Math - ACT Practice November
49. The standard region in the graph below represents the solution set to which of the following systems of inequalities? A. y < -x + 2 and (x - 1)² < 9 B. y > -x + 2 and (x - 1)² + (y - 2)² < 9 C. y > -x + 2 and (x - 1)² + (y - 2)² > 9 D. y < -x + 2 and (x - 1)² + (y - 2)² > 9 E. (y - 2) < 3 and (x - 1) > 3
A.
37. What is the difference between the mean and the median of the set {3, 8, 10, 15} ? A. 0 B. 1 C. 4 D. 9 E. 12
A. 0
9. A computer chip 0.32 cm thick is made up a layers of silicon. If the top and bottom layers are each 0.03 cm thick and the inner layers are each 0.02 cm thick, how many inner layers are there? A. 13 B. 15 C. 16 D. 52 E. 64
A. 13
23. Which of the following expressions is equivalent to 1/2y²(6x+2y+12x-2y) ? A. 9xy² B. 18xy C. 3xy² + 12x D. 9xy² - 2y³ E. 3xy² + 12x - y³ - 2y
A. 9xy^2
39. Trapezoid ABCD is graphed in the standard (x, y) coordinate plane below. What is the slope of CD? C(9, 4) and D(12, 1) A. -3 B. -1 C. 1 D. 5/21 E. 3/2
B. -1
33. A 15-foot wall is how many inches long in the scale drawing? A. 1.5 B. 1.875 C. 3 D. 3.375 E. 3.75
B. 1.875
13. In the figure below, C is the intersection of AD and BE. If it can be determined, what is the measure of ∠BAC? A. 80° B. 100° C. 110° D. 115° E. cannot be determined from the given information
B. 100°
15. This month, Kami sold 70 figurines in 2 sizes. The large figurines sold for $12 each, and the small figurines sold for $8 each. The amount of money he received from the sales of the large was equal to the amount of money he received from the sales of the small figurines. How many large figurines did Kami sell this month? A. 20 B. 28 C. 35 D. 42 E. 50
B. 28
25. Last month, Lucie had total expenditures of $900. The pie chart below breaks down these expenditures by category. The category in which Lucie's expenditures were greatest is what percent of her total expenditures, to the nearest 1%? Clothes = $254 Food = $219 Entertainment = $125 Insurance = $182 Gas = $120 A. 24% B. 28% C. 32% D. 34% E. 39%
B. 28%
53. A formula for the surface area (A) of the rectangular solid shown below is A = 2lw + 2lh + 2wh where 1 represents length; w, width; and h, height. By doubling each of the dimensions (l, w, and h), the surface area will be multiplied by what factor? A. 2 B. 4 C. 6 D. 8 E. 12
B. 4
21. To get a driver's license, an applicant must pass a written test and a driving test. Past records show 80% of the applicants pass the written test and 60% of those who have passed the written test pass the driving test. Based on these figures, how many applicants in a random group of 1,000 applicants would you expect to get driver's licenses? A. 200 B. 480 C. 600 D. 750 E. 800
B. 480
47. Only tenth, eleventh, and twelfth-grade students attend Washington High School. The ratio of tenth graders to the school's total student population is 86:225, and the ratio of eleventh graders to the school's total student population is 18:51. If 1 student is chosen at random from the entire school, which grade is that student most likely to be in? A. Tenth B. Eleventh C. Twelfth D. All grades are equally alike E. Cannot be determined fro, the given information
B. Eleventh
29. What is the product of the complex numbers (-3i + 4) and (3i + 4) ? A. 1 B. 7 C. 25 D. -7 + 24i E. 7 + 24i
C. 25
57. The functions y = sin x and y = sin(x + a) + b, for constants a and b, are graphed in the standard (x, y) coordinate plane below. The functions have the same maximum value. One of the following statements about the values of a and b is true. Which statement is it? A. a < 0 and b = 0 B. a < 0 and b > 0 C. a = 0 and b > 0 D. a > 0 and b < 0 E. a > 0 and b > 0
A. a < 0 and b = 0
