B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 11 страница

(C)

(D)

(E)

28. If 5 x + 7 y = 18 and 2 x − 4 y = 6, what is the value of 7 x + 3 y?

(A) 7

(B) 12

(C) 19

(D) 24

(E) 31

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 26

1. In the figure below, what is the value of a?

(A) 10

(B) 20

(C) 28

(D) 36

(E) 45

2. The Rivertown Little League is divided into d divisions. Each division has t teams, and each team has p players. How many players are there in the entire league?

(A) d + t + p

(B) dtp

(C)

(D)

(E)

3. What is the value of n if 2ⁿ⁺¹= 32?

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8

4. In the figure below, what is the value of a + b + c?

(A) 210

(B) 220

(C) 240

(D) 270

(E) 280

5. The chart below shows the number of tennis tournaments that Adam entered each year from 1990 through 1995. In what year did he enter 50% more tournaments than the year before?

(A) 1991

(B) 1992

(C) 1993

(D) 1994

(E) 1995

6. If, for any number b, b # = b + 1 and # b = b – 1, which of the following is not equal to (3#)(#5)?

(A) (1#)(#9)

(B) 7# + #9

(C) (4#)(#4)

(D) (7#)(#3)

(E)

7. If a is a multiple of 5 and b = 5 a, which of the following could be the value of a + b?

I. 60

II. 100

III. 150

(A) I only

(B) III only

(C) I and III only

(D) II and III only

(E) I, II, and III

8. If 3 ^a = b and 3 ^c = d, then bd =

(A) 3 ^ac

(B) 3 ^a+c

(C) 6 ^a+c

(D) 9 ^ac

(E) 9 ^a+c

9. If r and s are two nonzero numbers and if 78(r + s) = (78 + r) s, then which of the following must be true?

(A) r = 78

(B) s = 78

(C) r + s = rs

(D) r < 1

(E) s < 1

10. If it is now June, what month will it be 100 months from now?

(A) January

(B) April

(C) June

(D) October

(E) December

11. If the average (arithmetic mean) of three consecutive integers is A, which of the following must be true?

I. One of the numbers is equal to A.

II. The average of two of the three numbers is A.

III. A is an integer.

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I, II, and III

12. A bag contains 25 slips of paper, on each of which a different integer from 1 to 25 is written. Blindfolded, Scott draws one of the slips of paper. He wins if the number on the slip he draws is a multiple of 3 or 5. What is the probability that Scott wins?

(A)

(B)

(C)

(D)

(E)

13. If m ² = 17, then what is the value of (m + 1)(m – 1)?

(A)

(B)

(C) 16

(D) 18

(E) 288

14. Which of the following points lie on the interior of the circle whose radius is 10 and whose center is at the origin?

(A) (-9, 4)

(B) (5, -9)

(C) (0, -10)

(D) (10, -1)

(E) (-6, 8)

15. Several shoppers were surveyed at a supermarket and asked how many people were in their families and how much money they spend each week on food. The data were graphed in the following scatterplot diagram.

If the average weekly cost of food per person for each of the seven families, A–G, was calculated, which one would be the median?

(A) A

(B) C

(C) D

(D) E

(E) G

16. If p pencils cost c cents, how many pencils can be bought for d dollars?

(A) cdp

(B) 100 cdp

(C)

(D)

(E)

17. If a is increased by 10% and b is decreased by 10%, the resulting numbers will be equal. What is the ratio of a to b?

(A)

(B)

(C)

(D)

(E)

18. In the figure below, line segments and partition pentagon ABCDE into a rectangle and two triangles. For which of the following can the value be determined?

I. a + b

II. b + c

III. a+ b+ c + d

(A) II only

(B) I and II only

(C) II and III only

(D) I and III only

(E) I, II, and III

19. Which of the following cannot be expressed as the sum of two or more consecutive positive integers?

(A) 17

(B) 22

(C) 24

(D) 26

(E) 32

20. In the figure below, the legs of right triangle ACB are diameters of the two semicircles. If AB = 4 what is the sum of the areas of the semicircles?

