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(D) 100(a + b)² < 400

(E) 400(a + b)²

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 07

1. If x ² – 36 = 0, which of the following could be a value of x?

(A) - 6

(B) - 4

(D) 3

(E) 12

2. The length of a rectangular rug is 2 feet more than its width. If the length of the rug is 8 feet, what is the area of the rug in square feet?

(A) 16

(B) 48

(D) 80

(E) 96

3. If r = 2 t and t = 3, what is the value of 2 r?

(A) 2

(B) 4

(D) 8

(E) 12

4. If the statement below is true, which of the following must also be true?

Some integers in set X are even.

(A) If an integer is even, it is in set X.

(B) If an integer is odd, it is in set X.

(D) All integers in set X are odd.

(E) Not all integers in set X are odd.

5. A triangle has a perimeter of 13 and one side of length 3. If the lengths of the other two sides are equal, what is the length of each of them?

(A) 4

(B) 5

(D) 7

(E) 8

6. The grid below shows the number of hours worked last week by 12 students of various ages at after-school jobs. Which of the following is true, according to this grid?

(A) Half of the students worked more than 12 hours each.

(B) One student worked exactly 15 hours.

(D) More 18 year olds than 17 year olds worked at least 13 hours each.

(E) Most of the students were under 16 years old.

7. Squaring the product of z and 5 gives the same result as squaring the sum of z and 5. Which of the following equations could be used to find all possible values of z?

(A) 5 z ² = (z + 5)²

(B) (5 z)² = z ² + 5²

(D) (5 z)²= (z + 5)²

(E) 5 z ²= z ² + 5²

8. If as many 7-inch pieces of wire as possible are cut from a wire that is 3 feet long, what is the total length of the wire that is left over? (12 inches = 1 foot)

(A) 1 inch

(B) 2 inches

(D) 4 inches

(E) 5 inches

9. Which of the lettered points in the figure below has coordinates (x, y) such that | x | + | y | = 5?

(A) A

(B) B

(D) D

(E) E

10. If n is a member of both set A and set B bellow, which of the following must be true?

I. n is an integer.

II. 4 n is an integer.

III. n = 4

(A) None

(B) II only

(D) I and III only

(E) I, II, and III only

11. If y is directly proportional to x and if y = 20 when x = 6, what is the value of y when x = 9?

(A)

(B)

(D) 27

(E) 30

12. The n th term of a sequence is defined to be 4n + 3. The 50th term is how much greater than the 45th term?

(A) 5

(B) 16

(D) 23

(E) 24

13. Which of the rectangular solids shown below has a volume closest to the volume of a right circular cylinder with radius 2 and height 4?

(A) A

(B) B

(D) D

(E) E

14. If x is a negative integer, what is the ordering of j, k, and m from least to greatest?

(A) j < k < m

(B) j < m < k

(D) m < j < k

(E) m < k < j

15. Flour, water, and salt are mixed by weight in the ratio of 5:4:1, respectively, to produce a certain type of dough. In order to make 5 pounds of this dough, what weight of salt, in pounds, is required?

(A)

(B)

(C)

(D) 1

(E) 2

16. In rectangle ABCD below, the area of the shaded region is given by . If the area of the shaded region is 7 , what is the total area, to the nearest whole number, of the unshaded regions of rectangle ABCD?

(A) 4

(B) 6

(D) 9

(E) 10

17. The city library donated some children’s books to Mr. Clark’s first-grade class. If each student takes 4 books, there will be 20 books left. If 3 students do not take a book and the rest of the students take 5 books each, there will be no books left. How many books were donated to the class?

(A) 120

(B) 140

(D) 175

(E) 185

18. In the figure below, if line has a slope of - 2, what is the y -intercept of ?

(A) 7

(B) 8

(D) 10

(E) 12

19. For all positive integers w and y, where w > y, let the operation # be defined by w#y = . For how many positive integers w is w #1 equal to 4?

