Download Algebra I Semester 2 Study Guide

Algebra I
Final Exam Study Guide
1.1 Solving Simple Equations
1.2 Solving Multi-Step Equations
1.5 Solving Equations with variables on
both sides
1.6 Solving Absolute Value Equations
1.7 Rewriting Equations and Formulas
2.1 Writing and Graphing Inequalities
2.2 Solving Inequalities Using Addition
and Subtraction
2.3 Solving Inequalities Using
Multiplication and Division
2.4 Solving Multi-Step Inequalities
2.5 Solving Compound Inequalities
2.6 Solving Absolute Value Inequalities
3.1 Functions
3.2 Characteristics of Functions
3.3 Linear Functions
3.4 Function Notation
3.5 Graphing Linear Functions in
Standard Form
3.6 Graphing Linear Functions in SlopeIntercept Form
3.7 Transformations of Linear Functions
3.8 Graphing Absolute Value Functions
4.1 Writing Equations in Slope-Intercept
Form
4.2 Writing Equations in Point-Slope
Form
4.3 Writing Equations of Parallel and
Perpendicular Lines
5.1 Solving Systems of Linear Equations
by Graphing
5.2 Solving Systems of Linear Equations
by Substitution
5.3 Solving Systems of Linear Equations
by Elimination
5.4 Solving Special Systems of Linear
Equations
5.5 Solving Equations by Graphing
5.6 Graphing Linear Inequalities in Two
Variables
5.7 Systems of Linear Inequalities
6.1 Properties of Exponents
6.2 Radical and Rational Exponents
6.3 Exponential Functions
6.5 Solving Exponential Equations
7.1 Adding and Subtracting Polynomials
7.2 Multiplying and Dividing
Polynomials
7.3 Special Products of Polynomials
7.4 Solving Polynomial Equations in
Factored Form
7.5 Factoring 𝒙𝟐 + 𝒃𝒙 + 𝒄
7.6 Factoring 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄
8.1 Graphing 𝒇(𝒙) = 𝒂𝒙𝟐
8.2 Graphing 𝒇(𝒙) = 𝒂𝒙𝟐 + 𝒄
8.3 Graphing 𝒇(𝒙) = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄
8.4 Graphing 𝒇(𝒙) = 𝒂(𝒙 − 𝒉)𝟐 + 𝒌
8.5 Using Intercept Form
9.3 Solving Quadratic Equations Using
Square Roots
9.4 Solving Quadratic Equations by
Completing the Square
9.5 Solving Quadratic Equations Using
Quadratic Formula
9.6 Solving Nonlinear Systems of
Equations
Final Exam Study Guide
Algebra I
Practice Problems by Chapter
Chapter 1
Solve the equations for the variable:
𝑧 + 3 = −6
3
3
10
3
(𝑥
2
=𝑤+1
𝑛
2 = −2𝑡
4
5
3𝑦 + 11 = −16
− 2) − 5 = 19
−4(2𝑧 + 6) − 12 = 4
1
3𝑛 − 3 = 4𝑛 + 1
|𝑦 + 3| = 17
− 5 = −2
2𝑦 − 16 = 3 (𝑦 − 3)
2|𝑘 − 3| = 18
6=𝑦−3
6=1−𝑏
𝑛 + 5𝑛 + 7 = 43
1
5
7
5
6= 𝑤+ 𝑤−4
1
3(𝑛 + 4) = 2 (6𝑛 + 4)
|16𝑔 − 40| = −4|4𝑔 − 10|
|𝑥 − 2| = |4 + 𝑥|
3(2𝑥 + 𝑦) = −4𝑥 − 𝑦
𝑎 = 9𝑦 + 3𝑦𝑥
Solve the literal equation for 𝑦:
2𝑥 − 4𝑦 = 20
Chapter 2
8𝑥 − 3 = 5 + 4𝑦
9𝑏 = −3
Final Exam Study Guide
Algebra I
Solve the inequality. Graph the solution, if possible.
𝑝 + 4 < 10
3
−4𝑛 ≥ 3
6(2𝑡 + 9) ≤ 12𝑡 − 1
𝑟 − 4 > −6
3𝑥 > −21
3𝑥 − 4 > 11
−4 < 2 + 9
−4 ≤
𝑏
3
2𝑟 − 8 > 4 (𝑟 − 6)
Determine where each of the following are increasing,
decreasing, positive and negative.
