purpose: pssa review for 8th grade mathematics (can be used as enrichment or remediation for middle...

8TH GRADE COMPREHENSIVE REVIEW

MATHEMATICS

• Purpose: PSSA Review for 8th Grade Mathematics(Can be used as enrichment or remediation for middle school levels)

• Contents: Concept vocabulary & practice exercises/

solutions. Fill-in-the-blank, Multiple Choice, Short & Extended

Response

• Sources: PA Assessment Anchors & Eligible Content for 8th Grade

Mathematics PA Assessment Anchor Glossary for 7th & 8th Grade Mathematics PDE Standard Aligned Systems Online Resources

McGraw Hill Pre-Algebra & Algebra I 2012 SeriesHolt McDougal 8th Grade Mathematics 2012 Series

• Reinforcement: www.studyisland.com http://www.ixl.com/math/grades www.mathmaster.org PSSA Coach, Assessment Anchors

Measuring Up to the Pennsylvania Academic Standards

MATHEMATICS

http://www.studyisland.com/

http://www.ixl.com/math/grades

http://www.mathmaster.org/

3

INSTRUCTIONS

There are five categories tested; Numbers & Operations, Measurement, Geometry, Algebraic Concepts, Data Analysis & Probability.

Each category has a two page vocabulary (fill-in-the-blank) review, followed by multiple choice, short response, and extended response exercises that are aligned with each of the Assessment Anchor subcategories.

Navigate through the review as you would a regular PowerPoint slide show.

Fill-in-the-blank answers will appear, in order, at the click of a mouse. Exercise answers will also appear at the click of a mouse. Use the reference symbol to access the 8th Grade Formula Sheet if

needed. Use the symbol found on the Formula Sheet to return to your

previous slide.

PLEASE BEGIN!!

4

Numbers & OperationsVocabulary Review

1. The product of a number and its __________ is 1.

2. Any number that can be written as a fraction is called a _________.

3. ________________ is a short-hand way of writing extremely large or extremely small numbers.

4. The set of ____________ is the set of all rational and irrational numbers.

5. The product of an integer multiplied by itself is called a _____________.

Word Bank:Rational numberScientific notationOrder of OperationsProportion

ReciprocalUnit pricePerfect squareReal numbersSquare root

Expanded form

Reciprocal

Rational number

Scientific notation

Real numbers

Perfect square

5

Numbers & OperationsVocabulary Review

6. A number written as the sum of values of its digits is called _________.

7. A number that is multiplied by itself to form a product is called a ___________ of that product.

8. A(n) __________ is used to compare price per item.

9. Rules describing what sequence to use in evaluating expressions is known as __________________.

10.A ___________ is an equation showing that two ratios are equal.

Word Bank:Rational numberScientific notationOrder of OperationsProportion

ReciprocalUnit pricePerfect squareReal numbersSquare root

Expanded form

Expanded form

Square root

Unit price

Order of Operations

Proportion

6

Practice…Representing Numbers in equivalent forms.

Scientific Notation

The Earth is approximately 93,000,000 miles from the sun. What is the distance written in scientific notation?

A. 9.3 x 106

B. 93 x 106

C. 93 x 107

D. 9.3 x 107

Exponential Form

Which number represents 4.5 x 104 written in standard notation?

A. 0.00045

B. 0.000045

C. 45,000

D. 450,000

Numbers & Operations

7


Expanded Notation

Which expression is equivalent to the number 8,006,425?

A. (8x107)+(6x106)+(4x103)+(2x102)+(5x101)

B. (8x10)+(6x10)+(4x10)+(2x10)+(5x10)

C. (8x106)+(6x105)+(4x104)+(2x103)+(5x102)

D. (8x106)+(6x103)+(4x102)+(2x101)+(5x100)


8


Square Root

LeAnn got an answer of about 3.87 when she entered 15 on her calculator and pressed the (√) key. Which of the following statements is the most likely explanation for her to believe that her calculator’s answer is or not reasonable?

