ACT MATH TEST. Pre-Algebra and Elementary Algebra
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1 Pre-Algebra and Elementary Algebra Of the 60 questions, 14 will relate to pre-algebra and 10 to elementary algebra. The pre-algebra and elementary algebra questions will cover the following topics: Arithmetic operations Powers and roots Ratio and proportion Percent Number theory Linear equations with one variable Probability and statistics Variables and functional relationships Substitution Polynomials Quadratic equations Properties of exponent 1. On the final project in Juan's art class, 14 students earned a grade of B. Those 14 students were exactly 20% of the total number of students in the class. How many students were in the class? a. 28 b. 34 c. 56 d. 64 e What is the value of x in the following equation? a. 2 b. 3 c. 9 d. 12 e At a certain construction site, there is a pile containing 55 tons of sand. Four trucks, each of which holds 11.4 tons of sand, are filled from this pile. How many tons of sand remain in the pile? f. 9.4 g h j k What is the value of 2(x 3) + 15, if x = 2? a. 3 b. 0 c. 5 d. 13 e. 25
2 5. Simplify: f. 7 g. 0 h. 7 j. 14 k Rosie's boss is going to give her a raise of 8%. If her salary before the raise is $25,500, what will her salary be after the raise? a. $23,460 b. $26,500 c. $27,040 d. $27,540 e. $27, If x is a real number such that x 3 = 80, between which two consecutive integers does x lie on the number line? f. 2 and 3 g. 3 and 4 h. 4 and 5 j. 5 and 6 k. 6 and 7 8. If 67 + a = 191, then a = a. 258 b. 124 c. 113 d. 124 e Joel is 8 years older than Karen, and Karen is twice as old as Lina. If Lina is x years old, how old is Joel in terms of x? f. x + 8 g. 2x h. x 8 j. 2x k. 2x + 8
3 10. Which of the following is a simplified form of 3a + 9b 2a? f. 6a + 9b g. a + 9b h. 12ab 2a j. 3a + 7ba k. 10ab 11. If x is positive, and 2x 2 7x 9 = 0, then what is the value of x? a. 1 b. 2 c. 4.5 d. 7 e A portable radio that normally sells for $29.55 is marked down by 20%. What is the sale price of the radio, rounded to the nearest dollar? a. $20 b. $21 c. $22 d. $23 e. $ Which of the following is the factored form of 3d 4 e 3 15de 2? f. 3(d 4 e 3 15de 2 ) g. 3de 2 (d 3 e 5) h. 3(d 4 e 15de) j. 3d 4 e 3 15de 2 k. 12d 3 e 14. If 2u + 2 = 20, and v 2u = 2, what is the value of v? a. 12 b. 10 c. 12 d. 14 e. 16
4 15. At a certain store, a 7.5-pound bag of rice costs $4.80. What is the cost per ounce of rice? (There are 16 ounces in a pound.) f. $0.02 g. $0.03 h. $0.04 j. $0.05 k. $ On Farm X, farm workers work 6 days per week and earn $23.00 per day, plus $0.74 per bushel filled. If a certain farm worker earned $ in a week, how many bushels did she fill in that week? a. 7 b. 31 c. 37 d. 68 e The quantity is greater than which of the following? f. g. h. j. k. 18. What is the smallest possible sum of 2 positive integers whose product is 36? a. 9 b. 10 c. 12 d. 13 e Two numbers have a greatest common factor of 6 and a least common multiple of 36. Which of the following could be the pair of numbers? a. 6 and 12 b. 6 and 18 c. 12 and 18 d. 12 and 24 e. 18 and 24
5 20. In the standard (x, y) coordinate plane, a line passes through the origin and the point What is the slope of the line? a. b. c. d. e. 21. The scores of five bowlers during the first round of a tournament are indicated in the table below. What is the average score of the five bowlers for the first round? a. 186 b. 192 c. 224 d. 240 e Motorcycle A travels 50 miles per hour for 2.5 hours. Motorcycle B travels 30 miles per hour for 5 hours. What is the difference between the number of miles traveled by Motorcycle A and the number of miles traveled by Motorcycle B? f. 0 g. 25 h. 125 j. 150 k For which of the following values of q is (q 4)(q + 3) = 0? a. 3 b. 4 c. 5 d. 6 e. 7
