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1. What is the domain of the function ?
A. –7.5 < x < 7.5B. x < –7.5 or x > 7.5C. x < –2.7 or x > 2.7D. x < –3.2 or x > 3.2E. x < 1.9 or x > 1.9
2. A magazine has 1,200,000 subscribers, of whom 400,000 are women and 800,000 are men. Twenty percent of the women and 60 percent of the men read the advertisements in the magazine. What is the probability that a randomly selected subscriber reads the advertisements?
A. 0.3B. 0.36C. 0.4D. 0.47E. 0.52
3. Let S be the sum of the first n terms of the arithmetic sequence 3, 7, 11, ? ? ? , and let T be the sum of the first n terms of the arithmetic sequence 8, 10, 12, ? ? ? . For n > 1, S = T for
A. no value of n B. one value of n C. two values of n D. three values of n E. four values of n
4. On the interval , the function has a maximum value of
A. 0.78B. 1C. 1.1D. 1.2E. 1.4
5. A point has rectangular coordinates (3,4). The polar coordinates are (5,). What is the value of ?
A. 30°B. 37°C. 51°D. 53°E. 60°
6. If f(x) = x2 – 4, for what real number values of x will f(f(x)) = 0?
A. 2.4B. ±2.4C. 2 or 6D. ±1.4 or ±2.4E. no values
7. If f(x) = x log x and g(x) = 10x, then g(f(2)) =
A. 24B. 17C. 4D. 2E. 0.6
8. If , then
A. 1.4B. 1.5C. 1.6D. 2E. 2.7
The figure above shows the graph of 5x. What is the sum of the areas of the rectangles?
A. 32,550B. 16,225C. 2604D. 1302E. 651
10. (p,q) is called a lattice point if p and q are both integers. How many lattice points lie in the area between the two curves x2 + y2 = 9 and x2 + y2 – 6x + 5 = 0?
A. 0B. 1C. 2D. 3E. 4
11. If sin A = , 90° < A < 180°, cos B = , and 270° < B < 360°, the value of sin (A + B) is
A. –0.83B. –0.55C. –0.33D. 0.73E. 0.95
12. For all real numbers x, f(2x) = x2 – x + 3. An expression for f(x) in terms of x is
A. 2x2 – 2x + 3B. 4x2 – 2x + 3C. D. E. x2 – x + 3
13. For what value(s) of k is x2 – kx + k divisible by x – k?
A. only 0B. only 0 or C. only 1D. any value of k E. no value of k
14. If the graphs of x2 = 4(y + 9) and x + ky = 6 intersect on the x-axis, then k =
A. 0B. 6C. –6D. no real numberE. any real number
15. The length of the latus rectum of the hyperbola whose equation is x2 – 4y2 = 16 is
A. 1B. 2C. D. 2E. 16
and f1 = 3, then f5 =
A. 1B. 2C. 4D. 8E. 16
17. How many distinguishable rearrangements of the letters in the word CONTEST start with the two vowels?
A. 120B. 60C. 10D. 5E. none of these
18. Which of the following translations of the graph of y = x2 would result in the graph of y = x2 – 6x + k, where k is a constant greater than 10?
A. Left 6 units and up k unitsB. Left 3 units and up k + 9 unitsC. Right 3 units and up k + 9 unitsD. Left 3 units and up k – 9 unitsE. Right 3 units and up k – 9 units
19. How many positive integers are there in the solution set of ?
A. 0B. 2C. 4D. 5E. an infinite number
20. During the year 1995 the price of ABC Company stock increased by 125%, and during the year 1996 the price of the stock increased by 80%. Over the period from January 1, 1995, through December 31, 1996, by what percentage did the price of ABC Company stock rise?
A. 103%B. 205%C. 305%D. 405%E. 505%
21. If x0 = 3 and xn+ 1, then x3 =
A. 15.9B. 31.7C. 44.9D. 65.2E. 173.9
22. When the smaller root of the equation 3x2 + 4x – 1 = 0 is subtracted from the larger root, the result is
A. –1.3B. 0.7C. 1.3D. 1.8E. 2
23. Each of a group of 50 students studies either French or Spanish but not both, and either math or physics but not both. If 16 students study French and math, 26 study Spanish, and 12 study physics, how many study both Spanish and physics?
A. 4B. 5C. 6D. 8E. 10
24. If x, y, and z are positive, with xy = 24, xz = 48, and yz = 72, then x + y + z =
A. 22B. 36C. 50D. 62E. 96
25. sin–1 (cos 100°) =
A. –1.4B. –0.2C. 0.2D. 1E. 1.4
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