Name: _______________________________________________
Date: ___________
Algebra 8 Honors Final Exam Topics
JUNE 2014
Ch.5 – Systems of Linear Inequalities
5.1 Solving Inequalities by Addition and Subtraction
5.2 Solving Inequalities by Multiplication and Division
5.3 Solving Multi-Step Inequalities
5.4 Solving Compound Inequalities
5.5 Inequalities Involving Absolute Value
5.6 Graphing Inequalities in Two Variables
6.8 Systems of Inequalities
Ch.7 – Monomials, Scientific Notation, and Polynomials
7.1 Multiplying Monomials
7.2 Dividing Monomials
7.3 Scientific Notation
7.4 Introduction to Polynomials
7.5 Adding and Subtracting Polynomials
7.6 Multiplying a Polynomial by a Monomial
7.7 Multiplying Polynomials
7.8 Special Products
Ch.8 – Factoring
8.1 Monomials and Factoring
8.2 Using the Distributive Property
8.3 Factoring Quadratic Equations: 𝑥 2 + 𝑏𝑥 + 𝑐 = 0
8.4 Factoring Quadratic Equations: 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0
8.5 Factoring Quadratic Equations: Differences of Squares
8.6 Factoring Quadratic Equations: Perfect Square Trinomials
Ch.9 – Quadratic and Exponential Functions
9.1 Graphing Quadratic Functions
9.2 Graphing Quadratic Functions using critical values or factoring (if possible)
9.5 Solving Quadratic Equations by Using the Quadratic Formula
For all chapters, you should know the vocabulary at the end of each chapter and be able to define or describe the
words. I would also suggest you look at your previous quizzes and tests.
To review for mastery of a subject:
1. Complete this packet.
2. Review the quizzes and tests you have already taken and be sure that if you had the same test to take
today, you would get 100%.
3. Read the chapter summaries several times. Write down any ideas that are unclear.
4. Do the Chapter Test for each chapter – These should now be easy.
Lesson 5-1 Solving Inequalities by Addition and Subtraction
Solve each inequality. Check your solution, and then graph it on a number line.
1) 𝑐 + 9 ≤ 3
2) 𝑑— 3 < 13
3) 14𝑝 > 5 + 13𝑝
4)
1
2
1
3
2
𝑥 + 4 ≥ 2𝑥 − 3
Define a variable, write an inequality and solve each problem. Check your solution.
5) The sum of a number and a negative six is greater than 9.
6) Negative five times a number is less than the sum of negative six times the number and 12.
Lesson 5-2 Solving Inequalities by Multiplication and Division
Solve each inequality. Check your solution.
1) −5𝑗 < −60
2)
𝑥
3) − 8 < 4
4)
𝑝
5
2
3
<8
𝑚 ≥ −22
Define a variable, write an inequality, and solve each problem. Then check your solution.
5) Negative one times a number is greater than -7.
6) Three fifths of a number is at least negative 10.
Lesson 5-3 Solving Multi-Step Inequalities
Solve each inequality. Check your solution.
1) 3𝑦 − 4 > −37
2) −5𝑞 + 9 > 24
3) 15𝑡 − 4 > 11𝑡 − 16
4) 2(𝑤 + 4) ≥ 7(𝑤 − 1)
5) 8𝑐 − (𝑐 − 5) > 𝑐 + 17
6) 5𝑥 ≤ 10(3𝑥 + 4)
Lesson 5-4 Solving Compound Inequalities
Solve each compound inequality. Then graph the solution set.
1) 5𝑚 − 8 ≥ 10 − 𝑚 or 5𝑚 + 11 < −9
2) −9 < 2𝑧 + 7 < 10
3) 2ℎ − 2 ≤ 3ℎ ≤ 4ℎ − 1
Lesson 5-5 Inequalities Involving Absolute Value
Solve each inequality. Then graph the solution set.
1) |3𝑥 + 2| > 8
4) 2(𝑞 − 4) ≤ 3(𝑞 + 2) or 𝑞 − 8 ≤ 4 − 𝑞
3ℎ−5
2) |
2
|≤2
Lesson 5-6 Graphing Inequalities in Two Variables
Determine which ordered pairs are part of the solution set for the following inequality.
1) 2𝑥 + 𝑦 ≤ 8; {(0,0), (−1, −1), (3, −2), (8, 0)}
Graph each inequality.
