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1. If A is the angle formed by the line 2y = 3x + 7 and the x -axis, then A equals
A. -45°B. 0°C. 56°D. 72°E. 215°
2. A U.S. dollar equals 0.716 European euros, and a Japanese yen equals 0.00776 European euros. How many U.S. dollars equal a Japanese yen?
A. 0.0056B. 0.011C. 0.71D. 94.2E. 179.98
3. If (x - 4)2 + 4(y - 3)2 = 16 is graphed, the sum of the distances from any fixed point on the curve to the two foci is
A. 4B. 8C. 12D. 16E. 32
4. In the equation x2 + kx + 54 = 0, one root is twice the other root. The value(s) of k is (are)
A. -5.2B. 15.6C. 22D. ± 5.2E. ± 15.6
5. The remainder obtained when 3x4 + 7x3 + 8x2 - 2x - 3 is divided by x + 1 is
A. -3B. 0C. 3D. 5E. 13
6. If f(x) = ex and g(x) = f(x) + f-1(x ), what does g (2) equal?
A. 5.1B. 7.4C. 7.5D. 8.1E. 8.3
7. If x0 = 3 and , then x3 =
A. 2.65B. 2.58C. 2.56D. 2.55E. 2.54
8. For what values of k does the graph of pass through the origin?
A. only 0B. only 1C. ±1D. ±E. no value
A. 15°B. 30°C. 45°D. 60°E. 75°
10. If x2 + 3x + 2 < 0 and f(x) = x2 - 3x + 2, then
A. 0 < f(x) < 6B. C. f(x) > 12D. f(x) > 0E. 6 < f(x) < 12
11. If f(x) = |x | + [x ], the value of f(-2.5) + f(1.5) is
A. -2B. 1C. 1.5D. 2E. 3
12. If (sec x)(tan x) < 0, which of the following must be true?
I. tan x < 0
II. csc x cot x < 0
III. x is in the third or fourth quadrant
A. I onlyB. II onlyC. III onlyD. II and IIIE. I and II
13. At the end of a meeting all participants shook hands with each other. Twenty-eight handshakes were exchanged. How many people were at the meeting?
A. 7B. 8C. 14D. 28E. 56
14. Suppose the graph of f(x) = 2x2 is translated 3 units down and 2 units right. If the resulting graph represents the graph of g(x ), what is the value of g (-1.2)?
A. -1.72B. -0.12C. 2.88D. 17.48E. 37.28
Four points on the graph of a polynomial P are shown in the table above. If P is a polynomial of degree 3, then P(x) could equal
A. (x - 5)(x - 2)(x + 1)B. (x - 5)(x + 2)(x + 1)C. (x + 5)(x - 2)(x - 1)D. (x + 5)(x + 2)(x - 1)E. (x + 5)(x + 2)(x + 1)
16. If f(x) = ax + b, which of the following make(s) f(x) = f-1(x )?
I. a = -1, b = any real number
II. a = 1, b = 0
III. a = any real number, b = 0
A. only IB. only IIC. only IIID. only I and IIE. only I and III
In the figure above, A = 110°, a = and b = 2. What is the value of C ?
A. 50°B. 25°C. 20°D. 15°E. 10°
18. If vector and vector = (3,-2), find the value of
A. 5.4B. 6C. 7D. 7.2E. 52
19. If and , then g(f(3)) =
A. 0.2B. 1.7C. 2.1D. 3.5E. 8.7
In ABC above, a = 2x, b = 3x + 2, , and C = 60°. Find x.
A. 0.5B. 0.64C. 0.77D. 1.64E. 1.78
21. If loga 5 = x and loga 7 = y , then loga
A. xyB. x - yC. (x + y )D. (y - x )E.
22. If f(x) = 3x2 + 4x + 5, what must the value of k equal so that the graph of f(x - k) will be symmetric to the y-axis?
A. -4B. - C. - D. E.
23. If f(x) = cos x and g(x) = 2x + 1, which of the following are even functions?
I. f(x) ? g(x )
II. f(g(x ))
III. g(f(x ))
A. only IB. only IIC. only IIID. only I and IIE. only II and III
24. A cylinder whose base radius is 3 is inscribed in a sphere of radius 5. What is the difference between the volume of the sphere and the volume of the cylinder?
A. 88B. 297C. 354D. 448E. 1345
25. Under which conditions is negative?
A. 0 < y < xB. x < y < 0C. x < 0 < yD. y < x < 0E. none of the above
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