(A) None

(B) One

(D) Four

(E) More than four

20. The figure below represents four offices that will be assigned randomly to four employees, one employee per office. If Karen and Tina are two of the four employees, what is the probability that each will be assigned an office indicated with an X?

(A)

(B)

(C)

(D)

(E)

21. The figure below shows five lines. If || m, which of the following is not equal to 90?

(A) r

(B) s

(D) u

(E) v

22. Which of the following is divisible by 3 and by 5 but is not divisible by 10?

(A) 30

(B) 35

(D) 45

(E) 60

23. The table below gives values of the function f for several values of t. If the graph of f is a line, which of the following defines f (t)?

(A) f (t) = t - 1

(B) f (t) = t + 1

(D) f (t) = 2 t - 1

(E) f (t) = 1 – 2 t

24. In the figure below, the intersection of ray and ray is

(A) Segment

(B) Segment

(D) Ray

(E) Line

25. According to the graph below, if there are 6,000 registered voters aged 60 and over in Washington County, how many registered voters are under the age of 30?

(A) 1,000

(B) 2,000

(D) 4,000

(E) 5,000

26. Based on the graph of the function f below, what are the values of x for which f (x) is positive?

(A) – 2 < 1 or 8 < x 10

(B) – 2 < 1 or 4 < x < 8

(D) – 2 x 10

(E) 1 < x < 8

27. Bernardo drives to work at an average speed of 50 miles per hour and returns along the same route at an average speed of 25 miles per hour. If his total travel time is 3 hours, what is the total number of miles in the round-trip?

(A) 225

(B) 112.5

(D) 62.5

(E) 50

28. If x and y are integers such that x ² = 64 and y ³ = 64, which of the following could be true?

I. x = 8

II. y = - 4

III. x + y = - 4

(A) I only

(B) II only

(D) II and III only

(E) I, II, and III

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 08

1. If 3(m + n) + 3 = 15, then m + n =

(A) 2

(B) 3

(D) 5

(E) 6

2. If Elena reads at a rate of r pages per minute for a total of m minutes, which of the following represents the total number of pages that Elena reads?

(A) rm

(B)

(C)

(D)

(E)

3. In the figure below, if l is a line, a + b = 120 and b + c = 100, then what is the value of b?

(A) 10

(B) 20

(D) 40

(E) 50

4. If , then n =

(A) 2

(B) 3

(D) 6

(E) 8

5. If 4 x + b = x + 2, what is b in terms of x?

(A) 5 x + 2

(B) 3 x + 2

(D) 2 – 3 x

(E) 2 – 5 x

6. The tables below show the retail prices of two car models and the quantities of those models sold at a particular car dealership in three different years. Based on these tables, how much greater was the total value of cars sold in 2005 than in 1995?

(A) $5,500,000

(B) $6,500,000

(D) $10,500,000

(E) $12,000,000

7. An isosceles triangle has one angle with a measure greater than 95° and another with a measure of x °. Which of the following must be true?

(A) x > 85

(B) x = 85

(D) x < 42.5

(E) x > 42.5

8. When m is divided by 7, the remainder is 2. What is the remainder when 4 m is divided by 7?

(A) 1

(B) 2

(D) 4

(E) 5

9. If a is a multiple of 3 and b is an odd integer, then which of the following must be an odd integer?

(A)

(B) ab

(D) 2 a + b

(E) a + 2 b

10. The point (a, b) is reflected over the x - axis, and then the reflected point is reflected over the y-axis. If a and b are both positive, which of the following represents the coordinates of the point after the second reflection?

(A) (a, b)

(B) (b, a)

(D) (- b, - a)

(E) (a, - b)

11. A right circular cylinder with a radius of 1 and a height of 1 has a volume that is most nearly the same as the volume of a rectangular solid with dimensions

(A) 1 by 1 by 1

(B) 1 by 1 by 2

(D) 1 by 2 by 2

(E) 1 by 2 by 3

12. If the n th term of a sequence is 3 n ² - n, then how much greater is the 10th term than the 3rd term?

(A) 242

(B) 266

(D) 286

(E) 290

13. What is the maximum number of points of intersection between a circle and a square that lie in the same plane?

(A) 4

(B) 6

(D) 8

(E) 9

14. If x < x ³ < x ², then which of the following must be true?

(A) x < -1

(B) -1 < x < 0

(D) x > 1

(E) x is not a real number

15. If (m + n)² = 18 and mn = 4, then what is the value of m ² + n ²?

(A) 10

(B) 14

(D) 22

(E) 26

16. An isosceles triangle has two sides of length 5 and 12. Which of the following could be the perimeter of this triangle?

