B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 6 страница

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(A)

(B)

(D)

(E) 3

26. If 16^{w + 2} = 2¹¹, what is the value of w?

(A) 0.75

(B) 1.33

(D) 3.50

(E) 4.75

27. In the figure below, ABCD is a parallelogram and AE bisects ∠ DAB. What is the value of x?

(A) 24

(B) 28

(D) 36

(E) 40

28. The width of a rectangle is 75% the length of the rectangle. The perimeter of the rectangle is 84 centimeters. A circle is drawn that contains all four vertices of this rectangle. If the area of this circle is kπ square centimeters, what is the value of k?

(A) 160

(B) 175

(D) 210

(E) 225

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 14

1. If 2 x + 7 = 4 x + 5, what is the value of x?

(A) 1

(B) 2

(D) 5

(E) 8

2. If n is any positive integer, which of the following must be even?

(A) n + 2

(B) 2 n

(D) n ²

(E) n ³

3. The length of a nail rounded to the nearest inch is 5 inches. Which of the following could be the actual length of the nail, in inches?

(A) 4.46

(B) 4.48

(D) 5.51

(E) 5.89

4. The walls of Jane’s living room have an area of 340 square feet. If she can paint 60 square feet per hour, how many minutes after she starts painting will there be only 100 square feet left to paint?

(A) 120

(B) 150

(D) 240

(E) 270

5. In the right triangle below, what is the value of 3 x?

(A) 18.0

(B) 22.5

(D) 30.0

(E) 67.5

6. What is 50% of 60% of 180?

(A) 48

(B) 54

(D) 90

(E) 92

7. If = b ² + 4 b + 4 then c =

(A)

(B)

(C)

(D)

(E)

8. If the average of 3 y, 4 y, and (y − 5) is 9, what is the value of y?

(A) 1.50

(B) 1.75

(D) 3.25

(E) 4.00

9. In the figure below, right triangle ABC has side lengths as shown. What is the value of x?

(A) 2

(B) 3

(D) 5

(E) 6

10. Which of the following represents the set of all values of x for which is defined the function f (x) = ?

(A) x - 4

(B) x > - 4

(D) x > - 4 and x 6

(E) x 6

11. When the positive integer w is divided by 6, the remainder is 2. What is the remainder when 5 w is divided by 6?

(A) 1

(B) 2

(D) 4

(E) 5

12. Given the information in the table below, what is the value of x + y + z?

(A) 35

(B) 113

(D) 299

(E) 314

13. If a circle with center (3, 4) is tangent to the x -axis, what is the circumference of the circle?

(A) 4

(B) 6

(D) 12

(E) 16

14. If the length of line segment is 7 and the length of line segment is 9, which of the following could not be the length of line segment ?

(A) 6

(B) 8

(D) 16

(E) 18

15. In the figure below, line m passes through the origin. Which of the following points lies on line m?

I. (− 2, 1)

II. (− 2, − 2)

III. (1, 1)

(A) I only

(B) I and II only

(D) II and III only

(E) I, II, and III

16. In the figure below, WX = XZ = ZY. What is the value of b?

(A) 56

(B) 76

(D) 84

(E) 128

17. In one day, Mitchell spends 30% of the day sleeping, 35% of the day at work, 5% of the day at the gym, five additional hours at home, and the rest of the day in the car. How many minutes does he spend in the car each day? (1 hour = 60 minutes)

(A) 2.2

(B) 60

(D) 132

(E) 432

18. What is the slope of the line containing the point (2, 5) and the midpoint of the line segment with endpoints (8, 8) and (6, −2)?

(A)

(B)

(C)

(D)

(E)

19. A square has a diagonal of length m. Which of the following represents the area of the square in terms of m?

(A)

(B) 2 m

(D) m ³

(E)

20. In the figure below, line l is parallel to line n. Which of the following represents the value of x in terms of y and z?

(A) z - y

(B) z + y

(D) 180 – z + y

(E) 90 - y

21. Let x $ y be defined by the equation x $ y = x ^y+ 3. What is the value of 4$2?

(A) 9

(B) 11

(D) 20

(E) 25

22. If m + n = 7 and 2 n − 3 m = 6, what is the value of 3 n − 2 m?

(A) 7

(B) 13

(D) 17

(E) 18

23. In the triangle below, if x and y are integers and x < 40, what is the smallest possible value of y?

(A) 39

(B) 61

(D) 119

(E) 141

24. Triangle ABC has side lengths that are all integers. If two of the sides are 7 and 11, how many possible values are there for the third side length?

