1,296 ACT Practice Questions, 3rd Edition (2013)
ACT Practice Test 2
2. MATHEMATICS TEST
60 Minutes—60 Questions
DIRECTIONS: Solve each problem, choose the correct answer, and then darken the corresponding oval on your answer sheet.
Do not linger over problems that take too much time. Solve as many as you can; then return to the others in the time you have left for this test.
You are permitted to use a calculator on this test. You may use your calculator for any problems you choose, but some of the problems may best be done without using a calculator.
Note: Unless otherwise stated, all of the following should be assumed:
1. Illustrative figures are NOT necessarily drawn to scale.
2. Geometric figures lie in a plane.
3. The word line indicates a straight line.
4. The word average indicates arithmetic mean.
1. Violet is baking a mixed berry pie that contains blueberries, cherries, blackberries, and raspberries. She uses three times as many blackberries as cherries, twice as many blueberries as raspberries, and the same number of blackberries and raspberries. If Violet has 10 cherries, how many of each of the other berries must she use?
2. The expression (3x − 5)(x + 2) is equivalent to:
F. 3x2 − 10
G. 3x2 + x + 10
H. 3x2 + x − 10
J. 3x2 + 11x − 10
K. 3x2 − 11x − 10
3. A function f is defined by f(x,y) = x − (xy − y). What is the value of f(8,6)?
4. What is of 28% of 8,000?
5. If 6x + 3 = 12 + 3x, then x =?
6. The second term of an arithmetic sequence is −2, and the third term is 8. What is the first term?
(Note: An arithmetic sequence has a common difference between consecutive terms.)
7. Stacie has a bag of solid colored jellybeans. Each jellybean is orange, purple, or pink. If she randomly selects a jellybean from the bag, the probability that the jellybean is orange is , and the probability that it is purple is . If there are 72 jellybeans in the bag, how many pink jellybeans are in the bag?
8. A cellular phone company unveiled a new plan for new customers. It will charge a flat rate of $100 for initial connection and service for the first two months, and $60 for service each subsequent month. If Bob subscribes to this plan for one year, how much does he pay in total for the year?
9. A square and a regular pentagon (a 5-sided polygon with congruent sides and interior angles) have the same perimeter. One side of the pentagon measures 20 inches. How many inches long is one side of the square?
10. Two contractors bid on a job to build a brick wall in a yard. Contractor A charges a flat fee of $1,600 plus $2 per brick. Contractor B charges a flat fee of $400 plus $8 per brick. If x represents the number of bricks in the wall, which of the following equations could be solved to determine the number of bricks which would make B’s charge to build the wall equal to A’s charge?
F. 1600 + 2x = 400 + 8x
G. 1600 + 8x = 400 + 2x
H. 2x + 8x = x
J. 2x + 8x = 1600
K. 2x + 8x = 400
11. Given that E = ABCD, which of the following is an expression of B in terms of E, A, C, and D?
B. E + ACD
C. E − ACD
12. Lines and intersect at point V on line , as shown in the figure below. The measures of 2 angles are given in terms of a, in degrees. What is the measure of XVZ in degrees?
13. An outdoor thermometer in Hanover, NH reads 70°F. The temperature in Hanover is 25°F cooler than in New Orleans, LA. What is the temperature, C, in degrees Celsius, in New Orleans?
(Note: F = C + 32)
14. If 3x + 2y = 5, what is the value of the expression 6x + 4y − 7?
15. Mike sold 3 pounds of beef at his deli on Wednesday and 2 pounds of beef on Saturday. Which of the following ranges includes the total amount of beef, in pounds, Mike sold during these two days?
A. At least 5 and less than 5
B. At least 5 and less than 5
C. At least 5 and less than 6
D. At least 6 and less than 6
E. At least 6 and less than 6
16. Dave leaves his house and bikes directly east for 3 miles. He then turns and bikes directly south for 4 miles. How many miles is Dave from his house?
17. A sensor records a piece of data every .0000000038 seconds. The sensor will record 100,000,000,000 pieces of data in how many seconds?