36 < 2𝑞
2(−4𝑠 + 2) ≥ −5𝑠 − 10
−1 ≤ −2𝑑 + 7 < 10
Write: “A number 𝑥 is more than -6 and at most 8” as an inequality.
Chapter 3
𝑔
5
|𝑥| > 10
Final Exam Study Guide
Algebra I
Determine whether the following represent a linear or nonlinear function.
Evaluate the functions when 𝑥 = −3, 0, 𝑎𝑛𝑑 5 (find 𝑓(−3), 𝑓(0), 𝑎𝑛𝑑 𝑓(5)).
𝑓(𝑥) = 𝑥 + 8
𝑓(𝑥) = 3𝑥 − 9
Chapter 4
Graph the linear equations (use your own graph paper):
𝑥=6
𝑦 = 2𝑥 + 4
𝑦=3
2𝑥 + 3𝑦 = 6
𝑦 = 5𝑥 − 10
8𝑥 − 4𝑦 = 16
1
𝑥
2
− 𝑦 = −2
𝑥 + 3𝑦 = 9
Find the equation of the line:
Write the equation of a line that passes through the point (4,7) and has a slope of -1.
Write a linear equation given the following sets of points:
1. 𝑓(10) = 5, 𝑓(2) = −3
2. 𝑓(3) = −4, 𝑓(5) = −4
Determine which of the following (if any) are perpendicular or parallel:
3. 𝑓(6) = 8, 𝑓(9) = 3
Algebra I
Final Exam Study Guide
Write an equation of the line that passes through (1, 5) and is parallel to the line 𝑦 = −4𝑥 + 2
Write an equation of the line that passes through (2, −3) and is parallel to the line 𝑦 = −2𝑥 − 3
Chapter 5
Solve each system by graphing, substitution or elimination:
𝑦 = −3𝑥 + 1
5𝑥 + 5𝑦 = 15
𝑦 = −4𝑥 + 3
𝑦 =𝑥−7
2𝑥 − 2𝑦 = 10
4𝑥 − 2𝑦 = 6
3𝑥 + 𝑦 = −9
9𝑥 − 2𝑦 = 34
2𝑥 + 3𝑦 = 4
𝑦 = 5𝑥 + 7
5𝑥 + 2𝑦 = −6
𝑦 + 3𝑥 = 6
Determine if each graph has one solution, no solutions, or infinitely many solutions
Graph each inequality:
𝑦 > −4
−9𝑥 + 3𝑦 ≥ 3
Write the inequality that represents each graph:
5𝑥 + 10𝑦 < 40
Graph each system:
𝑦 ≤𝑥−3
𝑦 ≥𝑥+1
𝑦 > −2𝑥 + 3
1
𝑦 ≥ 𝑥−1
4
Final Exam Study Guide
Algebra I
Chapter 6
Simplify or evaluate each expression.
Solve the equations:
5𝑥 = 53𝑥−2
1
8𝑥+4 = 82𝑥−1
3𝑥−2 = 3
(3)2𝑥+3 = 3
(2𝑦 + 4)(2𝑦 − 4)
(𝑝 + 4)2
(−1 + 2𝑑)2
Chapter 7
Find the product:
(𝑥 + 9)(𝑥 − 9)
Solve the equation:
(𝑧 + 3)(𝑧 − 7) = 0
(𝑏 + 13)2 = 0
2𝑦(𝑦 − 9)(𝑦 + 4) = 0
𝑥 2 + 5𝑥 = 0
Factor the polynomial:
𝑝2 + 2𝑝 − 35
3𝑡 2 + 16𝑡 − 12
𝑥2 − 9
𝑏 2 + 18𝑏 + 80
𝑧 2 − 4𝑧 − 21
6𝑥 2 + 17𝑥 + 7
𝑦 2 − 100
𝑥 2 − 11𝑥 + 28
10𝑎2 − 13𝑎 − 3
𝑥 2 − 6𝑥 + 9
𝑚2 + 16𝑚 + 64
Algebra I
Chapter 8
Final Exam Study Guide
Algebra I
Final Exam Study Guide