Math 115 Sample Final. 5) 1 5 y y y

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1 Math 11 Sample Final Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Factor completel. If the polnomial is prime, state this. 1) A) ( - )( + 2) B) (2 + 2)( - ) C)(2 + )( - 2) D) ( + )( - 2) ) A) 1 ( + 3)( - 2) B) ( + 3) - 2 C) 1 ( - 3)( + 2) D) ( - 3) + 2 2) A) (9 + 6)2 B) 9(3-2)2 C)Prime D) (81-6)( - 6) 6) A) Prime B) ( + 8)( - 8) C)( - 8)2 D) ( + 8)2 3) A) (- 8)2 B) (3-8)2 C)(3 + 8)2 D) Prime 7) 4-16 A) (2 + 4)(2-4) B) ( + 2)2( - 2)2 C)(2 + 4)( - 2)( + 2) D) (2-4)( - 2)( + 2) 4) t3-30t2 + 4t A) t(t - 3)(t - 1) B) t(t - 3)2 C)t(t - 3)2 D) (t2-3t)(t - 3) 1

2 8) A) (6 + )(6 - ) B) (6 + )2 C)(36 + 1)( - 2) D) (6 - )2 11) A) (2 + 1)( + 12) B) (2 + 3)( + 4) C)(2-3)( - 4) D) ( + 1)( + 12) 9) A) 6(4 + 3)( - 3) B) 63( - 3)( + 3) C)63( + 3)( - 3) D) 3( )( - 3) 12) A) 4( - 2)( + 4) B) (- 2)( ) C)(42 + 8)( - 4) D) 4( + 2)( - 4) ) A) (4 + 3)( + 2) B) (4 + 1)( + 6) C)(4 + 3)( + 2) D) ( + 3)(4 + 2) 13) A) 32( - 2)( - ) B) 32( + 2)( - ) C)3( + 2)(3 + ) D) 2(3-2)( + ) 2

3 14) A) ( + 16)( - ) B) ( - )( + ) C)( - 16)( + ) D) ( - 16)( + ) 18) A) (- 14)( + 1) B) ( + 2)( - 7) C)Prime D) (- 2)( + 7) 1) A) (14-7)( + ) B) 7(2 + 1)( - ) C)(2-1)(7 + 3) D) 7(2-1)( + ) 19) A) (2-9)( + ) B) (2 - )( - 9) C)(2 + )( - 9) D) (2 + )( - 9) 16) 49k2-169m2 A) (49k + m)(k - 169m) B) (7k + 13m)2 C)(7k - 13m)2 D) (7k + 13m)(7k - 13m) Solve. 20) = = 2 A) -, -2 B), 1 4 C), 0 D) No solution 17) 4k4-28k3 + 49k2 A) (2k3-7k2)(2k - 7) B) k2(4k + 1)(k + 49) C)k2(2k - 7)2 D) k2(2k + 7)2 3

4 21) -7-6 = = -14 A) No solution B) (0, 7) C)(0, 8) D) (-1, 8) Find the equation for the graph. 24) Solve. 22) A rectangular Persian carpet has a perimeter of 232 inches. The length of the carpet is 26 inches more than the width. What are the dimensions of the carpet? A) 3 in., 129 in. B) 71 in., 97 in. C)4 in., 71 in. D) 90 in., 116 in. - A) = - 6 B) = + 6 C) = D) = Solve using the five-step problem-solving process. 23) The second angle of a triangle is 4 times as large as the first. The third angle is 0 more than the sum of the other two angles. Find the measure of the second angle. A) 3 1 B) 6 4 Perform the indicated operation. Simplif, if possible. b 2) b2-2 + b b A) 2(b - 6) (b + )(b - ) B) 6b 2-2b + 10 b(b + )(b - ) C) D) -2(b - 6) b(b + )(b - ) 2(b + 6) b(b + )(b - ) C)2 D) 13 4

5 26) A) B) C) D) - 20 ( - 2)( - 3)( - 4) ( - 6) ( - 3)( - 4) ( - 2)( - 3) - 6 ( - 3)( - 4) 28) A) B) C) + 3 D) Solve the formula for the indicated letter. 29) A = P(1 + nr) for r A) r = A - P Pn C)r = A n B) r = Pn A - P D) r = P - A Pn 27) A) C) B) D) ( + 4)( - 4) 30) V = 1 Bh for h 3 A) h = 3V B C)h = 3B V B) h = B 3V D) h = V 3B