6 24. If pqs 0, then f. g. h. j. 2p 5 q 7 s 9 k. 2p 3 q 3 s If a = 3 and b = 2, then a 3 b ab 3 = f. 108 g. 78 h. 48 j. 30 k If (x y) 2 = x 2 26x + y 2 for all real numbers x, then y = f. 26 g. 13 h. 13 j. 26 k Find the sum of the polynomials 5x 2 y 2xy 2 and 3xy 2 x 2 y. a. 3xy 2 + 2x 2 y b. 4x 2 y + xy 2 c. 5x 3 y 3 d. 6x 2 y + 5xy 2 e. 8x 2 y 3xy Which of the following is equivalent to ( 3x 2 ) 3? f. 3x 5 g. 3x 6 h. 9x 6 j. 27x 5 k. 27x 6
7 29. if calculate the value of 2x 2 4x + 2. f. 72 g. 28 h. 5 j. 5 k If 2x + 4y = 8 and 5x + 2y = 10, what is the value of y? a. b. c. d. e. 31. Which if the following is equivalent to (a + b) 2? f. 2a + 2b g. a 2 + b 2 h. (ab) 2 j. a 2 + 2ab + b 2 k. (ab) 4 Intermediate Algebra and Coordinate Geometry Of the 60 questions, 9 will cover intermediate algebra and 9 will cover coordinate geometry. The intermediate algebra and coordinate geometry questions will cover the following topics: Sequences Formulas Quadratic formula Functions Composition of functions Inequalities Rational expressions Roots of polynomials Logarithms Matrices Number line graphs Midpoints Slope Parallel lines Graphs of polynomials Conics 1. What is the sixth term of the arithmetic sequence 3, 6, 9, 12,...? f. 13 g. 15 h. 18 j. 21 k. 24
8 2. If line segment XY is bisected by point Z, then which of the following must be true? a. b. c. d. e. 3. A rectangle is graphed in the standard (x, y) coordinate plane. Three of the rectangle's corners have coordinates ( 4, 5), (2, 5), and ( 4, 2). What are the coordinates of the fourth corner? a. ( 5, 2) b. (4, 2) c. ( 2, 2) d. ( 4, 5) e. (2, 2) 4. What is the slope of the line 2x 6y = 10? f. g. h. 0 j. k Which of the following is the graph of the solution set for z + 2 < 8? a. b. c. d. e.
9 6. If x and y are positive numbers, f. 3x 4y g. h. j. k. 7. In the right triangle below, how long is side MN? a. 6 b. c. d. e. 8. Which of the answer choices best describes the graph on the number line below? f. 1 > x > 2.5 g. 1 < x < 2.5 h. 1 < x < 2.5 j. 1 > > 2.5 k. 1 < < In the right triangle below, how many meters long is side AC? f. 5 g. 7.5 h. 10 j. k.
10 10. The line 3x 8y = 16 is plotted on the (x, y) coordinate plane. What is the y-intercept of the line? a. 4 b. 3 c. 2 d. 2 e Among the points on the number line below, which is the closest to f. F g. G h. H j. J k. K 12. If m n = 2 and m + n = then what is the value of f. g. h. j. k A line is graphed on the (x, y) coordinate plane. The value of the x-coordinate for each point on the line is 5 more than three times the value of the y-coordinate of that point. What is the slope of the line? f. g. h. 1 j. 2 k The equation for a certain line is 3y x = 12. Which of the following points lies on the line? a. (0, 10) b. (1, 4) c. (5, 5) d. ( 6, 2) e. ( 20, (3)
11 15. What is the value of gh, if 3g 12 = h and a. b. c. 4 d. e. 16. X, Y, and Z are real numbers and XYZ = π. Which of the following must be true? f. XYZ 2 = π 2 g. h. XYZπ = 0 j. k. 17. How many different integer values of x satisfy the inequality a. 3 b. 4 c. 5 d. 6 e What is the distance, on a standard (x, y) coordinate plane, between the point ( 2, 3) and the point ( 5, 4)? f. 7 g. h. 8 j. 9 k. 19. Which of the following is equivalent to f. g. h. 1 j. 2 k.
