Algebra 1 Chapter 03 Review
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1 Name: Class: Date: ID: A Algebra 1 Chapter 0 Review Multiple Choice Identify the choice that best completes the statement or answers the question. Write the inequality in words. 1. n < 52 a. fifty-two less than three times n b. Three times n is less than fifty-two. c. Three times n is less than or equal to fifty-two. d. Three times n is greater than fifty-two. Graph the inequality. 2. k > 9 2 a. c. b. d.. x 5 a. b. c. d. 4. x a. b. c. d. 1
2 Name: ID: A Write an inequality for the graph. 5. a. x 8 b. x < 8 c. x > 8 d. x < 8 Write an inequality to model the situation. 6. A number exceeds 21. a. n 21 b. n 21 c. n > 21 d. n < 21 Solve the inequality. Then graph your solution. 7. q 1 2 > 1 a. q > 1 6 c. q > 5 6 b. q > 1 d. q < x 4 6 a. x 24 c. x 24 b. x 10 d. x x 8 a. x 4 c. x 4 b. x 6 d. x > 6 Solve the inequality q a. 15. q b. 16. q c. 15. q d. 16. q 2
3 Name: ID: A x a. x x 7 < 28 b. x c. x a. x > 7 b. x < 7 c. x > 21 5 d. x d. x < (b 8) > 12 a. b > 20 b. b > 6 c. b > 14 d. b < Jeanette wants to tile the floor of a room in her house. The square tiles measure 4 ft on each side. The room is 10 ft wide. a. Write an inequality to describe how many tiles are needed to make one row of tiles across the width of the room. b. Solve the inequality. c. How many tiles should Jeanette buy to form one row? a. 4 t 10; t 1 1 ; 1 c. 4 + t 10; t ; 10 b. 4 t 10; t 1 1 ; 1 1 d. 4 t 10; t 1 1 ; Alexandria wants to go hiking on Saturday. She will choose from several parks considering these conditions. She wants to hike for 2 hours. She wants to spend no more than 6 hours away from home. She can average 65 miles per hour to and from the park. Write and solve an inequality to find possible distances from Alexandria s home to a park that satisfies the conditions. a d b. 6 + d 65 6; d 16 miles c. 2 + d 65 2; d 92 miles d. 2 + d 65 6; d 260 miles 6; d 92 miles Write a compound inequality that represents each situation. Graph your solution. 16. On a road in the city of Rochester, the maximum speed is 50 miles per hour, and the minimum speed is 20 miles per hour. a. 20 > x > 50 c. 20 x 50 b. 20 < x < 50 d. 20 x 50
4 Name: ID: A Write a compound inequality that the graph could represent a. 2 x < 4 c. x 4 or x < 2 b. 4 < x 2 d. 4 x < 2 a. d > or d 1 c. d < or d 1 b. d < 1 or d d. 1 d < Write an inequality for the situation. 19. all real numbers at most 9.5 or at least 5.5 a. b 9.5 or b 5.5 c. b 9.5 or b 5.5 b. 9.5 b 5.5 d. b 9.5 or b 5.5 Solve the equation. If there is no solution, write no solution n 12 = 16 a. n = 14 or n = 14 c. no solution b. n = 26 or n = 0 d. n = h 7 = 28 a. no solution c. h = 7, h = 21 b. h = 21 d. h = 7, h = 21 Short Answer 22. Eduardo solved 4x > 120 by adding 4 to each side of the inequality. What mistake did he make? Essay 2. Suppose a classmate is having difficulty solving 4(x 7) > 6x x. Explain how to solve the inequality, showing all the necessary steps and identifying the properties you would use. 24. Three consecutive even numbers have a sum between 84 and 96. a. Write an inequality to find the three numbers. Let n represent the smallest even number. b. Solve the inequality. 25. Suppose you start with at least $52 in your savings account and deposit $27 each week. Write an inequality to describe how much money m you have after w weeks. If you do this for 11 weeks, will you have enough to buy a bicycle that costs $40? Show your work. 4
5 ID: A Algebra 1 Chapter 0 Review Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: L REF: -1 Inequalities and Their Graphs STA: CA A1 5.0 KEY: translating an inequality inequality 2. ANS: D PTS: 1 DIF: L2 REF: -1 Inequalities and Their Graphs STA: CA A1 5.0 TOP: -1 Example KEY: graphing inequality. ANS: B PTS: 1 DIF: L2 REF: -1 Inequalities and Their Graphs STA: CA A1 5.0 TOP: -1 Example KEY: graphing inequality 4. ANS: B PTS: 1 DIF: L2 REF: -1 Inequalities and Their Graphs STA: CA A1 5.0 TOP: -1 Example KEY: graphing inequality 5. ANS: C PTS: 1 DIF: L2 REF: -1 Inequalities and Their Graphs STA: CA A1 5.0 TOP: -1 Example 4 KEY: writing an inequality from a graph graphing 6. ANS: C PTS: 1 DIF: L2 REF: -1 Inequalities and Their Graphs STA: CA A1 5.0 KEY: modeling with inequalities translating an inequality 7. ANS: C PTS: 1 DIF: L REF: -2 Solving Inequalities Using Addition and Subtraction OBJ: -2.1 Using Addition to Solve Inequalities STA: CA A1 5.0 TOP: -2 Example 1 KEY: Addition Property of Inequality solving inequalities 8. ANS: C PTS: 1 DIF: L2 REF: - Solving Inequalities Using Multiplication and Division OBJ: -.1 Using Multiplication to Solve Inequalities STA: CA A1 5.0 TOP: - Example 1 KEY: Multiplication Property of Inequality for c > 0 solving inequalities 9. ANS: A PTS: 1 DIF: L2 REF: - Solving Inequalities Using Multiplication and Division OBJ: -.2 Using Division to Solve Inequalities STA: CA A1 5.0 TOP: - Example KEY: Division Property of Inequality solving inequalities 10. ANS: D PTS: 1 DIF: L REF: -2 Solving Inequalities Using Addition and Subtraction OBJ: -2.2 Using Subtraction to Solve Inequalities STA: CA A1 5.0 TOP: -2 Example KEY: Subtraction Property of Inequality solving inequalities like terms 11. ANS: A PTS: 1 DIF: L4 REF: -2 Solving Inequalities Using Addition and Subtraction OBJ: -2.2 Using Subtraction to Solve Inequalities STA: CA A1 5.0 TOP: -2 Example KEY: Subtraction Property of Inequality like terms solving inequalities 1
