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(C)

(D)

(E) 32

6. If x ⁴ = 10, what is x ⁶?

(A) 10

(B) 100

(D) 1000

(E) 1000

7. The circumference of the circle with center O shown bellow is 2 π. What is the area of the shaded region?

(A)

(B)

(D) 0.5

(E) 0.25

8. If is an integer, what is the remainder when a is divided by 5?

(A) 1

(B) 2

(D) 4

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

9. Brigitte’s average (arithmetic mean) on her six math tests this marking period is 75. Fortunately for Brigitte, her teacher drops each student’s lowest grade, thus raising Brigitte’s average to 85. What was her lowest grade?

(A) 20

(B) 25

(D) 40

(E) 50

10. If m is an integer, which of the following could be true?

I. is an even integer.

II. is an even integer.

III. 17 m is a prime.

(A) I only

(B) II only

(D) I and II only

(E) II and III only

11. Max purchased some shares of stock at $10 per share. Six months later the stock was worth $20 per share. What was the percent increase in the value of Max’s investment?

(A) 20%

(B) 50%

(D) 200%

(E) The answer depends on the number of shares purchased.

12. Benjamin can type a full report in h hours. At this rate, how many reports can he type in m minutes?

(A)

(B)

(C)

(D)

(E)

13. The estate of a wealthy man was distributed as follows: 10% to his wife, 5% divided equally among his three children, 5% divided equally among his five grandchildren, and the balance to a charitable trust. If the trust received $1,000,000, how much did each grandchild inherit?

(A) $10,000

(B) $12,500

(D) $62,500

(E) $100,000

14. If A, B, C, and D lie on the same straight line, and if AC = 2 CD = 3 BD, what is the value of the ratio

(A)

(B)

(C)

(D)

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

15. A car going 40 miles per hour set out on an 80 mile trip at 9:00 A M. Exactly 10 minutes later, a second car left from the same place and followed the same route. How fast, in miles per hour, was the second car going if it caught up with the first car at 10:30 A M.?

(A) 45

(B) 50

(D) 55

(E) 60

16. In the figure below, what is the ratio of y to x?

(A)

(B)

(C)

(D)

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

17. Which of the following is equal to 10 – 9?

Questions 17 and 18 refer to the following definition. For any positive integer n, n represents the sum of the integers from 1 to n. For example, 5 = 1 + 2 + 3 + 4 + 5 = 15.

(A) 1

(B) 2

(D) 4

(E) 5

18. If 1000 = 50,500 and 10 = 55, what is the value of 1010?

(A) 50,555

(B) 55,555

(D) 60,555

(E) 65,555

19. A school’s honor society has 100 members: 40 boys and 60 girls, of whom 30 are juniors and 70 are seniors. What is the smallest possible number of senior boys in the society?

(A) 0

(B) 5

(D) 15

(E) 20

20. In the figure below, the small circle is inscribed in the square, which is inscribed in the large circle. What is the ratio of the area of the large circle to the area of the small circle?

(A)

(B)

(D)

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

21. In a class, 20 children were sharing equally the cost of a present for their teacher. When 4 of the children decided not to contribute, each of the other children had to pay $1.50 more. How much, in dollars, did the present cost?

(A) 50

(B) 80

(D) 120

(E) 150

22. If Wally’s Widget Works is open exactly 20 days each month and produces 80 widgets each day it is open, how many years will it take to produce 96,000 widgets?

(A) less than 5

(B) 5

(D) 10

(E) more than 10

23. In the figure below, JL = KL = LM and m ∠ JLK = 70. This information is sufficient to determine the value of which of the following?

(A) a only

(B) b only

(D) b and c only

(E) a, b, and c

24. The equation |1- | = 7 has two solutions. What is the sum of these solutions?

(A) 0

(B) 9

(D) 20

(E) 298

25. A (5, 1) lies on a circle whose center is O (1, 5). If is a diameter, what are the coordinates of B?

(A) (3, 3)

(B) (6, 6)

(D) (–1, 10)

(E) (–3, 9)

26. What is the volume, in cubic inches, of a cube whose total surface area is 216 square inches?

(A) 6

(B) 18

(D) 216

(E) 1296

27. If f (x) = , how many integers are in the domain of f?

(A) None

(B) 3

(D) 7

(E) Infinitely many

28. If a point in the figure below is chosen at random, what is the probability that the point lies in the shaded outer ring?

(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)

TEST 29

1. If 2 x + 4 x + 6 x = –12, then x =

(A) -1

(B) -0.5

(D) 0.5

(E) 1

2. What is the average (arithmetic mean) number of students per class?

Questions 2 and 3 refer to the information in the following table, which shows the number of students in each of the five fifth-grade classes at Taft Elementary School and, for each class, the number of students in the school band.

(A) 23

(B) 24

(D) 25

(E) 26

3. Which class has the highest percent of students in the band?

(A) A

(B) B

(D) D

(E) E

4. What is the product of 1.1 and 1.9 rounded to the nearest tenth?

(A) 1.5

(B) 1.7

(D) 2.1

(E) 3.0

5. In the figure below, lines k and are parallel, and line k passes through D, one of the corners of square ABCD. What is the value of w?

