Math 115 Sample Final

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1 Math 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. ) ( - )( + ) ( + )( - ) C)( + )( - ) ( + )( - ) ) (9 + 6) 9( - ) C)Prime (8-6)( - 6) ) (- 8) ( - 8) C)( + 8) Prime 4) t - 0t + 4t t(t - )(t - ) t(t - ) C)t(t - ) (t - t)(t - ) ) ( + )( - ) ( + ) - C) ( - )( + ) ( - ) + 6) Prime ( + 8)( - 8) C)( - 8) ( + 8) 7) 4-6 ( + 4)( - 4) ( + )( - ) C)( + 4)( - )( + ) ( - 4)( - )( + ) 8) 6 - (6 + )(6 - ) (6 + ) C)(6 + )( - ) (6 - ) 9) (4 + )( - ) 6( - )( + ) C)6( + )( - ) (0 + 8)( - ) ) (4 + )( + ) (4 + )( + 6) C)(4 + )( + ) ( + )(4 + ) ) + + ( + )( + ) ( + )( + 4) C)( - )( - 4) ( + )( + ) ) ( - )( + 4) ( - )(4 + 6) C)(4 + 8)( - 4) 4( + )( - 4) ) ( - )( - ) ( + )( - ) C)( + )( + ) ( - )( + ) 4) ( + 6)( - ) ( - )( + ) C)( - 6)( + ) ( - 6)( + ) ) (4-7)( + ) 7( + )( - ) C)( - )(7 + ) 7( - )( + ) 6) 49k - 69m (49k + m)(k - 69m) (7k + m) C)(7k - m) (7k + m)(7k - m)

2 7) 4k4-8k + 49k (k - 7k)(k - 7) k(4k + )(k + 49) C)k(k - 7) k(k + 7) 8) (- 4)( + ) ( + )( - 7) C)Prime (- )( + 7) 9) ( - 9)( + ) ( - )( - 9) C)( + )( - 9) ( + )( - 9) Solve using the five-step problem-solving process. ) 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. 6 4 C) Find the equation for the graph. 4) Solve. 0) - 4 = + = , -, 4 C), 0 No solution ) -7-6 = -4 - = -4 No solution (0, 7) C)(0, 8) (-, 8) Solve. ) A rectangular Persian carpet has a perimeter of inches. The length of the carpet is 6 inches more than the width. What are the dimensions of the carpet? in., 9 in. 7 in., 97 in. C)4 in., 7 in. 90 in., 6 in. = - 6 = + 6 C) = = Perform the indicated operation. Simplif, if possible. b ) b - + b b (b - 6) (b + )(b - ) 6b - b + 0 b(b + )(b - ) C) -(b - 6) b(b + )(b - ) (b + 6) b(b + )(b - )

3 6) 7) 8) C) - 0 ( - )( - )( - 4) ( - 6) ( - )( - 4) ( - )( - ) - 6 ( - )( - 4) C) ( + 4)( - 4) + 9 C) Solve the formula for the indicated letter. 9) A = P( + nr) for r r = A - P Pn C)r = A n r = Pn A - P r = P - A Pn ) P = L + W for W W = P - L C)W = P - L Find decimal notation. ) Simplif. 4) W = P - L W = d - L C) (-) C) ) ( + 6) 8 6 C) ) C) ) V = Bh for h h = V B C)h = B V h = B V h = V B 7) + - ( - 8) C) ) a + b = c for c c = a + b c = ab(a + b) C)c = ab a + b c = a + b ab

4 8) a a a - 9 a a a - 9 a + 6a + 6 a + a + 8 C) a - 6a + 6 a - a + 8 9) ) - 9 C) a - 6a - 6 a - a - 8 a + a - 6 a + 8a ) ( - 7)( - - ) C) ) (-74)(4)(-9) -9 9 C) ) (9 - )(9 + ) C) ) ( - )( ) C) C) - List all numbers for which the rational epression undefined. Multipl ) , -8-9,-8 C)0-6, 6 4) (7 + 9) C) ) ( + )( - ) C) ) ( )( + + 4) C) ) ( + ) C)