18. Alan has a rectangular photograph that is 20 centimeters wide by 30 centimeters long. Alan wants to reduce the area of the photograph by 264 square centimeters by decreasing the width and length by the same amount. What will be the new dimensions (width by length), in centimeters?
F. 11 by 24
G. 12 by 22
H. 12 by 28
J. 14 by 24
K. 16 by 21
19. A quadrilateral has a perimeter of 36 inches. If the lengths of the sides are 4 consecutive, even integers, what is the length, in inches, of the shortest side?
20. In the standard (x, y) coordinate plane, what is the slope of the line with equation 7y − 3x = 21?
21. In the figure shown below, points A, B, C, and D are collinear, and distances marked are in feet. Rectangle ADEG has an area of 48 square feet. What is the area, in square feet, of the trapezoid BCEF?
Use the following information to answer questions 22−24.
Quadrilateral FGHJ is shown below in the standard (x,y) coordinate plane. For this quadrilateral, = 10, = 6, = , and = 12.
22. Which of the following is closest to the perimeter of quadrilateral FGHJ, in coordinate units?
23. What is the length of , in coordinate units?
24. Which of the following are the coordinates of the image of J under a 90° clockwise rotation about the origin?
25. Which of the following geometric figures has at least 1 rotational symmetry and at least 1 reflectional symmetry?
(Note: The angle of rotation for the rotational symmetry must be less than 360°.)
26. What is the coefficient of x8 in the product of the polynomials below?
(–x4 + 3x3 − 5x2 + x − 5)(5x4 − 2x3 + x2 − 5x + 2)
Use the following information to answer questions 27−28.
The stem-and-leaf plot below shows the scores for each golfer in a recent tournament at the Lehigh Valley Golf Club. There were 13 golfers participating in the tournament.
(Note: For example, a score of 72 would have a stem value of 7 and a leaf value of 2.)
27. Which of the following is closest to the mean score of all the golfers in the tournament?
28. If a score represented in the stem-and-leaf plot is selected randomly, what is the probability that the score selected is exactly 83?
29. What is the least common multiple of 8, 2, 3a, 6b, and 4ab?
30. Aleksandra began collecting model airplanes in May of 2008. The number of model airplanes that she owns in each month can be modeled by the function A(m) = 2m + 2, where m = 0 corresponds to May. Using this model, how many model airplanes would you expect Aleksandra to own in December of 2008?
31. In the standard (x,y) coordinate plane, line segment has end points C(−3,5) and D(11,−7). What is the midpoint of ?
B. (8, 2)
C. (7, 1)
D. (7, −6)
E. (4, −1)
32. Given x ≠ ±4, which of the following is equivalent to the expression ?
F. x − 1
33. Evan purchased 6 boxes of sugar cookies, each box containing 10 snack bags and each bag containing 12 cookies. Evan could have purchased the same amount of cookies by buying how many family-sized packs of 30 cookies each?
34. When , 16r4 − s4 =?
35. Emilia is going to bake cookies. She rolls out a square of dough that is 12 inches wide by 12 inches long and cuts 9 identical circular cookies from the dough, as shown in the figure below. Each circular cut-out is tangent to the circular cut-outs next to it and tangent to the edge or edges of the square piece of dough it touches. Approximately, what is the area, in square inches, of the remaining dough, as shown in the figure?
36. Which of the following lists contains only prime numbers?
F. 63, 73, and 97
G. 71, 87, and 91
H. 73, 89, and 91
J. 79, 89, and 97
K. 81, 87, and 97
37. The costs of tutoring packages of different lengths, given in quarter hours, are shown in the table below.
Each cost consists of a fixed charge and a charge per quarter hour. What is the fixed charge?
38. At 3 p.m., the afternoon sun shines over a building and its rays hit the ground at a 34° angle. The building is 100 meters tall and is perpendicular to the ground. How long, to the nearest meter, is the building’s shadow that is cast by the sun?
(Note: sin 34° ≈ 0.56, cos 34° ≈ 0.83, tan 34° ≈ 0.67)
39. In the standard (x,y) coordinate system, circle O has its center at (4,−3) and a radius of 12 units. Which of the following is an equation of the circle?
