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1. If 10y – 6 = 3k(5y – 3) for all y, then k =
A. B. C. D. E. 2
2. For what values of x and y is |x – y| |y – x|?
A. x < y B. y < x C. x > 0 and y < 0D. for no value of x and y E. for all values of x and y
3. If (a,b) is a solution of the system of equations , then the difference, a – b, equals
A. –12B. –10C. 0D. 2E. 4
4. If f(x) = x – 1, g(x) = 3x, and h(x) = , then f –1(g(h(5))) =
A. 4B. 2C. D. E.
5. A sphere is inscribed in a cube. The ratio of the volume of the sphere to the volume of the cube is
A. 0.79:1B. 1:02C. 0.52:1D. 01:03.E. 0.24:1
6. Find y if the slope of the line containing the point (–1, 3) and (4, y) is 0.75.
A. 0.75B. 1C. 6.75D. 8E. 9.67
7. The nature of the roots of the equation 3x4 + 4x3 + x – 1 = 0 is
A. three positive real roots and one negative real rootB. three negative real roots and one positive real rootC. one negative real root and three complex rootsD. one positive real root, one negative real root, and two complex rootsE. two positive real roots, one negative real root, and one complex root
8. For what value(s) of k is x2 + 3x + k divisible by x + k?
A. only 0B. only 0 or 2C. only 0 or –4D. no value of k E. any value of k
9. What number should be added to each of the three numbers 3, 11, and 27 so that the resulting numbers form a geometric sequence?
A. 2B. 3C. 4D. 5E. 6
10. What is the equation of the set of points that are 5 units from point (2,3,4)?
A. 2x + 3y + 4z = 5B. x2 + y2 + z2 – 4x – 6y – 8z = 25C. (x – 2)2 + (y – 3)2 + (z – 4)2 = 25D. x2 + y2 + z2 = 5E.
11. If 3x3/2 = 4, then x =
A. 1.1B. 1.2C. 1.3D. 1.4E. 1.5
12. If f(x) = x3 – 4, then the inverse of f =
A. – x3+4B. C. D. E.
13. If f is an odd function and f(a) = b, which of the following must also be true?
I. f(a) = –b
II. f(–a) = b
III. f(–a) = –b
A. only IB. only IIC. only IIID. only I and IIE. only II and III
14. For all , tan + cos + tan(–) + cos(–) =
A. 0B. 2tanC. 2cosD. 2(tan + cos)E. 2
15. The period of the function f(x) = k cos kx is . The amplitude of f is
A. B. C. 1D. 2E. 4
16. If , its graph will have
A. one horizontal and three vertical asymptotesB. one horizontal and two vertical asymptotesC. one horizontal and one vertical asymptoteD. zero horizontal and one vertical asymptoteE. zero horizontal and two vertical asymptotes
17. At a distance of 100 feet, the angle of elevation from the horizontal ground to the top of a building is 42°. The height of the building is
A. 67 feetB. 74 feetC. 90 feetD. 110 feetE. 229 feet
18. A sphere has a surface area of 36π. Its volume is
A. 84B. 113C. 201D. 339E. 905
19. A pair of dice is tossed 10 times. What is the probability that no 7s or 11s appear as the sum of the sides facing up?
A. 0.08B. 0.09C. 0.11D. 0.16E. 0.24
20. The lengths of two sides of a triangle are 50 inches and 63 inches. The angle opposite the 63-inch side is 66°. How many degrees are in the largest angle of the triangle?
A. 66°B. 67°C. 68°D. 71°E. 72°
21. Which of the following is an equation of a line that is perpendicular to 5x + 2y = 8?
A. 8x – 2y = 5B. 5x – 2y = 8C. 2x – 5y = 4D. 2x + 5y = 10E.
22. What is the period of the graph of the function
A. 4πB. 2πC. πD. E.
23. For what values of k are the roots of the equation kx2 + 4x + k = 0 real and unequal?
A. 0 < k < 2B. |k| < 2C. |k| > 2D. k > 2E. –2 < k < 0 or 0 < k < 2
24. A point moves in a plane so that its distance from the origin is always twice its distance from point (1,1). All such points form
A. a lineB. a circleC. a parabolaD. an ellipseE. a hyperbola
25. If f(x) = 3x2 + 24x – 53, find the negative value of f –1(0).
A. –58.8B. –9.8C. –8.2D. –1.8E. –0.2
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