Review for Grade 9 Math Exam - Unit 6 - Linear Equations and Inequalities
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1 Review for Grade 9 Math Exam - Unit 6 - Linear Equations and Inequalities Name: Date: Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Solve: a b. 9 c. 2 d Solve: a b. 3 c. 3 d Solve: a. 1.2 b. 0.4 c. 5.7 d Solve: a. 39 b. 2 c. 63 d Write an equation for this statement: A number divided by 2, plus 5, is 8. a. b. c. d. 6. Solve: a. 7 3 b. 6 c. 1 d A number times 5, minus 6, is 8. Write an equation to determine the number. a. b. c. d. 8. Solve: a. x = 3 b. c. d. x = 3 9. Solve: a. q = b. q = 7 24 c. q = 7 24 d. q = 3 3 7
2 10. Which of these graphs is a solution of? i) ii) t iii) t iv) t t a. Graph ii b. Graph iii c. Graph iv d. Graph i 11. Which of these graphs is a solution of? i) ii) c iii) c iv) c c a. Graph i b. Graph ii c. Graph iv d. Graph iii 12. Which of these graphs represent the solution of the inequality? i) ii) q iii) q iv) q q a. Graph ii b. Graph iv c. Graph iii d. Graph i
3 13. Solve: a. b. c. d. 14. Solve: a. b. c. d. 15. An equipment rental company charges a flat rate of $25, plus $13 per day for insurance. Kyle has $121. Write an inequality to represent the number of days, d, for which he can rent equipment. a. c. b. d. Short Answer 16. Here is a student s solution for this question: Solve: Identify any errors in the solution. 17. A student solved this equation: 4(3w - 6) = 3-6w 12w - 6 = -3w 12w = -3w w = -3w w - (-3w) = -3w (-3w) 15w = 6 w = Identify any errors the student made, and then solve the original equation above.
4 18. Solve: 19. Car Rental Company A charges $29 a week, plus $13 per kilometre driven. Car Rental Company B charges $85 a week, plus $6 per kilometre driven. Determine the distance you must drive for the two rental costs to be the same. Model the problem with an equation. 20. Solve: 21. Solve and graph:
5 22. A games room charges a $13 entrance fee, plus $2.35 per hour of play time. Anne-Marie has $ For how long can she play in the games room? a) Choose a variable and write an inequality for this problem. b) Solve the inequality. 23. The cost to rent a banquet hall is $500, plus $35 per person. A company s social committee has $4700 to put towards renting a banquet hall. How many people could attend the function if they rented the banquet hall? a) Choose a variable and write an inequality to solve the problem. b) Solve the inequality. Problem 24. Solve: Show your work. 25. Solve: Show your work.
6 26. A cell phone company offers two different plans. Plan A: Monthly fee of $28, plus $0.38 per minute Plan B: Monthly fee of $22, plus $0.46 per minute a) Write an equation to determine the time in minutes that results in the same monthly cost for both plans. b) Solve the equation. c) Verify the solution. 27. Solve: Show your work. 28. Company A charges $17, plus $11 per day to rent a piece of equipment. Company B charges $33, plus $9 per day to rent the same piece of equipment. a) How many days must the piece of equipment be rented for the cost to be the same at both companies? b) How many days must the piece of equipment be rented for Company B to be less expensive?
