Math test english 5

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– ACT MATH TEST PRACTICE – Trigonometry Basic trigonometric ratios, graphs, identities, and equations are covered in this section. B ASIC T RIGONOMETRIC R ATIOS opposite sin A = opposite refers to the length of the leg opposite angle A. hypotenuse adjacent cos A = hypotenuse adjacent refers to the length of the leg adjacent to angle A. opposite tan A = adjacent T RIGONOMETRIC I DENTITIES sin2 x + cos2 x = 1 sin x tan x = cos x sin 2x = 2sin x cos x cos 2x = cos2 x − sin2 x 2tan x tan 2x = 1 − tan2 x P ractice Questions Directions After reading each question, solve each problem, and then choose the best answer from the choices given. (Remember, the ACT Math Test is different from all the other tests in that each math question contains ﬁve answer choices.) When you are taking the ofﬁcial ACT, make sure you carefully ﬁll in the appropriate bub- ble on the answer document. You may use a calculator for any problem, but many problems are done more quickly and easily with- out one. Unless directions tell you otherwise, assume the following: ﬁgures may not be drawn to scale I geometric ﬁgures lie in a plane I “line” refers to a straight line I “average” refers to the arithmetic mean I Remember, the questions get harder as the test goes on. You may want to consider this fact as you pace yourself. 164
– ACT MATH TEST PRACTICE – 1. How is ﬁve hundred twelve and sixteen thousandths written in decimal form? a. 512.016 b. 512.16 c. 512,160 d. 51.216 e. 512.0016 2. 4 1 − 1 3 = ? 3 4 f. 2 172 g. 3 152 h. 3 2 3 i. 2 152 j. 1 1 8 3. Simplify |3 − 11| + 4 × 23. a. 24 b. 40 c. 96 d. 520 e. 32 4. The ratio of boys to girls in a kindergarten class is 4 to 5. If there are 18 students in the class, how many are boys? f. 9 g. 8 h. 10 i. 7 j. 12 5. What is the median of 0.024, 0.008, 0.1, 0.024, 0.095, and 0.3? a. 0.119 b. 0.095 c. 0.0595 d. 0.024 e. 0.092 165
– ACT MATH TEST PRACTICE – 6. Which of the following is NOT the graph of a function? f. g. h. i. j. 166
– ACT MATH TEST PRACTICE – 7. 4.6 × 105 = ? a. 4.60000 b. 0.000046 c. 4,600,000 d. 460,000 e. 0.0000046 8. What is the value of x 5 for x = 3? f. 15 g. 243 h. 125 5 i. 3 j. 1.6 9. What is the next number in the pattern below? 0, 3, 8, 15, 24, . . . a. 35 b. 33 c. 36 d. 41 e. 37 10. What is the prime factorization of 84? f. 42 × 2 g. 7 × 2 × 3 h. 22 × 3 × 7 i. 2 × 6 × 7 j. 23 × 7 11. Find the slope of the line 7x = 3y − 9. a. 3 b. −9 7 c. 3 d. −3 3 e. 7 167
– ACT MATH TEST PRACTICE – 12. The perimeter of a rectangle is 20 cm. If the width is 4 cm, ﬁnd the length of the rectangle. f. 6 cm g. 16 cm h. 5 cm i. 12 cm j. 24 cm 13. Find the area of the ﬁgure below. 10 in 3 in 7 in 7 in a. 79 square inches b. 91 square inches c. 70 square inches d. 64 square inches e. 58 square inches 14. Five cans of tomatoes cost $6.50. At this rate, how much will 9 cans of tomatoes cost? f. $13.00 g. $11.70 h. $1.30 i. $11.90 j. $12.40 15. For all x ≠ 0, 32x + 1 =? 5 2 a. 15x 10 + 3x b. 15 + x 10 + 3x c. 15x 2 d. 15 + x 1 e. 5x 168
– ACT MATH TEST PRACTICE – 16. Which inequality best represents the graph below? −3 −2 −1 0 1 f. −1.5 > x > −1 g. x ≤ 0 h. −0.5 > x > 0 i. −1.5 < x < 0 j. −1.5 ≤ x ≤ 0 17. Simplify −(6x4y3)2. a. −36x6y5 b. 36x2y c. −36x8y6 d. 36x8y4 e. −36xy 18. If 2x + 3y = 55 and 4x = y + 47, ﬁnd x − y. f. 28 g. 16 h. 5 i. 12 j. 24 19. Which inequality represents the graph below? −4 0 4 a. −4x < 0 b. −20x > 5 c. x < −4 d. −x ≤ − 4 e. −x < 4 3 16x5y 4. 20. Simplify 3 f. 2xy 2x2y g. 8x2y 3 h. 8xy 2 3 i. 2xy xy 3 j. 4x 2y 2 x 169