B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 8 страница

(A) 1:9

(B) 1:3

(C) 1:1

(D) 3:1

(E) 9:1

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

(C) 2²⁶

(D) 2²⁷

(E) 2³²

29. Find the second order derivatives of the function

(A)

(B)

(C)

(D)

(E)

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

(A)

(B)

(C)

(D)

(E)

TEST 19

1. A playground with an area of 3,600 square feet is to be divided into six different play stations. What is the average (arithmetic mean) area, in square feet, of the six stations?

(A) 400

(B) 500

(C) 600

(D) 700

(E) 800

2. If 3 a = 15 and 4 b = 10, what is the value of ?

(A)

(B)

(C)

(D) 2

(E)

3. The graph below shows the salaries of five employees at UltraCorp over an eight-year period. Which employee’s salary has risen at the fastest rate over this period?

(A) Employee 1

(B) Employee 2

(C) Employee 3

(D) Employee 4

(E) Employee 5

4. One bucket of fried chicken serves either three adults or five children. If the Memorial Day fair committee wants to have enough chicken to serve 100 children and 60 adults, how many buckets of chicken are needed?

(A) 29

(B) 32

(C) 35

(D) 40

(E) 45

5. (5 x − 3 x + 4)(3 x + 6 x − 2) =

(A) 9 x ² + 16 x − 4

(B) 18 x ² + 32 x − 8

(C) 18 x ² - 40 x + 8

(D) 72 x ² + 20 x − 8

(E) 72 x ² - 20 x + 8

6. In the figure below, l || m and z = 55. What is the value of a + b + c?

(A) 235

(B) 265

(C) 275

(D) 305

(E) 315

7. If + 16 = 79, what is the value of x?

(A) 3

(B) 6

(C) 9

(D) 27

(E) 81

8. Each term in a sequence of numbers, except for the first term, is 2 less than the square root of the previous term. If the third term of this sequence is 1, what is the first term?

(A) 1

(B) 9

(C) 11

(D) 121

(E) 123

9. In the figure below, rectangle ABCD has an area of 90 and is divided into 15 smaller squares. What is the sum of the areas of the shaded regions?

(A) 39

(B) 42

(C) 45

(D) 48

(E) 51

10. For all x greater than 2, let be defined as the sum of the positive integers less than x. What is the value of ?

(A) 27

(B) 29

(C) 42

(D) 45

(E) 54

11. In the correctly worked addition problem below, X and Y represent two different digits. What digit does X represent?

(A) 0

(B) 1

(C) 4

(D) 8

(E) 9

12. If the average (arithmetic mean) of the three numbers below is 3 x and x ≠ 0, what is y in terms of x?

(A)

(B) 2 x

(C) 3 x

(D) x + 7

(E) 3 x - 3

13. In the figure below, what is the value of x in terms of w?

(A) w - 2

(B) w - 1

(C) w

(D) w + 1

(E) w + 2

14. When r is divided by 10, the remainder is 9. What is the remainder when r + 2 is divided by 5?

(A) 0

(B) 1

(C) 3

(D) 4

(E) 14

15. If five distinct lines lie in a plane, then at most how many distinct points can lie on two or more of these lines?

(A) 6

(B) 7

(C) 8

(D) 9

(E) 10

16. A pile of playing cards consists of only kings, jacks, and queens. If the probability of randomly choosing a king is and the probability of randomly choosing a queen is , what is the probability of randomly choosing a jack?

(A)

(B)

(C)

(D)

(E)

17. In the figure below, Δ VXT is equilateral and WU = WY. If the measure of ∠ VWU is twice the measure of ∠ VUW, what is the measure of ∠ TUY?

(A) 55

(B) 60

(C) 65

(D) 70

(E) 75

18. If m and n are positive numbers, what percent of m − 4 is n + 2?

(A)

(B)

(C)

(D)

(E)

19. At time t = 0, a rocket was launched from a platform m meters below the ground. Until the rocket hit the ground, its height, in meters, after t seconds was given by the function h bellow. For which of the following values of t did the rocket have the same height as it did when t = 10?

(A) 8

(B) 12

(C) 14

(D) 16

(E) 18

20. The price of a certain stock was d dollars on January 1, 2003. The price decreased by 20% in January, increased by 40% in February, decreased by 25% in March, and increased by 25% in April. In terms of d, what was the price of the stock at the end of April?