(A) 30

(B) 40

(D) 50

(E) 60

6. Steve took a bike trip in which he covered half the total distance on Monday. After going 100 kilometers on Tuesday, he determined that he still had 10% of the trip to complete. What was the total length, in kilometers, of the trip?

(A) 200

(B) 250

(D) 500

(E) 600

7. A number, x, is chosen at random from the set of positive integers less than 10. What is the probability that ?

(A)

(B)

(C)

(D)

(E)

8. The members of the French Club conducted a fundraising drive. The average (arithmetic mean) amount of money raised per member was $85. Then Jean joined the club and raised $50. This lowered the average to $80. How many members were there before Jean joined?

(A) 4

(B) 5

(D) 7

(E) 8

9. R, S, and T are points with RT = 2 RS. Which of the following could be true?

I. R, S, and T are the vertices of a right triangle.

II. R, S, and T are three of the vertices of a square.

III. R, S, and T all lie on the circumference of a circle.

(A) I only

(B) III only

(D) I and III only

(E) I, II, and III

10. There are 12 men on a basketball team, and in a game 5 of them play at any one time. If the game is 1 hour long, and if each man plays exactly the same amount of time, how many minutes does each man play?

(A) 10

(B) 12

(D) 25

(E) 30

11. The volume of pitcher I is A ounces, and the volume of pitcher II is B ounces, with B > A. If pitcher II is full of water and pitcher I is empty, and if just enough water is poured from pitcher II to fill pitcher I, what fraction of pitcher II is now full?

(A)

(B)

(C)

(D)

(E)

12. In the figure below, w + x + y + z =

(A) 140

(B) 280

(D) 320

(E) 360

13. What is the greatest value of x that is a solution of the following equation?

| x – 5| + 10 = 15

(A) 0

(B) 5

(D) 20

(E) 30

14. What is the average (arithmetic mean) of x, y, and z?

x + y = 10, y + z = 15, x + z = 17

(A) 7

(B) 14

(D) 21

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

15. A number of people boarded a bus at the terminal. At the first stop, half of the passengers got off and 1 got on. At the second stop, of the passengers on the bus got off and 1 got on. If the bus then had 15 passengers, how many were there when the bus left the terminal?

(A) 40

(B) 48

(D) 60

(E) 62

16. Thirty years ago, Mr. and Mrs. Lopez purchased a house. On average, the value of the house has doubled every 6 years. If the house is worth $320,000 today, what did they pay for it 30 years ago?

(A) $5,000

(B) $10,000

(D) $160,000

(E) $320,000×2⁵

17. Which of the following statements concerning the triangle in the figure below must be true?

I. c = 80 – a

II. c = b – 50

III. a + b = c + d

(A) I only

(B) II only

(D) I and III only

(E) I, II, and III

18. If c carpenters can build a garage in d days, how many days will it take e carpenters, working at the same rate, to build 2 garages?

(A)

(B)

(C)

(D)

(E)

19. If a ² ≠ b ², then

(A) -2

(B) 0

(D)

(E)

20. Let A = total area of five circles of radius r, and let B = total area of three circles of radius s. If A = B, then

(A)

(B)

(C)

(D)

(E)

21. If (w + 12) – 12 = 12, w =

(A) -12

(B) 0

(D) 24

(E) 36

22. If 24 of the 40 students in a club are girls, what is the ratio of boys to girls in the club?

(A) 2:5

(B) 3:5

(D) 3:2

(E) 5:2

23. If 25 – 3 = 7, what is the value of x?

(A) -36

(B) -6

(D) 36

(E) There is no value of x that satisfies the equation

24. What is the area of the circle whose center is at O (2, –2) and that passes through point P (3, 3)?

(A) 2 π

(B) 6 π

(D) 25 π

(E) 26 π

25. At Music Outlet the regular price for a CD is d dollars. How many CDs can be purchased for m dollars when the CDs are on sale at 50% off the regular price?

(A)

(B)

(C)

(D)

(E)

26. If f (x) = 9 x + 9 ^x, what is the value of f ()?

(A) 3

(B) 6

C) 7.5

(D) 9

(E) 9.9

27. Which of the following is equivalent to ?

(A) 2

(B)

(C)

(D)

(E)

28. The first term of sequence I is 2, and each subsequent term is 2 more than the preceding term. The first term of sequence II is 2 and each subsequent term is 2 times the preceding term. What is the ratio of the 32nd term of sequence II to the 32nd term of sequence I?

(A) 1

(B) 2

(D) 2²⁷

(E) 2³²

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)

TEST 30

1. Which of the following numbers has the same digit in the hundreds and hundredths places?

(A) 2200.0022

(B) 2224.2442

D) 2246.2462

(E) 2246.6422

2. Beth has twice as many baseball cards as Bruce. If Beth has b cards, how many cards does Bruce have?

(A) 2 b

(B) b ²

(C)

(D)

(E) b + 2

3. Alexis programmed her VCR to record for exactly 225 minutes. If it began recording at 9:05 A.M., at what time did it stop recording?

(A) 11:30 AM.

(B) 12:00 PM.

D) 12:50 PM.

(E) 1:00 PM.

4. In the figure below, what is the value of x?

(A) 40

(B) 60

C) 70

(D) 80

(E) 140

5. If the difference of two numbers is greater than the sum of the numbers, which of the following must be true?

(A) Neither number is negative.

(B) At least one of the numbers is negative.

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