Chapter 3 Algebra (pearson)

Transcription

1 Class: Date: Chapter 3 Algebra (pearson) What inequality represents the verbal expression? 1. 8 less than a number n is less than 13 a. 8 n < 13 c. n 8 < 13 b < n d. 13 < 8 n Which number is a solution of the inequality? x 14 1 a. 9 b. 3 8 c. 2 d x 4 a. What is the graph of the inequality? b. c. d. What inequality represents the graph? 4. a. x > 1 b. x < 1 c. x < 1 d. x 1 What inequality describes the situation? 5. Let t = the amount Thomas earned. Thomas earned $97 or more. a. t 97 b. t > 97 c. t 97 d. t < 97 1

2 What are the solutions of the inequality? Graph the solutions. 6. q 1 2 > 1 3 a. q > 1 6 b. q > 1 c. q > 5 6 d. q < 0 What are the solutions of the inequality? Graph the solutions. 7. x a. x 14 b. x 14 c. x 6 d. x 10 2

3 8. q > 1 2 a. q > 1 6 b. q > 1 c. q > 5 6 d. q < 0 9. Your class hopes to collect at least 350 cans of food for the annual food drive. There were 125 cans donated the first week and 146 more the second week. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass your goal. How many cans are needed to meet or surpass your goal? a c > 350; c > 79 c c 350; c 621 b c; c 621 d c 350; c 79 What are the solutions of the inequality? Graph the solutions. 10. x 6 2 a. x 12 b. x 8 c. x 12 d. x 8 3

4 11. The French Club is sponsoring a bake sale. If their goal is to raise at least $130, how many pastries must they sell at $2.50 each in order to meet that goal? Write and solve an inequality. a. 2.50p 130; p 325 c. 2.50p 130; p b. 2.50p 130; p 52 d. 130p 2.50; p x 8 What are the solutions of the inequality? Graph the solutions. a. x 10 b. x 4 c. x 4 d. x > 10 What are the solutions of the inequality? Check the solutions x 10 < 7 8 a. x > b. x < c. x < d. x < The width of a rectangle is 33 centimeters. The perimeter is at least 776 centimeters. Write and solve an inequality to find the possible lengths of the rectangle. a ; 743 b. 2(33) ; 355 c. 2(33) ; 355 d ; 743 Which is a solution of the inequality? 15. q + 2 2(q 6) > 0 a. 16 b. 19 c. 12 d. 14 What are the solutions of the inequality? a 5(a + 9) a. a 12 b. a 15 c. a 12 d. a 18 4

5 17. 7m 14 24m + 3 a. m b. m c. m d. m 1 What are the solutions of the inequality? ( x 4) 4x 24 a. x 8 c. all real numbers b. x 20 d. no solution What compound inequality represents the phrase? Graph the solutions. 19. all real numbers that are greater than 4 and less than 4 a. 4 < x < 4 b. 4 x 4 c. 4 < x 4 d. 4 < x < 4 What are the solutions of the compound inequality? Graph the solutions x 4 < 10 a. 3 x < 9 b. 1 x < 7 c. 0 x < 4 d. 1 x < 3 5

6 21. A student scored 84 and 88 on her first two quizzes. Write and solve a compound inequality to find the possible values for a third quiz score that would give her an average between 85 and 90, inclusive. a. 85 b. 84 c. 90 d n 90; 1 n n 3 90; 79 n n 3 85; 98 n n 3 90; 83 n 98 What are the solutions of the compound inequality? Graph the solutions x 6 < 16 or 12x + 8 > 4 a. x < or x > 1 3 b. x < 2 or x > 1 c. x < 2 or x > 1 3 d. x < 15 or x > 24 6

7 What are the solutions of the equation? Graph and check the solutions. 23. x + 7 = 6 a. x = 1 b. x = 1 or x = 1 c. x = 0 d. no solution n 1 = 13 a. n = 2 b. n = 2 or n = 2 c. n = 7 or n = 7 d. no solution 25. Starting from 1.6 miles away, a car drives towards a speed check point and then passes it. The car travels at a constant rate of 45 miles per hour. The distance of the car from the check point is given by d = t. At what times is the car 0.1 miles from the check point? a. 120 s and 12.8 s c. 136 s and 12.8 s b. 120 s and 136 s d and 128 s 7

