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1. If , for what value(s) of x does the graph of f(x ) have a vertical asymptote?
A. -2, 0, and 2B. -2 and 2C. 2D. 0E. -2
2. What is the distance between the points with coordinates (-3,4,1) and (2,7,-4)?
A. 5.24B. 7.68C. 11.45D. 13E. 19.26
3. Log (a2 - b2) =
A. log a2 - log b2B. C. D. 2 · log a - 2 · log bE. log (a + b ) + log (a - b )
4. The sum of the roots of the equation
A. 1.9B. 2.2C. 2.5D. 3.3E. 6.8
5. If the graph of x + 2y + 3 = 0 is perpendicular to the graph of ax + 3y + 2 = 0, then a equals
A. -6B. - C. D. E. 6
6. The maximum value of 6 sin x cos x is
A. B. 1C. 2.6D. 3E. 6
7. If f(r ,) = r cos, then f(2,3)=
A. -3B. -1.98C. 0.1D. 1.25E. 2
8. If 5 and -1 are both zeros of the polynomial P(x), then a factor of P(x) is
A. x2 - 5B. x2 - 4x + 5C. x2 + 4x - 5D. x2 + 5E. x2 - 4x - 5
9. i14 + i15 + i16 + i17=
A. 0B. 1C. 2iD. 1 - iE. 2 + 2i
10. When the graph of y = sin 2x is drawn for all values of x between 10° and 350°, it crosses the x-axis
A. zero timesB. one timeC. two timesD. three timesE. six times
11. The third term of an arithmetic sequence is 15, and the seventh term is 23. What is the first term?
A. 1B. 6C. 9D. 11E. 13
12. A particular sphere has the property that its surface area has the same numerical value as its volume. What is the length of the radius of this sphere?
A. 1B. 2C. 3D. 4E. 6
A. B. C. D. E.
14. The pendulum on a clock swings through an angle of 1 radian, and the tip sweeps out an arc of 12 inches. How long is the pendulum?
A. 3.8 inchesB. 6 inchesC. 7.6 inchesD. 12 inchesE. 35 inches
15. What is the domain of the function
A. x 1.33B. x 1.53C. x 2.33D. x -1.33 or x 1.33E. x -2.33 or x 2.33
16. If x + y = 90°, which of the following must be true?
A. cos x = cos yB. sin x = -sin yC. tan x = cot yD. sin x + cos y = 1E. tan x + cot y = 1
17. The graph of the equation y = x3 + 5x + 1
A. does not intersect the x-axisB. intersects the x-axis at one and only one pointC. intersects the x-axis at exactly three pointsD. intersects the x-axis at more than three pointsE. intersects the x-axis at exactly two points
18. The length of the radius of the sphere x2 + y2 + z2 + 2x - 4y = 10 is
A. 3.16B. 3.38C. 3.46D. 3.74E. 3.87
The graph of y = x4 + 11x3 + 9x2 - 97x + c is shown above with the window shown below it. Which of the following values could be c ?
A. -2820B. -80C. 80D. 250E. 2820
20. Which of the following is the solution set for x (x - 3)(x + 2) > 0?
A. x < -2B. -2 < x < 3C. -2 < x < 3 or x > 3D. x < -2 or 0 < x < 3E. -2 < x < 0 or x > 3
21. Which of the following is the equation of the circle that has its center at the origin and is tangent to the line with equation 3x - 4y = 10?
A. x2 + y2 = 2B. x2 + y2 = 4C. x2 + y2 = 3D. x2 + y2 = 5E. x2 + y2 = 10
22. If f(x) = 3 - 2x + x2, then
A. t2 + 2xt - 2tB. x2t2 - 2xt + 3C. t + 2x - 2D. 2x - 2E. none of the above
23. If f(x) = x3 and g(x) = x2 + 1, which of the following is an odd function (are odd functions)?
A. only IB. only IIC. only IIID. only II and IIIE. I, II, and III
24. In how many ways can a committee of four be selected from nine men so as to always include a particular man?
A. 48B. 56C. 70D. 84E. 126
The figure above shows a portion of the graph of y = 2x. What is the sum of the areas of the three inscribed rectangles shown?
A. 14B. 28C. 128D. 256E. 384
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