(A) 11

(B) 12

(D) 14

(E) 15

25. In the figure below, what is the value of w?

(A) 15

(B) 14

(D) 12

(E) 11

26. In 1995, the Jones family sold their home for $192,500. They spent $175,000 to buy the house in 1988. What percent profit did they make on the sale?

(A) 9%

(B) 10%

(D) 12%

(E) 13%

27. How many different committees of four people can be assembled from a group of six people?

(A) 8

(B) 12

(D) 20

(E) 24

28. After the second term in the sequence below, each term is equivalent to the ratio of the preceding term to the term before that. For example, the third term, −2, is equal to the ratio of 6 to − 3. How many of the first 100 terms of this sequence are negative?

- 3, 6, - 2…

(A) 33

(B) 34

(D) 66

(E) 67

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 15

1. How many CD cases, each holding 120 CDs, are needed to hold 20 dozen CDs? (1 dozen = 12 CDs)

(A) 1

(B) 2

(D) 4

(E) 5

2. Which of the following has the digit 4 in both the units place and the thousandths place?

(A) 4,004.040

(B) 4,000.400

(D) 3,040.444

(E) 3,040.004

3. If f (x) = 2 x ² + 8, what is the value of f (8)?

(A) 116

(B) 133

(D) 256

(E) 264

4. In the figure below, points X, Y, and Z lie on line l, and bisects . If XZ = 8, what is the length of ?

(A) 2

(B) 3

(D) 4

(E) 5

5. At a science fair, the prize money of $3,000 is to be split in the ratio 3:2:1 by the first, second, and third place finishers, respectively. What is the amount of the third prize?

(A) $500

(B) $1,000

(D) $2,000

(E) $2,500

6. If (x − y) = − 2, then (x − y)²=

(A) - 4

(B) - 2

(D) 2

(E) 4

7. In the table below, all of the columns and rows have the same sum. What is the value of A + B + C + D?

(A) 48

(B) 56

(D) 74

(E) 90

8. If a < b < −1, which of the following has the greatest value?

(A) – 3 a + b

(B) – (a – b)

(D) 3 a

(E) a - b

9. A piece of paper is folded in half about side AB. Cuts are then made along the dotted lines. Which of the following best represents the result when unfolded?

(A)

(B)

(C)

(D)

(E)

10. How many integers from the set of all integers from 1 to 100 inclusive are not the cube of an integer?

(A) 93

(B) 94

(D) 96

(E) 97

11. In a pet store, there are three times as many goldfish as there are tropical fish. There are twice as many orange goldfish as there are black goldfish. What is the probability that a randomly selected fish from the store is a black goldfish?

(A)

(B)

(C)

(D)

(E)

12. The ideal gas law states that pressure, P, varies inversely as volume, V, and directly as the temperature, T. If P = 700 and V = 10, then T = 350. What is the value of T when P = 500 and V = 20?

(A) 20

(B) 120

(D) 350

(E) 500

13. Which of the following ordered pairs (x, y) is a solution of both of the inequalities below?

x – 2 y > 13

y + x < 13

(A) (3, - 1)

(B) (12, 3)

(D) (10, 2)

(E) (1, 5)

14. After Andrea gives Chris $10 and Liz $3, Chris gives $4 to Liz. At this point, Andrea has $10 more than Chris and $16 more than Liz. How much more money did Andrea have than Chris originally?

(A) 10

(B) 20

(D) 29

(E) 36

15. In the figure below, points U, T, and V lie on the same line and point T is the midpoint of . What is the ratio of the perimeter of square RSTU to the perimeter of triangle TVW?

(A) 2 + : 4

(B) 4: 2 +

(D) 4: 2 +

(E) 2 + : 6

16. A parking lot has 5 spots remaining and 5 different cars in line waiting to be parked. If one of the cars is too big to fit in the two outermost spots, in how many different ways can the five cars be arranged?