6 31) 1 a + 1 b = 1 c for c A) c = a + b B) c = ab(a + b) Simplif. 34) (-2)2 C)c = ab a + b D) c = a + b ab A) 1 2 C) 26 3 B) 1 4 D) ) P = 2L + 2W for W A) W = P - L 2 C)W = P - L B) W = P - 2L 2 D) W = d - 2L 3) (12 + 6) A) 181 B) 61 C)847 D) 121 Find decimal notation. 33) ) A) B) C) D) A) B) 7 17 C) D)

7 37) (32-8) A) B) C) D) ) A) B) C)1 D) -1 38) a a a - 9 a a a - 9 A) a a + 6 a2 + a + 8 C) a 2-16a + 6 a2 - a + 8 B) a 2-16a - 6 a2 - a - 8 D) a 2 + 2a - 6 a2 + 8a - 8 List all numbers for which the rational epression undefined ) A) 9, -8 B) -9,-8 C)0 D) -6, 6 39) A) C) B) -117 D) 13 9 Multipl. 42) (7 + 9)2 A) B) C) D)

8 43) (- 7)( ) A) B) C) D) ) (- 3)( ) A) B) C) D) ) (-74)(43)(-92) A) -229 B) 229 C) D) ) (2 + 1)(2-1) A) 42-1 B) C) D) ) (92-11)( ) A) B) C) D) ) ( )( ) A) B) C) D) ) 23(3 + 2) A) B) C) D) 303 8

9 0) 6 w 9 7w4-3w2 + 4 A) 3 6 w w w 9 B) 3 6 w 4-2 w C) 3 6 w 13-2 w w 9 D) 3 6 w w w 9 3) ( - 0.4)( + 0.4) A) B) C) D) Solve. 4) - 2 = = 8 A) Infinite number of solutions B) No solution C) - 8 3, 8 3 D) - 8 3, ) 1 3 m m - 2 A) 3 m 2-4m + 8 B) 3 m 2-4m + 4 C) 9 m 2-4m + 4 D) 6 m 2-4m + 4 2) (2a - 9)2 A) 2a2-36a + 81 B) 2a C)4a D) 4a2-36a + 81 ) = = -30 A) (-4, -6) B) (-3, -7) C) No solution D) Infinite number of solutions 9

10 6) r + 3s = 7r + 4s = 3 A) (, 0) B) No solution C)(-, -1) D) Infinite number of solutions 9) m2-2 m2 + m + 2 A) 1 m + C) m - m + B) m + m - D) 1 Simplif, if possible. b - a 7) 7a - 7b A) 1 7 B) b - a 7a - 7b 60) 2-4 ( - 2)2 A) B) 2-4 ( - 2)2 C) + 2 D) C) -7 D) ) t t + 36 t2-12t + 36 (t + 6) 7 2t - 12 (t - 6)7 t2-36 A) (t - 6) 2(t + 6)4 C) 2(t + 6) 6 (t - 6)9 B) 2(t - 6) (t + 6)6 D) (t + 6) 2(t - 6)9

11 Write an equation for the graph. 61) Solve using the addition and multiplication principles. 63) > A) { } B) { < -0} C){ > -0} D) { < } A) = + 8 B) = + 4 C) = 4 D) = 4 Find an equation of the line meeting the specified conditions. Write our final answer in slope-intercept form. 62) Containing the point 0, 3 4 to 9 + = 6 A) = and perpendicular B) = Multipl and, if possible, simplif. 64) - 7 ( + 4) (- 7)2 A) C) B) + 4 D) 1-7 C) = D) =

12 Graph the linear equation. C) 6) = A) - D) B) Find an equation of the line meeting the specified conditions. Write our final answer in slope-intercept form. 66) Containing the point 0, = and parallel to A) = B) = C) = D) =

13 Perform the indicated operation and, if possible, simplif. 67) A) C) B) D) Solve using the addition and multiplication principles. 70) 2 (2-1) < -2 3 A) { - 1} B) { 1} C){ < - 1} D) { < 1} Subtract. 68) ( ) - ( ) A) B) C) D) ) < 3 A) C) 4 1 B) < D) < ) A) B) C) D) ) A) { < 11} B) { > 11} C){ } D) { } 13

14 Graph the equation. 73) = D) A) Multipl and, if possible, simplif. 74) A) ( - 3)(4 + ) 2 B) ( + 3)(4 + ) 2 B) C) ( - 3)(4 - ) 2 D) ( - 3)(4 + ) C) - 7) A) 18( + 3) + 2 B) 6( + 3) - 2 C) 18( + 2)( + 3) 2-4 D) 18( + 3)

