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# B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 5 page

25. In the figure below, ABCD is a rectangle. DC = 8, AD = 4, and E and F are midpoints of sides AB and BC respectively. What is the area of DEF?

(A) 12

(B) 18

(C) 24

(D) 28

(E) 32

26. How many different four-digit integers can be formed using the digits 3, 4, 5, 6, 7, 8, 9 if the tens digit is 5 and no digit is repeated within an integer?

(A) 16

(B) 45

(C) 63

(D) 120

(E) 840

27. Zander drives to work at an average speed of 40 miles per hour and returns home along the same route at an average speed of 24 miles per hour. If his total travel time is 4 hours, what is the total number of miles in the roundtrip to and from work?

(A) 48

(B) 60

(C) 96

(D) 120

(E) 144

28. A swimming pool with a capacity of 20,000 gallons is one-quarter full. A pump can deliver

g gallons of water every m minutes. If a company charges d dollars per minute for the use of the pump, then in terms of g, m, and d, how much will it cost, in dollars, to fill the pool?

(A)

(B) 15,000gmd

(C)

(D)

(E)

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 10

1. If x = , then which of the following has the greatest value?

(A) x

(B) 0.5x

(C) x2

(D) 1 - x

(E) x3

2. If Alexa’s car can typically travel 300 miles on a full tank of gasoline, and if her car’s tank can hold 18 gallons, then at this rate how far should the car be able to travel on 12 gallons of gasoline?

(A) 120 miles

(B) 180 miles

(C) 200 miles

(D) 220 miles

(E) 240 miles

3. If m and n are positive integers where m > n and 6m + 2n = 22, what is the value of n?

(A) 1

(B) 2

(C) 3

(D) 4

(E) 5

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

(A) 50

(B) 60

(C) 70

(D) 80

(E) 90

5. If , , and are all integers, then n must be divisible by

(A) 54

(B) 64

(C) 65

(D) 68

(E) 72

6. A farmer has 10 baskets, numbered 1 through 10, each of which contains 10 apples. If he removes 1 apple from basket 1, 2 apples from basket 2, 3 apples from basket 3, and so on, until he removes 10 apples from basket 10, what percent of the original apples remain?

(A) 35%

(B) 40%

(C) 45%

(D) 50%

(E) 55%

7. Which of the following is equivalent to 4n2 + 4n + 2?

(A) 4(n2 + n +

(B) 2(2n + 1)2

(C) 2(2n3 + 1)

(D) (2n + 1)(2n + 2)

(E) (2n – 1)(2n – 2)

8. If a and b are positive integers, (3a)(3b) = 243, and (3a)b = 729, which of the following could be the value of a?

(A) 1

(B) 3

(C) 4

(D) 5

(E) 7

9. If 70% of the bananas in a particular harvest had an average (arithmetic mean) length of

7 inches and 30% of the bananas in that harvest had an average (arithmetic mean) length of 5 inches, what was the average (arithmetic mean) length, in inches, of all of the bananas in the harvest?

(A) 6.0

(B) 6.2

(C) 6.4

(D) 6.6

(E) 6.8

10. Point C lies in plane R. How many circles are there in plane R that have center C and an area of 16π square inches?

(A) None

(B) One

(C) Three

(D) Five

(E) More than five

11. Let the function h be defined by h(x) = ( - 4)2. If h (m) = 36, what is the value of m?

(A) 10

(B) 15

(C) 20

(D) 25

(E) 30

12. If line l (not shown) contains points A and B on the xy-plane below, which of the following could be the equation of a line perpendicular to line l?

(A) y = + 2

(B) y = + 2

(C) y = - + 2

(D) y = - + 2

(E) y = x + 2

13. If x = 2y and y = z + 2, then what is in terms of z?

(A) z + 1

(B) z + 2

(C) 2z

(D) 2z+1

(E) 2z + 1

14. If a, b, c, and d in the equations bellow are all positive integers, which of the following is true?

(A) d < b < c < a

(B) d < c < a < b

(C) c < d < b < a

(D) d < b < a < c

(E) d < b < d < a

15. If the sequence below continues according to the pattern shown, what is the sum of the first 36 terms of the sequence?

1, 2, 3, 1, 2, 3, 1, 2 …

(A) 36

(B) 42

(C) 48

(D) 64

(E) 72

16. The Venn diagram below shows the distribution of students who play lacrosse, soccer, or both. If the ratio of the number of lacrosse players to the number of soccer players is 3:4, then what is the value of a?

(A) 6

(B) 8

(C) 12

(D) 16

(E) 24

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

(A) 30

(B) 32

(C) 34

(D) 35

(E) 36

18. Let Ω p be defined as for all positive integers, p. If Ω n = s, and s is a positive integer, which of the following is a possible value for s?