5 0) 6 w 9 7w4 - w + 4 ) 6 w + w - 4 w 9 6 w 4 - w + 4 C) 6 w - w + 4 w 9 6 w + 6 w - 4 w 9 m - m - ) (a - 9) m - 4m + 8 m - 4m + 4 C) 9 m - 4m m - 4m + 4 a - 6a + 8 a + 8 C)4a + 8 4a - 6a + 8 6) r + s = 7r + 4s = (, 0) No solution C)(-, -) Infinite number of solutions Simplif, if possible. b - a 7) 7a - 7b 7 C) ) t + t + 6 t - t + 6 (t + 6) 7 t - (t - 6)7 t - 6 (t - 6) (t + 6)4 C) (t + 6) 6 (t - 6)9 b - a 7a - 7b (t - 6) (t + 6)6 (t + 6) (t - 6)9 ) ( - 0.4)( + 0.4) C) Solve. 4) - = 8 - = 8 Infinite number of solutions No solution 9) m - m + m + m + C) m - m + m + m - C) - 8, 8-8, ) - 4 ( - ) ( - ) C) ) = - + = -0 (-4, -6) (-, -7) C) No solution Infinite number of solutions

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

7 Solve using the addition and multiplication principles. 70) ( - ) < - { - } { } C){ < - } { < } - - 7) < < C) 4 < 4 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 = ) { < } { > } C){ } { } Graph the equation. 7) = + C) = + 8 = + 8 Perform the indicated operation and, if possible, simplif. 67) - C) Subtract. 68) ( ) - ( ) C) ) C)

8 - - 7) ( + ) + 8( + )( + ) C) - 4 6( + ) - 8( + ) - C) - - Simplif. Assume that no denominator is zero and that 00 is not considered. 76) (6)() 77) 0m p m9p 88 C) 8 8 6m6p 6mp C) 6p m6 6m 6 p - 78) 4 9z 6 9z 6 8z0 C) 6 7 8z z Multipl and, if possible, simplif. 74) C) ( - )(4 + ) ( - )(4 - ) ( + )(4 + ) ( - )(4 + ) Factor out the largest common factor. 79) ( ) 6( ) C)6( ) 6( ) 80) 6m8 - m4-40m m(6m6 - m - 40) 8(m8-4m4 - m) C) No common factor 8m(m6-4m - ) 8

9 8) ( ) No common factor C)4( ) 4( ) Solve. If no solution eists, state this. 86) = , 4 C)No solution 4 Divide and, if possible, simplif. 8) ) = C)6-8 6 C) ) = C) 7 8) ( - + 8) ( + ) ( - ) C)( + ) ( - 9) Determine whether the pair of equations represents perpendicular lines. 89) + = -4 = 0 - Yes No Solve. 84) A shopkeeper ordered a total of 6 lb of cashews and peanuts. If he ordered 4 less pounds of cashews than peanuts, then how man pounds of peanuts did he order? 8 lb 40 lb C)6 lb lb 8) 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? hr 7 hr C) 7 7 hr hr Evaluate the polnomial. 90) for = C) -6 Find an equation in point-slope form of the line having the specified slope and containing the point indicated. 9) m = - ; (-6,-) + = - (- 6) - = - ( + 6) C) + = - ( + 6) - = - (- 6) 9

10 Solve the equation. 9) = C) 9) -4 - = C) Factor completel. 99) ( + )( + 4) ( + 4)( + ) C)( - )( - 4) (- 4)( - ) 0) (9 + )( + ) ( + )(4-+)( + )(-+) C)(6 + )( + 6) (7 + )( + ) 94) -q +. = -4.-.q -4.7 C).6 9) -9b b = -b C) 4 Multipl. Leave the answer in factored form. - 4 ) ( - 4)( - ) ( + )( + ) ( - 4)( + ) C) ( + )(-) ( - 4)( + ) ( + )( - ) ( - 4)() ( + )( - ) 96) a - = - -8 C)8 - Find an equation of the line containing the given pair of points. Write our final answer in slope-intercept form. 97) (-, ) and (-, -6) = 7 - C) = = - = - - Find the slope of the line containing the given pair of points. If the slope is undefined, state so. 98) (8, -) and (-, -7) 6 6 Divide. ) ( ) ( + ) C) ) ( ) ( + 4) C) C) 9 9

11 Solve the problem. 4) A loaded moving truck is traveling 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. 9 mph mph C)90 mph 4 mph ) The product of two consecutive integers is 89 more than their sum. Find the integers. and 9, or -9, -8 C), or -9, -8-9 and -8 6) The height of a triangle is cm more than the length of the base. If the area of the triangle is cm, find the height and length of the base. height: 0 cm; base: cm height: 6 cm; base: cm C)height: 9 cm; base: 6 cm height: 8 cm; base: cm Evaluate. ) - = 6 7, 8-7,-8 C), 6-7, 8 ) ( + )( - ) = -, -7 -,- C), -, ) - m - (m - 4), for m = C) 8-74 Write the equation of the line on the graph in slope-intercept form. 4) 7) A 0-ft ladder is leaning against a building. If the bottom of the ladder is 8 ft from the base of the building, how high does the ladder reach? 4 ft 6 ft C)6 ft ft ) Two angles are complementar. Twice one angle plus the other is 9. Find the measure of each angle. 74, 6 69, C), 69, Solve b factoring and using the principle of zero products. 9) k = 0k - 0 -, -,- C), 0, = - + = C) = 7 + = Find the slope and the -intercept of the line. ) -4 + = - 4 ;(0, -) - ;(0, -) 4 C) 4 ;(0, ) - 4 ;(0, ) ) 7 = 4-4 7, 4 7 C) 4 7, , 0 7 4, 0