(A) π

(B) 2π

(C) 4π

(D) 8π

(E) 16π

21. At the Fancy Furniture Factory, Brian bought two chairs for $299 each and a coffee table for $140. He paid of the total cost at the time of purchase and the balance in 12 equal monthly installments. What was the amount of each month’s payment?

(A) $10.25

(B) $37.50

(C) $42.75

(D) $51.25

(E) $61.50

22. If f (x) = x² – 2 ^x, what is the value of f (4)?

(A) -16

(B) -8

(C) 0

(D) 8

(E) 16

23. The operation ** is defined as follows: For any positive numbers a and b, a ** b = .Which of the following is an integer?

(A) 11**5

(B) 4**9

(C) 4**16

(D) 7**4

(E) 9**9

24. Which of the following is a solution of the equation 3| x | + 5 = 23?

(A) –6

(B) –4

(C)

(D) 15

(E) The equation has no solution.

25. If circle O has its center at (1, 1), and line is tangent to circle O at P (4, –4), what is the slope of ?

(A)

(B)

(C)

(D) 1

(E)

26. If 25 – 2 = 7, then x =

(A) -81

(B) 9

(C) 36

(D) 81

(E) 256

27. What is the value of n if 3¹⁰ 27²= 81 ?

(A) 6

(B) 10

(C) 12

(D) 15

(E) 30

28. In the figure below, what is the area of the shaded triangle?

(A) 30

(B) 32

(C) 34

(D) 35

(E) 36

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 27

1. If 5 c + 3 = 3 c + 5, what is the value of c?

(A) -1

(B) 0

(C) 1

(D) 3

(E) 5

2. In the figure below, C is the only point that right triangle ABC and square CDEF have in common. What is the value of a + b?

(A) 135

(B) 180

(C) 210

(D) 225

(E) 270

3. A lacrosse team raised some money. The members used 74% of the money to buy uniforms, 18% for equipment, and the remaining $216 for a team party. How much money did they raise?

(A) $2400

(B) $2450

(C) $2500

(D) $2600

(E) $2700

4. For all positive numbers a and b, let ab = . If n > 1, what does n  equal?

(A)

(B)

(C)

(D)

(E) 1

5. In the figure below, what is the value of b?

(A) 30

(B) 36

(C) 45

(D) 60

(E) 72

6. In the figure below, if x is 150 more than y, what is the value of y?

(A) 10

(B) 15

(C) 20

(D) 25

(E) 30

7. Heidi wrote the number 1 on 1 slip of paper, the number 2 on 2 slips of paper, the number 3 on 3 slips of paper, the number 4 on 4 slips of paper, the number 5 on 5 slips of paper, and the number 6 on 6 slips of paper. All the slips of paper were placed in a bag, and Sally drew 1 slip at random. What is the probability that the number on the slip Sally drew was odd?

(A)

(B)

(C)

(D)

(E)

8. For how many positive numbers a is it true that = a + a + a?

(A) 0

(B) 1

(C) 2

(D) 3

(E) more than 3

9. Last year Jose sold a painting for $2000. If he made a 25% profit on the sale, how much had he paid for the painting?

(A) $1200

(B) $1500

(C) $1600

(D) $2400

(E) $2500

10. For any positive integer n > 1, n! represents the product of the first n positive integers. For example, 3! = = 6. Which of the following is (are) equal to ?

I. 5! – 4! – 3!

II.

III. 15(3!)

(A) I only

(B) II only

(C) III only

(D) I and III only

(E) I, II, and III

11. A rectangle is twice as long as it is wide. If the width is a, what is the length of a diagonal?

(A)

(B)

(C)

(D) 3 a

(E) 5 a

12. If abc = 1, which of the following could be the number of integers among a, b, and c?

I. 1

II. 2

III. 3

(A) None

(B) I only

(C) I and II only

(D) I and III only

(E) I, II, and III

13. At Essex High School 100 students are taking chemistry and 80 students are taking biology. If 20 students are taking both chemistry and biology, what is the ratio of the number of students taking only chemistry to the number taking only biology?