A. It is not reasonable, because the answer should be a whole number.

B. It is reasonable because 3 squared is 9 while 4 squared is 16.

C. It is not reasonable, because the answer should be only slightly more than 3.

D. It is reasonable, because 15 is and odd number.


9

3³ + 4(8-5) ÷ 6 =

A. 6.5

B. 11

C. 29

D. 27.5

Practice…Completing calculations by applying the order of operations.

Order of Operations

Evaluate

7 + 5[(3 + 2)² - (2³ + 1)]

A. 97

B. 87

C. 36

D. 22


10

Karen is solving this problem.

(3² + 4²)² = ?

Which step is correct in the process of solving this problem?

A. (3² + 4⁴)B. (9² + 16²)

C. (7²)²

D. (9 + 16)²

Practice…Completing calculations by applying the order of operations.

Order of Operations

Which statement is correct?

A. (2 x 3) + 5 ÷ 8 = 2

B. (2 x 3 + 5) ÷ 8 = 2

C. 2 x (3 + 5) ÷ 8 = 2

D. (2 x 3) + 5 ÷ 8 = 2


11

Practice… Represent or solve problems using rates, ratios, proportions and/or percents.

Rates

A secretary can type 56 words per minute. How much time will she need to type a 4200-word report?

A. 7 hours 30 minutes

B. 1 hour 4 minutes

C. 1 hour 28 minutes

D. 1 hour 15 minutes

Ratios

In 1991, and American, Ann Trason, set a world record by running 100km in

Which is the best estimate of her average speed?

A. 12 km per hr

B. 14 km per hr

C. 16 km per hr

D. 18 km per hr

Hours Minutes Seconds

7 50 09


13


Julio’s wages vary directly as the number of hours that he works. If his wages for 5 hours are $29.75, how much will he earn for 30 hours?

Proportions(Short Response)

Scoring Rubric:

**[2 points] $178.50, and appropriate work is shown, such as solving a proportion, using a table, or trial and error with at least three trials and appropriate checks.

*[1 point] An incorrect proportion is set up, but no solution or an incorrect solution is found.

*[1 point] $178.50, but no work is shown or fewer than three trials with appropriate checks are shown.

[0 points] A zero response is completely incorrect, irrelevant, or incoherent or is a correct response that was obtained by an obviously incorrect procedure.


14


Bob and Rebecca both drove to a baseball game at a college stadium. Bob lives 70 miles from the stadium and Rebecca lives 60 miles from it, as shown in the accompanying diagram. Bob drove at a rate of 50 miles per hour, and Rebecca drove at a rate of 40 miles per hour. If they both left home at the same time, who got to the stadium first?

Distance & Rates(Short Response)

Scoring Rubric:

**[2 points] Bob, and appropriate work is shown, such as using the distance formula to calculate the two travel times or setting up a proportion.

*[1 point] Appropriate work is shown, but one computational or conceptual error is made but an appropriate answer is found.

*[1 point] Appropriate work is shown, but no answer or an incorrect answer is found.

[0 points] Bob, but no work or inappropriate work is shown.


70 miles

60 miles

Bob’s House

Rebecca’s House


15

Practice… Using estimation strategies in problem-solving situations.

Ken bought a used car for $5,375. He had to pay an additional 15 percent of the purchase price to cover both sales tax and extra fees. Of the following, which is the closest to the total amount Ken paid?

A. $806

B. $5,510

C. $5,760

D. $6,180

Estimation

The state law requires that students attend school 180 days out of the 365 days in a year. Approximately what percent of a year must students attend school?

A. 2%

B. 50%

C. 75%

D. 200%


16

Fractions A grocery store sells brown sugar by the pound. The table below

shows how many cups of sugar a customer will get for the number of pounds purchased.

The pattern continues. What is the total number of cups of brown sugar in a 7-pound package?

