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The graph of y = g(x) is shown in the figure above. If g(x) = ax2 + bx + c for constants a, b, and c, and if abc ≠ 0, then which of the following must be true?
A. ac > 1B. c > 1C. ac < 0D. a > 0E. ac > 0
2. If = x, what is the value of 4x + 2 ?
A. 2B. 3C. 4D. 12E. 14
In the figure above, which of the following points lies within the shaded region?
A. (-1, 1)B. (1, -2)C. (4, 3)D. (5, -4)E. (7, 0)
4. Six cups of flour are required to make a batch of cookies. How many cups of flour are required to make enough cookies to fill 12 cookie jars, if each cookie jar holds 1.5 batches?
A. 108B. 90C. 81D. 78E. 72
5. If n is an even integer, which of the following must be an odd integer?
A. 3n - 2B. 3(n + 1)C. n - 2D. E. n2
6. In the coordinate plane, what is the midpoint of the line segment with endpoints at (3, 4) and (0, 0) ?
A. (1.5, 2)B. (5, 0)C. (2.5, 0)D. (3.5, 3.5)E. (1.75, 1.75)
7. x - x =
A. -5xB. -xC. -xD. xE. 3x
The chart above shows the number of red and blue parrots Toby sold in May and the average weight of each type of bird sold. If Toby sold no other parrots, what was the average (arithmetic mean) weight, in pounds, of the parrots that Toby sold in May?
A. 2B. 2C. 2D. 5E. 9
In the figure above, the perimeter of square FCDE is how much smaller than the perimeter of rectangle ABDE ?
A. 2B. 3C. 4D. 7E. 16
In ΔABC above, if AC = 8, what is the length of ?
A. 8B. 8C. 6D. 4E. 3
11. If , what is the value of x ?
A. 4B. 16C. 16D. 32E. 64
12. If b equals 40% of a, then in terms of b, 40% of 4a is equal to which of the following?
A. B. C. bD. 4bE. 16b
13. Question below refers to the following definition.
For all real numbers x, let f(x) = 2x2 + 4.
What is the value of f(4)?
A. 16B. 18C. 20D. 36E. 72
14. Question below refers to the following definition.
Which of the following is equal to f(3) + f(5)?
A. f(4)B. f(6)C. f(8)D. f(10)E. f(15)
15. If the circle with center O has a diameter of 9, then what is the area of the circle with center O ?
A. 81πB. πC. πD. 18πE. 9π
16. The graph of which of the following equations is parallel to the line with equation y = -3x - 6?
A. x - 3y = 3B. x - y = 2C. x + y = 4D. x + y = 5E. x + 3y = 6
17. How many solutions exist to the equation |x| = |2x – 1|?
A. 0B. 1C. 2D. 3E. 4
18. There are k gallons of gasoline available to fill a tank. After d gallons have been pumped, in terms of k and d, what percent of the gasoline has been pumped?
A. B. C. D. E.
19. Ray and Jane live 150 miles apart. Each drives toward the other's house along a straight road connecting the two, Ray at a constant rate of 30 miles per hour and Jane at a constant rate of 50 miles per hour. If Ray and Jane leave their houses at the same time, how many miles are they from Ray's house when they meet?
A. 40B. 51C. 56D. 75E. 93
20. A bag contains 4 red hammers, 10 blue hammers, and 6 yellow hammers. If three hammers are removed from the bag at random and no hammer is returned to the bag after removal, what is the probability that all three hammers will be blue?
In the figure above, x || y. What is the value of a in terms of b and c ?
A. b + cB. 2b – cC. 180 – b + cD. 180 – b – cE. 360 – b – c
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