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Math 9 Fall 2014 Unit 1 Powers and Roots Practice Exam Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Write the quotient of B. 2 A. ____ as a single power. C. D. 2. Which square roots are correct to the nearest tenth? i) ii) iii) iv) v) A. i, iii ____ B. i, iii, v C. ii, iv, v D. i, ii, v C. i, ii, and iv D. iii and iv 3. Which power is positive? i) ii) iii) iv) A. i and iv B. i and ii ____ 4. State which operation you would do first to evaluate . A. Subtract 5 from 6 C. Add 8 and 9 B. Multiply 9 and 6 D. Square 6 ____ 5. Evaluate: A. 100 B. 1 000 000 001 000 ____ ____ ____ 6. Write A. B. C. 10 001 000 D. 10 000 000 000 as a product of powers. C. D. 7. Write as a power. A. 8 B. 8. Write A. C. D. as a power. B. C. D. ____ 9. A square has an area of 24.1 cm2. Determine the perimeter of the square, to the nearest tenth of a centimeter. A. 19.6 cm B. 4.9 cm C. 24.0 cm D. 6.1 cm ____ 10. Name the two whole numbers whose squares (areas) are closest to 52.5. A. 49, 64 B. 4, 9 C. 7, 8 D. 16, 25 ____ 11. Write A. ____ B. C. D. C. iii D. ii C. i and ii D. i and iv C. 35 741 in standard form. D. 35 740 12. Which number is the greatest? i) ii) 5645 iii) iv) 5780 A. iv ____ as a quotient of powers. B. i 13. Which expressions have positive values? i) ii) iii) iv) A. ii and iv B. ii and iii ____ 14. Write 1 000 000 as a power of 10. A. B. 105 C. D. 106 ____ 15. Write A. 35 746 B. 3574 ____ 16. List all the whole numbers between 63 and 101 that are perfect squares. A. 64, 81, 96 C. 64, 81, 100 B. 64, 81 D. 64, 72, 81, 100 ____ 17. Which fraction is a perfect square? i) ii) iii) iv) A. ii ____ 18. Use benchmarks to determine the value of A. ____ B. iii B. C. iv D. i . C. D. 19. The lengths of the two legs of a right triangle are 6.5 cm and 3.4 cm. Determine the length of the hypotenuse to 1 decimal place. A. 53.8 cm B. 7.3 cm C. 5.5 cm D. 3.1 cm Numeric Response 1. Determine the value of , to the nearest tenth. 2. The lengths of the two legs of a right triangle are 6.5 cm and 3.4 cm. Determine the length of the hypotenuse to 1 decimal place. 3. Evaluate: 4. Evaluate: 5. Correct the errors in the work below and then record the correct answer. 6. Express in the form . Place the value of n in the numerical response box. Short Answer 1. Use benchmarks to estimate 2. To estimate the value of to the nearest tenth. , determine the two whole number perfect squares closest to 159.5 and their square roots. 3. Write 50 986 using powers of 10. 4. Write as a product of powers. 5. Simplify, then evaluate. 6. A field measures 105 m by 104 m. a) Write an expression for the area of the field, using powers of 10. b) Write an expression for the perimeter of the field, using powers of 10. 7. Insert brackets to make each statement true. a) b) 8. Write the number of unit cubes in the large cube as a power. 9. Calculate the number whose square root is 10. Replace . with a fraction to make this statement true. Problem 1. Simplify, then evaluate. Show your work. 2. Identify, then correct, any errors in the work shown. 3. a) Write 128 as a power of 2. b) Write 243 as a power of 3. 4. Write the expression so that the powers have the same base. Simplify, then evaluate. 5. Where possible, replace with a “+” or “” sign to make each product positive. a) b) c) d) Can all products be made positive? Explain. 6. The side length of square PQRS is half the side length of square ABCD. Square ABCD has area 121 cm2. a) What is the area of square PQRS? b) What is the length of each side of square PQRS? D S C R P A Q B 7. Determine the value of . Math 9 Fall 2014 Answer Section Unit 1 Powers and Roots MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: C C A D C B C D A C B A D D A C A D B NUMERIC RESPONSE 1. 2. 3. 4. 5. ANS: ANS: ANS: ANS: ANS: 8.8 7.3 29 0.3 261 6. ANS: DIF: SHORT ANSWER 1. ANS: Moderate DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: DIF: Easy Moderate Moderate Easy Moderate Easy Easy Easy Moderate Easy Easy Moderate Moderate Easy Moderate Easy Easy Moderate Moderate Practice Exam Between 4 and 5 but closer to 5 DIF: Moderate 2. ANS: 144 and 169 DIF: Easy 3. ANS: DIF: Easy 4. ANS: DIF: Easy 5. ANS: DIF: Moderate 6. ANS: a) Area of the field: b) Perimeter of the field: DIF: Difficult 7. ANS: a) b) DIF: Moderate 8. ANS: As a power, the number of unit cubes is DIF: Easy 9. ANS: DIF: Easy 10. ANS: . Between DIF: and Moderate PROBLEM 1. ANS: DIF: Difficult 2. 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: DIF: Moderate 3. ANS: a) b) DIF: Difficult 4. ANS: DIF: Difficult 5. ANS: a) Replace with a “” sign. b) Replace with a “+” sign. c) 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 is always positive, which means DIF: Difficult 6. ANS: a) Area of PQRS = b) PQ = DIF: Moderate 7. ANS: DIF: Difficult area of ABCD cm = 5.5 cm . is always negative.