C) Exactly one of the numbers is negative.

(D) Both numbers are negative.

(E) None of these statements must be true.

6. (3 a ² b ³)³ =

(A) 9 a ⁵ b ⁶

(B) 9 a ⁶ b ⁹

(C) 27 a ⁵ b ⁶

(D) 27 a ⁶ b ⁹

(E) 27 a ⁸ b ²⁷

7. Anne-Marie was x years old y years ago. How old will she be in z years?

(A) x + y + z

(B) x – y + z

(C) z – x – y

(D) y – x + z

(E) x – y – z

8. 10 is what percent of A?

(A) 10 A %

(B)

(C)

(D)

(E)

9. A rectangle has a perimeter equal to the circumference of a circle of radius 3. If the width of the rectangle is 3, what is its length?

(A) 3π – 3

(B) 4.5π – 3

(C) 6π – 3

(D) 9π – 3

(E) It cannot be determined from the information given.

10. If Anthony had 3 times as many marbles as he actually has, he would have as many marbles as Billy has. What is the ratio of the number of marbles Anthony has to the number of marbles Billy has?

(A) 1:9

B) 1:3

(C) 1:1

(D) 3:1

(E) 9:1

11. In the figure below, . If R represents the perimeter of rectangle ABCD, and T represents the perimeter of CBE, what is the value of R – T?

(A) 2

B) 8

(C) 20

(D) 12 – 4

(E) It cannot be determined from the information given.

12. Two cylindrical tanks have the same height, but the radius of one tank equals the diameter of the other. If the volume of the larger is k % more than the volume of the smaller, k =

(A) 50

(B) 100

(C) 200

(D) 300

E) 400

13. For any numbers a, b, c, d, is defined to be a number box if ac = bd and a = b + c + d.

If is a number box, then x + y =

(A) 8

(B) 10

(C) 12

(D) 14

(E) 24

14. If f (x) = 3 x + 8, for what value of a is f (a) = a?

A) -4

(B) -2

(C) -

(D) 0

(E)

15. In the figure below, if the perimeter of square ABCD is 8, what is the perimeter of square RSTU?

(A) 4 + 4

(B) 8

(C) 12

(D) 16

(E) It cannot be determined from the information given.

16. If x + y = a, y + z = b, and x + z = c, what is the average (arithmetic mean) of x, y, and z?

(A)

(B)

(C)

(D)

(E) It cannot be determined from the information given.

17. A circular grass field has a circumference of 120 meters. If Eric can mow 400 square meters of grass per hour, how many hours will he take to mow the entire field?

(A) 4

(B) 5

(C) 6

(D) 8

(E) 9

18. If X = , what is the result on X of doubling a, tripling b, and quadrupling c?

(A) X is multiplied by 1.5.

(B) X is multiplied by 3.

(C) X is multiplied by 4.5.

(D) X is multiplied by 6.

(E) X is multiplied by 9.

19. A sequence of numbers begins 1, 1, 1, 2, 2, 3 and then repeats this pattern of six numbers forever. What is the sum of the 135th, 136th, and 137^th numbers in the sequence?

(A) 3

(B) 4

(C) 5

(D) 6

(E) 7

20. The measures of the three angles of a triangle are in the ratio of 5:5:10, and the length of the longest side is 10. From this information, which of the following can be determined?

I. The area of the triangle

II. The perimeter of the triangle

III. The length of each of the three altitudes

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I, II, and III

21. If A is the set of odd positive integers less than 10, and B is the set of prime numbers less than 10, how many members does A ∪ B have?

(A) 3

B) 5

(C) 6

(D) 9

(E) 10

22. Mr. Brock wrote a number on the blackboard. When he added 3 to the number, he got the same result as when he multiplied the number by 3. What was the number he wrote?

(A) -3

(B) 0

C) 1.5

(D)

(E) 3

23. What positive number n satisfies the equation (16)(16)(16) n = ?

(A)

B) 1

(C) 4

(D) 8

(E) 16

24. If A (2, –1) and B (4, 7) are the endpoints of a diameter of a circle, what is the area of the circle?

(A) 16π

(B) 17π

(C) 18π

(D) 144π

(E) 1156π

25. In the figure below, arcs and are semicircles. If a point is chosen at random inside the figure, what is the probability that the point lies in the shaded region?

(A)

(B)

(C)

(D)

(E)

26. If r and s are positive numbers satisfying the inequality < , which of the following must be true?

(A) r < s

(B) s < r

(C) r > 1

(D) s > 1

(E) r and s can be any numbers as long as r ≠ s.

27. If f (x) = 3 + , which of the following cannot be a value of f (x)?

(A) -

(B) -

C) 0

(D)

(E) 3

28. A square and an equilateral triangle each have sides of length 5. What is the ratio of the area of the square to the area of the triangle?

(A)

(B)

(C)

(D)

(E)

29. Differentiate the function in the below.

(A)

(B)

(C)

(D)

(E)

30. Find the integral of the function in the below.

(A)

(B)

(C)

(D)

(E)

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