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What a freshman should know
to take Geometry in the 9th
Grade at St. Francis
Algebra in 9th Grade
H. Algebra 1
Algebra 1
A Grade and
Recommendation
Geometry
H. Geometry
A Grade,
Recommendation,
and Summer Work
Algebra 2
H. Alg 2 / Trig
A Grade,
Recommendation, and
Summer Trig Course
Trig / Pre-Calc
AP Calculus AB
Geometry in 9th Grade
H. Geometry
Geometry
A Grade and
Recommendation
Algebra 2
H. Alg 2 / Trig
Trig / Pre-Calc
AP Calculus AB
AP Calculus AB
AP Statistics
Algebra
Structure and
Method Book 1
McDougal Littell
Brown, Dolciani,
Sorgenfrey, Cole
1 - Introduction to Algebra
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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
x
• Write equation(s) using these variables
x+1
9 feet
x  x 1  9
• Solve the equation(s)
2x 1  9
2x  8
x4
x 1  5
• Write the answer in sentence form and give units if applicable
The lengths of the two pieces are 4 and 5 feet.
2 - Working with Real Numbers
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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
Con s odd int x, x  2, x  4
• Write equation(s) using these variables
x  x  2  x  4  x  30
• Solve the equation(s)
3x  6  x  30
2 x  24
x  12
• Write the answer in sentence form and give units if applicable
Twelve is even, therefore no solution.
3 - Solving Equations and Problems
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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 x  12
x 3
+
x3
-
x  3
x  3
4 - Polynomials
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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
Solve for the unknown
 3x  5 2 x  3   x 1 6 x  5
6 x  9 x  10 x  15  6 x  5x  6 x  5
2
2
6 x  x 15  6 x  x  5
2
2
2 x  10
x5
5 - Factoring Polynomials
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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.
Aold  20  23  460
20-x
23-x
Anew  460  120   20  x  23  x 
460 120  460  20 x  23x  x2
0  x  43x  120
2
0   x  3 x  40 
x  3, 40
40 is not possible  x  3
6 - Fractions
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Simplifying Fractions
Multiplying Fractions
Dividing Fractions
Least Common Denominator
Adding and Subtraction Fractions
Mixed Expressions
Polynomial Long Division
Simplify
2y
y

2
y  25 y  5
2y
y

 y  5 y  5 y  5

2y
y  y 5


 
  y  5 y  5 y  5  y  5
2 y  y  y  5
 y  5 y  5
2 y  y2  5 y
 y  5 y  5
 y2  3y
 y  5 y  5
7 – Applying Fractions
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Ratios
Proportions
Equations with Fractional Coefficients
Fractional Equations
Percents
Percent Problems
Mixture Problems
Work Problems
Negative Exponents
Scientific Notation
Solve for the unknown
3a
4
4

 2
a 1 a  1 a 1
3a
4
4


a  1 a  1  a  1 a  1
 3a

4
4



  a  1 a  1
 a  1 a  1  a  1 a  1 
3a  a  1  4  a  1  4
3a2  3a  4a  4  4
3a 2  a  0
a  3a  1  0
1
a  0,
3
8 – Introduction to Functions
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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).
y 7   1
m

x
63

8
3
• Slope intercept form or Point slope form
y  mx  b
8
7   6  b
3
7  16  b
b  9
8
y  x9
3
y  m x
8
 y  1   x  3
3
9 – Systems of Linear Equations
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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?
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Establish variables or draw a labeled diagram
A is # of adult’s tickets sold and C is # of child’s tickets sold
Write equation(s) using these variables
A  C  785
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5 A  2C  3280
Solve the equation(s)
A  785  C
5  785  C   2C  3280
3925  5C  2C  3280
3C  645
C  215
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Write the answer in sentence form and give units if applicable
There were 215 child’s tickets sold.
10 - Inequalities
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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.
x y 5
x  2y  4
x
0
5
y
5
0
5
4
3
y
x
0
-2
4
0
2
1
-8
-6
-4
-2
2
-1
-2
-3
-4
-5
4
6
8
11 – Rational and Irrational Numbers
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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
Solve for the unknown
x 1  1 x
2
x  1  1  x 
2
2
x 1  1  2x  x
2
0  2x
x0
2
12 – Quadratic Functions
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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.
x  int  y  0
y  x2  4x  1
y  int  x  0
y 1
0  x2  4 x  1
b  b 2  4ac
x
2a
x
4  42  4 11
2 1
4  16  4
2
4  12

2
4  2 3

2
x
x  2  3