I. 22

II. 29

III. 30

(A) II only

(B) I and II only

(D) II and III only

(E) I, II, and III

17. The figure below shows a digital counter above a dial counter showing the digits 0 through 5. Both counters are initially set to 0 and count upward together in increments of 1. For instance, when the digital counter reads 5 the dial counter also reads 5, but when the digital counter reads 6, the dial counter resets back to 0. What will the dial counter read when the digital counter reads 1000?

(A) 0

(B) 1

(D) 4

(E) 5

18. In a mixture of raisins and dates, the ratio by weight of raisins to dates is 7 to 3. How many pounds of raisins will there be in 7 pounds of this mixture?

(A) 2.1

(B) 2.3

(D) 3.0

(E) 4.9

19. If m and n are integers and m = n - then which of the following could be the value of m?

I. –5

II. –3

III. –1

(A) II only

(B) II and III only

(D) I and III only

(E) I, II, and III

20. Each of the k girls in a club agreed to raise an equal amount of money to give to a charity to which the club had pledged a total of x dollars. If p more girls later join the club and also agree to raise an equal share of the pledged amount, how much less would each of the original club members have to raise, in dollars, than she had originally agreed to raise?

(A)

(B)

(C)

(D)

(E)

21. If 4 m – 2 = m + 7, what is the value of m?

(A) 3.0

(B) 4.5

(D) 7.5

(E) 9.0

22. In the figure below, l and m are lines. What is the value of x?

(A) 10

(B) 20

(D) 40

(E) 80

23. If of m is 48, what is of m?

(A) 80

(B) 64

(D) 40

(E) 30

24. Let represent the nth term of a particular sequence. If = 54 and each term except the first is equal to the previous term divided by 3, then what is the first term that is not an integer?

(A)

(B)

(C)

(D)

(E)

25. If is an integer, which of the following could not be the value of n?

(A) 2

(B) 8

(D) 18

(E) 32

26. Four of the six faces of a cube are painted black, and the other two faces are painted white. What is the least number of vertices on this cube that could be shared by two or more black faces?

(A) Eight

(B) Seven

(D) Five

(E) Four

27. If y varies directly as x, and if y = 8 when x = a and y = 12 when x = a + 10, what is the value of a?

(A) 5

(B) 8

(D) 15

(E) 20

28. The figure below shows the graph of the function f (x) = ax + b, where a and b are constants.

What is the slope of the graph of the function g (x) = –2 f (x)?

(A) -3

(B) -

(C)

(D)

(E) 3

29. Differentiate the function in the below.

, for some constant a and b

(A)

(B)

(C)

(D)

(E)

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

(A)

(B)

(C)

(D)

(E)

TEST 09

1. If b = 4 and c = 7, what is the value of 3 b − 5 c?

(A) - 27

(B) - 23

(D) 6

(E) 20

2. If the average (arithmetic mean) of 4 and w is equal to the average of 2, 8, and w, what is the value of w?

(A) 2

(B) 4

(D) 8

(E) 10

3. In the figure below, the length of MN is equal to the length of QR. What is the value of x?

(A) - 3

(B) - 1

(D) 5

(E) 6

4. The cost of a highway toll was $0.75 in 2005. The following year the cost of the toll increased to $1.00. By what percent did the toll increase?

(A) 10%

(B) 20%

(D) 33%

(E) 50%

5. The cost of four oranges is d dollars. At this rate, what is the cost of 40 oranges?

(A)

(B)

(D) 20 d

(E) 40 d

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