![Name: ______________________ ID: A
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23. Write 704 065 using powers of 10.
.
24. Evaluate: 4
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− [6 ÷ (−2)]
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25. Simplify, then evaluate.
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7
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6
.
26. Simplify, then evaluate.
2
2
8
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Á
Á
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Á
Á
Á
ˆ
¯
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3
.
27. State which operation you would do first to evaluate (6)
0
+ [8 ÷ (−2)]
2
− 5.
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Math_9_Chapter_2_Practice_Test.pdf
- 1. Name: ______________________ Class: _________________ Date: _________ ID: A 1 Unit Two Practice Test: Powers and Exponent Laws Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Write the base of −(−6) 5 . a. 6 b. −6 c. −6 × 5 d. 5 ____ 2. Evaluate: 4 6 a. 1296 b. 4096 c. 10 d. 24 ____ 3. Write one billion as a power of 10. a. 109 b. 108 c. 1010 d. 108 ____ 4. Evaluate: (−15) 0 a. –1 b. 1 c. 0 d. –15 ____ 5. Evaluate: −(10 0 ) 7 a. −7 b. 1 c. 7 d. −1 ____ 6. State which operation you would do first to evaluate 8 + 9 × 6 2 − 5. a. Square 6 c. Subtract 5 from 6 b. Add 8 and 9 d. Multiply 9 and 6 ____ 7. Evaluate: 5 3 − −6 ( ) 3 a. 33 b. –91 c. 341 d. –3 ____ 8. Evaluate: (2 + 3) 2 − (3 − 5) 3 a. 17 b. –85 c. 16 d. 33 ____ 9. Write the product of 5 2 × 5 4 as a single power. a. 10 6 b. 5 6 c. 25 6 d. 5 8
- 2. Name: ______________________ ID: A 2 ____ 10. Write the quotient of 6 8 6 4 as a single power. a. 6 4 b. 2 c. 6 2 d. 6 12 ____ 11. Express −5 ( ) 6 × −5 ( ) 6 −5 ( ) 4 as a single power. a. (−5) 9 b. (−5) 8 c. (−5) 32 d. (−5) 3 ____ 12. Write −4 ( ) × −5 ( ) È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ 5 as a product of powers. a. −4 ( ) 5 + −5 ( ) 5 c. −4 ( ) 5 × −5 ( ) 5 b. 4 5 × 5 5 d. 5 −4 ( ) + 5 −5 ( ) ____ 13. Write 5 3 Ê Ë Á Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ ˜ 3 as a quotient of powers. a. 5 3 − 3 3 b. 2 3 c. 5 3 3 1 d. 5 3 3 3 ____ 14. Evaluate: −4 ( ) 0 È Î Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ 5 a. 5 b. −5 c. 1 d. −1 ____ 15. Which answer is negative? i) (−7) 10 ii) −(7) 10 iii) −(−7) 10 a. i only b. i and iii c. i and ii d. ii and iii ____ 16. Evaluate: 107 a. 100 000 000 b. 10 000 000 c. 1 000 000 d. 70
- 3. Name: ______________________ ID: A 3 ____ 17. Which is the correct value of 2 2 + 3 × 5 − 3? i) 14 ii) 10 iii) 16 iv) 32 a. ii b. iii c. i d. iv ____ 18. Evaluate: −2 ( ) 4 × −2 ( ) 2 ÷ −2 ( ) 0 a. –32 b. 64 c. 256 d. –64 ____ 19. Evaluate: 10 4 × 10 3 + 10 5 a. 1 000 000 000 000 c. 120 b. 10 100 000 d. 1 000 000 100 000 ____ 20. Write −7 ( ) × 2 È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ 5 as a product of powers. a. −7 ( ) 5 × 2 5 b. −7 ( ) 5 + 2 5 c. −5 ( ) 5 d. 5 −7 ( ) × 2 ____ 21. Which expressions have positive values? i) −7 ( ) 6 È Î Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ 7 ii) − −7 ( ) 6 È Î Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ 7 iii) − 7 6 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 7 iv) − − −7 ( ) 6 È Î Í Í Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ ˙ ˙ 7 a. ii and iv b. i and iv c. i and ii d. ii and iii Short Answer 22. Write the base and the exponent of this power: (−8) 4 .