35. CC Installations' estimate consists of a $650.00 charge for labor, plus a fixed charge per cabinet. The labor charge and the charge per cabinet remain the same for any number of cabinets built and installed. CC Installations would give Gianna what estimate if the craft room were to have twice as many cabinets as Gianna is planning to have? A. $2,800.00 B. $3,000.00 C. $3,450.00 D. $3,650.00 E. $4,300.00
D. $3,650.00
19. In scientific notation, 670,000,000 + 700,000,000 = ? A. 1.37 x 10⁻⁹ B. 1.37 x 10⁷ D. 1.37 x 10⁹ E. 137 x 10¹⁵
D. 1.37 x 10^9
17. In a plane, the distinct lines AB and CD intersect at A, where A is between C and D. The measure of ∠BAC is 47°. What is the measure of ∠BAD? A. 43° B. 47° C. 94° D. 133° E. 137°
D. 133
45. Given that a[2 6 1 4] = [x 27 y x] for some real number a, what is x + z? A. 4/3 B. 27/2 C. 26 D. 27 E. 48
D. 27
31. To make a 750-piece jigsaw puzzle more challenging, a puzzle compnay includes 5 extra pieces in the box along with the 750 pieces, and those 5 extra pieces do not fit anywhere in the puzzle. If you buy such a puzzle box, break the seal on the box, and immediately select 1 piece at random, what is the probability that it will be 1 of the extra pieces? A. 1/5 B. 1/755 C. 1/750 D. 5/755 E. 5/750
D. 5/755
1. The blood types of 150 people were determined for a study. O = 62 people; A = 67 people; B = 15 people; AB = 6. If 1 person from this study is randomly selected, what is the probability that this person has either Type A or Type AB blood? A. 62/150 B. 66/150 C. 68/150 D. 73/150 E. 84/150
D. 73/150
43. A formula to estimate the monthly payment, p dollars, on a short-term loan is p = (1/2ary + a)/12y where a dollars is the amount of the loan, r is the annual interest rate expressed as a decimal, and y years is the length of the loan. When a is multiplied by 2, what is the effect on p? A. p is divided by 6 B. p is divided by 2 C. p does not change D. p is multiplied by 2 E. p is multiplied by 4
D. p is multiplied by 2
59. As part of a probability experiment, Elliott is to answer a 4 multiple-choice questions. For each question, there are 3 possible answers, only 1 of which is correct. If Elliott randomly and independently answers each question, what is the probability that he will answer the 4 questions correctly? A. 27/81 B. 12/81 C. 4/81 D. 3/21 E. 1/81
E. 1/81
5. If ƒ(x) = (3x + 7)², then ƒ(1) = ? A. 10 B. 16 C. 58 D. 79 E. 100
E. 100
51. If x:y= 5:2 and y:z = 3:2, what is the ratio of x:z? A. 3:1 B. 3:5 C. 5:3 D. 8:4 E. 15:4
E. 15:4
27. What is the perimeter of the isosceles right triangle, whose hypotenuse is 8√2 inches long? A. 8 B. 8 + 8√2 C. 8 + 16√2 D. 16 E. 16 + 8√2
E. 16 + 8√2
7. The first term is 1 in the geometric sequence 1, -3, 9, -27.... . What is the SEVENTH term of the geometric sequence? A. -243 B. -30 C. 81 D. 189 E. 729
E. 729
55. Kelly asked 120 students questions about skiing. The results of the poll are shown in the table below. 1. Have you skied either cross-country or downhill? 65 yes and 55 no 2. If you answered Yes to Question 1, did you ski downhill? 28 yes and 37 no 3. If you answered Yes to Question 1, did you ski cross-country? 45 yes and 20 no After completing the poll, Kelly wondered how many of the students polled had skied both cross-country and downhill. How many of the students polled indicated that they had skied both cross-country and downhill? A. 73 B. 65 C. 47 D. 18 E. 8
E. 8
3. On a particular road map, 1/2 inch represents 18 miles. About how many miles apart are 2 towns that are 2.5 inches apart on this map? A. 18 B. 22.5 C. 36 D. 45 E. 90
E. 90
41. Which of the following vertical lines cuts ABCD into 2 trapezoids with equal areas? A. x = 2.5 B. x = 3.5 C. x = 4.5 D. x = 5.5 E. x = 6.5
E. x = 6.5
40. When ABCD is reflected over the y-axis to A'B'C'D', what are the coordinates of D'? F. (-12, 1) G. (-12, -1) H. (12, -1) J. (1, 12) K. (1, -12)
