UNIVERSITY OF WISCONSIN SYSTEM

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1 Name UNIVERSITY OF WISCONSIN SYSTEM MATHEMATICS PRACTICE EXAM Check us out at our website:

2 GENERAL INSTRUCTIONS: You will have 90 minutes to complete the mathematics practice test. Work rapidl but carefull. Do not spend too much time on an one question. If ou have time after ou have finished the test, ou ma go back and review our answers. PLEASE NOTE that the use of a non-graphing calculator on this test is optional. No question on this test requires the use of a calculator. GRAPHING CALCULATORS ARE NOT ALLOWED. You ma not share a calculator. When ou take the official Math Placement Test, our placement will be based on three math scores which will be used in combination to determine our optimal math placement. In order to get the most accurate assessment using this practice test, ou should tr to duplicate the actual testing situation as closel as possible. When taking the test, ou should not use an additional materials or look up the answers to the questions. You should onl allow ourself 90 minutes to take this test and should take the entire test in one sitting. If possible, take the test in a quiet room where ou will not be interrupted. When ou have completed the test, ou should score our test using the answer ke and scoring instructions provided on the last page.

3 . (a + b) + (a + (b + = a) (a + b + d) (a + b) b) 7a + b c e) 7a + b + 6c 7a b + c. ( ) = a) d) + 9 b) + 9 e) % of 60 is a) d) b) 7 e) What is the area of the given figure?. The area of triangle XYZ is Y a) d) 0 b) e) 0 7 X 0 a) 0 d) Z 7. In which triangle is the sum of the measures of the angles the greatest? b) e) 0 8 N S V Y M O R T U W X Z. a) d) 6 b) e) 8 a) MNO d) XYZ b) RST e) None of these UVW MATH PRACTICE TEST FORM

4 8. Fifteen ounces of concentrate is mied with ounces of water to make 60 ounces of orange juice. What percent of the orange juice is concentrate? a) d) 0 b) e). Subtracting n from added to three times n is equal to a) n d) n b) n + e) n + n +. Which best describes how angles K, L, and M are related? 9. = a) 7 d) b) e) None of these K L a) K + L = M d) K + L + M = 80 b) K + L > M e) More information needed K + L < M M 0. + = 0 0 b) e) 9 0. ( ) + ( ) = a) 7 d) b) e) square ards is a) square foot d) 8 square foot b) square foot e) square foot 7 square foot 6

5 . If =, then = Solve for : + ( ) = ( + ) a) = d) = b) = e) = b) e) 8 = 6. If ABCD is a rectangle, then A F E B 9. Which of the following has been reduced to lowest terms? 6 6 b) e) D C a) DCEA is a rectangle. b) DCBF is a parallelogram. DCEF is a trapezoid. d) DCEF is a parallelogram. e) DCEF is a rhombus. 0. (a ) = a) 6a d) 9a 6 b) 6a 6 e) 9a 9 9a F + 7. If d =, then p = p a) d(f + ) d) b) df e) d F + F + d d F. Epress in scientific notation. a) b) d) e) MATH PRACTICE TEST FORM 7

6 . If a train travels 60 miles in 0 minutes, what is its average speed in miles per hour? a) 0 d) 60 b) 00 e) Right triangle ABC has AC = and AB =. The area of triangle ABC is a) 78 B b) 6 60 d) 0 A C e) None of these ( ) n (A B). Find the value of when C n =, A =, B = and C =. a) 6 d) b) e) = a) 60 d) b) 7 e) 0. The remainder when is divided b is a) d) 7 b) e) 9 8. Which of the functions listed below has this graph? a) f() = b) f() = f() =. If h() =, which of the following is not defined? a) h(0) d) h() b) h() e) h( ) h( ) d) f() = log e) f() = log 8

7 9. The slope of the line with the equation = 7 + is a) d) b) 7 e) a 6 = a) a 6 d) a 8 9 b) a e) a 67 a 0. () (9 ) = a) 7 d) b) e) 9. What fraction of the rectangle s area is shaded? 6 6. Find all values of for which ( + )( ) = 0 a), d), b) e) b), e),,. Which of the following represent(s) functions of? i ii iii a) i onl d) i and iii b) ii onl e) i, ii, and iii iii onl MATH PRACTICE TEST FORM 9