(A) 0.80 d

(B) 0.84 d

(C) 1.05 d

(D) 1.12 d

(E) 1.20 d

21. Eric earns a 5% commission on each $200 stereo that he sells. How many stereos must he sell to earn $100?

(A) 5

(B) 10

(C) 15

(D) 20

(E) 25

22. Jane’s Discount Music Superstore sells both new and used CDs and DVDs. On the basis of the information listed below, how many used DVDs were sold during the holiday season?

(A) 2,500

(B) 3,000

(C) 4,000

(D) 6,500

(E) 7,000

23. One bag of potatoes of a certain brand weighs 40 ounces. Five pounds of these potatoes cost $4.00. If Larry has exactly $20.00 to spend on potatoes, what is the maximum number of bags he can buy? (1 pound = 16 ounces)

(A) 7

(B) 8

(C) 9

(D) 10

(E) 11

24. What is the area of the shaded region in the figure below?

(A) 15

(B) 20

(C) 25

(D) 30

(E) 35

25. The rectangular solid below is constructed of 12 cubes that each have a volume of 8 cubic inches. What is the surface area of the solid?

(A) 32

(B) 48

(C) 96

(D) 128

(E) 144

26. Set M consists of the consecutive integers from −15 to y, inclusive. If the sum of all of the integers in set M is 70, how many numbers are in the set?

(A) 33

(B) 34

(C) 35

(D) 36

(E) 37

27. In a round robin tennis tournament involving seven players, each player will play every other player twice. How many total matches will be played in the tournament?

(A) 21

(B) 28

(C) 42

(D) 48

(E) 56

28. The figure below shows a right prism, the base of which is a quarter of a circle with center C. If the area of each base of the prism is 12.5π and the volume of the solid is 300π, what is the distance from point A to point B?

(A) 24

(B) 26

(C) 28

(D) 30

(E) 32

29. Find the second order derivatives of the function

(A)

(B)

(C)

(D)

(E)

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

(A)

(B)

(C)

(D)

(E)

TEST 20

1. In the figure below, if the coordinates of points J and K are added together, this sum will be the coordinate of a point between

(A) -3 and -2

(B) -2 and -1

(C) 0 and 1

(D) 1 and 2

(E) 2 and 3

2. If 6 x + 9 y = 8, then 2 x +3 y =

(A)

(B)

(C) 2

(D)

(E) 3

3. Glenna had three boxes of pencils, each of which contained y pencils. She distributed these pencils by giving one to each student in her class, and had 9 pencils left over. If there are 21 students in Glenna’s class, what is y?

(A) 3

(B) 4

(C) 6

(D) 8

(E) 10

4. If an integer n is divisible by both 12 and 20, then it must also be divisible by

(A) 15

(B) 24

(C) 32

(D) 80

(E) 240

5. A container in the shape of a right circular cylinder contains 12 liters of liquid when it is filled to of its height. How many liters does it contain when it is completely filled?

(A) 18

(B) 16

(C) 15

(D) 10

(E) 9

6. The profit that a company earns is equal to its revenue minus its expenses. If the revenue, in dollars, that a company makes for selling x items is given by the function R (x) = 12 x and the expenses it must pay for selling those x items is given by the function E (x) = 3 x + 12, then which of the following expresses the profit, in dollars, that the company earns for selling those x items?

(A) P (x) = 15 x + 12

(B) P (x) = 15 x –12

(C) P (x) = 9 x + 12

(D) P (x) = 9 x –12

(E) P (x) = 12 – 9 x

7. The average (arithmetic mean) of x and y is m, where m 0. What is the average (arithmetic mean) of x, y, and 2 m?

(A) m

(B)

(C)

(D)

(E) 2 m

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

(A) 30

(B) 40

(C) 50

(D) 60

(E) 70

9. For all real values of x and y, let x ♦ y be defined by the equation x ♦ y = 2 – xy. If –1 < a < 0 and 0 < b < 1, then which of the following must be true?