12 Factor completel. Add. 6) ( + 4) + ( + 4) ( + 4)( + ) ( + )( + 4) C)( + 4)( + ) ( - 4)( - ) 7) ( ) + ( ) C) Choose the most appropriate translation of the question. 8) 84 is 7% of what number? p 84 = 7 p = 0.84p C)84 = 0.7p p = Translate the problem to an equation. Do not solve. 9) 8 minus twice a number equals more than the number. 8 - = = + C)8 - = + Factor b grouping. 0) (- )( - 7) ( + )( - 7) C)6( - )( + 7) ( - )( + 7) Find the intercepts for the equation. ) = 4 (-, ), (-, 4) (-, 0), (, 0) C)(0, -), (0, ) (-, 0), (0, -) Find an equation of the line having the specified slope and containing the indicated point. Write our answer in slope-intercept form. 4) m = -9; (-7, 6) = 9-9 = -9-7 C) = -9-6 = -9-8 Determine whether the pair of equations represents parallel lines. ) + 4 = = 4 No Yes Find the - and -intercepts for the equation. Then graph the equation. 6) = (0, -4), (-6, 0) 0 ) ( + 4)( + ) ( + )( + 4) C)( - )( - 4) ( - 4)( - ) Perform the indicated operation. ) ( ) (-9) C)

13 (0, 6), (-6, 0) 0 Find the slope-intercept equation for the line with the indicated slope and -intercept. 8) Slope - 4 ; -intercept (0, 8) = = C) = = C)(0, 4), (-6, 0) -0 0 Add or subtract, as indicated. 9) ( + ) - ( + ) - ( + ) C) (0, 4), (-4, 0) Solve the sstem of equations b graphing. If there is no solution or an infinite number of solutions, state this. 0) + = + = Evaluate as requested. -0 7) Evaluate the polnomial z + + for =, = -4, and z = C)4 7 (, 6) Infinite number of solutions C)(-, 6) No solution

14 Answer Ke Testname: MATHSAMPLEFINAL ) D ) B ) B 4) B ) C 6) D 7) C 8) A 9) C ) A ) B ) A ) A 4) A ) D 6) D 7) C 8) B 9) D 0) C ) B ) C ) C 4) D ) C 6) B 7) A 8) B 9) A 0) A ) C ) B ) A 4) D ) D 6) D 7) B 8) B 9) C 40) D 4) B 4) C 4) B 44) B 4) A 46) D 47) A 48) A 49) C 0) C 4

15 Answer Ke Testname: MATHSAMPLEFINAL ) C ) D ) B 4) C ) B 6) A 7) D 8) A 9) C 60) A 6) D 6) D 6) C 64) A 6) D 66) A 67) B 68) D 69) D 70) C 7) D 7) C 7) C 74) A 7) D 76) D 77) C 78) B 79) C 80) D 8) D 8) A 8) B 84) B 8) D 86) C 87) D 88) A 89) B 90) A 9) C 9) A 9) C 94) D 9) C 96) A 97) C 98) D 99) A 0) B

16 Answer Ke Testname: MATHSAMPLEFINAL ) B ) B ) B 4) D ) C 6) C 7) A 8) B 9) D ) B ) D ) C ) A 4) A ) A 6) C 7) B 8) C 9) C 0) D ) B ) B ) D 4) B ) B 6) C 7) A 8) A 9) D 0) A 6

C) x m A) 260 sq. m B) 26 sq. m C) 40 sq. m D) 364 sq. m. 7) x x - (6x + 24) = -4 A) 0 B) all real numbers C) 4 D) no solution

C) x m A) 260 sq. m B) 26 sq. m C) 40 sq. m D) 364 sq. m. 7) x x - (6x + 24) = -4 A) 0 B) all real numbers C) 4 D) no solution Sample Departmental Final - Math 46 Perform the indicated operation. Simplif if possible. 1) 7 - - 2-2 + 3 2 - A) + - 2 B) - + 4-2 C) + 4-2 D) - + - 2 Solve the problem. 2) The sum of a number and its