15 Simplif. Assume that no denominator is zero and that 00 is not considered. 76) (63)(2) A) 88 B) 121 C) 81 D) 128 Factor out the largest common factor. 79) A) 3( ) B) 6( ) C)63( ) D) 63( ) 77) 30m 3p2 m9p A) 6m6p2 B) 6mp C) 6p m6 D) 6m 6 p 80) 16m8-32m4-40m2 A) m2(16m6-32m2-40) B) 8(2m8-4m4 - m2) C) No common factor D) 8m2(2m6-4m2 - ) 78) 4 9z 2 A) 16 9z12 B) 16 81z20 81) A) 4( ) B) No common factor C)42( ) D) 422( ) C) z20 D) z12 1

16 Divide and, if possible, simplif. 82) A) B) ) A contractor finds that it takes Julie 9 hours to construct a wall of a certain size. It takes Leann 8 hours to construct the same wall. How long would it take if the worked together? A) 1 hr B) 17 hr C) 2 26 D) 92 6 C) hr D) hr 83) ( ) A) 1 ( + 2)2 B) 1 ( - 2)2 C)( + 2)2 D) ( - 9)2 Solve. 84) A shopkeeper ordered a total of 6 lb of cashews and peanuts. If he ordered 24 less pounds of cashews than peanuts, then how man pounds of peanuts did he order? A) 28 lb B) 40 lb C)16 lb D) 32 lb Solve. If no solution eists, state this. 86) = A) -4 B) -4, 4 C)No solution D) 4 16

17 87) = A) 24 B) 8 C)16 D) -8 Determine whether the pair of equations represents perpendicular lines. 89) + 13 = -4 = 30-1 A) Yes B) No Evaluate the polnomial. 90) for = -2 A) -24 B) -34 C)12 D) ) 3 = A) 1 7 B) 7 C) 7 D) 1 Find an equation in point-slope form of the line having the specified slope and containing the point indicated. 91) m = -1 ; (-6,-3) 2 A) + 3 = -1 (- 6) 2 B) - 3 = -1 ( + 6) 2 C) + 3 = -1 ( + 6) 2 D) - 3 = -1 (- 6) 2 17

18 Solve the equation. 92) = ) -9b b = -3b + 14 A) -14 B) -9 C) D) 14 A) C) 2 1 B) D) ) a = -3 A) -8 B) C)8 D) - 93) -4-2 = A) 13 2 C) B) D) ) -q = q A) -114 B).7 C).6 D) 12 Find an equation of the line containing the given pair of points. Write our final answer in slope-intercept form. 97) (-, 1) and (-2, -6) A) = C) = B) = D) =

19 Find the slope of the line containing the given pair of points. If the slope is undefined, state so. 98) (8, -) and (-1, -7) A) 13 6 C) 9 2 B) D) Multipl. Leave the answer in factored form ) A) ( - 4)( 2-2) (2 + )( + 1) ( - 4)( + 1) C) (2 + 2)(-2) ( - 4)( + 1) B) (2 + )(2-2) ( - 4)(1) D) (2 + )(2-2) Factor completel. 99) A) ( + 2)(32 + 4) B) ( + 4)(32 + 2) C)( - 2)(32-4) D) (- 4)(32-2) Divide. 2) ( ) ( + 2) 4 A) C) B) D) ) A) (9 + 1)(3 + 1) B) (2 + 1)(4-2+1)( + 1)(2-+1) C)(6 + 1)(3 + 6) D) (7 + 1)(2 + 1) 19

20 3) ( ) (22 + 4) A) B) C) D) ) The product of two consecutive integers is 89 more than their sum. Find the integers. A) and 11 B) 9, or -9, -8 C), 11 or -9, -8 D) -9 and -8 Solve the problem. 4) A loaded moving truck is traveling 1 mph faster than a freight train. In the time it takes the train to travel 60 miles, the truck travels 90 miles. Find the speed of the truck. A) 9 mph B) 1 mph C)90 mph D) 4 mph 6) The height of a triangle is 3 cm more than the length of the base. If the area of the triangle is 12 cm2, find the height and length of the base. A) height: 20 cm; base: 1 cm B) height: 16 cm; base: 13 cm C)height: 19 cm; base: 16 cm D) height: 18 cm; base: 1 cm 20

21 7) A 30-ft ladder is leaning against a building. If the bottom of the ladder is 18 ft from the base of the building, how high does the ladder reach? A) 24 ft B) 6 ft C)26 ft D) 22 ft Solve b factoring and using the principle of zero products. 9) 2k2 = 30k - 0 A) -, B) -,- C), 20 D), 1) 72 = 4 A) - 4 7, 4 7 B) 4 7, 0 C) 4 7, 7 4 D) 7 4, 0 8) Two angles are complementar. Twice one angle plus the other is 19. Find the measure of each angle. A) 74, 16 B) 69, 21 C)3, 3 D) 69, ) 2 - = 6 A) 7, 8 B) -7,-8 C)1, 6 D) -7, 8 21