- 4. Name: ______________________ ID: A 4 23. Write 704 065 using powers of 10. . 24. Evaluate: 4 2 − [6 ÷ (−2)] 3 . 25. Simplify, then evaluate. −2 ( ) 5 × −2 ( ) 7 ÷ −2 ( ) 6 . 26. Simplify, then evaluate. 2 2 8 0 Ê Ë Á Á Á Á Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ 3 . 27. State which operation you would do first to evaluate (6) 0 + [8 ÷ (−2)] 2 − 5. .
- 5. Name: ______________________ ID: A 5 28. Insert brackets to make each statement true. a) 3 2 + 4 × 5 − 2 2 = 13 b) 3 2 + 4 × 5 − 2 2 = 61 . 29. Simplify, then evaluate. −2 ( ) 4 × −2 ( ) 2 −2 ( ) 4 × −2 ( ) 0 . 30. Write 11 × −12 ( ) × 13 È Î Í Í Í Í ˘ ˚ ˙ ˙ ˙ ˙ 3 as a product of powers. . 31. Simplify, then evaluate. 2 4 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 3 × 2 2 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 4 2 2 × 2 6 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 .
- 6. Name: ______________________ ID: A 6 32. Simplify, then evaluate. 4 9 ÷ 4 6 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 − 2 8 ÷ 2 6 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 . Problem 33. Evaluate: 5(3) 3 − 3(−5) 3 Show your steps. . 34. One estimate shows that the number of people without access to safe drinking water is about one billion. How much water is required if each person who does not have access to safe drinking water is given 10 L of safe drinking water? Give your answer in standard form and using powers of 10. .
- 7. Name: ______________________ ID: A 7 35. Evaluate: (10) 2 − (4) 2 (6) 2 − 2(2) 2 Show your calculations. . 36. Identify, then correct, any errors in the work shown. 3 3 × 3 4 ÷ 3 6 = 3 3×4÷6 = 3 2 = 6 .
- 8. Name: ______________________ ID: A 8 37. Identify, then correct, any errors in the work shown. 32 × 33 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 2 = 32×3 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 2 = 36 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 2 = 36+2 = 38 = 6561 . 38. Where possible, replace with a “+” or “−” sign to make each product positive. a) −( 8) 11 b) (−8) 12 c) −( 8) 12 d) (−8) 11 Can all products be made positive? Explain. .
- 9. Name: ______________________ ID: A 9 39. These are two samples of student work. Are they correct? Explain. Student A: 3 3 × 3 4 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 = 3 12 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 = 3 14 Student B: 3 3 × 3 4 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 = 3 7 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 = 3 14 . 40. Simplify, then evaluate. Show your work. 102 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 4 × 53 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 4 54 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 2 × 102 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 5 × 105 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 3 × 24 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 3 22 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 4 × 102 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 2 .