(A) 15

(B) 54

(D) 96

(E) 120

17. Seven students took a quiz and their average (arithmetic mean) score was 83. If the average score for three of the students was 79, what was the average score for the other four students?

(A) 85

(B) 86

(D) 88

(E) 89

18. According to the data listed in the table below, the minimum wage in 1980 was what percent larger than the minimum wage in 1974?

(A) 30%

(B) 55%

(D) 110%

(E) 155%

19. After the first two terms in the sequence below, each subsequent term is the sum of the two immediately preceding numbers. For example, 21 = 13 + 8. How many of the first 60 terms of this sequence are odd?

8, 13, 21…

(A) 20

(B) 30

(D) 40

(E) 44

20. A snow-removal company charges a business d dollars for removing any amount of snow from their parking lot up to 6 inches, and f dollars for each additional inch of snow. Which of the following represents the cost of hiring the company to shovel p inches of snow from the parking lot, if p > 6?

(A) pd + pf

(B) fd + p

(D) fp – 6f + 6d

(E) f (p – 6) + d

21. If 3 − x = 2 x − 6, what is the value of x?

(A) 1

(B) 2

(D) 6

(E) 9

22. In the correctly worked addition problem below, R, P, and T, represent different digits. What is the value of R?

(A) 0

(B) 2

(D) 8

(E) 9

23. In the figure below, what is the value of w + v?

(A) 40

(B) 125

(D) 220

(E) 300

24. One number is twice as large as another positive number, and their difference is 4. What is the greater of the two numbers?

(A) 4

(B) 6

(D) 10

(E) 12

25. In a movie theater, of the seats were filled when the previews started. After 50 more people came in, of the seats were filled. How many seats are in the movie theater?

(A) 90

(B) 120

(D) 170

(E) 190

26. How many of the first fifty positive integers contain the digit 4?

(A) 12

(B) 13

(D) 15

(E) 16

27. If 3 x = y + z, y = 6 − z, and z + x = 8, what is the value of ?

(A) 0

(B) 2

(D) 5

(E) 7

28. In the figure below, the four vertices of square RSTU lie on circle O, which has a radius of 8. What is the area of the shaded region?

(A) 32

(B) 96

(D) 150

(E) 166

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 16

1. If x = 3 and 5 x = 3 x + y, then y =

(A) 1.5

(B) 2

(D) 4

(E) 6

2. A store sells a package of 6 batteries for $4 and a package of 24 of the same batteries for $12. If you need to buy 48 of these batteries, how much money will you save by buying them in packages of 24 rather than packages of 6?

(A) $4

(B) $8

(D) $16

(E) $20

3. Which of the following points does not lie in the shaded region below?

(A) (1, 1)

(B) (1, 4)

(D) (4, 1)

(E) (5, 5)

4. If of 2 x is 5, what is of 4 x?

(A) 5

(B) 10

(D) 20

(E) 25

5. If n is a positive integer that is divisible by 12 and 16, then n must also be divisible by

(A) 28

(B) 32

(D) 96

(E) 192

6. In the figure below, if a − b = 10, then a =

(A) 60

(B) 65

(D) 75

(E) 80

7. If n is an integer, which of the following must be an even integer?

(A)

(B) n + 2

(D) n²

(E) n²+ n

8. Mike sold a total of 48 sodas at a snack stand. The stand sells only cola and root beer. If he sold twice as many colas as root beers, how many root beers did he sell?

(A) 32

(B) 24

(D) 16

(E) 8

9. If m and n are both squares of integers, which of the following is not necessarily the square of an integer?

(A) 9 m

(B) mn

(D) 9 mn

(E) 9 m – 9 n

10. If a + b = 9, a − c = 14, and a = 10, then c − b =

(A) - 5

(B) - 3

(D) 5

(E) 23

11. If the average (arithmetic mean) of a, b, 4, and 10 is 8, what is the value of a + b?

(A) 4

(B) 6

(D) 15

(E) 18

12. With the exception of the shaded squares, every square in the figure below contains the sum of the number in the square directly above it and the number in the square directly to its left. For example, the number 4 in the unshaded square bellow is the sum of the 2 in the square above it and the 2 in the square directly to its left. What is the value of x?

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