(A) 1

(B) 3

(C) 5

(D) 6

(E) 8

19. The graph in the xy-plane of the quadratic function f contains the points (0, 0), (1, 5), and (5, 5). What is the maximum value of f(x)?

(A) 12

(B) 11

(C) 10

(D) 9

(E) 8

20. A 60° wedge is cut from a paper circle with radius 12 centimeters and the paper is then folded into a cone, as shown in the figure below. What is the height, in centimeters, of this cone?

(A)

(B)

(C)

(D)

(E)

21. The three interior angles of a triangle have measures of a°, a°, and b°. If b = 80, what is the value of a?

(A) 30

(B) 40

(C) 50

(D) 60

(E) 100

22. If x is a number greater than 0 and less than 1, which of the following is greatest?

(A) 1 - x

(B)

(C) -

(D) x

(E) x2

23. Which of the following is a multiple of 3, 5, and 7?

(A) 35

(B) 70

(C) 75

(D) 105

(E) 112

24. A deluxe box of crayons contains 10 more crayons than a regular box of crayons. If a regular box contains m crayons, how many crayons do 5 deluxe boxes contain?

(A) 5m + 10

(B) 5m + 50

(C) 5(m + 50)

(D) 10m + 50

(E) 10(m + 50)

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

(A) 100

(B) 90

(C) 80

(D) 70

(E) 60

26. Which of the following could be true about the relationship between x and y shown in the table below?

(A) y is directly proportional to x.

(B) y is inversely proportional to x.

(C) y is directly proportional to the square of x.

(D) x is inversely proportional to the square of y.

(E) y is inversely proportional to the square of x.

27. The figure below shows the arrangement of 5 cages in the primate house of a zoo. Each cage is to house one specimen from the following five species: capuchin, lemur, macaque, squirrel monkey, and tamarin. The lemur must be in a cage on one end, and the tamarin must be in the center cage. If the capuchin must be in a cage next to the macaque, and the tamarin must be in a cage next to the squirrel monkey, how many arrangements of these primates in these cages are possible?

(A) 2

(B) 3

(C) 4

(D) 6

(E) 8

28. In the equation below, h and b are constants. If the equation is true for all values of y, what is the value of b?

(A) - 24

(B) - 8

(C) 6

(D) 8

(E) 24

29. Differentiate the function in the below.

, for some fixed a > 0 and x > 0

(A)

(B)

(C)

(D)

(E)

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

(A)

(B)

(C)

(D)

(E)

TEST 11

1. There are 5 CD racks in a room. Each rack contains at least 10 CDs but not more than 14 CDs. Which of the following could be the total number of CDs on all five racks?

(A) 25

(B) 35

(C) 55

(D) 75

(E) 85

2. If x is 4 less than p and p is 2 more than m, then what is the value of x when m = 2?

(A) - 1

(B) 0

(C) 1

(D) 2

(E) 4

3. The drawing below is to be rotated 90° about point X in the direction indicated. Which of the following shows the end result of this rotation?

(A)

(B)

(C)

(D)

(E)

4. The price of admission to the New Haven Children’s Museum is \$6 more for adults than for children. If a group of 6 adults and 18 children pays a total of \$108 to visit the museum, what is the cost, in dollars, of the ticket for one adult?

(A) \$7.00

(B) \$9.00

(C) \$10.00

(D) \$12.00

(E) \$13.00

5. In the figure below, circular region X represents cars with DVD players, circular region Y represents cars with navigation systems, and circular region Z represents cars with all-wheel drive. What is represented by the shaded region?

(A) cars with DVD players, navigation systems, and all-wheel drive

(B) cars with DVD players and all-wheel drive, but without navigation systems

(C) cars with navigation systems and all-wheel drive (some possibly with DVD players)

(D) cars with DVD players and all-wheel drive (some possibly with navigation systems)

(E) cars with DVD players and navigation systems (some possibly with all-wheel drive)

6. The tick marks on the number line below are equally spaced and their coordinates are shown. Of these coordinates, which has the smallest nonnegative value?

(A) a

(B) b

(C) c

(D) d

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

7. In a recent mayoral election, a total of 200,000 votes were cast for two candidates, Julie Sanders and Bob Tanks. If Julie Sanders won by a ratio of 7 to 3, what was the total number of votes cast for Bob Tanks?

(A) 30,000

(B) 60,000

(C) 90,000

(D) 120,000

(E) 140,000

8. Which of the following numbers provides a counterexample to the statement below?

“All multiples of 3 are odd.”