A. 15 2/3

B. 16 1/3

C. 16 2/3

D. 17 1/3

Practice… Computing and/ or explaining operations with integers, fractions and/ or decimals.

Number of Pounds Number of Cups

3 7

4 9 1/3

5 11 2/3

6 14


17

Fractions

Subtract (-)

14 5/8

- 6 3/8

A. 8 3/8

B. 7 2/8

C. 8 1/4

D. 9

Decimals

Divide (÷)

3

0.24

A. 0.08

B. 8.0

C. 0.72

D. 12.5



18

Subtracting Negatives

Solve:

27 – (-9)

A. -3

B. -18

C. 18

D. 36

Adding Negatives

Solve:

-4 + 23

A. -19

B. 19

C. 20

D. -27



19

Practice… Calculating mean.

TOP Electronics is a small business with five employees. The mean (average) weekly salary for the five employees is $360. If the weekly salaries of four of the employees are $340, $340, $345, and $425, what is the salary of the fifth employee?

Average(Short Response)

Scoring Rubric:

**[2 points] $350, and appropriate work is shown, such as (1450 +x) ÷ 5 = 360, or trial and error with at least trials and appropriate checks.

*[1 point] Appropriate work is shown, but one computational error is made

*[1 point] The total of the five salaries is shown to be 5 · 360 = 1800, but no further correct work is shown.

*[1 point] $350, but no work is shown or fewer than three trials with appropriate checks are shown.



20

1. ____________ is the sum of the areas of all the faces of a 3-D figure.

2. The sum of ___________________ is equal to 180°.

3. A _______ is a 2-D shape that can be folded to create a 3-D figure.

4. A 3-D solid that has two congruent and parallel faces is known as a _______.

5. The sum of ____________________ is equal to 90°.

Word Bank:NetCircumferencePrismSupplementary angles

Complementary anglesFormulaInterior angle Polygon Surface area

Volume

Measurement Vocabulary ReviewSurface area

Supplementary angles

Complementary angles

Net

Prism

21

6. A(n) _____________ is an angle inside of a shape.

7. A (n) _________ is a closed plane figure formed by three or more line segments that intersect only at their endpoints (vertices).

8. The number of cubic units needed to fill a given space is known as ________.

9. ______________ is the measured distance around a circle.

10.A ________ is a rule showing relationships among quantities.

Word Bank:NetCircumferencePrismSupplementary angles

Complementary anglesFormulaInterior angle Polygon Surface area

Volume

Measurement Vocabulary Review

Interior angle

Polygon

Volume

Circumference

Formula

22

Customary measurements

How many feet are in 15 miles?

A. 352

B. 35,200

C. 79,200

D. 89,760

Metric measurements

Greg is 150 centimeters tall. How many meters is that?

A. 0.500

B. 1.5

C. 15

D. 15,000

Practice… Converting measurements.

Measurement

24

In a quadrilateral, each of two angles has a measure of 115°. If the measure of a third angle is 70°, what is the measure of the remaining angle?

A. 60°

B. 70°

C. 130°

D. 140°

Find the measure in degrees, of the smallest angle in this triangle:

A. 20

B. 40

C. 60

D. 80

Practice… Determining the measurement of a missing side(s) or angle(s) in a polygon.

Missing Angles

3x

2x 4x

Measurement

26


In the accompanying diagram of ∆BCD, m<C=70, m<CDE=130, and side BD is extended to A and to E. Find m<CBA.

Missing Angles(Short Response)

Scoring Rubric:

**[2 points] 120, and appropriate work is shown, such as m<CDB= 180 – 130 = 50 and m<CBA = 70 + 50 = 120 or correctly labeled angles in a diagram.

*[1 point] Appropriate work is show, but one computational error is made.

*[1 point] Appropriate work is show, but one conceptual error is made.

*[1 point] m<CBD = 60 is found, but no further correct work is shown.

*[1 point] 120, but no work is shown


A B

C

D E

70°

130°

Measurement

27

The length of each side of a figure below is 4 inches (in.).

