what a freshman should know to take geometry in the 9 ...sfhs.net/pdf/math ppt.pdftrig / pre-calc...

What a freshman should know to take Geometry in the 9th

Grade at St. Francis

Algebra in 9th Grade H. Algebra 1

H. Geometry

Trig / Pre-Calc

Algebra 2

Geometry

H. Alg 2 / Trig

AP Calculus AB

A Grade and Recommendation

Algebra 1

A Grade, Recommendation, and Summer Work

A Grade, Recommendation, and Summer Trig Course

Geometry in 9th Grade

AP Statistics

H. Geometry

Trig / Pre-Calc

Algebra 2 H. Alg 2 / Trig

AP Calculus AB

A Grade and Recommendation

Geometry

AP Calculus AB

Algebra Structure and

Method Book 1 McDougal Littell Brown, Dolciani, Sorgenfrey, Cole

1 - Introduction to Algebra

• Variables • Grouping Symbols • Equations • Translating Words into Symbols • Translating Sentences into Equations • Translating Problems into Equations • A Problem Solving Plan • Number Lines • Opposites and Absolute Value

A ribbon 9 feet long is cut into two pieces. One piece is 1 foot longer than the other. What are the lengths of the pieces?

• Establish variables or draw a labeled diagram

• Write equation(s) using these variables

• Solve the equation(s)

• Write the answer in sentence form and give units if applicable

The lengths of the two pieces are 4 and 5 feet.

9 feet

x+1x

1 9x x

2 1 9

2 8

4

1 5

x

x

x

x

2 - Working with Real Numbers

• Basic Assumptions • Addition on a Number Line • Rules for Addition • Subtracting Real Numbers • The Distributive Property • Rules for Multiplication • Problem Solving: Consecutive Integers • The Reciprocal of a Real Number • Dividing Real Numbers

The sum of three consecutive odd integers is thirty more than the first. Find the integers?

• Establish variables or draw a labeled diagram




Twelve is even, therefore no solution.

s int , 2, 4Con odd x x x

2 4 30x x x x

3 6 30

2 24

12

x x

x

x

3 - Solving Equations and Problems

• Transforming Equations: Add and Subt

• Transforming Equations: Multi and Div

• Using Several Transformations

• Using Equations to Solve Problems

• Equations with Variables on Both Sides

• Problem Solving: Using Charts

• Cost, Income, and Value Problems

• Proof in Algebra

Solve for the unknown

+ -

9 x 3 5 x 3 12

9 x 3 5 x 3 12

4 12x

3x

3x 3

3

x

x

4 - Polynomials

• Exponents • Adding and Subtracting Polynomials • Multiplying Monomials • Powers of Monomials • Multiplying Polynomials by Monomial • Multiplying Polynomials • Transforming Formulas • Rate-Time-Distance Problems • Area Problems • Problems without Solutions


3 5 2 3 1 6 5x x x x

2 26 9 10 15 6 5 6 5x x x x x x 2 26 15 6 5x x x x

2 10x

5x

5 - Factoring Polynomials

• Factoring Integers • Dividing Monomials • Monomial Factors of Polynomials • Multiplying Binomials Mentally • Differences of Two Squares • Squares of Binomials • Factoring Patterns for Trinomials • Factoring by Grouping • Using Several Methods of Factoring • Solving Equations by Factoring • Using Factoring to Solve Problems

Originally the dimensions of a rectangle were 20 cm by 23 cm. When both dimensions were decreased by the same amount, the area of the rectangle

decreased by 120 cm2. Find the dimensions of the new rectangle.

23-x

20-x 20 23 460oldA

460 120 20 23newA x x

2460 120 460 20 23x x x 20 43 120x x

0 3 40x x

3, 40x

40 3is not possible x

6 - Fractions

• Simplifying Fractions

• Multiplying Fractions

• Dividing Fractions

• Least Common Denominator

• Adding and Subtraction Fractions

• Mixed Expressions

• Polynomial Long Division

Simplify

2

2

25 5

y y

y y

2

5 5 5

y y

y y y

2 5

5 5 5 5

y y y

y y y y

2 5

5 5

y y y

y y

22 5

5 5

y y y

y y

2 3

5 5

y y

y y

7 – Applying Fractions

• Ratios • Proportions • Equations with Fractional Coefficients • Fractional Equations • Percents • Percent Problems • Mixture Problems • Work Problems • Negative Exponents • Scientific Notation


2

3 4 4

1 1 1

a

a a a

3 4 4

1 1 1 1

a

a a a a

3 4 41 1

1 1 1 1

aa a

a a a a

3 1 4 1 4a a a

23 3 4 4 4a a a 23 0a a

3 1 0a a

10,

3a

8 – Introduction to Functions

• Equations in Two Variables • Points, Lines, and Their Graphs • Slope of a Line • The Slope-Intercept Form of a Linear Equation • Determining an Equation of a Line • Function Defined by Tables and Graphs • Function Defined by Equations • Linear and Quadratic Functions • Direct and Inverse Variations

Write the equation of a line that goes through the points (3, -1) and (6, 7).

• Slope intercept form or Point slope form

7 1

6 3

ym

x

8

3

y mx b y m x

8

7 63

b

7 16 b

9b

89

3y x

8

1 33

y x

9 – Systems of Linear Equations

• The Graphing Method

• The Substitution Method

• Solving Problems with Two Variables

• The Addition – or – Subtraction Method

• Multiplication with Add / Subt Method

• Wind and Water Current Problems

• Puzzle Problems

A movie theater charges $5 for an adult’s ticket and $2 for a child’s ticket. One Saturday the theater sold 785 tickets for $3280. How many child’s tickets

were sold for the movie that Saturday? • Establish variables or draw a labeled diagram

• A is # of adult’s tickets sold and C is # of child’s tickets sold




There were 215 child’s tickets sold.

785A C 5 2 3280A C

785A C

5 785 2 3280C C

3925 5 2 3280C C

3 645C

215C

10 - Inequalities

• Order of Real Numbers

• Solving Inequalities

• Solving Problems Involving Inequalities

• Solving Combined Inequalities

• Absolute Value in Open Sentences

• Absolute Values of Product in Open Sentences

• Graphing Linear Inequalities

• Systems of Linear Inequalities

Graph the solution set to the system of linear inequalities.

5

2 4

x y

x y

5

5

0

0

yx

4

-2

0

0

yx

5

4

3

2

1

-1

-2

-3

-4

-5

-8 -6 -4 -2 2 4 6 8

11 – Rational and Irrational Numbers

• Properties of Rational Numbers • Decimal Form of Irrational Numbers • Rational Square Roots • Irrational Square Roots • Square Roots of Variable Expressions • The Pythagorean Theorem • Multiplying, Dividing, and Simplifying Radicals • Adding and Subtracting Radicals • Multiplication of Binomials Containing Radicals • Simple Radical Equations


2 1 1x x

22 1 1x x

2 21 1 2x x x

0 2x

0x

12 – Quadratic Functions

• Quadratic Equation with Perfect Squares • Completing the Square • The Quadratic Formula • Graphs of Quadratic Equations • The Discriminate • Methods of Solutions • Solving Problems Involving Quadratics • Direct and Inverse Variation Involving Squares • Joint and Combined Variations

Find the x & y intercepts of the quadratic function.

int 0y x

1y

int 0x y 20 4 1x x

2 4

2

b b acx

a

24 4 4 1 1

2 1x

4 16 4

2

4 12

2

4 2 3

2

x

2 3x

2 4 1y x x

what a freshman should know to take geometry in the 9 ...sfhs.net/pdf/math ppt.pdftrig / pre-calc...

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