(A) 9

(B) 12

(C) 13

(D) 14

(E) 15

9. For how many integer values of x is |x − 2.5| < 12?

(A) 20

(B) 21

(C) 22

(D) 23

(E) 24

10. If the average of 8 and x is 10 and the average of 7 and y is 11, what is the average of x and y?

(A) 9.0

(B) 10.5

(C) 12.0

(D) 13.5

(E) 15.0

11. Of the 360 students at a private school , were from Connecticut. If of the students lived on campus, what was the least possible number of students who lived on campus and were from Connecticut?

(A) 55

(B) 63

(C) 72

(D) 135

(E) 155

12. This year, 200 men and 250 women attend State College. If the male population were to increase by 10% next year, what is the maxi-mum possible increase in the female population that would produce no more than an 8% increase in the overall student population next year?

(A) 16

(B) 17

(C) 20

(D) 22

(E) 26

13. In the figure below, if C is the center of the circle and 20 < r < 40, then which of the following expresses all possible values of s?

(A) 30 < s < 50

(B) 50 < s < 70

(C) 70 < s < 80

(D) 75 < s < 90

(E) 140 < s < 160

14. If a and b are positive integers such that (a4)(b – 5) = 0, what is the least possible value of a + b?

(A) 5

(B) 6

(C) 8

(D) 10

(E) 11

15. A meal that costs m dollars is to be split equally among a group of coworkers. In terms of m, how many dollars less will each person pay for the meal if there are 6 people in the group instead of 4?

(A)

(B)

(C)

(D)

(E) 10m

16. If the length of is 12 and the length of is 13, which of the following could be the length of ?

(A) 24

(B) 26

(C) 28

(D) 29

(E) 30

17. In the figure bellow, points P and R are to be consecutive vertices of square PRST (not shown). What is the area of square PRST?

(A) 16

(B) 20

(C) 22

(D) 24

(E) 25

18. Based on the portions of the graphs of the functions f and g shown below, what are the values of x between −5 and 5 for which g(x) < f(x)?

(A) −2 < x < −1 only

(B) −1 < x < 2 only

(C) −1 < x < 3 only

(D) 2 < x < 5 only

(E) −5 < x < −1 and 2 < x < 5

19. If m and n are positive integers in the inequalities above and m > n, what is the value of m?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9

20. A student is instructed to arrange four cards in a row on a table. She has six cards to choose from, each of which has a different color: black, red, blue, green, yellow, and brown. If the student follows these instructions but other-wise chooses her cards randomly, what is the probability that her arrangement will be blue, red, yellow, and green, in that order?

(A)

(B)

(C)

(D)

(E)

21. If x = 4 and 3x + 2 = y, what is the value of y?

(A) 2

(B) 4

(C) 8

(D) 14

(E) 18

22. In the figure below, three lines intersect at a point. If x = 71 and u = 64, what is the value of z?

(A) 40

(B) 45

(C) 50

(D) 55

(E) 60

23. According to the graph below, for which month did Sarah earn \$400 more than Emma?

(A) January

(B) February

(C) March

(D) April

(E) May

24. If the average (arithmetic mean) of 3, 7, 10, and x is 7, then what is the median of 3, 7, 10, and x?

(A) 5.5

(B) 6

(C) 6.5

(D) 7

(E) 7.5

25. A home appliance salesperson makes a commission of p percent of the selling price of a dishwasher. Which of the following represents the commission, in dollars, on 4 dishwashers that sold for \$650 each?

(A)

(B)

(C) 26p

(D) 650p

(E) 2,600p

26. The graph of y = x2 + 2 is shown below. If the graph were to be shifted up 2 and left 3, which of the following would be the equation of the transformed function?

(A) y = (x − 3)2 + 4

(B) y = (x + 3)2 - 2

(C) y = (x + 3)2 + 4

(D) y = (x - 3)2 + 2

(E) y = (x + 3)2 + 2

27. In the figure below, C lies on . In terms of a, which of the following must be equivalent to b?

(A) a - 15

(B)

(C)

(D)

(E)

28. If x and y are positive numbers, what percent of (x − 2) is y?

(A)

(B)

(C)

(D)

(E)

29. Differentiate the function in the below.

, for x > 3

(A)

(B)

(C)

(D)

(E)

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

(A)

(B)

(C)

(D)

(E)

TEST 12

1. If a = 3 + b and a = 2b, then b =

(A) 1.5

(B) 2

C) 3

(D) 4

(E) 6

2. If 1 pound of cheese costs \$1.50 and 2 pounds of beef costs \$4.00, then how much more expensive is 6 pounds of beef than 6 pounds of cheese?

Date: 2015-12-24; view: 2306

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