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B) The mild temperature was lowered by a heavy rain in the morning, and the temperature dropped lower by evening. 10 page(D) 2000 (E) 2001
24. When a positive integer, m, is divided by 7, the remainder is 4. Which of the following expressions will yield a remainder of 3 when it is divided by 7?
(A) m + 2 (B) m + 3 (C) m + 4 (D) m + 5 (E) m + 6
25. If a2 − b2 = 12, and (a − b) = 4, then what is the value of ab?
(A) -1 (B) -0.5 (C) 0 (D) 3.5 (E)
26. For all numbers x and y, let x♣y be defined as x♣y = x2 − 2xy + y2. What is the value of (2♣4)♣8?
(A) 1 (B) 4 (C) 12 (D) 16 (E) 20
27. 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 (C) 120 (D) 132 (E) 432
28. In the figure below, the circle with center O is inscribed in square WXYZ. What is the area of the shaded portion of the figure?
(A) 8 - 2π (B) 8 - π (C) 4 - 2π (D) 2 - π (E) 4 - π
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 22
1. If one of the angles in a triangle is 100°, what is the average (arithmetic mean) of the measures, in degrees, of the other two angles?
(A) 20° (B) 30° (C) 40° (D) 60° (E) 80°
2. If k is an integer that is 1 less than a multiple of 6, which of the following could be k + 1?
(A) 16 (B) 17 (C) 18 (D) 19 (E) 20
3. Which of the following expresses the number that is 15 more than the product of 3 and m − 2?
(A) 3m - 21 (B) 3m - 13 (C) 3m - 6 (D) 3m + 9 (E) 3m + 13
4. In the figure below, four line segments intersect at a single point. What is the value of m + n?
(A) 45 (B) 50 (C) 60 (D) 65 (E) 85
5. If x% of 30 is 12, what is 4x% of 15?
(A) 6 (B) 12 (C) 18 (D) 24 (E) 48
6. If 0 < x < 1 then which of the following must be true? I. II. x2 > x III. −x < −1
(A) None (B) I only (C) II only (D) III only (E) I and III only
7. If every gadget costs p dollars to make, and each one sells for m dollars, then which of the following expressions represents the profit made if 10 gadgets are made but only 9 are sold?
(A) 10m 9p (B) 9m 10p (C) 10(m - p) 9m (D) 9p + 10m (E) 10(m p) + 9m
8. If y = f(x) such that y varies inversely as x, and the points (4, 6) and (2, m) lie on the graph of y = f(x), what is the value of m?
(A) 4 (B) 6 (C) 8 (D) 10 (E) 12
9. A machine can fill 200 boxes of cereal in 5 minutes. At this rate, how many hours will it takes this machine to fill 24,000 boxes of cereal? (60 minutes = 1 hour)
(A) 10 (B) 24 (C) 100 (D) 210 (E) 600
10. In the figure below, what is the value of x in terms of n?
(A) (B) (C) (D) (E)
11. Which of the following represents all possible solutions to the equation below? (r 5)2 = (r + 2)2
(A) -5 and 2 only (B) 5 and -2 only (C) 3.5 only (D) 1.5 only (E) 0 only
12. A certain class has 8 boys and 10 girls. How many different sets of four class officers-president, vice president, treasurer and secretary-can be formed from students in this class if the president and treasurer must be girls and the vice president and secretary must be boys?
(A) 25,600 (B) 6,400 (C) 5,040 (D) 3,200 (E) 2,520
13. In the figure below, if the shaded region has an area of 15, what is the slope of AB?
(A) (B) (C) (D) 1 (E)
14. If m > 1, then
(A) m + 1 (B) m (C) m - 1 (D) -1 (E)
15. If a circle on the coordinate plane has a center at (6, −6), which of the following could not be the number of points on the circle that also lie on a coordinate axis? I. 1 II. 2 III. 3
(A) I only (B) II only (C) I and II only (D) I and III only (E) II and III only
16. A certain car race consists of three legs of equal distance. On the first two legs of the race, a car travels an average of 50 miles per hour. On the last leg of the race, the car travels at an average of 75 miles per hour. What is the average speed, in miles per hour, for this car over the entire race?
