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1. If x and y are integers such that 4x – 8 > 0 and 4y + 8 < 0, then which of the following must be true?
A. xy is even.B. xy is odd.C. xy is negative.D. xy is positive.E. xy is equal to zero.
2. A rectangle with length 16 and width 6 has an area that is 3 times the area of a triangle with height 8. What is the length of the base of the triangle?
A. 4B. 8C. 12D. 16E. 22
Note: Figure not drawn to scale.
A right circular cone is drawn above, with two circles centered at A on its base as shown. AB is the height of the cone, the measure of ∠ABC is 60°, and has a length of y. If bisects ∠ABC, which of the following gives the area of the smaller circle in terms of y ?
A. 8πB. 4πC. yπD. E.
4. During the past week, a factory produced 10,000 computer disks, of which 30 were found to be defective. At this rate, if the factory produced 1,000,000 computer disks, approximately how many would be defective?
A. 3B. 30C. 300D. 3,000E. 30,000
In the figure above, lines k and l are tangent to the circle with center O at points A and C, respectively. If OB = 4, OA = AB, AB = BC, and ⊥ then OA =
A. B. 2C. 2D. 4E. 4
6. If it costs z dollars to buy n pizzas, how much will it cost, in dollars, to buy b pizzas at the same rate?
A. B. C. D. E. znb
In the figure above, if l1 || l2 and x = 55, then y + z =
A. 120B. 145C. 175D. 180E. 195
In the circle above with center O, OQ = QR. If the radius of the circle is 8, what is the area of ΔOPQ ?
A. 4B. 4C. 8D. 8E. 16
9. Eighty students went on a class trip. If there were 14 more boys than girls on the trip, how many girls were on the trip?
A. 26B. 33C. 40D. 47E. 66
10. For all x, let f(x) = (10 – x)2. If p = f(6), which of the following is equal to 4p ?
A. f(24)B. f(18)C. f(12)D. f(8)E. f(4)
11. If b is a positive number not equal to 1, which of the following must also be positive?
A. B. C. D. 2 – bE. 2b – 1
12. What is the distance between the x-intercept and the y-intercept of the line y = x - 6?
A. 9B. 15C. (approximately 9.43)D. (approximately 10.82)E. 15 + (approximately 25.82)
The figures above show the graphs of the functions f and g. The function f is defined by f(x)= 2x3 + 5x2 – x. The function g is defined by g(x) = f(x – h) – k, where h and k are constants. What is the value of hk ?
A. –2B. –1C. 0D. 1E. 2
14. Which of the following is equal to 3x + 9y +12 ?
A. 3(x + 3y + 9)B. 3(x + 3y) + 12C. 3(x + 3y) + 4D. 3(x + 6y + 9)E. 3x(3y + 4)
15. To ship boxes of books, Luis charges $4.95 per box plus a one-time service fee of $7.00 per order. If he receives an order for 12 boxes of books, how much will Luis charge?
A. $11.95B. $23.95C. $66.40D. $84.00E. $143.40
16. If f (x) = , what is the smallest possible value of f (x) ?
A. There is no such value.B. 0C. D. 1E. 2
17. Question below refers to the following chart.
How many cars did the 9th grade class wash during the car wash?
A. 5B. 51C. 122D. 180E. 255
18. Question below refers to the following chart.
How many more cookies were sold by the 10th grade than were sold by the 12th grade?
A. 60B. 90C. 120D. 150E. 180
If C and D represent digits in the correctly worked multiplication problem above, then C + D =
A. 2B. 7C. 8D. 13E. 15
In the figure above, is the diameter of the circle with center O. The shaded portion of the figure has an area of 25π and is the area of the entire circle. What is the length of arc RST ?
A. 15πB. 25πC. 30πD. 112.5πE. 125π
21. If x2 - |5x| = -6, then what is one possible value of x ?
A. -5B. -2C. 0D. 5E. 6
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