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1. A central angle of two concentric circles is . The area of the large sector is twice the area of the small sector. What is the ratio of the lengths of the radii of the two circles?
A. 0.25:1B. 0.50:1C. 0.67:1D. 0.71:1E. 1:01
2. If the region bounded by the lines , x = 0, and y = 0 is rotated about the y-axis, the volume of the figure formed is
A. 18.8B. 37.7C. 56.5D. 84.8E. 113.1
3. If there are known to be 4 broken transistors in a box of 12, and 3 transistors are drawn at random, what is the probability that none of the 3 is broken?
A. 0.25B. 0.255C. 0.375D. 0.556E. 0.75
4. What is the domain of ?
A. x > 0B. x > 2.47C. –2.47 < x < 2.47D. –3.87 < x < 3.87E. all real numbers
5. Which of the following is a horizontal asymptote to the function f(x) = ?
A. y = –3.5B. y = 0C. y = 0.25D. y = 0.75E. y = 1.5
6. When a certain radioactive element decays, the amount at any time t can be calculated using the function , where a is the original amount and t is the elapsed time in years. How many years would it take for an initial amount of 250 milligrams of this element to decay to 100 milligrams?
A. 125 yearsB. 200 yearsC. 458 yearsD. 496 yearsE. 552 years
7. If n is an integer, what is the remainder when 3x(2n+ 3) – 4x(2n + 2) + 5x(2n+ 1) – 8 is divided by x + 1?
A. –20B. –10C. –4D. 0E. The remainder cannot be determined.
8. Four men, A, B, C, and D, line up in a row. What is the probability that man A is at either end of the row?
A. B. C. D. E.
A. 260B. 50C. 40D. 5E. none of these
10. The graph of y4 – 3x2 + 7 = 0 is symmetric with respect to which of the following?
I. the x -axis
II. the y-axis
III. the origin
A. only IB. only IIC. only IIID. only I and IIE. I, II, and III
11. In a group of 30 students, 20 take French, 15 take Spanish, and 5 take neither language. How many students take both French and Spanish?
A. 0B. 5C. 10D. 15E. 20
12. If f(x) = x2, then
A. 0B. hC. 2xD. 2x + hE.
13. The plane whose equation is 5x + 6y + 10z = 30 forms a pyramid in the first octant with the coordinate planes. Its volume is
A. 15B. 21C. 30D. 36E. 45
14. What is the range of the function ?
A. All real numbersB. All real numbers except 5C. All real numbers except 0D. All real numbers except -1E. All real numbers greater than 5
15. Given the set of data 1, 1, 2, 2, 2, 3, 3, x, y, where x and y represent two different integers. If the mode is 2, which of the following statements must be true?
A. If x = 1 or 3, then y must = 2.B. Both x and y must be > 3.C. Either x or y must = 2.D. It does not matter what values x and y have.E. Either x or y must = 3, and the other must = 1.
16. If and g(x)=x2, for what value(s) of x does f(g(x)) = g(f(x))?
A. –0.55B. 0.46C. 5.45D. –0.55 and 5.45E. 0.46 and 6.46
17. If 3x – x2 2 and y2 + y 2, then
A. –1 xy 2B. –2 xy 2C. –4 xy 4D. –4 xy 2E. xy = 1, 2, or 4 only
18. In ABC, if sin A = and sin B = , sin C =
A. 0.14B. 0.54C. 0.56D. 3.15E. 2.51
19. The solution set of is
A. 0 < x < B. x < C. x > D. < x < 1E. x > 0
20. Suppose the graph of f(x) = –x3 + 2 is translated 2 units right and 3 units down. If the result is the graph of y = g(x), what is the value of g (–1.2)?
A. –33.77B. –1.51C. –0.49D. 31.77E. 37.77
In the figure above, the bases, ABC and DEF, of the right prism are equilateral triangles of side s. The altitude of the prism BE is h. If a plane cuts the figure through points A, C, and E, two solids, EABC, and EACFD, are formed. What is the ratio of the volume of EABC to the volume of EACFD?
22. A new machine can produce x widgets in y minutes, while an older one produces u widgets in w hours. If the two machines work together, how many widgets can they produce in t hours?
23. The length of the major axis of the ellipse 3x2 + 2y2 – 6x + 8y – 1 = 0 is
A. B. C. D. 4E.
24. A recent survey reported that 60 percent of the students at a high school are girls and 65 percent of girls at this high school play a sport. If a student at this high school were selected at random, what is the probability that the student is a girl who plays a sport?
A. 0.1B. 0.21C. 0.32D. 0.39E. 0.42
25. If x – 7 divides x3 – 3k3x2 – 13x – 7, then k =
A. 1.19B. 1.34C. 1.72D. 4.63E. 5.04
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