(A) 52.00 (B) 56.25 (C) 58.33 (D) 62.50 (E) 66.67
17. In the figure below, what is the length of line segment AE in terms of x?
(A) 3x + 11 (B) 5x + 14 (C) 7x + 8 (D) 6x + 11 (E) 6x + 17
18. A video store charges an annual account fee of $3.00 per customer and has a total of 5,400 members. If everyone pays the fee, what is the total amount collected from the members?
(A) $16.20 (B) $162.00 (C) $1,620.00 (D) $16,200.00 (E) $162,000.00
19. A plastic container contains 2 pints of water. If 8 tablespoons of water are poured out, what fraction of the original amount remains? 1 pint = 2 cups, 1 cup = 16 tablespoons.
(A) (B) (C) (D) (E)
20. Lines m and n intersect, as shown, in the figure below. What is the value of y?
(A) 52 (B) 58 (C) 62 (D) 68 (E) 72
21. Elysha uses air-conditioning year round and spends, on average, $125 per month to cool her apartment. A new energy-efficient air conditioning system would cost her $3,000 to install and only $25 per month thereafter to cool the apartment. If she installs the new system, how many months will it take for her total savings in cooling costs to equal the cost of the system?
(A) 30 (B) 35 (C) 40 (D) 45 (E) 50
22. In the correctly worked addition problem below, A, B, and C represent different digits. What is the value of B?
(A) 0 (B) 1 (C) 4 (D) 5 (E) 8
23. The radius of the base of the right circular cone below is 4 inches and the height of the cone is 14 inches. A cut is made parallel to the circular base such that it produces a smaller cone with a radius of 3 inches. What is the height, in inches, of the smaller cone?
(A) 3.5 (B) 6.0 (C) 7.0 (D) 10.5 (E) 11.0
24. A right triangle has side lengths of x − 1, x + 1, and x + 3. What is its perimeter?
(A) 7 (B) 24 (C) 28 (D) 32 (E) 36
25. In the repeating decimal below, what is the 3,000th digit to the right of the decimal? 0.
(A) 2 (B) 4 (C) 5 (D) 1 (E) 6
26. The pie graph below shows the housing situation of families in Glenville. If there are 12,000 families in Glenville, then how many families own homes?
(A) 3,000 (B) 4,000 (C) 6,000 (D) 8,000 (E) 9,000
27. In the figure below, BD || CE. What is the length of DE?
(A) 6 (B) 6 (C) 2 (D) 4 (E) 3
28. Given the graph of y = f(x) below, which of the following represents the graph of y = f(x + 3) + 3?
(A)
(B)
(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 23
1. If x3y = x9 and x > 1, then y =
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
2. The ratio of 1 to 1.4 is equal to the ratio of
(A) 1 to 4 (B) 3 to 4 (C) 5 to 7 (D) 7 to 5 (E) 4 to 3
3. A line and a ray intersect as shown below. What is the value of 2x + 5?
(A) 20 (B) 25 (C) 40 (D) 45 (E) 50
4. When three times a number is divided by two, the result is 39. What is that number?
(A) 20 (B) 21 (C) 24 (D) 26 (E) 30
5. How much greater is x + 5 than x − 5?
(A) 2 (B) 5 (C) 7 (D) 10 (E) 12
6. Rectangle M has an area of A square feet. The length and width of another rectangle, N, are each triple the length and width of rectangle M. What is the area of rectangle N in terms of A?
(A) 2A (B) 3A (C) 6A (D) 9A (E) 12A
7. If a circle has a circumference of 10, what is the ratio of the circumference of the circle to its diameter?
(A) 1:2π (B) 1:π (C) π:1 (D) 2π:1 (E) π:2
8. What is the distance from point A to point B in the figure below?
(A) 1 (B) 3 (C) 4 (D) 5 (E) 7
9. A theater purchases $500 worth of Sticky Bears and Chocolate Bombs. Each bag of Sticky Bears costs $1.50 and each bag of Chocolate Bombs costs $1.00. If a total of 400 bags of candy were purchased, how many bags of Chocolate Bombs did the theater buy?
(A) 100 (B) 150 (C) 200 (D) 250 (E) 300
10. The median of a set of seven consecutive even integers is 10. What is the average (arithmetic mean) of this set?
(A) 8 (B) 10 (C) 12 (D) 14 (E) 16
11. The total revenue collected for movie tickets at the Bijou is what percent of the total revenue collected for movie tickets at the Community Cinema?
