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1. If point (a,b) lies on the graph of function f, which of the following points must lie on the graph of the inverse f ?
A. (a,b)B. (–a,b)C. (a,–b)D. (b,a)E. (–b,–a)
2. Harry had grades of 70, 80, 85, and 80 on his quizzes. If all quizzes have the same weight, what grade must he get on his next quiz so that his average will be 80?
A. 85B. 90C. 95D. 100E. more than 100
3. Which of the following is an asymptote of ? tan πx ?
A. x = –2B. x = –1C. D. x = 1E. x = 2
4. If logb x = p and logb y = q, then logb xy =
A. pqB. p + qC. D. p – qE. pq
5. The sum of the roots of 3x3 + 4x2 – 4x = 0 is
A. B. C. 0D. E. 4
6. If then
A. 0B. C. D. E. 1
7. If f(x) = log(x + 1), what is f–1(3)?
A. 0.6B. 4C. 999D. 1001E. 10,000
8. If f(x) 0 for all x, then f(2 – x) is
A. –2B. 0C. 2D. 0E. 2
9. How many four-digit numbers can be formed from the numbers 0, 2, 4, 8 if no digit is repeated?
A. 18B. 24C. 27D. 36E. 64
10. If x –1 is a factor of x2 + ax – 4, then a has the value
A. 4B. 3C. 2D. 1E. none of the above
11. If 10 coins are to be flipped and the first 5 all come up heads, what is the probability that exactly 3 more heads will be flipped?
A. 0.0439B. 0.1172C. 0.125D. 0.3125E. 0.6
12. If and n is a positive integer, which of the following statements is FALSE?
A. i4n = 1B. i4n + 1 = –iC. i4n + 2 = –1D. in + 4 = inE. i4n + 3 = –i
13. If logr 3 = 7.1, then logr
A. 2.66B. 3.55C. D. E.
14. If f(x) = 4x2 and g(x) = f(sin x) + f(cos x), then g(23°) is
A. 1B. 4C. 4.29D. 5.37E. 8
15. What is the sum of the roots of the equation
A. – 0.315B. – 0.318C. 1.414D. 3.15E. 4.56
16. Which of the following equations has (have) graphs consisting of two perpendicular lines?
I. xy = 0
II. |y | = |x |
III. |xy | = 1
A. only IB. only IIC. only IIID. only I and IIE. I, II, and III
17. A line, m, is parallel to a plane, X, and is 6 inches from X. The set of points that are 6 inches from m and 1 inch from X form
A. a line parallel to mB. two lines parallel to mC. four lines parallel to mD. one pointE. the empty set
In the figure above, if VO = VY, what is the slope of segment VO?
A. B. C. D. E. Cannot be determined from the given information.
19. A cylindrical bar of metal has a base radius of 2 and a height of 9. It is melted down and reformed into a cube. A side of the cube is
A. 2.32B. 3.84C. 4.84D. 97.21E. 113.1
20. The graph of y = (x + 2)(2x – 3) can be expressed as a set of parametric equations. If x = 2t – 2 and y = f(t), then f(t) =
A. 2t(4t – 5)B. (2t – 2)(4t – 7)C. 2t(4t – 7)D. (2t – 2)(4t – 5)E. 2t(4t + 1)
21. If points and lie on the graph of y = x3 + ax2 + bx + c, and y1 – y2 = 3, then b =
A. 1.473B. 1.061C. –0.354D. –0.939E. –2.167
22. Rent-a-Rek has 27 cars available for rental. Twenty of these are compact, and 7 are midsize. If two cars are selected at random, what is the probability that both are compact?
A. 0.0576B. 0.0598C. 0.481D. 0.521E. 0.541
23. If a and b are real numbers, with a > b and |a| < |b|, then
A. a > 0B. a < 0C. b > 0D. b < 0E. none of the above
24. If [x] is defined to represent the greatest integer less than or equal to x, and the maximum value of f(x) is
A. –1B. 0C. D. 1E. 2
A. 0B. 1C. 2D. 3E.
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