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1. A right circular cone whose base radius is 4 is inscribed in a sphere of radius 5. What is the ratio of the volume of the cone to the volume of the sphere?
A. 0.222 : 1B. 0.256 : 1C. 0.288 : 1D. 0.333 : 1E. 0.864 : 1
2. If x0 = 1 and then x3 =
A. 1.26B. 1.361C. 1.396D. 1.408E. 1.412
3. The y-intercept of is
A. 0.22B. 0.67C. 1.41D. 1.49E. 4.58
4. If the center of the circle x2 + y2 + ax + by + 2 = 0 is point (4,–8), then a + b =
A. –8B. –4C. 4D. 8E. 24
5. If p(x) = 3x2 + 9x + 7 and p(a) = 2, then a =
A. only 0.736B. only –2.264C. 0.736 or 2.264D. 0.736 or –2.264E. –0.736 or –2.264
6. If i is a root of x4 + 2x3 – 3x2 + 2x – 4 = 0, the product of the real roots is
A. –4B. –2C. 0D. 2E. 4
7. If and 270° B 360°, sin(A + B) =
A. –0.832B. –0.554C. –0.333D. 0.733E. 0.954
8. If a family has three children, what is the probability that at least one is a boy?
A. 0.875B. 0.67C. 0.5D. 0.375E. 0.25
9. If sec 1.4 = x, find the value of csc(2 tan-1x).
A. 0.33B. 0.87C. 1D. 1.06E. 3.03
10. The graph of |y – 1| = |x + 1| forms an X. The two branches of the X intersect at a point whose coordinates are
A. (1,1)B. (–1,1)C. (1,–1)D. (–1,–1)E. (0,0)
11. For what value of x between 0° and 360° does cos 2x = 2 cos x ?
A. 68.5° or 291.5°B. only 68.5°C. 103.9° or 256.1°D. 90° or 270°E. 111.5° or 248.5°
12. For what value(s) of x will the graph of the function have a maximum?
A. B. C. D. E.
13. For each positive integer n, let Sn = the sum of all positive integers less than or equal to n. Then S51 equals
A. 50B. 51C. 1250D. 1275E. 1326
14. If the graphs of 3x2 + 4y2 – 6x + 8y – 5 = 0 and (x – 2)2 = 4(y + 2) are drawn on the same coordinate system, at how many points do they intersect?
A. 0B. 1C. 2D. 3E. 4
15. If logx 2 = log3x is satisfied by two values of x, what is their sum?
A. 0B. 1.73C. 2.35D. 2.81E. 3.14
16. Which of the following lines are asymptotes for the graph of
I. x = –1
II. x = 5
III. y = 3
A. I onlyB. II onlyC. I and IID. I and IIIE. I, II, and III
17. If and 0° 180°, then =
A. 0°B. 0° or 180°C. 80.5°D. 0° or 80.5°E. 99.5°
18. If f(x,y) = 2x2 – y2 and g(x) = 2x, which one of the following is equal to 22x?
A. f(x,g(x))B. f(g(x),x)C. f(g(x),g(x))D. f(g(x),0)E. g(f(x,x))
19. Two positive numbers, a and b, are in the sequence 4, a, b, 12. The first three numbers form a geometric sequence, and the last three numbers form an arithmetic sequence. The difference b – a equals
A. 1B. C. 2D. E. 3
20. A sector of a circle has an arc length of 2.4 feet and an area of 14.3 square feet. How many degrees are in the central angle?
A. 63.4°B. 20.2°C. 14.3°D. 12.9°E. 11.5°
21. The y- coordinate of one focus of the ellipse 36x2 + 25y2 + 144x – 50y – 731 = 0 is
A. –2B. 1C. 3.32D. 4.32E. 7.81
In the figure above, ABCD is a square. M is the point one-third of the way from B to C. N is the point one-half of the way from D to C. Then =
A. 50.8°B. 45.0°C. 36.9°D. 36.1°E. 30.0°
23. If f is a linear function such that f(7) = 5, f(12) = –6, and f(x) = 23.7, what is the value of x?
A. –3.2B. –1.5C. 1D. 2.4E. 3.1
24. Under which of the following conditions is negative?
A. x < y < 0B. y < x < 0C. 0 < y < xD. x < 0 < yE. all of the above.
25. The binary operation * is defined over the set of real numbers to be . What is the value of 2 * (5 * 3)?
A. 1.84B. 2.14C. 2.79D. 3.65E. 4.01
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