(A) 25% (B) 50% (C) 75% (D) 100% (E) 200%
12. If the ticket revenue at the Triplex is greater than the ticket revenue at the Village Theater, what is the least possible value of x?
(A) 137 (B) 138 (C) 139 (D) 140 (E) 141
13. How many integers between 100 and 1000 contain only the digits 3, 4 or 5, if any digit may be repeated?
(A) 16 (B) 18 (C) 20 (D) 24 (E) 27
14. If
(A) (B) (C) (D) (E)
15. The inscribed circle touches square ABCD at points E, F, G, and H, which are all midpoints of their respective sides. If the length of one side of the square is 6, what is the area of the shaded region?
(A) 36 − 9π (B) 36 − 36π (C) 24 − 9π (D) 36π −36 (E) 24 − 9π
16. A chef spends c hours each day at her restaurant,
(A) (B) (C) (D) 24c (E)
17. If the rectangles shown below have the same perimeter, what is the value of x?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
18. If b represents a positive integer, which of the following expressions necessarily represents an even integer?
(A) 2b (B) b + 2 (C) 2b + 1 (D) 3b (E) 2b − 1
19. Two lines intersect as shown in the figure below, what is the value of x?
(A) 54 (B) 56 (C) 57 (D) 59 (E) 62
20. If x and y are both positive, which of the following is equivalent to (x6y4)
(A) (B) (C) (D) (E)
21. Based on the information in the table below, what is the median final exam grade for Mr. Prices class?
(A) 75 (B) 80 (C) 85 (D) 90 (E) 95
22. If a = b3, and b is positive, then by what factor does a increase if b is tripled?
(A) 3 (B) 8 (C) 9 (D) 27 (E) 81
23. If f(x) = (x − 2)2 + 4, what is the least possible value of f(x)?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
24. If 20w = 53 × 43, what is the value of w?
(A) 1 (B) 3 (C) 6 (D) 8 (E) 10
25. Which of the following represents the result if the three operations below are performed in sequence? Step 1: Subtract 5 from x Step 2: Multiply this difference by 2 Step 3: Add 6 to this product
(A) x 4 (B) 2x + 1 (C) 2x 4 (D) 2x 6 (E) 2x + 2
26. If
(A) 3 (B) 6 (C) 9 (D) 27 (E) 81
27. Two towns located x miles apart are p centimeters apart on a roadmap that is drawn to scale. How many miles apart are two towns that are p + 5 centimeters apart on this map?
(A) (B) (C) (D) (E)
28. For any positive integer, n, let For example,
(A) (B) (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 24
1. Which of the following integers is 2 greater than a multiple of 7?
(A) 14 (B) 15 (C) 16 (D) 17 (E) 18
2. A store sells oranges for 20 cents each, but for every four oranges you buy, you may buy a fifth for only 5 cents. How many oranges can you buy from this store for $3.40?
(A) 14 (B) 17 (C) 18 (D) 19 (E) 20
3. If r is a positive number and s is a negative number, all of the following must represent positive numbers except
(A) −r + s (B) r − s (C) (D) rs2 (E) (rs)2
4. Which of the following expresses the number that is 12 less than the product of 3 and x + 1?
(A) x − 8 (B) x + 37 (C) 3x − 11 (D) 3x − 9 (E) 3x + 15
5. One bag of grass seed covers 5,000 square feet. If each bag costs $25, how much will it cost to buy enough grass seed to cover a square area that is 200 feet by 200 feet?
(A) $25 (B) $100 (C) $200 (D) $1,000 (E) $2,000
6. In the right triangle below, what is the value of w?
Date: 2015-12-24; view: 924 |
< x
=
= 0.245162451624516
, which of the following represents the value of y in terms of x?
hours of which she spends preparing desserts. At this rate, after how many days will the chef have spent 24 hours preparing desserts?
+ 16 = 79, what is the value of x?
be defined as the integer obtained when each digit in n has been replaced with the corresponding digit in the table below, ignoring any leading zeroes.
= 548 and 
= 08 = 8. Which of the following is equivalent to 
+ 
?