A. (x − 4)2 + (y + 3)2 = 12
B. (x + 4)2 + (y + 3)2 = 12
C. (x + 4)2 − (y + 3)2 = 12
D. (x − 4)2 + (y − 3)2 = 144
E. (x − 4)2 + (y + 3)2 = 144
40. What is the least integer value of x that makes the inequality true?
41. When f(a) = a2 + 2a + 5, what is the value of f(a + b)?
A. a2 + b2 + 2ab + 5
B. a2 + b2 + 2a + 2b + 10
C. a2 + b2 + 2a + 2b + 5
D. (a + b)2 + a + b + 5
E. (a + b)2 + 2a + 2b + 5
42. In the figure below, M is on and O is on . and are parallel. The dimensions given are in feet. What is the length, in feet, of ?
43. Gina watched as a plane took off from the runway and climbed to 30,000 feet. She calculated the plane’s height, h feet, t seconds after takeoff to be given by h = 1,200 + 32t. To the nearest second, how many seconds did it take the plane to climb to a height of 2 miles? (Note: 1 mile = 5,280 feet)
44. In ABC, the measures of A, B, and C are 2x°, 3x°, and 5x°, respectively. What is the measure of C?
45. A basketball player has attempted 30 free throws and made 12 of them. Starting now, if he makes every free throw attempted, what is the least number of additional free throws he must attempt to raise his free-throw percentage to at least 55%?
(Note: Free-throw percentage =
46. If y is a negative integer, which of the following has the least value?
47. Jonathan, Ellery, and 3 other groomsmen are rehearsing for a wedding by walking down an aisle one at a time, one groomsman in front of the other. Each time all 5 walk down the aisle, the groom tells them to walk in a different order from first to last. What is the greatest number of times the groomsmen can walk down the aisle without walking in the same order twice?
48. In the circle below, O is the center and measures 5 inches from chord . The area of the circle is 169π square inches. What is the length of , in inches?
49. What is the x–intercept of the line that passes through points (−3,7) and (6,4) in the standard (x,y) coordinate plane?
50. Which of the following equations represent a graph that intersects the x-axis at x = 7?
F. y = (x + 7)2
G. y = (x − 7)2
H. y = (–x − 7)2
J. y − 7 = x2
K. y + 7 = x2
51. If 0° < θ < 90° and tan θ = , what is sin θ + cos θ?
52. In the figure below, = , and is a radius of the circle, having a length of 8 inches. What is the area of OAB, in square inches?
53. In XYZ, shown below, = 30. Which of the following represents the length of ?
(Note: For a triangle with sides of lengths x, y, and z, and respective opposite angles measuring X, Y, and Z, it will be true that: , according to the law of sines.)
54. Points P and Q lie on circle O with radius of 9 feet. The measure of POQ is 120°. What is the length, in feet, of minor arc ?
56. If function f is defined by f(x) = −2x3, then what is the value of f(f(1))?
57. The function y varies directly as x for all real numbers in the (x, y) coordinate plane. Which of the following could be the graph of y?
58. Gopi took 5 quizzes for which the scores are integer values ranging from 0 to 10. The median of her scores is 9. The mean of her scores is 8. The only mode of her scores is 10. Which of the following must be true about her quiz scores?
F. Her lowest score is 4.
G. Her lowest score is 5.
H. The median of the 3 lowest scores is 6.
J. The sum of the 5 scores is 50.
K. The sum of the 2 lowest scores is 11.
59. To make a cardboard table for her dollhouse, Ouisie uses a rectangular piece of cardboard measuring 40 inches wide and 60 inches long. She cuts out four equal-sized squares from each corner and folds down the sides at a 90° angle. If the top of the table measures 800 square inches, how tall, in inches, is the table?
60. Which of the following expressions gives the area, in square feet, of ABC shown below with the given side lengths in feet?
F. 50 tan 35°
G. 50 cos 35°
H. 50 sin 35°
J. 100 cos 35°
K. 100 sin 35°
END OF TEST 2
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