# MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Math 2 Stud Guide-Chapters 8 and 9 Name Date: Time: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all square roots of the number. ) 600 9, -9 B) 60, -60 C) 6, -6 D) 6, -6 ) Find the square root. 2) B) 62 C) Not a real number D) 8 2) ) ) Not a real number B) - 2 C) 9 D) - 9 Find the square of the radical epression. 4) 9 9 4) 9 2 B) 20 9 C) 9 9 D) Identif the given number as ʺRationalʺ, ʺIrrationalʺ, or ʺNot a real numberʺ. If the number is rational, give its eact value. If the number is irrational, give a decimal approimation to the nearest thousandth. ) -2 ) Irrational, B) Not a real number C) Irrational,.489 D) Rational, ) - 2 Rational, -.0 B) Not a real number C) Irrational,.0 D) Irrational, -.0 6) Find the length of the unknown side of a right triangle with legs a and b and hpotenuse c. Round to the nearest thousandth, if necessar. 7) b = 7, c = 7) a = B) a = 9 C) a = 7.4 D) a = 6.40 Find the square root. Epress the answer as a whole number or as a square root. Do not use a calculator. 8) (-) B) 24 C) 7 D) 74 8)

2 Solve the problem. Give the answer to the nearest thousandth if necessar. 9) The length of a rectangle is 72 meters, and the width is 2 meters. Find the measure of the diagonal of the rectangle. 72 meters 9) 2 meters 80 meters B) 7 meters C) 76 meters D) 74 meters Find the root. ) -2 2 B) -2 C) -6.4 D) Not a real number ) Use a calculator with a cube root ke to find the root. Round to the nearest thousandth. ) B) C) D) -.2 ) Find the product and simplif, if possible. 2), 0 6 B) 6 C) 0 D) 2 2) Simplif the radical. ) 66 Cannot be simplified B) 2 C) 2 D) 4 ) 4) B) 84 C) 8 D) 4 2 4) Simplif the epression. ) 7 2 ) 2 B) 7 C) D) Simplif the radical. Assume that all variables represent nonnegative real numbers. 6) m8 n8, n 0 m 9 n4 B) m 9 n 4 C) m 9 n8 D) m 8 n4 6) 2

3 7) k6 2 7) k 6 B) k C) k 2 D) k Simplif the radical. 8) 8) B) C) 4 D) 6 9 9) ) 4 9 B) 8 27 C) 2 D) ) k 27 20) k 27 B) k C) k 8 D) k Solve the problem. 2) A cube-shaped bo must be constructed to contain 28 ft. What should the side length of the bo be? Give our answer in eact form. 2) 4 2 ft B) 4 8 ft C) 4 2 ft D) 4 ft Simplif and add or subtract wherever possible. 22) ) 2 B) C) 6 2 D) - 2 Simplif the epression b performing the indicated operations. 2) ) B) C) D) Perform the indicated operations. Assume that all variables represent nonnegative real numbers. 24) 6 4 m9p6 - m2p 4 mp2 24) m2p 4 mp2 B) C) 9m2p 4 mp2 D) Cannot simplif

4 2) B) 8 C) 8 D) 6 2) Find the perimeter of the figure. 26) 26) B) 40 8 C) 40 2 D) 20 2 Rationalize the denominator and simplif. 27) ) - 6 B) C) - D) - Simplif. 28) ( 2-6) ( m - ) 2m - 6-2m + 2 B) 2m + 6-6m + 2 C) 2m - 6-6m + 2 D) 2m - 6-6m ) Rationalize the denominator. Assume that all variables represent positive real numbers. 29) B) 7 C) 77 D) 77 29) Rationalize the denominator. 0) 4 2 0) 4 B) 4 2 C) 4 D) 4 Simplif the epression. ) ( - ) B) 4-8 C) 9-9 D) ) Simplif the radical epression. Assume that all variables represent nonnegative real numbers. 2) ( 9a + b) 2 8a ab + b2 B) 9a + 9ab + b C) 9a + 2 9ab + b D) 8a2 + 9ab + b2 2) 4