8 . One factor of is a) + d) b) + e) + 8. The graph of + = crosses the ais at a) = d) = b) = e) = 6 = 6. ( + )( ) = a) b) d) + 7 e) When ou solve the equation + = 0, how man roots are greater than? a) no root d) three roots b) one root e) all roots two roots 7. An equation of the circle with center (, k) and radius is a) + = k b) ( ) + ( + k) = 0. The graph of a function = f() is given b ( ) + ( + k) = d) ( + ) + ( k) = e) ( + ) + ( k) = The domain of the inverse f () is the set of real numbers between a) 0 and d) and b) and e) and and 0

9 . Find the area of the shaded region between the lines.. If (a + ) = a 6 + 9, then a = a) b) 6 8 (0,) (0,6) (,0) a) d) b) e) 6 d) 0 e). In lowest terms, = + ( ) ( )( + ) 6. If log = log 8, then = 8 b) e) log 8 log 8 8 b) 8 e) = < 9 is equivalent to a) < < d) < < b) < < e) < < b) e) 6 6. < One factor of 8 + is a) + d) b) e) Which of the following equations has the same solution as =? + a) = 0 b) 9 + = = 0 d) = 0 e) = 0 MATH PRACTICE TEST FORM

10 9. If f() = +, then equals a) d) + h b) h e) + h + h f( + h) f() h. A value in the solution of } + = 9 + = 0 a) 0 d) is b) e) 6 0. ( ) + = a) 0 d) b) e) + ( ) +. A 90 pound coil of cable is 00 feet long. If a 0 foot length is cut off, what is the weight in pounds of the remaining cable? a) 9 d) 80 b) e) The distance between the points (,) and (,) is a) ( + ) ( + ) b) + ( ) + ( ) d) ( ) + ( ). The number of bees, P, in a colon doubles ever ears. If t is measured in ears and P is the initial number of bees, then a) P = P t/ d) P = P t o b) P = P t e) P = P t/ o P = P t o o o o e) ( ) + ( )

11 . The function f() is graphed over the interval from = to = 8. Which statement is true about f() over the given interval? (,) f() (,/) (0,) (,0) 6 8 (6, ) a) The largest value of the function is 8. b) The maimum value of f() is. The solution to f() = 0 is. d) f() = 0 when =. e) None of these 7. The function f() = + multiplies the input b then adds. Then f (), the inverse of f, a) multiplies the input b, then subtracts. b) multiplies the input b, then subtracts. subtracts from the input, then multiplies b. d) adds to the input, then mulitiplies b. e) multiplies the input b, then subtracts. 6. How man real numbers are solutions for + 7 = 0? a) none d) three b) one e) more than three two 8. The line = 0 is parallel to a) 8 = 6 6 b) = 0 = d) = 7 e) = 0 9. If ( + a) = 0 + a, then a = a) d) b) e) 0 MATH PRACTICE TEST FORM

12 60. A line not parallel to = a is a) = a d) a = + b) = a a e) a = a = a 6. Which of the following equations has a graph that is a straight line? a) = + b) + = = d) = 6. The cost, in thousands of dollars, of producing thousand tetbooks is C() = The revenue, also in thousands of dollars, is R() =. Find the profit or loss if thousand tetbooks are produced. (Profit = Revenue Cost) a) 0 thousand dollar loss e) None of these 6. Let A, B, C be distinct points on a circle with diameter AB. Then we ma conclude that C b) thousand dollar loss thousand dollar loss d) 0 thousand dollar profit A B e) thousand dollar profit 6. The total production costs C to manufacture S skateboards are shown below for a week period. Write a linear equation that represents this data. # OF PRODUCTION SKATEBOARDS COSTS WEEK $8,00 WEEK $9,96 WEEK 08 $,08 a) AC is longer than AB. b) angle ABC is greater than angle BAC. angle BAC is greater than angle ACB. d) angles BAC and ACB are complementar. e) angle ACB is a right angle. a) C = 8S +,76 b) C = 8S +,00 C = 8S + 8,00 d) C = 6.70S + 8,00 e) C = 90.86S +,00