What is the perimeter of the figure?

A. 12 in.

B. 16 in.

C. 20 in.

D. 24 in.

The interior angles of a sign total 1080°. What type of polygon is the sign?

A. Hexagon

B. Pentagon

C. Heptagon

D. Octagon


Missing Sides

4 in.

Measurement

29

A farmer has a rectangular field that measures 100 feet by 150 feet. He plans to increase the area of the field by 20%. He will do this by increasing the length and width by the same amount, x. Which equation represents the area of the new field?

A. (100 + 2x)(150 + x) = 18,000

B. 2(100 + x) + 2(150 + x) = 15,000

C. (100 + x)(150 + x) = 18,000

D. (100 + x)(150 + x) = 15,000

Scaling Area

Measurement

Practice… Determining measures of perimeter, circumference, area, surface area and/ or volume.

30

Surface Area The box pictured below is open

at the top. Find its outside surface area.

A. 45 cm²

B. 1150 cm²

C. 1300 cm²

D. 3750 cm²

Volume The volume of the rectangular

solid below is 1,440 cubic inches.

What could be the length and width of this rectangular solid?

A. 4 inches by 10 inches

B. 8 inches by 20 inches

C. 10 inches by 48 inches

D. 30 inches by 40 inches


10 cm15 cm

20 cm 3 in

Measurement

32

Perimeter Delroy’s sailboat has two sails

that are similar triangles. The larger sail has sides of 10 feet, 24 feet, and 26 feet. If the shortest side of the smaller sail measures 6 feet, what is the perimeter of the smaller sail?

A. 15 ft

B. 36 ft

C. 60 ft

D. 100 ft

Circumference The circumference of a circle

is 16∏. What is the radius of the circle?

A. 4

B. 8

C. 16

D. 32


Measurement

34

Perimeter How does the perimeter of a

rectangle change when each side is increased by 2 units

A. The perimeter doubles

B. The perimeter quadruples

C. The perimeter increases by 4 units

D. The perimeter increases by 8 units

Area If the diameter of a car tire is

30 cm, what is the area of that circle? Round your answer.

A. 30.14 cm²

B. 314 cm²

C. 7,070 cm²

D. 707 cm²


Measurement

36

1. When a transversal intersects two lines, ___________________ are on the same side of the transversal and on the same side of the given lines. (Also, similar or congruent figures.)

2. A(n) _________________ has exactly two congruent sides.

3. The ____________________ is a formula for finding the length of a side of a right triangle when the lengths of two sides are given.

4. A pair of ________________ angles are located outside a set of parallel lines and on opposite sides of the transversal.

5. A pair of opposite congruent angles formed when two lines intersect are called _____________.

Word Bank:Isosceles triangleAdjacent anglesCoordinate plane

Acute triangle

Corresponding anglesPythagorean TheoremScalene triangle

Vertical anglesAlternate exterior

Alternate interior

Geometry Vocabulary Review

Corresponding angles

Isosceles triangle

Pythagorean Theorem

Alternate exterior

Vertical angles

37

6. A(n) _______________ has no congruent sides.

7. A (n) ____________ has each angle measuring less than 90°.

8. A pair of _______________ angles are located between a set of parallel lines and on opposite sides of the transversal.

9. A ________________ is a 2-D system which contains both horizontal and vertical axes.

10._______________ share a common side and common vertex and do not overlap.

Word Bank:Isosceles triangleAdjacent anglesCoordinate plane

Acute triangle

Corresponding anglesPythagorean TheoremScalene triangle

Vertical anglesAlternate exterior

Alternate interior

Geometry Vocabulary Review

Scalene triangle

Acute triangle

Alternate interior

Coordinate plane

Adjacent angles

38

Circular Geometry A duck swims from the edge of a circular pond to a fountain in

the center of the pond. Its path is represented by the dotted line in the diagram below.

What term describes the duck’s path?