5 Rationalize the denominator. Write the quotient in lowest terms. ) B) - - C) + - D) - - ) Write the quotient in lowest terms. 4) ) B) C) D) Perform the indicated operation and epress the answer in simplest form. ) ( - 2)( ) ) B) 7 C) D) Solve the problem. 6) If an investment of P dollars grows to A dollars in two ears, the annual rate of return on the investment is given b r = A - P P. Angela Ramos invested \$40 in a mone market fund. Two ears later, her investment was worth \$720. Find the approimate annual rate of return on her investment. Round to the nearest tenth of a percent..% B).% C) 6.7% D).8% 6) Solve the equation. 7) p2-2p + 8 = p + 7 {-2} B) - C) {2} D) {9} 7) 8) = B) - 4 C) 6 D) 2 8) 9) 6 - = 6 - {0, 4} B) {4, 8} C) {4, -4} D) {0, -4} 9) 40) = 6 {-7} B) {-7, -} C) D) {-} 40) 4) 8 - = 9 - {0, 9} B) {0, -9} C) {9, 8} D) {9, -9} 4)

6 42) = 2 {-4, 2} B) {-2, 8} C) {-8, 2} D) {-2, 4} 42) Solve the problem. 4) A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 2 feet and the height from the ground to the front doors is 6 feet, how long is the ramp? 8. ft B) 22.2 ft C) 2.8 ft D).4 ft 4) Simplif the epression. 44) -2-4/ 62 B) - 62 C) -62 D) 62 44) Simplif the epression. Write our answer in eponential form with onl positive eponents. 66/7 4) 6/7 6-2/7 6/7 B) 69/7 C) 6/7 D) 69/7 4) Simplif the epression. Write our answer in eponential form with onl positive eponents. Assume that all variables represent positive numbers. 4 -/2 46) 46) 6 2 B) 2 C) 2 D) 2 Simplif the radical. Give the answer as an integer or a radical in simplest form. Assume that all variables represent nonnegative numbers. 47) ) 6 B) 26/ C) 7 D) 26 Use the eponential ke on a calculator to find the root. If the root is irrational, round it to the nearest thousandth. 48) B).47 C).9 D) ) Solve the problem. 49) In an economics stud, three quantities m, p, and q have been found to be related b the equation m = p/2 q/2. Find m, if p = 9 and q = 6. 8 B) 24 C) 9 D) 8 49) 6

7 Provide an appropriate response. 0) Write an equivalent epression in radical form. 24/2-24 B) 24. C) 24 D) 2 0) Find the distance between the pair of points. ) 2, 2 4 and - 2, 4 ) 26 B) 29 C) D) 29 Chapter 9 Solve the equation. Epress radicals in simplest form. 2) 2 = { } B) {± } C) {±2.} D) {2} 2) Solve the equation. Epress radicals in simplest form. ) 2 = 2 ) ± B) ± C) ± D) ± 4) 9p2-9 = 4) B) ± C) {-, 7} D) ± ) = 72 ) { , } B) { , } 7 C) { , } D) {42 2-6, } 6) ( - 7)2 = 2 {2} B) {2, 2} C) {2, -2} D) {, -} 6) Use a calculator to solve the equation. Round to the nearest hundredth, if necessar. 7) (.44p )2 =.47 {.9, -.9} B) {.84, -.84} C) {-.9, -7.0} D) {7.0, -.9} 7) Solve the problem. 8) The area of a circle is found b the equation A = πr2. If the area A of a certain circle is 44π square centimeters, find its radius r. r = 2π cm B) r = ± 2 cm C) r = 2 cm D) r = 2 π cm 8) 7