- 10. ID: A 1 Unit Two Practice Test: Powers and Exponent Laws Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Easy REF: 2.1 What Is a Power? LOC: 9.N1 TOP: Number KEY: Conceptual Understanding 2. ANS: B PTS: 1 DIF: Moderate REF: 2.1 What Is a Power? LOC: 9.N1 TOP: Number KEY: Procedural Knowledge 3. ANS: A PTS: 1 DIF: Easy REF: 2.2 Powers of Ten and the Zero Exponent LOC: 9.N1 TOP: Number KEY: Procedural Knowledge 4. ANS: B PTS: 1 DIF: Easy REF: 2.2 Powers of Ten and the Zero Exponent LOC: 9.N1 TOP: Number KEY: Procedural Knowledge 5. ANS: D PTS: 1 DIF: Moderate REF: 2.2 Powers of Ten and the Zero Exponent LOC: 9.N1 TOP: Number KEY: Procedural Knowledge 6. ANS: A PTS: 1 DIF: Easy REF: 2.3 Order of Operations with Powers LOC: 9.N1 TOP: Number KEY: Conceptual Understanding 7. ANS: C PTS: 1 DIF: Moderate REF: 2.3 Order of Operations with Powers LOC: 9.N1 TOP: Number KEY: Procedural Knowledge 8. ANS: D PTS: 1 DIF: Moderate REF: 2.3 Order of Operations with Powers LOC: 9.N1 TOP: Number KEY: Procedural Knowledge 9. ANS: B PTS: 1 DIF: Easy REF: 2.4 Exponent Laws I LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 10. ANS: A PTS: 1 DIF: Easy REF: 2.4 Exponent Laws I LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 11. ANS: B PTS: 1 DIF: Moderate REF: 2.4 Exponent Laws I LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 12. ANS: C PTS: 1 DIF: Easy REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 13. ANS: D PTS: 1 DIF: Easy REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 14. ANS: C PTS: 1 DIF: Moderate REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 15. ANS: D PTS: 1 DIF: Moderate REF: 2.1 What Is a Power? LOC: 9.N1 TOP: Number KEY: Conceptual Understanding 16. ANS: B PTS: 1 DIF: Easy REF: 2.2 Powers of Ten and the Zero Exponent LOC: 9.N1 TOP: Number KEY: Procedural Knowledge 17. ANS: B PTS: 1 DIF: Moderate REF: 2.3 Order of Operations with Powers LOC: 9.N1 TOP: Number KEY: Procedural Knowledge
- 11. ID: A 2 18. ANS: B PTS: 1 DIF: Moderate REF: 2.4 Exponent Laws I LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 19. ANS: B PTS: 1 DIF: Moderate REF: 2.4 Exponent Laws I LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 20. ANS: A PTS: 1 DIF: Easy REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 21. ANS: B PTS: 1 DIF: Moderate REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Conceptual Understanding SHORT ANSWER 22. ANS: Base: −8 Exponent: 4 PTS: 1 DIF: Easy REF: 2.1 What Is a Power? LOC: 9.N1 TOP: Number KEY: Conceptual Understanding 23. ANS: 704 065 = (7 × 10 5 ) + (4 × 10 3 ) + (6 × 10 1 ) + (5 × 10 0 ) PTS: 1 DIF: Moderate REF: 2.2 Powers of Ten and the Zero Exponent LOC: 9.N1 TOP: Number KEY: Procedural Knowledge 24. ANS: 43 PTS: 1 DIF: Moderate REF: 2.3 Order of Operations with Powers LOC: 9.N1 TOP: Number KEY: Procedural Knowledge 25. ANS: −2 ( ) 6 = 64 PTS: 1 DIF: Moderate REF: 2.4 Exponent Laws I LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 26. ANS: 2 2 8 0 Ê Ë Á Á Á Á Á Á Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ 3 = 2 2 1 Ê Ë Á Á Á Á Á Á Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ ˜ 3 = 2 6 = 64 PTS: 1 DIF: Moderate REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 27. ANS: Divide 8 by −2 PTS: 1 DIF: Easy REF: 2.3 Order of Operations with Powers LOC: 9.N1 TOP: Number KEY: Conceptual Understanding