A. Chord

B. Radius

C. Diameter

D. Central angle

Practice…Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders..

Duck’s Path

Geometry

39

Parallelograms

The height of a parallelogram is 13.5 feet. The base is four times the height. What is the area of the parallelogram?

A. 45.5625 ft²

B. 54 ft²

C. 182.25 ft²

D. 729 ft²


Prisms

What is the volume of a rectangular prism with a length of 16 inches, a height or 4 inches, and a width of 12 inches?

A. 48 in.³

B. 768 in.³

C. 1810 in.³

D. 2413 in.³

Geometry

41

Parallelograms(Short Response)

Is it possible for two parallelograms to have the same area but not be congruent? Explain why or why not.


Geometry

Scoring Rubric:

**[2 points] Yes, two parallelograms can have the same area but not be congruent. Let one parallelogram have a base of 6 units and a height of 4 units. Its area is 24 square units. Let another parallelogram have a base of 8 units and a height of 3 units. Its area is also 24 units, but the two parallelograms are not congruent.

*[1 point] Yes, two parallelograms can have the same area but not be congruent. No explanation or example is given.

*[1 point] Yes, two parallelograms can have the same area but not be congruent. A poor or incorrect explanation is given.


42

Which angles are complementary?

A. <2 and <3

B. <3 and <4

C. <4 and <5

D. <1 and <2


1 23

45

The ratio of two supplementary angles is 2:7. What is the measure of the smaller angle?

A. 10°

B. 14°

C. 20°

D. 40°

Angles

Geometry

43

Net Which of the following figures is the net of a square based pyramid?

A. 1 C. 3

B. 2 D. 4


Geometry

44

Regular Polygons(Extended Response)

The top of the picnic table shown has the shape of a regular polygon.

a. Sketch and classify the polygon. Is it convex or concave?

b. Draw a single segment that divides the polygon in your sketch into two trapezoids.

c. Find the sum of the measures of the angles of the polygon.


Geometry

Solution:a–b. The polygon is a regular hexagon. It is convex.

c. 360 + 360 = 720The sum of the measures of the angles of the polygon is 720°.

46

Line p is parallel to line k in the figure shown below

Which statement about the lines in the figure is true?

A. Line k is parallel to line m.

B. Line m is parallel to line j.

C. Line p is perpendicular to line k.

D. Line j is perpendicular to line p.

In the diagram below, line l is parallel to line m and line p is parallel to line q?

Which angle has the same measure as <1?

A. <2

B. <3

C. <4

D. <5

Practice…Identifying, using, and/or describing properties of angles, triangles, quadrilaterals, circles, pyramids, cubes, prisms, spheres, cones and/or cylinders.

Angles & Lines

2 1

34 5

l m

q

p

j

m

kp

Geometry

47

Mr. Kyle drives eight miles south and then six miles east. What was the diagonal distance from his starting point?

A. 2 miles

B. 10 miles

C. 14 miles

D. 48 miles

What is the length of the missing side in this triangle?

A. 14

B. 15

C. 16

D. 18

Practice…Computing measures of sides of right triangles using the Pythagorean Theorem.

Pythagorean Theorem

12

x

20

Geometry

49

Which building is located at (-2, 3)?

A. School

B. Library

C. Market

D. Bank

At what point does the line intersect the y-axis?

A. (5, 0)

B. (0, 5)

C. (0,-3)

D. (-3, 0)

Practice…Plot and/or identify ordered pairs on a coordinate plane.

Coordinate System

Library

School

Bank

Market

Geometry

50

1. A ______________ is an equation whose graph in a coordinate plane is a straight line.

2. _____________ is the distance of a number from zero on a number line; shown by | |.