13 6. If sin A = and 0 < A < 90, then cos A = 68. Let θ be the angle formed b the line = and the positive ais. Then 8 b) e) sin θ equals a) 0 d) b) 0 e) Suppose a triangle has the dimensions indicated below: 69. If h is an altitude of the triangle, then the area is b = 0 π A = a = 0 B θ a h c Then sin B equals a) 60 d) b) 6 e) b a) bc d) ab sin θ b) ab e) ab cos θ ab tan θ 67. cos θ tan θ = a) sin θ d) cot θ b) cos θ sin θ e) sec θ MATH PRACTICE TEST FORM

14 70. A sketch of the graph of = tan() is a) d) 7. If cos θ = and 0 < θ < 90, then cos (90 θ) equals a) d) b) e) b) e) 7. The cosine of the angle θ in the figure is θ, 7. Given ABC with D the midpoint of side AC and E the midpoint of side BC. B E A D C b) e) Then which of the following is not true? a) AB DE b) AB = DE ADE = DEC d) A = EDC 7. In the figure below, ABD = 90 and BCD = 90. The length of BC is A B e) ABC is similar to DEC D C a) d) b) e) 6 6

15 7. Which of the following statements is false? a) All squares are similar. b) All congruent rectangles are similar. All equiangular triangles are similar. 78. The triangle ABC is circumscribed about a circle with P, Q, and R as the points of tangenc. If AR = 0, CQ = 8, and BQ =, then the length of AB is A d) All equilateral triangles are similar. e) All right triangles are similar. R P C Q B 76. If cos = 0.70, then cos ( ) = a) 0.70 d) 0.0 b) 0.0 e) 0.70 a) 0 d) 6 b) e) The solutions to sin = in the interval 0 π are 77. Suppose a foot ladder is leaning against a vertical wall, where the bottom of the ladder is a distance of feet from the wall. Then the angle θ that the ladder makes with the ground is given b π a) =, 6 π b) =, π 6 π π π π =,,, 7π π π π d) =,,, π π 7π e) =,,, π π 6 θ a) d) cos b) cos e) cos cos MATH PRACTICE TEST FORM 7

16 80. Let f() have the graph shown below: 8. tan 0 = π π π π b) e) Then f() could be a) sin d) sin () b) cos () e) sin () 8. An angle of radian measure,, has degree measure of 80 π 80 π cos π b) e) None of these 80 π sin () + cos () = a) 9 d) cos (6) b) e) None of these 8. sin θ = a) sin θ b) cos θ sin θ cos θ d) sin θ + cos θ 8. In the figure below, AB = BD and BE is perpendicular to AC. If AC = and AD = 8, find AE. B e) sin θ sin θ A E D C a) d) b) e) None of these 8 END OF TEST

17 ANSWER KEY: The answers to this practice test are given below. Give ourself one point for each question ou answered correctl and zero points for each question ou answered incorrectl. Add up our points for each section: Math Basics, Algebra, and Trigonometr. An average score on Math Basics is between and 9. An average score on Algebra is between 0 and 6 and an average score on Trigonometr is between and. Placement into a remedial level math course is determined solel b our score on the Math Basics section of the test. Therefore, ou would need to score 0 or higher on the Math Basics section to test out of a remedial level math course. Math Basics Algebra Trigonometr. B. D. A. D. D 6. C 7. E 8. C 9. D 0. E. C. A. D. D. D 6. C 7. D 8. B 9. B 0. D. D. C. D. B. B 6. D 7. C 8. B 9. E 0. D. C. E. C. B. B 6. E 7. E 8. E 9. C 0. C. B. A. E. D. D 6. B 7. A 8. D 9. E 0. E. D. C. E. A. D 6. A 7. C 8. D 9. D 60. C 6. B 6. B 6. D 6. E 6. A 66. D 67. A 68. E 69. D 70. D 7. C 7. B 7. B 7. B 7. E 76. A 77. D 78. C 79. E 80. E 8. C 8. C 8. B 8. D 8. C