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1. Which of the following equations has 3 as a solution?
I.x2 - 9x = 0
II.x2 + x - 12 = 0
III.x2 + 6x + 9 = 0
A. I onlyB. II onlyC. III onlyD. I and IIE. II and III
2. A sequence of numbers is created by starting with k, and then adding 3 to the previous number to create each new number. If the 20th number in this sequence is 55, then k equals
A. -5B. -2C. 1D. 5E. 35
If the diameter of circle O is 10 cm, and ABCD is a square, then the area of the shaded region in cm2 is which of the following?
A. 25π - 50B. 25π - 25C. 50π - 50D. 50π - 100E. 100π - 100
4. If 3a + 2b = -4, and 2a + 3b = -11, then 5a - 5b =
A. -15B. 5C. 7D. 15E. 35
In the drawing above, line segment XY is parallel to line segment AB. If AB = 10, XY = 6, and the area of triangle ABC is 50, then the area of triangle XYC is
A. 18B. 24C. 30D. 36E. 44
6. Biking with the wind, a cyclist took 40 minutes to complete a ride. Biking against the wind, the cyclist took 60 minutes to complete the same ride. Assuming that the cyclist bikes 30 miles per hour without any wind, and that the wind's speed was constant, the speed of the wind, in miles per hour, was
A. 5B. 6C. 8D. 10E. There is not enough information given.
7. If k is an integer less than 8, then the greatest possible value of 2k - 1 is
A. 6B. 7C. 13D. 14E. 15
8. The sum of the odd numbers from 3 to 11, including both 3 and 11, is
A. 24B. 32C. 35D. 45E. 63
In the diagram above, lines p and q are parallel. The measure of the angle marked x is
A. 30°B. 40°C. 50°D. 60°E. 70°
10. The price of a certain train ticket is directly proportional to the number of miles traveled. If a ten-mile trip costs $3.75, then a 24-mile trip would cost
A. $6.15B. $9.00C. $10.50D. $15.00E. $17.75
11. If a Δ b = b2 - 3a, then -4 Δ -2 =
A. -22B. -16C. -8D. 16E. 22
12. A function is defined by . For
what value(s) of x would the function equal 25?
A. 12.5 onlyB. 12.5 or C. 81 onlyD. 81 or -81E. none of the above
Each box in the shape above is a square. If the total area of the shape is 48 square units, then the length of AB is
A. 5 unitsB. 10 unitsC. 20 unitsD. 40 unitsE. 80 units
14. A bag of candy was divided among four children. The first child got exactly one-fourth of the candy. Then, the second child got one-third of the candy that was left. Next, the third child got one-half of the candy remaining. Finally, the fourth child got everything left over. Which child now has the least candy?
A. The first child got the least.B. The second child got the least.C. The third child got the least.D. The third and fourth children are tied for the least.E. All four children got the same amount of candy.
In the diagram above, O is the center of the large circle, and A and B are the centers of the two smaller circles. If the length of NP is 8, then the area of the shaded region is
A. 4πB. 8πC. 16πD. 32πE. 48π
The graph above shows y = f(x). Which point would have to appear on the graph of y = 2f(x) + 4?
A. (-1, 0)B. (0, 1)C. (1, 0)D. (2, -2)E. (10, 0)
17. On a hike, a student walked 10 kilometers due north, 5 kilometers due east, and 2 kilometers due south. Her distance, in a straight line, from her starting point is now closest to
A. 2.6 kilometersB. 8 kilometersC. 9.4 kilometersD. 12.1 kilometersE. 17 kilometers
18. The expression (x - 5)2 is equivalent to
A. x2 - 10x + 25B. x2 + 25C. x2 - 10D. x2 - 5x + 25E. x2 - 25
19. Let a ~ b equal:
2a, if a > b
b + 3, if b > a
5, if a = b
Which of the following would equal 14?
A. 5 ~ 7B. 7 ~ 8C. 7 ~ 7D. 7 ~ 5E. 11 ~ 7
20. If it takes x widgets to make one thingumajig, and one thingumajig can produce y whatchamacallits, then the number of widgets needed to produce n whatchamacallits is
A. B. nxyC. D. E.
21. In a deck of 12 cards, each card has one of the symbols below on each side. Some cards have the same symbols on both sides; some cards have different symbols. If every symbol appears on at least two different cards, and Symbols A and B together appear on a total of 13 sides, what is the maximum number of cards that could have Symbol D on both sides?
A. OneB. TwoC. ThreeD. FourE. Five
The diagram above shows two rectangles, ABCD and PQRS. If AP = 4, QR = 7, and RD = , then the area of PQRS is
A. 84B. C. 147D. 231E.
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