3. A(n) __________________ is a group of two or more equations that contain two or more variables.

4. A phrase that contains operations, numbers, and/or variables is a(n) ____________.

5. A relationship that has exactly one output for each input is called a ________.

Word Bank:FunctionFunction tableSystem of equationsAbsolute value

ExpressionInverse operationsTermsEquationInequality

Linear function

Algebraic Concepts Vocabulary Review

Linear equation

Absolute value

System of equations

Expression

Function

51

6. An _________ shows the relationship between quantities that are not equal.

7. A sentence that shows that two expressions are equivalent is a(n) ________.

8. ______ in an expression are set apart by plus or minus signs.

9. A table of ordered pairs that represent solutions of a function is called a _____________.

10._________________ undo each other; addition and subtraction, multiplication and division.

Word Bank:FunctionFunction tableSystem of equationsAbsolute value

ExpressionInverse operationsTermsEquationInequality

Linear function

Algebraic Concepts Vocabulary Review

Inequality

Equation

Terms

Function table

Inverse operations

52

Fiona created a pattern using numbers as shown below.

0, 2, 6, 12

The pattern continues. What is the next number in the pattern?

A. 14

B. 18

C. 20

D. 24

Practice…Analyzing, extending or developing descriptions of patterns or functions.

Patterns

List the next two values in this sequence:

4, 10, 22, __, __

A. 34, 46

B. 34, 48

C. 40, 62

D. 46, 94

Algebraic Concepts

53

What is the solution of

x > -3?.

3

A. x < -1

B. x > -1

C. x < -9

D. x > -9

Practice…Analyzing, extending or developing descriptions of patterns or functions.

Functions

The table below shows a relationship between the values of x and y.

Which equation describes the relationship?

A. y = x – 3

B. y = x +3

C. y = -x -3

D. y = -x +3

x y

-7 -10

-2 -5

3 0

8 5

Algebraic Concepts

54

Dora owns a card store. After a full week, she made $250.00 by selling cards (c). Using the equation 1.25c = 250, how many cards did Dora sell that week?

A. 125

B. 200

C. 251

D. 312

In which equation is m = 28 the solution?

A. m – 3 = 5

5

B. m – 3 = 5

5

C. m – 3 = 5

5

D. (m – 3)5 = 5

Practice…Select and/ or use a strategy to simplify an expression, solve an equation or inequality and/ or check the solution for accuracy.

Solving Equations

Algebraic Concepts

55

Expressions

If k can be replaced by any number, how many different values can the expression k + 6 have?

A. One

B. Six

C. Seven

D. Infinitely many

Inequalities

There is $150 in Dave’s bank account. He deposits $200 into the account each month. Dave needs at least $700 to buy a used car. The inequality below can be solved for x to find the number of deposits Dave must make to reach his goal.

200x + 150 ≥ 700

How many deposits must Dave make?

A. x ≥ 2.75

B. x ≤ 2.75

C. x ≥ 4.25

D. x ≤ 4.25

Practice…Selecting and/ or using a strategy to simplify an expression, solve an equation or inequality and/ or check the solution for accuracy.

Algebraic Concepts

56

Practice… Selecting and/ or using a strategy to simplify an expression, solve an equation or inequality and/ or check the solution for accuracy.

Brett was given the problem: “Evaluate 2x² + 5 when x = 3.” Brett wrote that the answer was 41. Was Brett correct? Explain your answer.

Checking for Accuracy(Short Response)

Scoring Rubric:

**[2 points] No, and an appropriate explanation is given or the expression is evaluated correctly.

*[1 point] No, and the correct order of operations is used to evaluate 2(3)² + 5, but one computational error is made.

*[1 point] One conceptual error is made in evaluating the expression, but the question is answered appropriately.

*[1 point] Appropriate work is shown, but the question is not answered.

[0 points] No, but no explanation or an inappropriate explanation is given.


Algebraic Concepts

57

Inequalities

When Bernie earns 5 times more than the amount (a) of money he has plus another $1,000, he will have at least $16,000 to start a small business. Which statement represents this situation?