6 ID: A 12. ANS: A PTS: 1 DIF: L2 REF: -4 Solving Multi-Step Inequalities OBJ: -4.1 Solving Inequalities With Variables on One Side STA: CA A1 4.0 CA A1 5.0 TOP: -4 Example 1 KEY: modeling with inequalities multi-step inequality with variables on one side solving inequalities 1. ANS: C PTS: 1 DIF: L2 REF: -4 Solving Multi-Step Inequalities OBJ: -4.1 Solving Inequalities With Variables on One Side STA: CA A1 4.0 CA A1 5.0 TOP: -4 Example KEY: solving inequalities using the Distributive Property like terms solving inequalities 14. ANS: D PTS: 1 DIF: L4 REF: - Solving Inequalities Using Multiplication and Division OBJ: -.1 Using Multiplication to Solve Inequalities STA: CA A1 5.0 TOP: - Example 4 KEY: Multiplication Property of Inequality for c > 0 problem solving word problem solving inequalities multi-part question 15. ANS: C PTS: 1 DIF: L4 REF: -4 Solving Multi-Step Inequalities OBJ: -4.1 Solving Inequalities With Variables on One Side STA: CA A1 4.0 CA A1 5.0 TOP: -4 Example 2 KEY: solving inequalities problem solving word problem solving inequalities 16. ANS: C PTS: 1 DIF: L2 REF: -5 Compound Inequalities OBJ: -5.1 Solving Compound Inequalities Containing And STA: CA A1.0 TOP: -5 Example KEY: writing a compound inequality compound inequality solving inequalities 17. ANS: D PTS: 1 DIF: L REF: -5 Compound Inequalities OBJ: -5.1 Solving Compound Inequalities Containing And STA: CA A1.0 TOP: -5 Example 4 KEY: writing a compound inequality compound inequality 18. ANS: C PTS: 1 DIF: L REF: -5 Compound Inequalities OBJ: -5.2 Solving Compound Inequalities Joined by Or STA: CA A1.0 TOP: -5 Example 4 KEY: writing a compound inequality compound inequality 19. ANS: D PTS: 1 DIF: L2 REF: -5 Compound Inequalities OBJ: -5.2 Solving Compound Inequalities Joined by Or STA: CA A1.0 TOP: -4 Example 4 KEY: writing a compound inequality compound inequality translating an inequality 20. ANS: A PTS: 1 DIF: L REF: -6 Absolute Value Equations and Inequalities OBJ: -6.1 Solving Absolute Value Equations STA: CA A1.0 TOP: -6 Example 1 KEY: absolute value Addition Property of Equality 21. ANS: C PTS: 1 DIF: L REF: -6 Absolute Value Equations and Inequalities OBJ: -6.1 Solving Absolute Value Equations STA: CA A1.0 TOP: -6 Example 2 KEY: absolute value Division Property of Equality 2
7 ID: A SHORT ANSWER 22. ANS: He should have divided each side by 4. PTS: 1 DIF: L REF: - Solving Inequalities Using Multiplication and Division OBJ: -.2 Using Division to Solve Inequalities STA: CA A1 5.0 TOP: - Example KEY: Division Property of Inequality writing in math error analysis ESSAY 2. ANS: [4] 4(x 7) > 6x x 4x 28 > 6x x Use the Distributive Property 4x 28 > 14x + 2 Combine like terms. 4x 28 4x > 14x + 2 4x Subtraction Property of Inequality 28 > 10x + 2 Simplify > 10x Subtraction Property of Inequality 0 > 10x Simplify > 10x Division Property of Inequality 10 > x Simplify. [] one computational or property error [2] two computational or property errors [1] computational steps or properties missing PTS: 1 DIF: L REF: -4 Solving Multi-Step Inequalities OBJ: -4.2 Solving Inequalities With Variables on Both Sides STA: CA A1 4.0 CA A1 5.0 TOP: -4 Example 5 KEY: multi-step inequality extended response rubric-based question writing in math
8 ID: A 24. ANS: [4] a. 84 n + (n + 2) + (n + 4) 96 b. 84 n + n n n n n n n 0 [] one computational error [2] incorrect inequality OR two computational errors [1] one or more answers missing PTS: 1 DIF: L4 REF: -5 Compound Inequalities OBJ: -5.1 Solving Compound Inequalities Containing And STA: CA A1.0 TOP: -5 Example KEY: writing a compound inequality solving a compound inequality containing AND problem solving word problem extended response rubric-based question 25. ANS: [4] m w w = 11, so m (11) m m 49 yes; because there is at least $49 in your account [] one computational error or wrong conclusion [2] two computational errors or no work shown [1] no conclusion and one or more errors PTS: 1 DIF: L REF: -2 Solving Inequalities Using Addition and Subtraction OBJ: -2.2 Using Subtraction to Solve Inequalities STA: CA A1 5.0 KEY: translating an inequality modeling with inequalities problem solving word problem extended response rubric-based question 4
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