Algebra II: Chapter 6 Test Review
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1 Class: Date: Algebra II: Chapter 6 Test Review 1. Simplify 8 4 /. 1 2 a. c. 2 b. 8 d Which is equivalent to 81 1/4? a. 9 b. c. 1 9 d. 1. The volume of a sphere can be given by the formula V = r. You have to design a spherical container that will hold a volume of 55 cubic inches. What should the radius of your container be? a. 1.1 in. b. 2.6 in. c..62 in. d in. 4. Rewrite 11 1 / 4 using radical notation. True or False: 5. For any integer a 0, a 1 / n = 1 a n. Evaluate: / 4 7. Use a calculator to evaluate 16 1 /. Round the result to three decimal places. 8. The volume of a dodecahedron (a solid with 12 regular pentagons as faces) is V a, where a is the length of an edge. Find the edge length of a dodecahedron whose volume is 1000 cubic centimeters. Simplify: Simplify: a. 16 b c. 8 2 d a. 6 b. 60 c. 24 d. 6 1
2 a c b d Simplify: 1. Ê Ë Á w 25 x 20 ˆ 4/5 14. Which is 24 a. 2 b. 2 6 written in simplest form? c. 2 d. 4 6 Simplify the expression Simplify the expression. Assume all variables are positive x (10x 0. ) 17. Let g(x) = 5x 2. Find g(g( 1)). a. 5 c. 625 b. 125 d Let f(x) = x 2 5 and g(x) = x 2. Find g(f(x)). a. x 4 0x c. x 4 5 b. x 4 15 d. 9x Let f(x) = x 2 4 and g(x) = x 2. Find f(g(x)). a. x c. 9x 4 4 b. x x 2 48 d. x Find the inverse of the relation (1, 5), (2, ), (, 1), (4, 1). 21. Find the inverse of the relation (1, 1), (2, 2), (1, ), (4, 4). 22. Which is an equation for the inverse of the relation y = 4x + 2? a. y = 2x + 4 c. y = x b. y = 4x 2 d. y = x
3 2. Write an equation for the inverse of the relation y = 22x Which of the following is an equation for the inverse of the function f(x) = 2x + 2? a. g(x) = 1 2 x + 1 c. g(x) = 1 2 x + 2 b. g(x) = 1 2 x 1 d. g(x) = 1 2 x Which shows the graph of y = 2x 2 2 and its reflection over the line y = x and correctly states whether the reflection is the graph of a function? a. c. Yes No b. d. No Yes
4 26. Sketch the graph of the function f( x) = 2 4x and its inverse on the same coordinate plane. 27. Sketch the graph of the function f( x) = x 2 1. Is the inverse of f(x) a function? Graph the function f. Then use the graph to determine whether the inverse of f is a function. 28. f( x) = 5x 6, x 0 4
5 29. Which is the graph of f(x) = x 6? a. c. b. d. 5
6 Refer to the function g( x) = 1 + x Sketch the graph of g(x). 6
7 1. Which represents the graph of y = x + 4? State the domain and range of the function. a. c. b. Domain:x 4; Range: y 0 d. Domain: x 4; Range:y 0 Domain:x 0; Range: y 4 Domain: x 0; Range:y 4 7
8 Graph: 2. Which is the graph of f(x) = x 4? a. c. b. d.. A certain gas will escape from a storage tank according to the formula e = 10 p, where e represents the amount escaping in cubic meters per minute at atmospheric pressure, and p represents the pressure in kilopascals. How much gas is escaping when the pressure is 484 kilopascals? Round your answer to the nearest whole number. a. 5 cubic meters c. 1,460 cubic meters b. 251 cubic meters d cubic meters Graph the function. Then state the domain and range. 4. f( x) = 2 ( x 4) 1 / 1 8