1) 3𝑦 − 2𝑥 ≤ 2
2) 𝑦 > 4𝑥 − 1
Lesson 6-8 Systems of Inequalities
Solve each system of inequalities.
1) 𝑦 ≤ 𝑥 + 4
𝑦−𝑥 ≥1
2) 𝑦 ≤ −1
3𝑥 − 2𝑦 > 6
Lesson 7-1 Multiplying Monomials
Determine whether each expression is a monomial. Write yes or no. Explain your reasoning.
1) 𝑛2 − 3
2) 53
Simplify each expression.
3) 𝑎5 (𝑎)(𝑎7 )
4) (−3𝑚𝑝2 )(5𝑚3 𝑝2 )
1
2
5) (2 𝑤 3 ) (6𝑤 4 )2
Lesson 7-2 Dividing Monomials
Simplify. Assume that no denominator is equal to zero.
1)
4)
𝑏6 𝑐 5
𝑏3 𝑐 2
2)
(−𝑥)3 𝑦 3
2𝑎2 𝑏4
3) ( 3 )
3𝑎 𝑏
𝑥3𝑦6
(3𝑎𝑏2 𝑐)−3
(2𝑎2 𝑏𝑐 2 )2
2
5𝑛−1 𝑚2
5) (
2𝑚−2
0
)
Lesson 7-3 Scientific Notation
Express each number in scientific notation
1) 1,400,322
2) 0.004500
Express each number in standard form
3) 5.3 × 103
4) 4.7 × 10−6
Evaluate. Express the results in both scientific notation and standard form.
5) (5.23 × 10−7 )(8.2 × 105 )
3.344×106
6)
4.2×10−3
Lesson 7-4 Intro to Polynomials
State whether each expression is a polynomial. If so, identify it as a monomial, a binomial, or a trinomial.
5
2) 0
1) 5𝑥 2 𝑦 + 3𝑥𝑦 − 7
3) 𝑘 − 𝑘 2 𝑦
Find the degree of each polynomial.
4) 𝑎 + 5𝑐
5) 14𝑎𝑏𝑐𝑑 − 6𝑑 3
Arrange the terms of each polynomials in standard form.
6) 2𝑥 2 − 3𝑥 + 4𝑥 3 − 𝑥 5
7) 𝑥 8 + 2𝑥 2 − 𝑥 6 + 1
Lesson 7-5 Adding and Subtracting Polynomials
Find each sum or difference.
1) (3𝑎2 + 5) + (4𝑎2 − 1)
2) (4𝑑 + 3𝑒 − 8𝑓) − (−3𝑑 + 10𝑒 − 5𝑟 + 6)
3) (−7𝑐 2 − 2𝑐 − 5) + (9𝑐 − 6) + (16𝑐 2 + 3) + (−9𝑐 2 − 7 + 7)
Lesson 7-6 Multiplying a Polynomial by a Monomial
Find each product.
1) −3(8𝑥 + 5)
2) 7𝑥𝑦(5𝑥 2 − 𝑦 2 )
3) 4𝑚2 (9𝑚2 𝑛 + 𝑚𝑛 − 5𝑛2 )
Simplify each expression.
4) −3𝑎(2𝑎 − 12) + 5𝑎
5) −2𝑥(𝑥 + 3) + 3(𝑥 + 3)
Solve each equation.
6) −6(11 − 2𝑥) = 7(−2 − 2𝑥)
7) 𝑥(𝑥 − 3) + 4𝑥 − 3 = 8𝑥 + 𝑥(3 + 𝑥)
8) −3(𝑥 + 5) + 𝑥(𝑥 − 1) = 𝑥(𝑥 + 2) − 3
Lesson 7-7 Multiplying Polynomials
Find each product.
1) (𝑑 + 2)(𝑑 + 5)
2) (2𝑥 − 5)(𝑥 + 6)
3) (−𝑛 + 2)(−2𝑛2 + 𝑛 − 1)
Lesson 7-8 Special Products
Find each product.
1) (𝑡 + 7)2
4) (𝑥 2 + 𝑥 + 1)(𝑥 2 − 𝑥 − 1)
2) (𝑤 − 12)(𝑤 + 12)
3) (𝑞 − 4ℎ)2
Lesson 8-1 Monomials and Factoring
Factor each monomial completely.