(A) –2 < a ♦ b < –1

(B) –1 < a ♦ b < 0

(C) 0 < a ♦ b < 1

(D) 1 < a ♦ b < 2

(E) 2 < a ♦ b < 3

10. The figure below shows a circle with an area of 25π square units. If each vertex of the rectangle is on the circle as shown, what is the area of the rectangle, in square units?

(A) 30

(B) 36

(C) 42

(D) 48

(E) 54

11. Line l passes through the origin and is perpendicular to the line given by the equation 2 x + y = 8. Which of the following points is not on line l?

(A) (-4, -2)

(B) (-1, 1)

(C) (2, 1)

(D) (4, 2)

(E) (7, 3.5)

12. If a and b are positive numbers, which of the following is equivalent to a % of 5 b?

(A)

(B)

(C)

(D)

(E)

13. If the triangle in the figure below is reflected over line l, what will be the coordinates of the reflection of point A?

(A) (4, 1)

(B) (6, 1)

(C) (10, 1)

(D) (11, 1)

(E) (12, 1)

14. How many positive 3-digit integers contain only odd digits?

(A) 15

(B) 75

(C) 125

(D) 225

(E) 500

15. If k is a positive odd integer greater than 4, which of the following always represents the product of two even integers?

(A) k ² = – 4

(B) k ² + 4 k –5

(C) k ² + 5 k + 6

(D) k ² + 3 k – 10

(E) k ² + k –20

16. The figure below shows the graph of the function f (x) = x ² – k. Points A and B lie on the graph of the function and are the vertices of rectangle ABCD. If AB = 6 and the area of rectangle ABCD is 20, what is the value of k?

(A)

(B)

(C)

(D)

(E)

17. In the figure below, if the coordinates of points P and Q are multiplied together, the result will be closest to which of the following points?

(A) A

(B) B

(C) C

(D) D

(E) E

18. If = 5 z and =5 y then xy =

(A) 3

(B) 4

(C) 12

(D) 24

(E) 36

19. When a positive integer p is divided by 7, the remainder is 2. Which of the following expressions will yield a remainder of 4 when divided by 7?

(A) p + 2

(B) p + 3

(C) p + 4

(D) p + 5

(E) p + 6

20. Which of the following graphs best represents the information in the table below?

(A)

(B)

(C)

(D)

(E)

21. Four hundred dollars was invested at a yearly simple interest rate of x percent. If at the end of one year the investment had grown to 500 dollars, what is the value of x?

(A) 20

(B) 25

(C) 30

(D) 45

(E) 40

22. In the figure below, which of the following line segments (not shown) has a slope of − 3?

(A)

(B)

(C)

(D)

(E)

23. In a parking lot, ³/₄ of the vehicles are cars and ¹/₃ of the cars are more than 3 years old. If 20 cars in the lot are more than 3 years old, how many vehicles are there in total?

(A) 30

(B) 40

(C) 60

(D) 80

(E) 90

24. What is the average (arithmetic mean) of 8 consecutive odd integers if the smallest of those integers is n?

(A) n + 5

(B) n + 6

(C) n + 7

(D) n + 8

(E) n + 9

25. If w is an integer and w 0, which of the following must be a positive even integer?

(A) w ⁴

(B) (w – 2)³

(C) 4 w ²

(D) 4 w

(E) 3(w ²)

26. In the circle below, W is the center of the circle and the length of ZY is 8. If the area of the circle is 64π, what is the value of x?

(A) 40

(B) 50

(C) 60

(D) 70

(E) 80

27. Which of the following expressions is equivalent to 16 x ⁴?

I. (64 x ⁶)^2/3

II.

III.

(A) I only

(B) II only

(C) II and III only

(D) I and II only

(E) I, II, and III

28. In April of 2004, d dogs and c cats lived in an animal shelter. If 4 cats arrived at the shelter in May of 2004 and the ratio of dogs to cats remained unchanged, in terms of c and d, how many dogs arrived at the shelter in May of 2004?

(A) 4

(B)

(C)

(D)

(E)

29. Find the second order derivatives of the function

(A)

(B)

(C)

(D)

(E)

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

(A)

(B)

(C)

(D)

(E)

TEST 21

1. A cookie recipe requires 2.5 cups of flour and makes 36 cookies. At this rate, how many cups of flour are required to make 54 cookies?

(A) 3

(B) 3

(C) 3

(D) 4

(E) 4

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

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