Review Unit 2. Multiple Choice Identify the choice that best completes the statement or answers the question.
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1 Review Unit 2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Identify the index of. a. b. 3 c. 7 d Identify the radicand of. a. 4 b. c. 6 d Between which two consecutive integers on a number line would you locate? a. 2 and 3 b. 3 and 4 c. 2 and 3 d. 1 and 2 4. Write in simplest form. a. b. 6 3 c. d. 5. Write as an entire radical. 6. Write 7 14 as an entire radical. 7. Write as an entire radical. 8. Evaluate a b c d Evaluate a. 18 c b. 32 d Evaluate a without using a calculator. b. 1 6 c d. 1 6 Short Answer 11. Write an equivalent form of 6 as a fifth root. 12. Which of these numbers is the greatest?,,,, 13. Evaluate. 14. Write as a power. 15. Evaluate without using a calculator.
2 Problem 16. This diagram shows a cube with volume V cubic units and edge length s units. s V cubic units Provide a value of V for which s is rational. 17. Here is Tanisha s solution for evaluating a power: Identify the errors Tanisha made. Write a correct solution. 18. At a distance of 1 m from a light source, the intensity of the light is 2 mw/m 2 (milliwatts per square metre). The intensity, I, at a distance d metres from the source is given by the formula: I = 2d 2. Determine the intensity of the light 2.5 m from the source. 19. Koli wants to invest enough money on January 1st to pay his daughter $900 at the end of each year for the next 6 years. The investment savings account pays 3.3% compounded annually. The amount, A dollars, that Koli must invest on January 1st is given by the formula:, where P is the annual payment in dollars, r is the annual interest rate expressed as a decimal, and t is the time in years that the money will be invested. How much must Koli invest on January 1st? 20. A tree farmer used the formula to estimate the volume, V cubic metres, of a tree with height h metres and mean trunk diameter d metres. The height of a tree is 20 times its mean trunk diameter, and its volume is 230 m. What is the mean trunk diameter of this tree to the nearest metre?
3 Review Unit 2 Answer Section MULTIPLE CHOICE 1. ANS: B PTS: 1 DIF: Easy REF: 4.1 Estimating Roots LOC: 10.AN2 KEY: Procedural Knowledge 2. ANS: B PTS: 1 DIF: Easy REF: 4.1 Estimating Roots LOC: 10.AN2 KEY: Procedural Knowledge 3. ANS: A PTS: 1 DIF: Easy REF: 4.2 Irrational Numbers 4. ANS: B PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals 5. ANS: C PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals 6. ANS: C PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals 7. ANS: B PTS: 1 DIF: Easy REF: 4.3 Mixed and Entire Radicals 8. ANS: D PTS: 1 DIF: Moderate REF: 4.4 Fractional Exponents and Radicals 9. ANS: B PTS: 1 DIF: Moderate REF: 4.4 Fractional Exponents and Radicals 10. ANS: D PTS: 1 DIF: Easy REF: 4.5 Negative Exponents and Reciprocals SHORT ANSWER 11. ANS: PTS: 1 DIF: Moderate REF: 4.1 Estimating Roots 12. ANS: PTS: 1 DIF: Moderate REF: 4.3 Mixed and Entire Radicals 13. ANS: 0.9 PTS: 1 DIF: Easy REF: 4.4 Fractional Exponents and Radicals
4 14. ANS: or PTS: 1 DIF: Easy REF: 4.4 Fractional Exponents and Radicals 15. ANS: PTS: 1 DIF: Easy REF: 4.5 Negative Exponents and Reciprocals PROBLEM 16. ANS: The formula for the volume, V, of a cube with edge length s units is: V = s 3 To determine the value of s, take the cube root of each side. For s to be rational, V must be a positive number that is a perfect cube. For example, V = 125 PTS: 1 DIF: Moderate REF: 4.2 Irrational Numbers LOC: 10.AN1 KEY: Problem-Solving Skills Communication 17. ANS: Tanisha made an error in the first line when she wrote the square root symbol ( ) instead of the ( ) symbol. Also, the exponent outside the bracket should have been 2, not 7. (The numerator of a fractional exponent represents the index of the radical and the denominator represents the exponent of the power.) A correct solution: PTS: 1 DIF: Moderate REF: 4.4 Fractional Exponents and Radicals KEY: Problem-Solving Skills Communication 18. ANS: Use the formula. Substitute: d = 2.5
5 0.32 At a distance of 2.5 m, the intensity of light is 0.32 mw/m 2. PTS: 1 DIF: Moderate REF: 4.5 Negative Exponents and Reciprocals KEY: Problem-Solving Skills 19. ANS: Use the formula. Substitute: P = 900, r = 0.033, t = 6 Koli should invest $ on January 1st. PTS: 1 DIF: Moderate REF: 4.5 Negative Exponents and Reciprocals KEY: Problem-Solving Skills 20. ANS: Use the formula. Substitute: V = 230 and h = 20d d The mean trunk diameter is approximately 3 m. PTS: 1 DIF: Moderate REF: 4.6 Applying the Exponent Laws KEY: Problem-Solving Skills
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