A. 5a + 1,000 ≥ 16,000

B. 5 + 1,000a ≤ 16,000

C. 5a +1,000 ≤ 16,000

D. 5 + 1,000a ≥ 16,000

Expressions

Which expression represents 4 times the sum of x squared and 6?

A. 4x² + 6

B. 4(x² + 6)

C. 4(x + 6)²

D. (4x + 6)²

Practice…Creating and/ or interpreting expressions, equations or inequalities that model problem situations.

Algebraic Concepts

58

A wooden box with 8 DVDs inside weighs 4.2 kilograms. The box weighs 0.6 kg when empty. Using w to represent the weight of one DVD, which of the following describes this situation?

A. 8w = 4.2

B. 8w + 0.6 = 4.2

C. 8w – 0.6 = 4.2

D. 8(w + 0.6) = 4.2

Which equation shows that the sum of x and 2 is twice as much as 6?

A. x = 2 · 2 · 6

B. x + 2 · 2 =6

C. 2(x +2) = 6

D. x + 2 = 2 · 6

Practice…Creating and/ or interpreting expressions, equations or inequalities that model problem situations.

Creating Equations

Algebraic Concepts

59

Tables Which linear function is

graphed below?

A. y = x + 3

B. y² = 3x

C. y = 3

D. x = 3

Functions Given the function y = ½x -2,

which set of numbers completes the table?

A. {4, 3, 2}

B. {-4, -3, -2}

C. {-4, 3, 2}

D. {4, -3, -2}

Practice…Represent relationships with tables or graphs on the coordinate plane.

x y

-4

-2

0

Algebraic Concepts

60

1. ___________ describes the relationship between two sets of data.

2. A graphic method for showing a summary using median, quartiles and extremes of data is known as a(n) ____________________.

3. A(n) ___________ is a possible order or arrangement of a set of items.

4. A statement of _____________________ is based on the results of a series of trials.

5. Two events that cannot occur at the same time are known as _______________________.

Word Bank:Compound eventStem-and-leaf plotTheoretical probability

Box-and-whisker plot

Experimental probabilityIndependent eventsPermutation

Mutually exclusive events

Scatter plotCorrelation

Data Analysis & ProbabilityVocabulary ReviewCorrelation


Permutation

Experimental probability


61

6. ___________________ is a statement of the probability of an event without doing an experiment or analyzing.

7. A _______________ is made up of two or more simple events.

8. Two events in which the outcome of one event does not affect the outcome of the other event are known as _________________.

9. A graph with points plotted to show a relationship between two variables is called a ___________.

10.A(n) ________________ displays groups of data arranged by place value.

Data Analysis & ProbabilityVocabulary Review

Word Bank:Compound eventStem-and-leaf plotTheoretical probability


Experimental probabilityIndependent eventsPermutation


Scatter plotCorrelation

Theoretical probability

Compound event

Independent events

Scatter plot

Stem-and-leaf plot

62

Charts According to the graph, what

percent of the students chose generic brands?

A. 15%

B. 14%

C. 17%

D. 16%

Brand A; 8%Brand B;

5%

Brand C; 15%

Brand D; 30%

Brand E; 27%

Generic brands

Favorite Sneakers at Sherman High School

Stem-and-Leaf Plots The table below shows test

scores for a class. How many students scored in the 80’s?

A. 2 students

B. 6 students

C. 7 students

D. 9 students

Practice…Choosing, displaying or interpreting data.

Stem Leaf

9 0 1 1 5 7

8 0 0 2 4 6 7 9

7 7 7 8 9

6 9

5 2 3

4 4

Data Analysis & Probability

63

Interpreting Data The test scores for 10 students in Ms. Sampson’s homeroom were

61, 81, 83, 87, 88, 89, 90, 98, and 100. Which frequency table is accurate for this set of data?

A. 1) C. 3)

B. 2) D. 4)

Practice…Choosing, displaying or interpreting data.