F. (-12, 1)
20. For Trapezoid ABCD show below, AB||DC, the measures of the interior angles are distinct, and the measure of ∠D is x⁰. What is the degree measure of ∠A in terms of x? F. (180-x)⁰ G. (180-0.5x)⁰ H. (180+0.5x)⁰ J. (180+x)⁰ K. x⁰
F. (180 - x)⁰
4. Given ƒ = cd³, ƒ = 450, and d = 10, what is c? F. 0.45 G. 4.5 H. 15 J. 45 K. 150
F. 0.45
18. In which of the following are 1/2, 5/6, and 5/8 arranged in ascending order? F. 1/2 < 5/8 < 5/6 G. 5/6 < 1/2 < 5/8 H. 5/6 < 5/8 < 1/2 J. 5/8 < 1/2 < 5/6 K. 5/8 < 5/6 < 1/2
F. 1/2 < 5/8 < 5/6
50. You can find the volume of an irregularly shaped solid object by completely submerging it in water and calculating the volume of water the object displaces. You completely submerge a solid object in a rectangular tank that has a base 40 centimeters by 30 centimeters and is filled with water to a depth of 20 centimeters. The object sinks to the bottom, and the water level goes up 0.25 centimeters. What is the volume, in cubic centimeters, of the object? F. 300 G. 240 H. 200 J. 150 K. 75
F. 300
38. Which of the following describes a true relationship between the functions f(x) = (x - 3)² + 2 and g(x) = 1/2x + 1 graphed below in the standard (x, y) coordinate plan? F. f(x) + g(x) for exactly 2 values of x G. f(x) = g(x) for exactly 1 value of x H. f(x) < g(x) for all x J. f(x) > g(x) for all x K. f(x) is the inverse of g(x)
F. f(x) + g(x) for exactly 2 values of x
48. 4/√2 + 2/√3 = ? F. (4√3 + 2√2)/√5 G. (4√3 + 2√2)/√6 H. 6/(√2 + √3) J. 6/√5 K. 8/√6
G. (4√3 + 2√3)/√6
26. In the figure below, the measure of ∠BAC is (x + 20)⁰ and the measure of ∠BAD is 90⁰. What is the measure of ∠CAD? F. (x - 70)⁰ G. (70 - x)⁰ H. (70 + x)⁰ J. (160 - x)⁰ K. (160 + x)°
G. (70 - x)°
44. The points E(6, 4) and F(14, 12) lie in the standard (x,y) coordinate plane shown below. Point D lies on EF between E and F such that the length of EF is 4 times the length of DE. What are the coordinates of D? F. (7, 5) G. (8, 6) H. (8, 8) J. (10, 8) K. (12, 10)
G. (8, 6)
30. The radius of the base of the right circular cone shown below is 5 inches, and the height of the cone is 7 inches. Solving which of the following equations gives the measure, θ, of the angle formed by a slant height of the cone and a radius? F. tan θ = 5/7 G. tan θ = 7/5 H. sin θ = 5/7 J. sin θ = 7/5 K. cos θ = 7/5
G. tan θ = 7/5
6. Jorge's current hourly wage for working at Denti Smiles is $12.00. Jorge was told that at the beginning of next month, his new hourly wage will be an increase of 6% of his current hourly wage. What will be Jorge's new hourly wage? F. $12.06 G. $12.60 H. $12.72 J. $18.00 K. $19.20
H. $12.72
8. The shipping rate for customers of Ship Quick consists of a fee per box and a price per pound for each box. Less than 10 pounds = $5.00 fee and $1.00 per pound; 10-25 pounds = $10.00 fee and $0.65 per pound; More than 25 pounds = $20.00 fee and $0.30 per pound. Gregg wants Ship Quick to ship 1 box that weighs 15 pounds. What is the shipping rate for this box? F. $9.75 G. $16.50 H. $19.75 J. $20.00 K. 24.50
H. $19.75
2. The monthly fees for single rooms at 5 colleges are $370, $310, $380, $340, and $310. What is the mean of these monthly fees? F. $310 G. $340 H. $342 J. $350 K. $380
H. $342
22. If a, b, and c are positive integers such that a^b = x and c^b = y, then xy= ? F. ac^b G. ac^2b H. (ac)^b J. (ac)^2b K. (ac)^b²
H. (ac)^b
52. Which of the following is the solution statement for the inequality shown below? -5 < 1 - 3x < 10 F. -5 < x < 10 G. -3 < x H. -3 < x < 2 J. -2 < x > 3 K. x < -3 or x > 2
H. -3 < x > 2