8 Decide whether the statement is true or false. If it is false, tell wh. 9) If k = 0, then 2 = k will have eactl one real solution. False; the equation will have no real solution. B) True C) False; the equation will have two real solutions. 9) Complete the trinomial so that it is a perfect square. 60) B) 6 C) 26 D) 64 60) 6) ) 2 B) C) 2 2 D) 4 2 Solve the equation b completing the square. 62) k2 + 8k + 8 = 0 {-9} B) {± 9} C) {-8} D) {9} 62) 6) = 0, B) 0, C) -, D) -, 6) 64) d2 + 7d + 20 = 0, 4 B) -, - 4 C) -, - 4 D), 4 64) Solve the equation b completing the square. Then (i) give the eact solutions and (ii) give the solutions rounded to the nearest thousandth. 6) 2 = - 8 6) (i) {-4 ± 2} (ii) {0.8, -8.8} B) (i) {- ± 2} (ii) {.8, -.8} C) (i) {4 + 2} (ii) {8.8} D) (i) {-4 ± 2 2} (ii) {.6} Solve the problem. 66) A ball is thrown verticall upward from the top of a building 44 feet tall with an initial velocit of 28 feet per second. The height, s (in feet), of the ball after t seconds is given b s = -6t2 + 28t After how man seconds will the ball pass the top of the building on its wa down? 44 B) C) 7 D) 8 66) 67) Find the dimensions of a rectangular enclosure with a perimeter of 4 d and an area of 60 d2. d b d B) 6 d b 2 d C) d b 2 d D) 6 d b d 67) 8

9 If necessar, write the equation in the standard form a2 + b + c = 0. Then identif the values of a, b, and c. Do not actuall solve the equation. 68) 82 = 2 68) a =, b = 2, c = 0 B) a = 8, b = -2, c = 0 C) a = 8, b = 0, c = 2 D) a = 8, b = -2 69) (9 + )(4-4) = ( + 7) a = -, b =, c = - B) a =, b = -, c = -2 C) a = 6, b = 29, c = -2 D) a = 7, b = 9, c = 2 69) Use the quadratic formula to solve the equation. Simplif an radicals. 70) p2-22p + 2 = 0 {0, } B) {} C) {± } D) {0, 22} 70) 7) 2 = 7-8 {- ± 2} B) {4 + 2} C) {-4 ± 2 2} D) {-4 ± 2} 7) Use a calculator to find an approimate solution to the equation. Round our answer to the nearest thousandth. 72) = -9 72) {.0,.697} B) {-.97, -.97} C) {., -8.} D) {-.697, -.0} Solve the equation. Epress radicals in simplest form. 7) b2 + 4 b = - 7) 0, 4 B) 4 C) D) 4 ± 74) m 2 = - 6 m ) 2, - B) - 2 C) - 2, D) 7) = 0.6 { ± 7} B) { + 7} C) {2 ± 7} D) {2-7} 7) Solve the problem. 76) Solve the formula V = πr2h + πr 2h for r b writing it in the form ar2 + br + c = 0 and then using 76) the quadratic formula. r = ± (V - πr2h) πh B) r = ± (V - πr2h)(πh) πh C) r = ± (V - πr2h) πh D) r = ± (V - πr2h)(πh) πh 9

10 77) The position of an object moving in a straight line is given b s = 2t2 - t, where s is in meters and t is the time in seconds the object has been in motion. How long (to the nearest tenth) will it take the object to move meters? 2. sec B) 2. sec C) 6.0 sec D). sec 77) Answer the question. 78) Which one of the following methods cannot be used to solve the equation = 0? Quadratic formula B) All of the methods can be used. C) Completing the square D) Factoring 78) Write the number as a multiple of i. 79) -4 2i B) -i 2 C) ±2i D) -2i 79) 80) i B) -2i 7 C) 2i 7 D) ) Perform the indicated operation. Give the result in standard form. 8) (9-9i) + (7 + 4i) 6 - i B) -6 + i C) 2 + i D) 6 + i 8) 82) ( + i) - ( + 4i) + (6 + 7i) 6 + 6i B) i C) -6-8i D) 6 + 4i 82) Find the product. 8) (4 + 7i)(6 + 7i) 7 + 4i B) i C) -2-70i D) 49i2 + 70i ) Write the quotient in standard form i 84) 7 + i 7 - B) 7 + i C) i 48 D) i 2 84) Solve the equation for comple solutions. Write our answer in standard form. 8) ( - )2 = -6 {±4} B) {9, } C) {, -9} D) { ± 4i} 8) 86) (8z + )2 = -7 {- ± i } B) 8 ± 8 i C) - 8 ± i D) {- ± i } 8 86) 87) = 0 {6, -2} B) {4 ± 8i} C) {-2 ± 4i} D) {2 ± 4i} 87)