- 12. ID: A 3 28. ANS: a) 3 2 + 4 × (5 − 2 2 ) = 13 b) (3 2 + 4) × 5 − 2 2 = 61 PTS: 1 DIF: Moderate REF: 2.3 Order of Operations with Powers LOC: 9.N1 TOP: Number KEY: Problem-Solving Skills 29. ANS: −2 ( ) 2 = 4 PTS: 1 DIF: Moderate REF: 2.4 Exponent Laws I LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 30. ANS: 11 3 × −12 ( ) 3 × 13 3 PTS: 1 DIF: Easy REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 31. ANS: 2 4 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 3 × 2 2 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 4 2 2 × 2 6 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 = 2 20 2 16 = 2 4 = 16 PTS: 1 DIF: Moderate REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Procedural Knowledge 32. ANS: 4 9 ÷ 4 6 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 − 2 8 ÷ 2 6 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 = 4 3 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 − 2 2 Ê Ë Á Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ ˜ 2 = 4 6 − 2 4 = 4080 PTS: 1 DIF: Moderate REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Procedural Knowledge PROBLEM 33. ANS: 5(3) 3 − 3(−5) 3 = 5 × 27 − 3 × (−125) = 135 + 375 = 510 PTS: 1 DIF: Difficult REF: 2.1 What Is a Power? LOC: 9.N1 TOP: Number KEY: Problem-Solving Skills
- 13. ID: A 4 34. ANS: Each person is to be given 10 L of safe drinking water. 1 billion ×10 L = 1 000 000 000 × 10 = 10 000 000 000 = 1 × 10 10 L 1 × 10 10 L = 10 000 000 000 L The amount of water required is about 1 × 10 10 L, or 10 000 000 000 L. PTS: 1 DIF: Moderate REF: 2.2 Powers of Ten and the Zero Exponent LOC: 9.N1 TOP: Number KEY: Problem-Solving Skills | Communication 35. ANS: (10) 2 − (4) 2 (6) 2 − 2(2) 2 = 100 − 16 36 − 8 = 84 28 = 3 PTS: 1 DIF: Moderate REF: 2.3 Order of Operations with Powers LOC: 9.N1 TOP: Number KEY: Problem-Solving Skills | Communication 36. ANS: Errors: The exponents should be added and subtracted, not multiplied and divided. The result of 3 2 is 3 × 3, not 3 × 2. Correction: 3 3 × 3 4 ÷ 3 6 = 3 3+4−6 = 3 1 = 3 PTS: 1 DIF: Difficult REF: 2.4 Exponent Laws I LOC: 9.N2 TOP: Number KEY: Problem-Solving Skills | Communication
- 14. ID: A 5 37. ANS: Errors: In line 1, the exponents of 3 should be added instead of multiplied. In line 3, the exponents of 3 should be multiplied instead of added. Correction: 32 × 33 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 2 = 32+3 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 2 = 35 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 2 = 35×2 = 310 = 59 049 PTS: 1 DIF: Moderate REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Problem-Solving Skills | Communication 38. ANS: a) Replace with a “−” sign. b) Replace with a “+” sign. c) −( 8) 12 is always negative. d) Replace with a “−” sign. Not all products can be made positive. In part c, there is an even number of factors in the power ( 8) 12 . ( 8) 12 is always positive, which means −( 8) 12 is always negative. PTS: 1 DIF: Difficult REF: 2.1 What Is a Power? LOC: 9.N1 TOP: Number KEY: Problem-Solving Skills | Communication 39. ANS: Both final answers are correct but the method Student A used is wrong. When two powers of 3, 33 and 34, are multiplied, the exponents 3 and 4 should be added. When a power of 3, 312, is raised to the exponent 2, the exponents 12 and 2 should be multiplied. PTS: 1 DIF: Moderate REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Communication
- 15. ID: A 6 40. ANS: 102 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 4 × 53 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 4 54 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 2 × 102 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 5 × 105 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 3 × 24 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 3 22 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 4 × 102 Ê Ë Á Á Á Á ˆ ¯ ˜ ˜ ˜ ˜ 6 = 108 × 512 58 × 1010 × 1015 × 212 28 × 1012 = 10 (8+15) × 512 × 212 10 (10+12) × 58 × 28 = 1023 × 512 × 212 1022 × 58 × 28 = 101 × 54 × 24 = 10 × 625 × 16 = 100 000 PTS: 1 DIF: Difficult REF: 2.5 Exponent Laws II LOC: 9.N2 TOP: Number KEY: Problem-Solving Skills