28. The equation y = ax² + bx + c is graphed in the standard (x,y) coordinate plane for real values of a, b, and c. When y = 0, which of the following best describes the solutions for x? F. 2 distinct positive real solutions G. 2 distinct negative real solutions H. 1 positive real solution and 1 negative real solution J. 2 real solutions that are not distinct K. 2 distinct solutions that are not real
H. 1 positive real solution and 1 negative real solution
34. Gianna will install tile on the portion of the floor that will not be covered by cabinets. What is the area, in square feet, of the portion of the floor that will NOT be covered by cabinets? F. 72 G. 90 H. 140 J. 156 K. 164
H. 140
14. Antwan drew the circle graph below describing his dime spent at school in 1 day. His teacher said that the numbers of hours listed were correct, but that the central angle measures for the sectors were not correct. What should be the central angle measure for the Core subjects sector? Core subjects = 4 hours; Electives = 3 hours; Lunch and passing time = 1 hour; Choir = 1 hour; F. 72° G. 80° H. 160° J. 200° K. 288°
H. 160°
24. An artist makes a profit of (500p - p²) dollars from selling p paintings. What is the fewest number of paintings the artist can sell to make a profit of at least $60,000? F. 100 G. 150 H. 200 J. 300 K. 600
H. 200
16. A car accelerated from 88 feet per second (fps) to 220 fps in exactly 3 seconds. Assuming the acceleration was constant, what was the car's acceleration, in feet per second, from 88 fps to 220 fps? F. 1/144 G. 29 1/3 H. 44 J. 75 1/3 K. 102 2/3
H. 44
36. Which of the following if the graph of the region 1 < x + y < 2
J.
60. The sides of an acute triangle measure 14 cm, 18 cm, and 20 cm, respectively. Which of the following equations, when solved for θ, gives the measure of the smallest angle of the triangle? F. sinθ/14 = 1/18 G. sinθ/14 = 1/20 H. sinθ/20 = 1/14 J. 14² = 18² + 20² - 2(18)(20)cosθ K. 20² = 14² + 18² - 2(14)(18)cosθ
J. 14² = 18² + 20² -2(18)(20)cosθ
46. A container is 1/8 full of water. After 10 cups of water are added, the container is 3/4 full. What is the volume of the container in cups? F. 13 1/3 G. 13 1/2 H. 15 J. 16 K. 40
J. 16
58. Which of the following number line graphs shows the solution set to the inequality |x - 5| < -1?
K.
56. The square below is divided into 3 rows of equal area. In the top row, the region labeled A has the same area as the region labeled B. In the middle row, the 3 regions have equal areas. What fraction of the square's area is in a region labeled A? F. 1/9 G. 3/9 H. 6/9 J. 13/12 K. 13/36
K. 13/36
32. What fraction lies exactly halfway between 2/3 and 3/4 ? F. 3/5 G. 5/6 H. 7/12 J. 9/16 K. 17/24
K. 17/24
10. These are the number cars Jing sold each month last year. What is the median of the data in the table? January = 25, February = 15; March = 22; April = 19; May = 16; June = 13; July = 19; August = 25; September = 25; October = 27; November = 28; December = 29 F. 13 G. 16 H. 19 J. 20.5 K. 23.5
K. 23.5
42. Given ƒ(x) = x - 1/x and g(x) = 1/x, what is ƒ(g(1/2))? E. -3 G. -3/2 H. -2/3 J. 0 K. 3/2
K. 3/2
12. The length of a rectangle with area 54 square centimeters is 9 centimeters. What is the perimeter of the rectangle? F. 6 G. 12 H. 15 J. 24 K. 30
K. 30
54. A dog eats 7 cans of food in 3 days. At this rate, how many cans of food does the dog eat in 3 + d days? F. 7/3 + d G. 7/3 + d/3 H. 7/3 + 7/3d J. 7 + d/3 K. 7 + 7d/3
K. 7 + 7d/3
11. Students studying motion observed a cart rolling at a constant rate along a straight line. The table below gives the distance, d feet, the cart was from a reference point point at 1-second intervals from t = 0 seconds to t = 5 seconds. t = 0, 1, 2, 3, 4, 5; d = 14, 20, 26, 32, 38, 44 Which of the following equations represents this relationship between d and t? A. d = t + 14 B. d = 6t + 8 C. d = 6t + 14 D. d = 14t + 6 E. d = 34t
c. d = 6t + 14