(A)

(B)

(C)

(D)

(E) It cannot be determined from the information given

14. In the figure below, a small square is drawn inside a large square. If the shaded area and the white area are equal, what is the ratio of the side of the large square to the side of the small square?

(A)

(B)

(C)

(D)

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

15. In rectangle ABCD below, diagonal makes a 30° angle with side . If AC = 10, what is the area of the rectangle?

(A) 25

(B) 25

(C) 48

(D) 50

(E) 100

16. The value of 10 pounds of gold is d dollars, and a pound of gold has the same value as p pounds of silver. What is the value, in dollars, of one pound of silver?

(A)

(B)

(C)

(D)

(E)

17. If a and b are positive integers such that (a – 4)(b – 5) = 0, what is the least possible value of a + b?

(A) 5

(B) 6

(C) 8

(D) 10

(E) 11

18. The number of cells growing in a particular Petri dish doubles every 30 minutes. If at 8:00 A.M. there were 60 cells in the dish, how many were there at noon of the same day?

(A)

(B)

(C)

(D)

(E)

19. The distance between Ali’s house and college is exactly 135 miles. If she drove of the distance in 135 minutes, what was her average speed, in miles per hour?

(A) 40

(B) 45

(C) 60

(D) 67.5

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

20. The average (arithmetic mean) weight of five students is 150.4 pounds. If no student weighs less than 130 pounds and if no two students’ weights are within 5 pounds of each other, what is the most, in pounds, that any one of the students can weigh?

(A) 172

(B) 192

(C) 202

(D) 232

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

21. What is the absolute value of the product of all the integers from –6 to 3, inclusive?

(A) -120

(B) -15

(C) 0

(D) 15

(E) 120

22. If of a number is 7 more than of the number, what is of the number?

(A) 12

(B) 15

(C) 18

(D) 20

(E) 24

23. If A is the set of multiples of 5 less than 200 and B is the set of multiples of 7 less than 200, how many members are there in A ∩ B?

(A) 0

(B) 5

(C) 11

(D) 62

(E) 67

24. If + 3 = 5, then x =

(A) -9

(B) 3

(C) 7

(D) 9

(E) 26

25. Let the lengths of the sides of a triangle be represented by x + 3, 2 x – 3, and 3 x – 5. If the perimeter of the triangle is 25, what is the length of the shortest side?

(A) 5

(B) 7

(C) 8

(D) 10

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

26. What is the maximum number of points of intersection between a square and a circle?

(A) less than 4

(B) 4

(C) 6

(D) 8

(E) more than 8

27. In square ABCD, vertex A is at (–1, –1) and vertex C is at (4, 2). What is the area of square ABCD?

(A) 9

(B) 15

(C) 17

(D) 25

(E) 34

28. If f (x) = x + 5, which of the following is a solution of f (3 a) + 2 = f (2 a) + 3?

(A) 1

(B) 2

(C) 5

(D) 6

(E) There are no solutions.

29. Differentiate the function in the below.

(A)

(B)

(C) 0

(D) 1

(E)

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

(A)

(B)

(C)

(D)

(E)

TEST 28

1. If 3 x = 12,5 x =

(A) 2.4

(B) 14

(C) 15

(D) 20

(E) 60

2. In the figure below, x =

(A) 33

(B) 57

(C) 67

(D) 123

(E) 147

3. If 8 – (8 – m) = 8, then m =

(A) –16

(B) –8

(C) 0

(D) 8

(E) 16

4. If of the members of the school chorus are boys, what is the ratio of girls to boys in the chorus?

(A)

(B)

(C)

(D)

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

5. In the figure below, what is the perimeter of pentagon ABCDE, formed by right triangle EAB and square BCDE?

(A) 20

(B) 8 + 12

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