8 26. 2 x = 14 a. x = b. x = or c. x = or d. no solution 27. d What are the solutions of the inequality? Graph the solution. a. d 9 b. d 9 or d 3 c. d 9 or d 3 d. d The optimal operating temperature of a given car engine is within 15 F of 230 F. Write an absolute value inequality for the range of acceptable temperatures and solve the inequality. a. x ; x 215 or x 245 c. x ; x 215 or x 245 b. x ; 215 x 245 d. x ; 215 x 245 8

9 Chapter 3 Algebra (pearson) Answer Section 1. ANS: C PTS: 1 DIF: L3 REF: 3-1 Inequalities and Their Graphs OBJ: To write, graph, and identify solutions of inequalities NAT: CC A.REI.3 TOP: 3-1 Problem 1 Writing Inequalities KEY: solution of an inequality 2. ANS: D PTS: 1 DIF: L3 REF: 3-1 Inequalities and Their Graphs OBJ: To write, graph, and identify solutions of inequalities NAT: CC A.REI.3 TOP: 3-1 Problem 2 Identifying Solutions by Evaluating KEY: solution of an inequality 3. ANS: A PTS: 1 DIF: L2 REF: 3-1 Inequalities and Their Graphs OBJ: To write, graph, and identify solutions of inequalities NAT: CC A.REI.3 TOP: 3-1 Problem 3 Graphing an Inequality KEY: solution of an inequality 4. ANS: B PTS: 1 DIF: L2 REF: 3-1 Inequalities and Their Graphs OBJ: To write, graph, and identify solutions of inequalities NAT: CC A.REI.3 TOP: 3-1 Problem 4 Writing an Inequality From a Graph KEY: solution of an inequality 5. ANS: C PTS: 1 DIF: L3 REF: 3-1 Inequalities and Their Graphs OBJ: To write, graph, and identify solutions of inequalities NAT: CC A.REI.3 TOP: 3-1 Problem 5 Writing Real-World Inequalities KEY: create inequalities in one variable solution of an inequality 6. ANS: C PTS: 1 DIF: L4 REF: 3-2 Solving Inequalities Using Addition or Subtraction OBJ: To use addition or subtraction to solve inequalities TOP: 3-2 Problem 1 Using the Addition Property of Inequality KEY: equivalent inequalities 7. ANS: B PTS: 1 DIF: L3 REF: 3-2 Solving Inequalities Using Addition or Subtraction OBJ: To use addition or subtraction to solve inequalities TOP: 3-2 Problem 3 Using the Subtraction Property of Inequality KEY: equivalent inequalities 8. ANS: A PTS: 1 DIF: L4 REF: 3-2 Solving Inequalities Using Addition or Subtraction OBJ: To use addition or subtraction to solve inequalities TOP: 3-2 Problem 3 Using the Subtraction Property of Inequality KEY: equivalent inequalities 9. ANS: D PTS: 1 DIF: L3 REF: 3-2 Solving Inequalities Using Addition or Subtraction OBJ: To use addition or subtraction to solve inequalities TOP: 3-2 Problem 4 Writing and Solving an Inequality KEY: equivalent inequalities 1

