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1. The operation # is defined by the equation a # b = . What is the value of k if 3 #k = k # 2?
A. 2.0B. 2.4C. 3.0D. 5.5E. 6.0
2. If 7x–1 = 6x, find x.
A. –13.2B. 0.08C. 0.22D. 0.52E. 12.6
3. A red box contains eight items, of which three are defective, and a blue box contains five items, of which two are defective. An item is drawn at random from each box. What is the probability that one item is defective and one is not?
A. B. C. D. E.
4. If (log3 x)(log5 3) = 3, find x.
A. 5B. 9C. 25D. 81E. 125
5. If and , then f(g(h(2))) =
A. 1.2B. 1.4C. 2.9D. 4.7E. 8.5
6. In ABC, A = 45°, B = 30°, and b = 8. Side a =
A. 6.5B. 11C. 12D. 14E. 16
7. The equations of the asymptotes of the graph of 4x2 – 9y2 = 36 are
A. y = x and y = – x B. y = 0 and x = 0C. and D. and E. and
8. If g(x – 1) = x2 + 2, then g(x) =
A. x2 – 2x + 3B. x2 + 2x + 3C. x2 – 3x + 2D. x2 + 2E. x2 – 2
9. If f(x) = 3x3 – 2x2 + x – 2, then f(i) =
A. –2i – 4B. 4i – 4C. 4i D. –2i E. 0
10. If the hour hand of a clock moves k radians in 48 minutes, k =
A. 0.3B. 0.4C. 0.5D. 2.4E. 5
11. If the longer diagonal of a rhombus is 10 and the large angle is 100°, what is the area of the rhombus?
A. 37B. 40C. 42D. 45E. 50
12. Let and g(x) = 3x. The sum of all values of x for which f(x) = g(x) is
A. –8.5B. 0C. 8D. 9E. 9.4
13. How many subsets does a set with n elements have?
A. n2B. 2nC. D. n E. n!
14. If f(x) = 23x – 5, find f –1(16).
A. 1B. 2C. 3D. 4E. 5
15. For what positive value of n are the zeros of P(x) = 5x2 + nx + 12 in ratio 2:3?
A. 0.42B. 1.32C. 4.56D. 15.8E. 25
16. If f(–x) = – f(x) for all x and if the point (–2, 3) is on the graph of f, which of the following points must also be on the graph of f ?
A. (–3, 2)B. (2, –3)C. (–2, 3)D. (–2, –3)E. (3, –2)
17. A man piles 150 toothpicks in layers so that each layer has one less toothpick than the layer below. If the top layer has three toothpicks, how many layers are there?
A. 15B. 17C. 20D. 148E. 11,322
18. If the circle x2 + y2 – 2x – 6y = r2 – 10 is tangent to the line 12y = 60, the value of r is
19. If a0 = 0.4 and an + 1 = 2|an| – 1, then a5 =
A. –0.6B. –0.2C. 0.2D. 0.4E. 0.6
20. If 5.21p = 2.86q, what is the value of ?
A. –0.60B. 0.55C. 0.6D. 0.64E. 1.57
21. As , find the limit of the product .
A. 1.9B. 2C. 2.1D. 2.2E. 2.3
22. There is a linear relationship between the number of chirps made by a cricket and the air temperature. A least-squares fit of data collected by a biologist yields the equation:
estimated temperature in °F = 22.8 + (3.4) (the number of chirps per minute)
What is the estimated increase in temperature that corresponds to an increase of 5 chirps per minute?
A. 3.4°FB. 17.0°FC. 22.8°FD. 26.2°FE. 39.8°F
23. If the length of the diameter of a circle is equal to the length of the major axis of the ellipse whose equation is x2 + 4y2 – 4x + 8y – 28 = 0, to the nearest whole number, what is the area of the circle?
A. 28B. 64C. 113D. 254E. 452
24. The force of the wind on a sail varies jointly as the area of the sail and the square of the wind velocity. On a sail of area 50 square yards, the force of a 15-mile-per-hour wind is 45 pounds. Find the force on the sail if the wind increases to 45 miles per hour.
A. 135 poundsB. 225 poundsC. 405 poundsD. 450 poundsE. 675 pounds
If the riser of each step in the drawing above is 6 inches and the tread is 8 inches, what is the value of |AB|?
A. 40 inchesB. 43.9 inchesC. 46.6 inchesD. 48.3 inchesE. 50 inches
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