9 5. Which gives the solution(s) of the equation x 5 = 6? a. 211, 221 c. 221 b. 41 d. 211 Solve the equation. Check for extraneous solutions. 6. y 2 = 5 7. A certain gas will escape from a storage tank according to the formula e = 150 p, where e represents the amount escaping in cubic meters per minute at atmospheric pressure, and p represents the pressure in megapascals. What is the pressure on the gas when about 00 cubic meters per minute are escaping? Round your answer to the nearest tenth. a megapascals c. 2.0 megapascals b. 4.0 megapascals d. 0.5 megapascals 8. The velocity of sound in air is given by the equation v = t where v is the velocity in meters per second and t is the temperature in degrees Celsius. Find the temperature when the velocity of sound in air is 10 meters per second. Round the answer to the nearest degree. a. C c. 51 C b. 452 C d. 48 C 9. Which gives the solution(s) of x + 72 = x? a. 8 b. 9 c. no solution d. 9, Which gives the solution of 5x + 4 a. 5 b = 6? c. 1 d. none of these 9
10 Algebra II: Chapter 6 Test Review Answer Section 1. ANS: D PTS: 1 DIF: Level B REF: MAL2087 STA: MI.MIGLC.MTH A1.1.4 KEY: rational exponent 2. ANS: D PTS: 1 DIF: Level B REF: MAL20871 STA: MI.MIGLC.MTH A1.1.4 KEY: rational exponent. ANS: B PTS: 1 DIF: Level B REF: MAL2089 STA: MI.MIGLC.MTH A1.1.4 KEY: nth root formula volume sphere BLM: Application 4. ANS: 4 11 PTS: 1 DIF: Level A REF: MAL20867 NAT: NCTM 9-12.NOP.1.a KEY: rational exponent index radical form BLM: Knowledge 5. ANS: False PTS: 1 DIF: Level B REF: MAL20868 KEY: rational exponent BLM: Comprehension 6. ANS: 2 PTS: 1 DIF: Level B REF: MAL20874 STA: MI.MIGLC.MTH A1.1.4 KEY: rational exponent 7. ANS: 0.97 PTS: 1 DIF: Level A REF: MAL20879 NAT: NCTM 9-12.NOP..a STA: MI.MIGLC.MTH A1.1.4 KEY: rational exponent 1
11 8. ANS: 5.07 cm PTS: 1 DIF: Level B REF: MAL20894 STA: MI.MIGLC.MTH A1.1.4 KEY: nth root formula volume dodecahedron BLM: Application 9. ANS: 8 25 PTS: 1 DIF: Level B REF: MAL20901 TOP: Lesson 6.2 Apply Properties of Rational Exponents KEY: radicals product property 10. ANS: C PTS: 1 DIF: Level B REF: MAL20912 TOP: Lesson 6.2 Apply Properties of Rational Exponents KEY: radical expression like radicals 11. ANS: A PTS: 1 DIF: Level B REF: MAL20914 TOP: Lesson 6.2 Apply Properties of Rational Exponents KEY: radical expression like radicals 12. ANS: C PTS: 1 DIF: Level B REF: MAL20916 TOP: Lesson 6.2 Apply Properties of Rational Exponents KEY: radical expression like radicals 1. ANS: w 20 x 16 PTS: 1 DIF: Level B REF: MAL20920 TOP: Lesson 6.2 Apply Properties of Rational Exponents KEY: rational exponents power of a quotient BLM: Knowledge 14. ANS: C PTS: 1 DIF: Level B REF: MAL20864 TOP: Lesson 6.2 Apply Properties of Rational Exponents KEY: radical expression simplest form 15. ANS: 27 PTS: 1 DIF: Level B REF: 7f70547-cdbb-11db-b f7 TOP: Lesson 6.2 Apply Properties of Rational Exponents KEY: radical expression evaluate nth root BLM: Knowledge 16. ANS: 1004x 0.9 PTS: 1 DIF: Level B REF: 7f cdbb-11db-b f7 TOP: Lesson 6.2 Apply Properties of Rational Exponents KEY: rational exponent power of a power BLM: Knowledge 2
12 17. ANS: D PTS: 1 DIF: Level B REF: MAL2092 NAT: NCTM 9-12.ALG.1.d STA: MI.MIGLC.MTH A2.2.5 TOP: Lesson 6. Perform Function Operations and Composition KEY: function composition of functions BLM: Comprehension 18. ANS: A PTS: 1 DIF: Level B REF: MAL2094 NAT: NCTM 9-12.ALG.1.d STA: MI.MIGLC.MTH A2.2.5 TOP: Lesson 6. Perform Function Operations and Composition KEY: function composition of functions BLM: Comprehension 19. ANS: C PTS: 1 DIF: Level B REF: MAL2097 NAT: NCTM 9-12.ALG.1.d STA: MI.MIGLC.MTH A2.2.5 TOP: Lesson 6. Perform Function Operations and Composition KEY: function composition