12 20. A cookie recipe calls for a 3:1 ratio of flour to sugar. If you put 2 cups of flour into the batter, how many cups of sugar do you need? a. b. 1 c. d. 3 e Line AB has points (3, 1) and (2, 4) in the standard (x, y) coordinate plane. Line CD is parallel to line AB. What is the slope of line CD? a. 4 b. 3 c. d. e If log = x, then x = a. b. c. 3 d. 25 e At what point do the lines with the following two equations intersect? y = 14x x = 2y 8 a. b. ( 3, 2) c. ( 3, 2) d. (3, 2) e. (3, 2) Plane Geometry and Trigonometry Of the 60 questions, 14 will cover plane and solid geometry and 4 will cover trigonometry. The plane geometry and trigonometry questions will cover the following topics: Lines and angles Perimeter Area Triangle Right triangles Similar figures Properties of polygons Circles
13 1. In the figure below, points G, H, and I are on the same line. What is the measure of? f. 35 g. 55 h. 75 j. 125 k In the parallelogram below, what is the measure of WZY? a. 55 b. 75 c. 90 d. 105 e A certain triangle has sides of lengths 40, 50, and 60 inches. If a similar triangle has a perimeter of 300 inches, how many inches long is that triangle's longest side? f. 45 g. 60 h. 80 j. 100 k A garden needs to be covered with grass sod. The garden has the dimensions shown below. How many square feet of sod are required to cover the garden? f. 720 g. 864 h. 984 j. 1,056 k. 1, A right triangle has sides of length 15, 20, and 25 meters. What is the area of the triangle in square meters? a. 60 b. 150 c. 250 d. 625 e. 7,500
14 6. Two sides of a triangle are 17 and 18 feet. Which of the following CANNOT be the length of the third side? a. 2 b. 8 c. 15 d. 18 e If the sine of a certain angle is and its cosine is what is the angle's tangent? a. b. c. d. e. 8. In the figure below, lines a and b are parallel to each other, and lines c and d are parallel to each other. If the two angles have measures 40 and 115, as shown, what is the measure of angle x? f. 25 g. 35 h. 50 j. 65 k What is the length of the radius of a circle with an area of 4π? f g. 2 h j. 2.5 k What is the area of the shaded region below, if the radius of the inner circle is 2.5 inches and the radius of the outer circle is 5 inches? f. 2.5π g. 6.25π h. 7.5π j. 12π k π
15 11. A square measuring w inches on each side is removed from a rectangle of length (w + 6) inches and width (w 1) inches. What is the remaining area, in square inches, of the rectangle? a. 11 b. 5w 6 c. 2w + 5 d. w 2 + 5w e. 5w A tin of candy contains three flavors. There are twice as many grape candies in a tin as there are cherry candies. There are three times as many lemon candies as grape candies. If a number of apple candies, equal to the number of cherry candies already in the tin, is added to the tin, what is the probability of randomly selecting a lemon candy from the tin? f. g. h. j. k. 13. In tossing a fair coin three consecutive times, what is the probability of getting heads on 2 consecutive tosses but NOT on three consecutive tosses? (A fair coin has an equal likelihood of a heads or tails outcome.) f. g. h. j. k. 14. In the parallelogram ABCD shown below, AD is 7 inches long. If the perimeter of the parallelogram is 42 inches, how many inches long is CD? f. 35 g. 29 h. 22 j. 14 k. 15. A ten-foot long ladder is propped up against an eight-foot tall building. If the ladder reaches the top of the building, what is the cosine of the angle formed by the ladder and the building? f. g. h. 2 j. 18 k. 80
16 16. All angles in the figure below are right angles. What is the perimeter, in inches (in), of the figure below? a. 35 b. 66 c. 70 d. 200 e In the figure below, if the height, width, and length are all doubled, the new surface area will be how many times its original size? a. 2 b. 4 c. 6 d. 8 e. 24 Peterson's Practice Tests for the ACT *
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