10 10. ANS: C PTS: 1 DIF: L3 REF: 3-3 Solving Inequalities Using Multiplication or Division OBJ: To use multiplication or division to solve inequalities NAT: CC N.Q.2 CC A.CED.1 CC A.REI.3 TOP: 3-3 Problem 1 Multiplying by a Positive Number 11. ANS: B PTS: 1 DIF: L3 REF: 3-3 Solving Inequalities Using Multiplication or Division OBJ: To use multiplication or division to solve inequalities NAT: CC N.Q.2 CC A.CED.1 CC A.REI.3 TOP: 3-3 Problem 3 Dividing by a Positive Number KEY: create inequalities in one variable problem solving 12. ANS: B PTS: 1 DIF: L3 REF: 3-3 Solving Inequalities Using Multiplication or Division OBJ: To use multiplication or division to solve inequalities NAT: CC N.Q.2 CC A.CED.1 CC A.REI.3 TOP: 3-3 Problem 4 Dividing by a Negative Number 13. ANS: A PTS: 1 DIF: L4 REF: 3-4 Solving Multi-Step Inequalities TOP: 3-4 Problem 1 Using More Than One Step 14. ANS: B PTS: 1 DIF: L3 REF: 3-4 Solving Multi-Step Inequalities TOP: 3-4 Problem 2 Writing and Solving a Multi-Step Inequality KEY: create inequalities in one variable problem solving 15. ANS: C PTS: 1 DIF: L3 REF: 3-4 Solving Multi-Step Inequalities TOP: 3-4 Problem 3 Using the Distributive Property 16. ANS: C PTS: 1 DIF: L3 REF: 3-4 Solving Multi-Step Inequalities TOP: 3-4 Problem 4 Solving an Inequality With Variables on Both Sides 17. ANS: D PTS: 1 DIF: L2 REF: 3-4 Solving Multi-Step Inequalities TOP: 3-4 Problem 4 Solving an Inequality With Variables on Both Sides 18. ANS: C PTS: 1 DIF: L3 REF: 3-4 Solving Multi-Step Inequalities TOP: 3-4 Problem 5 Inequalities With Special Solutions 19. ANS: D PTS: 1 DIF: L3 REF: 3-6 Compound Inequalities OBJ: To solve and graph inequalities containing the word and TOP: 3-6 Problem 1 Writing a Compound Inequality KEY: compound inequality create inequalities in one variable 20. ANS: B PTS: 1 DIF: L3 REF: 3-6 Compound Inequalities OBJ: To solve and graph inequalities containing the word and TOP: 3-6 Problem 2 Solving a Compound Inequality Involving And KEY: compound inequality 2

11 21. ANS: D PTS: 1 DIF: L3 REF: 3-6 Compound Inequalities OBJ: To solve and graph inequalities containing the word and TOP: 3-6 Problem 3 Writing and Solving a Compound Inequality KEY: compound inequality create inequalities in one variable problem solving 22. ANS: B PTS: 1 DIF: L3 REF: 3-6 Compound Inequalities OBJ: To solve and graph inequalities containing the word or TOP: 3-6 Problem 4 Solving a Compound Inequality Involving Or KEY: compound inequality 23. ANS: D PTS: 1 DIF: L3 NAT: CC A.SSE.1.b CC A.CED.1 TOP: 3-7 Problem 1 Solving an Absolute Value Equation KEY: absolute value 24. ANS: B PTS: 1 DIF: L3 NAT: CC A.SSE.1.b CC A.CED.1 TOP: 3-7 Problem 1 Solving an Absolute Value Equation KEY: absolute value 25. ANS: B PTS: 1 DIF: L3 NAT: CC A.SSE.1.b CC A.CED.1 TOP: 3-7 Problem 2 Solving an Absolute Value Equation KEY: create absolute-value inequalities absolute value problem solving 26. ANS: D PTS: 1 DIF: L3 NAT: CC A.SSE.1.b CC A.CED.1 TOP: 3-7 Problem 3 Solving an Absolute Value Equation With No Solution KEY: absolute value 27. ANS: B PTS: 1 DIF: L3 NAT: CC A.SSE.1.b CC A.CED.1 TOP: 3-7 Problem 4 Solving an Absolute Value Inequality Involving Greater Than or Equal To KEY: absolute value 28. ANS: D PTS: 1 DIF: L3 NAT: CC A.SSE.1.b CC A.CED.1 TOP: 3-7 Problem 5 Solving an Absolute Value Inequality Involving Less Than or Equal To KEY: create absolute-value inequalities absolute value problem solving 3