1) 240𝑚𝑛
2) −231𝑥𝑦 2 𝑧
Find the GCF of each set of monomials.
3) 4𝑥𝑦, −6𝑥
4) −14𝑥𝑦, −12𝑦, −20𝑥
Lesson 8-2 Using the Distributive Property
Use the Distributive Property to factor each polynomial.
1) 10𝑎2 + 40𝑎
2) 2𝑚3 𝑛2 − 16𝑚𝑛2 + 8𝑚𝑛
3) 2𝑎𝑥 + 6𝑥𝑐 + 𝑏𝑎 + 3𝑏𝑐
4) 2𝑒 2 𝑔 + 2𝑓𝑔 − 4𝑒 2 ℎ − 4𝑓ℎ
Solve each equation. Check your solutions.
5) 𝑎(𝑎 − 9) = 0
7) 10𝑥 2 − 20𝑥 = 0
Lesson 8-3 Quadratic Equations: 𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎
Factor each trinomial.
1) 𝑥 2 − 9𝑥 + 14
3) 𝑎2 − 9𝑎 − 36
Solve each equation. Check your solution.
5) 𝑎2 + 3𝑎 − 4 = 0
7) 𝑥 2 − 57 = 16𝑥
6) (2𝑦 + 6)(𝑦 − 1) = 0
8) 15𝑎2 = 60𝑎
2) 𝑠 2 + 15𝑠 + 36
4) 𝑘 2 − 27𝑘 − 90
6) 𝑛2 − 9𝑛 = −18
8) −20𝑦 + 19 = −𝑦 2
Lesson 8-4 Quadratic Equations: 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 = 𝟎
Factor each trinomial, if possible. If the trinomial cannot be factored using integers, write prime.
1) 4𝑎2 + 4𝑎 − 63
2) 5𝑥 2 − 17𝑥 + 14
3) 2𝑛2 − 11𝑛 + 13
4) 10𝑥 2 − 20𝑥𝑦 + 10𝑦 2
Solve each equation. Check your solutions.
5) 8𝑡 2 + 32𝑡 + 24 = 0
6) 4𝑥 2 − 4𝑥 − 4 = 4
Lesson 8-5 Quadratic Equations: Differences of Squares
Factor each polynomial, if possible. If the polynomial cannot be factored, write prime.
1) 𝑥 2 − 9
2) 75𝑟 2 − 48
Solve each equation by factoring. Check your solutions.
3) 4𝑥 2 = 16
4) 9𝑛2 − 4 = 0
Lesson 9-1 Graphing Quadratic Functions
Use a table of values to graph each function. State the domain and range.
1) 𝑦 = 𝑥 2 + 6𝑥 + 8
2) 𝑦 = −𝑥 2 + 3𝑥
X
Y
y-intercept: _______________
Domain: _________________
Range: __________________
X
Y
y-intercept: _______________
Domain: _________________
Range: __________________
Find the vertex, the equation of the axis of symmetry, and the y-intercept.
3) 𝑦 = −𝑥 2 + 2𝑥 − 3
4) 𝑦 = 3𝑥 2 + 6𝑥 + 3
Consider each equation.
a. Determine whether the function has maximum or minimum.
b. State the maximum or minimum value.
c. Write the domain and range of the function.
5) 𝑦 = 4𝑥 2 − 1
6) 𝑦 = −𝑥 2 − 1
Lesson 9-2 Solving Quadratic Equations by Graphing
Solve each equation by graphing.
1) 𝑎2 − 25 = 0
3) 𝑏 2 − 18𝑏 + 81 = 0
2) 𝑥 2 + 3𝑥 + 27 = 0
4) – 𝑦 2 − 3𝑦 + 10 = 0
Lesson 9-5 Solving Quadratic Equations by Using the Quadratic Formula
Solve each equation by using the Quadratic Formula. Round to the nearest tenth if necessary.
1) 𝑐 2 + 6 = −5𝑐
2) 2𝑡 2 − 𝑡 − 15 = 0
3) 𝑡 2 + 16 = 0
4) 3𝑘 2 + 2 = −8𝑘
State the value of the discriminant for each equation. Then determine the number of real solutions of the
equation.
5) 3𝑓 2 + 2𝑓 = 6
6) 3𝑤 2 − 2𝑤 + 8 = 0
7) 4𝑟 2 − 12𝑟 = −9