22 112) ( + 2)( - ) = -3 A), -37 B) -2,-2 C), 3 D) -2, Write the equation of the line on the graph in slope-intercept form. 114) Evaluate. 113) -11 m2-3(m - 4), for m = 7 A) - 42 B) C) D) A) = - + B) = C) = 7 + D) = Find the slope and the -intercept of the line. 11) -4 + = - A) 4 ;(0, -1) B) -11 ;(0, -1) 4 C)1 1 4 ;(0, 1) D) - 4 ;(0, 1) 22

23 Factor completel. 116) 32( + 4) + 2( + 4) A) (32 + 4)( + 2) B) (12 + 2)( + 4) C)( + 4)(32 + 2) D) ( - 4)(32-2) Translate the problem to an equation. Do not solve. 119) 8 minus twice a number equals 2 more than the number. A) 8-2 = 2 + B) 8-2 = C)8-2 = 2 + Add. 117) ( ) + ( ) A) B) C) D) Factor b grouping. 120) A) (- )( - 7) B) (2 + )(3-7) C)6( - )( + 7) D) (2 - )(3 + 7) 121) A) (3 + 4)( + 2) B) (3 + 2)( + 4) C)(3-2)( - 4) D) (3-4)( - 2) Choose the most appropriate translation of the question. 118) 84 is 7% of what number? A) p 84 = 7 B) p = 0.84p C)84 = 0.7p D) p =

24 Perform the indicated operation. 122) ( ) (-93) A) B) C) D) Determine whether the pair of equations represents parallel lines. 12) = = 14 A) No B) Yes Find the - and -intercepts for the equation. Then graph the equation. 126) = Find the intercepts for the equation. 123) -2-4 = 4 A) (-2, 2), (-1, 4) B) (-1, 0), (2, 0) C)(0, -1), (0, 2) D) (-2, 0), (0, -1) A) (0, -4), (-16, 0) 20 Find an equation of the line having the specified slope and containing the indicated point. Write our answer in slope-intercept form. 124) m = -9; (-7, 6) A) = 9-9 B) = -9-7 C) = -9-6 D) =

25 B) (0, 16), (-16, 0) 20 Evaluate as requested. 127) Evaluate the polnomial 2z + + for = 1, = -4, and z = 1. A) -7 B) -4 C)4 D) C)(0, 4), (-16, 0) 20 Find the slope-intercept equation for the line with the indicated slope and -intercept. 128) Slope - 4 ; -intercept (0, 8) 3 A) = B) = C) = D) = D) (0, 4), (-4, 0) Add or subtract, as indicated. 129) (22 + 3) - (2 + 22) - ( + 2) A) B) C) D)

26 Solve the sstem of equations b graphing. If there is no solution or an infinite number of solutions, state this. 130) 2 + = + 2 = A) (2, 6) B) Infinite number of solutions C)(-2, 6) D) No solution 26

27 Answer Ke Testname: M11SAMPLEFINAL 1) D 2) B 3) B 4) B ) C 6) D 7) C 8) A 9) C ) A 11) B 12) A 13) A 14) A 1) D 16) D 17) C 18) B 19) D 20) C 21) B 22) C 23) C 24) D 2) C 26) B 27) A 28) B 29) A 30) A 31) C 32) B 33) A 34) D 3) D 36) D 37) B 38) B 39) C 40) D 41) B 42) C 43) B 44) B 4) A 46) D 47) A 48) A 49) C 0) C 27

28 Answer Ke Testname: M11SAMPLEFINAL 1) C 2) D 3) B 4) C ) B 6) A 7) D 8) A 9) C 60) A 61) D 62) D 63) C 64) A 6) D 66) A 67) B 68) D 69) D 70) C 71) D 72) C 73) C 74) A 7) D 76) D 77) C 78) B 79) C 80) D 81) D 82) A 83) B 84) B 8) D 86) C 87) D 88) A 89) B 90) A 91) C 92) A 93) C 94) D 9) C 96) A 97) C 98) D 99) A 0) B 28

29 Answer Ke Testname: M11SAMPLEFINAL 1) B 2) B 3) B 4) D ) C 6) C 7) A 8) B 9) D 1) B 111) D 112) C 113) A 114) A 11) A 116) C 117) B 118) C 119) C 120) D 121) B 122) B 123) D 124) B 12) B 126) C 127) A 128) A 129) D 130) A 29