B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 4 page

(A) 4

(B) 6

(C) 8

(D) 9

(E) 10

17. The city library donated some childrens books to Mr. Clarks 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

(C) 160

(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

(C) 9

(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

(C) Two

(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

(C) t

(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

(C) 40

(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

(C) f(t) = 2t + 1

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

(E) f(t) = 1 2t

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

(A) Segment

(B) Segment

(C) Ray

(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

(C) 3,000

(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

(C) 1 < < 4 or 8 < x 10

(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

(C) 100

(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

(C) I and III 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

(C) 4

(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

(C) 30

(D) 40

(E) 50

4. If , then n =

(A) 2

(B) 3

(C) 5

(D) 6

(E) 8

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

(A) 5x + 2

(B) 3x + 2

(C) 2 - x

(D) 2 3x

(E) 2 5x

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

(C) $9,000,000

(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

(C) x = 42.5

(D) x < 42.5

(E) x > 42.5

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

(A) 1

(B) 2

(C) 3

(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

(C) a + b

(D) 2a + b

(E) a + 2b

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)

(C) (- a, - b)

(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

(C) 1 by 1 by 3

(D) 1 by 2 by 2

(E) 1 by 2 by 3

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

(A) 242

(B) 266

(C) 281

(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

(C) 7

(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

(C) 0 < x < 1

(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

(C) 18

(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

(C) I and III 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

(C) 2

(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

(C) 2.8

(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

(C) I and II 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 4m 2 = m + 7, what is the value of m?

(A) 3.0

(B) 4.5

(C) 6.0

(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

(C) 30

(D) 40

(E) 80

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

(A) 80

(B) 64

(C) 60

(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

(C) 12

(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

(C) Six

(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

(C) 10

(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) = 2f(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 3b − 5c?

(A) - 27

(B) - 23

(C) 3

(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

(C) 6

(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

(C) 2

(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%

(C) 25%

(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)

(C) 10d

(D) 20d

(E) 40d

6. If the areas of the two triangles in the figure below are equal, which of the following could be the coordinates of point P?

(A) (3, - 4)

(B) (4, - 6)

(C) (2, - 4)

(D) (2, - 5)

(E) (1, - 7)

7. If a b = - 4, what is the value of a^{2} 2ab + b^{2}?

(A) - 32

(B) - 16

(C) 0

(D) 16

(E) 32

8. Between which two months did the Franklin Office Supply Depot experience the greatest change in the number of units sold?

(A) February to March

(B) March to April

(C) April to May

(D) June to July

(E) August to September

9. The ratio of r to s is 3 to 4. The ratio of s to t is 2 to 9. What is the ratio of r to t?

(A) 1 to 3

(B) 1 to 6

(C) 2 to 9

(D) 3 to 10

(E) 4 to 5

10. Points A, B, C, and D lie on a line, in that order. If CD > BC > AB and the length of CD is 6, which of the following could be the length of AD?

(A) 17

(B) 18

(C) 19

(D) 20

(E) 21

11. The table below gives values of the linear function f for selected values of x. Which of the following functions defines f?

(A) f(x) = + 4

(B) f(x) = x - 3

(C) f(x) = 2x + 2

(D) f(x) = 3x − 3

(E) f(x) = 4x − 6

12. In the figure below, if l || n, which of the following is not necessarily equal to e?

(A) a

(B)

(C)

(D)

(E) d

13. If k is a positive integer, which of the following is equivalent to ?

(A)

(B)

(C)

(D)

(E)

14. If t is 40 percent greater than p, and p is 40 percent less than 600, what is the value of t − p?

(A) 144

(B) 240

(C) 360

(D) 504

(E) 1008

15. In the sequence below, each term after the second can be found by multiplying the two preceding terms together. For example, the third term is −2 × 4 = − 8. How many of the first 139 terms of this sequence are negative?

- 2, 4, 8

(A) 46

(B) 70

(C) 74

(D) 92

(E) 93

16. In the figure below, if the value of h(5) = k, then what is the value of h(2k)?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9

17. In a bag of marbles, of the marbles are red, of the marbles are white, and of the marbles are blue. If the remaining 10 marbles are green, how many marbles are in the bag?

(A) 15

(B) 20

(C) 35

(D) 45

(E) 50

18. If x and y are positive numbers greater than 1, and then w =

(A)

(B)

(C)

(D)

(E)

19. In the quadrilateral below, ON = OM = OP. If MN = MP, then what is the value of x?

(A) 15

(B) 20

(C) 25

(D) 30

(E) 35

20. There are five roads from Wilton to Norwalk and four roads from Norwalk to Darien. If

Kristina drives from Wilton to Darien and back, passes through Norwalk in both directions, and does not travel any road twice, how many different routes are possible for the round trip?

(A) 16

(B) 32

(C) 160

(D) 240

(E) 360

21. If pens cost $3 each and binders cost $2 each, which of the following represents the cost, in dollars, of p pens and b binders?

(A) 5(b + p)

(B) 3bp

(C) 3p + 2b

(D) 2(p + b)

(E) 6bp

22. Which of the following integers is divisible by 4 and 6, but is not divisible by 8?

(A) 12

(B) 24

(C) 48

(D) 64

(E) 72

23. If 8,755 = 85(x + 2), then x =

(A) 12

(B) 14

(C) 100

(D) 101

(E) 102

24. Let be defined by the equation for all non-zero numbers x, y, and z. Which of the following is equal to an odd integer?