7 Review for Grade 9 Math Exam - Unit 6 - Linear Equations and Inequalities Answer Section MULTIPLE CHOICE 1. ANS: D PTS: 1 DIF: Easy REF: 6.1 Solving Equations by Using Inverse Operations LOC: 9.PR3 TOP: Patterns and Relations (Variables and Equations) 2. ANS: B PTS: 1 DIF: Easy REF: 6.1 Solving Equations by Using Inverse Operations LOC: 9.PR3 TOP: Patterns and Relations (Variables and Equations) 3. ANS: D PTS: 1 DIF: Easy REF: 6.1 Solving Equations by Using Inverse Operations LOC: 9.PR3 TOP: Patterns and Relations (Variables and Equations) 4. ANS: C PTS: 1 DIF: Easy REF: 6.1 Solving Equations by Using Inverse Operations LOC: 9.PR3 TOP: Patterns and Relations (Variables and Equations) 5. ANS: D PTS: 1 DIF: Moderate REF: 6.1 Solving Equations by Using Inverse Operations LOC: 9.PR3 TOP: Patterns and Relations (Variables and Equations) KEY: Conceptual Understanding 6. ANS: C PTS: 1 DIF: Moderate REF: 6.1 Solving Equations by Using Inverse Operations LOC: 9.PR3 TOP: Patterns and Relations (Variables and Equations) 7. ANS: B PTS: 1 DIF: Easy REF: 6.2 Solving Equations by Using Balance Strategies LOC: 9.PR3 TOP: Patterns and Relations (Variables and Equations) KEY: Conceptual Understanding Procedural Knowledge 8. ANS: D PTS: 1 DIF: Moderate REF: 6.2 Solving Equations by Using Balance Strategies LOC: 9.PR3 TOP: Patterns and Relations (Variables and Equations) 9. ANS: D PTS: 1 DIF: Difficult REF: 6.2 Solving Equations by Using Balance Strategies LOC: 9.PR3 TOP: Patterns and Relations (Variables and Equations) 10. ANS: C PTS: 1 DIF: Easy REF: 6.3 Introduction to Linear Inequalities LOC: 9.PR4 TOP: Patterns and Relations (Variables and Equations) KEY: Conceptual Understanding 11. ANS: B PTS: 1 DIF: Easy REF: 6.3 Introduction to Linear Inequalities LOC: 9.PR4 TOP: Patterns and Relations (Variables and Equations) 12. ANS: C PTS: 1 DIF: Easy REF: 6.4 Solving Linear Inequalities by Using Addition and Subtraction 13. ANS: A PTS: 1 DIF: Moderate REF: 6.4 Solving Linear Inequalities by Using Addition and Subtraction
8 14. ANS: C PTS: 1 DIF: Easy REF: 6.5 Solving Linear Inequalities by Using Multiplication and Division 15. ANS: C PTS: 1 DIF: Moderate REF: 6.5 Solving Linear Inequalities by Using Multiplication and Division SHORT ANSWER 16. ANS: Error: If the student is going to divide by 3 first, each term must be divided by 3. Alternatively, the student could subtract 5 from each side first, then divide each side by 3. PTS: 1 DIF: Moderate REF: 6.1 Solving Equations by Using Inverse Operations Communication 17. ANS: Errors: The student forgot to multiply by 6 when using the distributive property. 3-6w is not equal to -3w. Correct solution: 4(3w - 6) = 3-6w 12w - 24 = 3-6w 12w = 3-6w w = -6w w - (-6w) = -6w (-6w) 18w = 27 w = or 1 or 1 or 1.5 PTS: 1 DIF: Moderate REF: 6.2 Solving Equations by Using Balance Strategies Communication \
9 18. ANS: x = PTS: 1 DIF: Difficult REF: 6.2 Solving Equations by Using Balance Strategies 19. ANS: Let d represent the distance driven. PTS: 1 DIF: Difficult REF: 6.2 Solving Equations by Using Balance Strategies 20. ANS: PTS: 1 DIF: Moderate REF: 6.4 Solving Linear Inequalities by Using Addition and Subtraction 21. ANS: PTS: 1 DIF: Easy REF: 6.5 Solving Linear Inequalities by Using Multiplication and Division 22. ANS: a) Let h represent the number of hours of play time. b) h 7 PTS: 1 DIF: Moderate REF: 6.5 Solving Linear Inequalities by Using Multiplication and Division 23. ANS: a) Let p represent the number of people. b) PTS: 1 DIF: Moderate REF: 6.5 Solving Linear Inequalities by Using Multiplication and Division
10 PROBLEM 24. ANS: PTS: 1 DIF: Difficult REF: 6.1 Solving Equations by Using Inverse Operations 25. ANS: So, p =, or PTS: 1 DIF: Difficult REF: 6.2 Solving Equations by Using Balance Strategies
11 26. ANS: a) Let t represent the number of minutes. b) The monthly costs for both plans are the same at 75 min. c) Verify: Substitute into the original equation. Left side Right side Since the left side equals the right side, is the correct solution. PTS: 1 DIF: Difficult REF: 6.2 Solving Equations by Using Balance Strategies KEY: Problem-Solving Skills Communication 27. ANS: Multiply each side of the inequality by 12. PTS: 1 DIF: Difficult REF: 6.4 Solving Linear Inequalities by Using Addition and Subtraction
12 28. ANS: a) Let d represent the number of days to rent the piece of equipment. The piece of equipment must be rented for 8 days for the cost to be the same at both companies. b) Let d represent the number of days to rent the piece of equipment. The piece of equipment must be rented for 9 or more days for Company B to be less expensive. PTS: 1 DIF: Difficult REF: 6.5 Solving Linear Inequalities by Using Multiplication and Division KEY: Problem-Solving Skills Communication
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