11 88) = ± 67 i B) ± 67 i 8 88) C) -7 ± 67 8 D) 7 ± 67 8 Give the coordinates of the verte and sketch the graph of the equation. 89) = 2-89) (0, ) - B) (-, 0) C) (, 0) D) (0, -)

12 90) = ) (-4, 9) B) (-0., 7.2) C) (4, 9) D) (-4, -9) Decide from the graph = f() how man real solutions f() = 0 has. Then give the solution set of real solutions. 9) 9) Two; {0, 4} B) One; {0} C) One; {4} D) None; 2

13 92) 92) Two; {, - 9} B) Two; {-2, 4} C) One; {} D) One; {-8} Give the domain and range of the function. Assume the ends of the function continue on. 9) 6 9) Domain (-, ); Range (-, ) B) Domain (-, ); Range [0, ) C) Domain [-, 0); Range [0, ) D) Domain (-, 0); Range [-4, ) Solve the problem. 94) Given f() = , find f(0). 0 B) 6 C) -4 D) 4 94) 9) Given f() = , find f(-). -4 B) 46 C) -0 D) -20 9)

14 96) The cross section of a large telescope having a diameter of 60 feet and a maimum depth of 6 feet is depicted below. 96) 90 (-80, 6) (80, 6) 4 What is the equation of this parabola? Not enough information B) = 2 C) = 40 2 D) = ) The length and width of a rectangle have a sum of 80. What dimensions give the maimum area? Length 9 and width 4 B) Length 0 and width 0 C) Length 40 and width 40 D) Length and width 49 97) 98) Given f() = , find f(-2) 2 B) C) D) 98) Solve the equation b completing the square. 99) a2 + 8a = 9 {0, -9} B) {, -9} C) {-, 9} D) {± -9} 99) 4

15 Give the coordinates of the verte and sketch the graph of the equation. 0) = ( - )2 0) (-, 0) B) (, 0) C) (0, ) D) (0, -)

16 Answer Ke Testname: MATH 2 STUDY GUIDE CHAPTERS 8 AND 9 ) B 2) C ) D 4) C ) B 6) D 7) C 8) D 9) B ) B ) B 2) B ) A 4) D ) D 6) A 7) B 8) C 9) C 20) D 2) A 22) A 2) A 24) A 2) B 26) C 27) C 28) C 29) C 0) C ) B 2) C ) D 4) C ) D 6) A 7) C 8) D 9) A 40) D 4) A 42) C 4) C 44) B 4) C 46) A 47) A 48) C 49) D 0) C 6

17 Answer Ke Testname: MATH 2 STUDY GUIDE CHAPTERS 8 AND 9 ) D 2) B ) A 4) D ) B 6) B 7) C 8) C 9) B 60) D 6) A 62) A 6) D 64) B 6) A 66) D 67) C 68) B 69) B 70) B 7) D 72) D 7) C 74) C 7) A 76) B 77) B 78) D 79) A 80) C 8) A 82) A 8) B 84) B 8) D 86) C 87) D 88) B 89) D 90) A 9) D 92) B 9) B 94) C 9) A 96) D 97) C 98) D 99) B 0) B 7

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