Interval Frequency

61-70 2

71-80 2

81-90 7

91-100 10


Interval Frequency

61-70 2

71-80 0

81-90 8

91-100 10

Interval Frequency

61-70 2

71-80 2

81-90 8

91-100 10

Interval Frequency

61-70 2

71-80 0

81-90 6

91-100 2

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There are 15 girls and 11 boys in a mathematics class. If a student is selected at random to run an errand, what is the probability that a boy will be selected?

A. 4/26

B. 11/26

C. 15/26

D. 11/15

There are 9 packages, 5 red and 4 green. There are calculators inside 4 of the red packages and inside 2 of the green packages. What is the probability of choosing a package containing a calculator from the entire group of packages?

A. 4/5

B. 2/3

C. 1/2

D. 4/9

Practice…Calculating the probability of an event.

Probability


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While watching a game at a carnival where participants guess which of three cups is covering a ball, Jeremy tallies that following results.

Find the experimental probability of the following as a fraction in its simplest form AND an approximate percentage.

a. Find the experimental probability of the ball being under the right cup.

b. Find the experimental probability of the ball not being under the middle cup.

Practice…Calculating the probability of an event.

Probability


33 or about 50%67

49 or about 73%67

Ball Location left middle

right

Frequency 16 18 33

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Combination

Sarah and Tom belong to a soccer league that has 8 teams. Each team will play all of the other teams twice. How many games will be played in all?

A. 16

B. 28

C. 56

D. 64

Permutation

Edward conducts a simulation using a coin, a number cube, and a spinner as shown below.

What is the number of outcomes for this simulation?

A. 3

B. 8

C. 12

D. 48

Practice…Determining the number of combinations and/ or permutations for an event.


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Practice…Determining the number of combinations and/ or permutations for an event.

In Jackson County, Wyoming, license plates are made with two letters (A through Z) followed by three digits (0 through 9). The plates are made according to the following restrictions:

• the first letter must be J or W, and the second letter can be any of the 26 letters of the alphabet

• no digit can be repeated How many different license plates can be made with these restrictions?

Combinations(Short Response)

Scoring Rubric:

**[2 points] 37,440 and appropriate work is shown, such as 2 x 26 x 10 x 9 x 8 or 2P1 x 26P1 x 10P3.

*[1 point] Appropriate work is show, but one computational error is made.

*[1 point] Appropriate work is shown for at least one restriction, such as 2x26 or 10 x 9 x 8.

*[1 point] 37,440 but no work is shown.



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Drawing Conclusions

From a batch of 3000 light bulbs, 100 were selected at random and tested. If 5 of the light bulbs in the sample were found to be defective, about how many defective light bulbs would be expected in the entire bunch?

A. 15

B. 60

C. 150

D. 300

Correlation

The data represented in the scatter plot below can be described as having…

A. Positive correlation

B. Negative correlation

C. No correlation

D. Both positive and negative correlation

Practice…Drawing conclusions, making inferences and/ or evaluate hypotheses based on statistical and data displays.


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Drawing Conclusions

An animal shelter needs to find homes for 40 dogs and 60 cats. If 15% of the dogs are female and 25% of the cats are female, what percent of the animals are female?

A. 21%

B. 22%

C. 40%

D. 42%

Correlation

Which data sets have a negative correlation?

A. A person’s eye color and height

B. A person’s height and weight

C. The distance traveled and the time it takes to travel

D. The outdoor temperature and the number of hours a heater is used



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Drawing Conclusions John left his home and walked 3 blocks to his school, as shown in

the accompanying graph.

What is one possible interpretation of the section of the graph from point B to point C?

A. John reached the top of a hill and began walking on level ground.

B. John waited before crossing a busy street.

C. John arrived at school and stayed throughout the day.

D. John returned home to get his mathematics homework.


A

B C

D

1

3

2

Time


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Good luck to all!!!

Feel free to repeat the review as many times as you like or continue studying

your own additional resources!

purpose: pssa review for 8th grade mathematics (can be used as enrichment or remediation for middle...

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