of functions BLM: Comprehension 20. ANS: (5, 1), (, 2), (1, ), ( 1, 4) PTS: 1 DIF: Level A REF: MAL20945 NAT: NCTM 9-12.ALG.1.b TOP: Lesson 6.4 Use Inverse Functions KEY: inverse relation 21. ANS: (1, 1), (2, 2), (, 1), (4, 4) PTS: 1 DIF: Level A REF: MAL20946 NAT: NCTM 9-12.ALG.1.b TOP: Lesson 6.4 Use Inverse Functions KEY: inverse relation 22. ANS: D PTS: 1 DIF: Level B REF: MAL20941 TOP: Lesson 6.4 Use Inverse Functions KEY: inverse relation 2. ANS: y = x PTS: 1 DIF: Level B REF: MAL20949 TOP: Lesson 6.4 Use Inverse Functions KEY: inverse relation 24. ANS: B PTS: 1 DIF: Level B REF: MAL2094 NAT: NCTM 9-12.ALG.1.d STA: MI.MIGLC.MTH A2.2.4 TOP: Lesson 6.4 Use Inverse Functions KEY: Inverse function inverse relation 25. ANS: B PTS: 1 DIF: Level B REF: MAL20952 TOP: Lesson 6.4 Use Inverse Functions KEY: function inverse relation inverse function reflection horizontal line test BLM: Comprehension
13 26. ANS: f 1 ( x) = 1 4 x PTS: 1 DIF: Level B REF: MAL20958 NAT: NCTM 9-12.ALG.1.b TOP: Lesson 6.4 Use Inverse Functions KEY: inverse functions graph reflection 27. ANS: No PTS: 1 DIF: Level B REF: MAL20962 NAT: NCTM 9-12.ALG.1.b STA: MI.MIGLC.MTH A2.2.4 MI.MIGLC.MTH A2.2.6 TOP: Lesson 6.4 Use Inverse Functions KEY: inverse relations inverse functions graph reflection horizontal line test 28. ANS: The inverse of f is a function. PTS: 1 DIF: Level B REF: 7f4711dc-cdbb-11db-b f7 TOP: Lesson 6.4 Use Inverse Functions KEY: inverse relations inverse functions graphing horizontal line test reflection BLM: Comprehension 4
14 29. ANS: B PTS: 1 DIF: Level A REF: MAL20968 TOP: Lesson 6.5 Graph Square Root and Cube Root Functions KEY: square root graph radical function domain range BLM: Knowledge 0. ANS: PTS: 1 DIF: Level B REF: MAL20974 TOP: Lesson 6.5 Graph Square Root and Cube Root Functions KEY: square root graph radical function 1. ANS: A PTS: 1 DIF: Level A REF: MAL20979 TOP: Lesson 6.5 Graph Square Root and Cube Root Functions KEY: square root radical function graph 2. ANS: D PTS: 1 DIF: Level B REF: MAL2098 TOP: Lesson 6.5 Graph Square Root and Cube Root Functions KEY: radical function graph cube root BLM: Comprehension. ANS: D PTS: 1 DIF: Level A REF: MCS80780 TOP: Lesson 6.5 Graph Square Root and Cube Root Functions KEY: radical function square root evaluate formula BLM: Application 4. ANS: domain: all real numbers range: all real numbers PTS: 1 DIF: Level C REF: 7f68b06a-cdbb-11db-b f7 TOP: Lesson 6.5 Graph Square Root and Cube Root Functions KEY: radical function parent function vertical shrink transformation graph translation 5. ANS: D PTS: 1 DIF: Level A REF: MAL20988 TOP: Lesson 6.6 Solve Radical Equations KEY: radical equation 5
15 6. ANS: y = 127 PTS: 1 DIF: Level A REF: MAL20989 TOP: Lesson 6.6 Solve Radical Equations KEY: radical equation extraneous solution BLM: Knowledge 7. ANS: B PTS: 1 DIF: Level B REF: MAL20992 TOP: Lesson 6.6 Solve Radical Equations KEY: radical equation formula BLM: Application 8. ANS: A PTS: 1 DIF: Level B REF: MAL2099 TOP: Lesson 6.6 Solve Radical Equations KEY: radical equation formula velocity BLM: Application 9. ANS: B PTS: 1 DIF: Level B REF: MAL20997 TOP: Lesson 6.6 Solve Radical Equations KEY: radical equation extraneous solutions BLM: Knowledge 40. ANS: A PTS: 1 DIF: Level B REF: MAL20885 TOP: Lesson 6.6 Solve Radical Equations KEY: radical equation extraneous solutions BLM: Knowledge 6
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