility

.mod

el

App

ly.t

he.A

ddit

ion.

Ru

le,.

P(A

.or.

B).=

.P(A

).+.P

(B).–

.P(A

.and

.B),.

and.

inte

rpre

t.th

e.an

swer

.in.t

erm

s.of

.th

e.m

odel

.

S-C

P.7

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Con

dit

iona

l.P

roba

bilit

y.an

d.th

e.R

ule

s.of

.P

roba

bilit

y

Use

.the

.ru

les.

of.p

roba

bilit

y.to

.com

pute

.pr

obab

iliti

es.o

f.co

mpo

und

.eve

nts.

in.a

.un

iform

.pr

obab

ility

.mod

el

(+).A

pply

.the

.gen

eral

.Mu

ltipl

icat

ion.

Ru

le.in

.a.u

nifo

rm.p

roba

bilit

y.m

odel

,.P

(A.a

nd.B

).=.P

(A)P

(B|A

).=.P

(B)P

(A|B

),.an

d.in

terp

ret.

the.

answ

er.in

.ter

ms.

of.

the.

mod

el.

S-C

P.8

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Con

dit

iona

l.P

roba

bilit

y.an

d.th

e.R

ule

s.of

.P

roba

bilit

y

Use

.the

.ru

les.

of.p

roba

bilit

y.to

.com

pute

.pr

obab

iliti

es.o

f.co

mpo

und

.eve

nts.

in.a

.un

iform

.pr

obab

ility

.mod

el

(+).U

se.p

erm

utat

ion

s.an

d.co

mbi

nati

ons.

to.c

ompu

te.p

roba

bilit

ies.

of.c

ompo

und

.ev

ents

.and

.sol

ve.p

robl

ems.

S-C

P.9

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Usi

ng.

Pro

babi

lity.

to.

Mak

e.D

ecis

ion

s

Cal

cula

te.

expe

cted

.val

ues.

and.

use.

them

.to.

solv

e.pr

oble

ms

(+).D

efin

e.a.

rand

om.v

aria

ble.

for.

a.q

uant

ity.

of.in

tere

st.b

y.as

sig

nin

g.a.

num

eric

al.v

alue

.to.

each

.eve

nt.in

.a.

sam

ple.

spac

e;.g

raph

.the

.cor

resp

ond

ing.

prob

abili

ty.d

istr

ibut

ion.

usin

g.th

e.sa

me.

gra

phic

al.d

ispl

ays.

as.fo

r.da

ta.

dis

trib

utio

ns.

S-M

D.1

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Usi

ng.

Pro

babi

lity.

to.

Mak

e.D

ecis

ion

s

Cal

cula

te.

expe

cted

.val

ues.

and.

use.

them

.to.

solv

e.pr

oble

ms

(+).C

alcu

late

.the

.exp

ecte

d.va

lue.

of.a

.ra

ndom

.var

iabl

e;.in

terp

ret.

it.a

s.th

e.m

ean.

of.t

he.p

roba

bilit

y.d

istr

ibut

ion.

S-M

D.2

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Usi

ng.

Pro

babi

lity.

to.

Mak

e.D

ecis

ion

s

Cal

cula

te.

expe

cted

.val

ues.

and.

use.

them

.to.

solv

e.pr

oble

ms

(+).D

evel

op.a

.pro

babi

lity.

dis

trib

utio

n.fo

r.a.

rand

om.v

aria

ble.

defi

ned.

for.

a.sa

mpl

e.sp

ace.

in.w

hic

h.th

eore

tica

l.pro

babi

litie

s.ca

n.be

.cal

cula

ted;

.find

.the

.exp

ecte

d.va

lue.

S-M

D.3

X

Hig

h.Sc

hool

-St

atis

tics.

and.

Prob

abili

ty

Usi

ng.

Pro

babi

lity.

to.

Mak

e.D

ecis

ion

s

Cal

cula

te.

expe

cted

.val

ues.

and.

use.

them

.to.

solv

e.pr

oble

ms

(+).D

evel

op.a

.pro

babi

lity.

dis

trib

utio

n.fo

r.a.

rand

om.v

aria

ble.

defi

ned.

for.

a.sa

mpl

e.sp

ace.

in.w

hic

h.pr

obab

iliti

es.a

re.

assi

gne

d.em

piri

cally

;.fin

d.th

e.ex

pect

ed.

valu

e.

S-M

D.4

X


Appendixes

Com

mon

Cor

e S

tate

Sta

nd

ard

sA

P C

ours

e

Gra

de

Dom

ain

Clu

ster

Sta

nd

ard

Sk

ill

Cod

e

AP

C

alcu

lus

AB

AP

C

alcu

lus

BC

AP

S

tati

stic

s A

P

Com

pu

ter

Sci

ence

Hig

h.Sc

hool

-St

atis

tics

.an

d.Pr

obab

ility

Usi

ng.

Pro

babi

lity.

to.

Mak

e.D

ecis

ion

s

Use

.pro

babi

lity.

to.e

valu

ate.

outc

omes

.of.

deci

sion

s

(+).W

eigh

.the

.pos

sibl

e.ou

tcom

es.o

f.a.

deci

sion

.by.

assi

gn

ing.

prob

abili

ties

.to.

payo

ff.va

lues

.and

.find

ing.

expe

cted

.va

lues

.

Fin

d.th

e.ex

pect

ed.p

ayof

f.fo

r.a.

gam

e.of

.cha

nce.

S-M

D.5

aX

Hig

h.Sc

hool

-St

atis

tics

.an

d.Pr

obab

ility

Usi

ng.

Pro

babi

lity.

to.

Mak

e.D

ecis

ion

s

Use

.pro

babi

lity.

to.e

valu

ate.

outc

omes

.of.

deci

sion

s

(+).W

eigh

.the

.pos

sibl

e.ou

tcom

es.o

f.a.

deci

sion

.by.

assi

gn

ing.

prob

abili

ties

.to.

payo

ff.va

lues

.and

.find

ing.

expe

cted

.va

lues

.

Eva

luat

e.an

d.co

mpa

re.

stra

teg

ies.

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S-M

D.5

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S-M

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.

S-M

D.7

X

ConneCtion11b-3443