Enter keyword(s) Home | Registration | Test Prep | Scores | College Planning | Financial Aid | Career Planning | Student Blog | FAQs Sample Tests English Test Set 1 Questions / Answers Set 2 Questions / Answers Set 3 Questions / Answers Set 4 Questions / Answers Set 5 Questions / Answers Mathematics Test Set 1 Questions / Answers Set 2 Questions / Answers Set 3 Questions / Answers Set 4 Questions / Answers Set 5 Questions / Answers Reading Test Set 1 Questions / Answers Set 2 Questions / Answers Set 3 Questions / Answers Set 4 Questions / Answers ACT Assessment Sample Question Answer Key and Question Explanations Set 4: Mathematics 1. The correct answer is C. 5a = 25 so a = = 5; a2 = 5 · 5 = 25 A. If a2 = 5, then a = B. If a2 = 20, then a = and 5a = 5 25 so a2 5. = and 5a = 5 25 so a2 = D. If a2 = 125, then a = and 5a = 5 E. If a2 = 625, then a = = 25 and 5a = 5(25) = 125 = 20. 25 so a2 25 so a2 125. 625. 2. The correct answer is H. 30% of $1,000,000 is 0.3($1,000,000) = $300,000. When split equally among 5 group members, each gets ($300,000) = $60,000. F. If each got $30,000, the group's share would be 5($30,000) = $150,000, but that's only 15% of $1,000,000. G. If each got $50,000, the group's share would be 5($50,000) = $250,000, but that's only 25% of $1,000,000. Science Test Set 1 Questions / Answers Set 2 Questions / Answers Set 3 Questions / Answers Set 4 Questions / Answers Set 5 Questions / Answers Writing Test Sample Essay 1 Sample Essay 2 Sample Essay 3 Sample Essay 4 Return to Test Prep J. If each got $200,000, the group's share would be 5($200,000) = $1,000,000, but that's 100% of $1,000,000. K. If each got $300,000, the group's share would be 5($300,000) = $1,500,000, and that's more than the amount of sales generated. 3. The correct answer is B. 42 – k(4) – 12 = 0, so 4 – 4k = 0, k = 1 when x = 4, x2 – x – 12 = 42 – 4 – 12 = 0. A. If k = 7, then x2 – 7x – 12 should be 0 when x = 4. But 42 – 7(4) – 12 = –24 C. If k = –1, then x2 + x – 12 should be 0 when x = 4. But 42 + 4 – 12 = 8 0. 0. Test Descriptions D. If k = –3, then x2 + 3x – 12 should be 0 when x = 4. But 42 + 3(4) – 12 = 16 0. E. If k = –7, then x2 + 7x – 12 should be 0 when x = 4. But 42 + 7(4) – 12 = 32 0. 4. The correct answer is H. = = F. Incorrect because = only when x = , since = G. Incorrect because = only when x = , since = J. Incorrect because = 6 only when x = –3, since = K. Incorrect because = 8 only when x = – , since = = = = =6 = = =8 5. The correct answer is E. = , so 5(u + 4) = (u – 2)15, 5u + 20 = 15u – 30, 10u = 50, u = 5. Check: A. If u = –3, = and = = = = –1 and = = 15 and –1 = = – and = = 15, so –3 doesn't satisfy the equation. B. If u = –1, = 5 and – 5, so –1 doesn't satisfy the equation. C. If u = 3, = = 5 and = = and 5 , so 3 doesn't satisfy the equation. D. If u = 4, = = and = = and , so 4 doesn't satisfy the equation. 6. The correct answer is H. Parallel lines have equal slopes; kx + 2y = 8, so 2y = –kx + 8, y = x + 4. 18x + ky = 12, so ky = –18x + 12, y = = x+ . The slopes must be equal, so , –k2 = –36, k = ±6. A positive value is required, so k = 6. F. If k = 0, the lines are 2y = 8 or y = 4, which is horizontal, and 18x = 12 or x = , which is vertical. A horizontal line cannot be parallel to a vertical line. G. If k = 2, the lines are 2x + 2y = 8 or y = 4 – x, which has slope –1, and 18x + 2y = 12 or y = 6 – 9x, which has slope –9. –1 –9, so the lines cannot be parallel. J. If k = 8, the lines are 8x + 2y = 8 or y = 4 – 4x, which has slope –4, and 18x + 8y = 12 or y = – x, which has slope – . –4 – , so the lines cannot be parallel. K. If k = 12, the lines are 12x + 2y = 8 or y = 4 – 6x, which has slope –6, and 18x + 12y = 12 or y = 1 – x, which has slope – . –6 – , so the lines cannot be parallel. 7. The correct answer is E. A = r2 so A = 2 = A. In order for to be the area, the radius would have to be radius is inch, not inch. , since 2= , but the B. In order for to be the area, the radius would have to be radius is inch, not inch. , since 2= , but the C. In order for to be the area, the radius would have to be radius is inch, not inch. , since 2= , but the D. In order for to be the area, the radius would have to be radius is inch, not inch. , since 2= , but the 8. The correct answer is J. Since sin x = cos(90° – x) for all x, if sin x = cos y, then Y = 90° – X and X + Y = X + (90 X) = 90°. Conversely, if X + Y = 90°, Y = 90° – X, cos Y = cos(90° – X) = cos 90° cos X + sin 90° sin X = 0 · cos X + 1 · sin X = sin X. F. If X + Y = 30°, then Y = 30° – X and sin X = cos(30° – X) sin X = cos 30° cos X + sin 30° sin X sin X = cos X + sin X sin X = cos X = tan X = , so X = 60°, Y = –30°. But both X and Y must be between 0° and 90°, so X + Y 30°. G. If X + Y = 45°, then Y = 45° – X and sin X = cos(45° – X) sin X = cos 45° cos X + sin 45° sin X sin X = cos X + sin X 1– sin X = cos X = tan X = + 1, so X = 67.5°, Y = –22.5°. But both X and Y must be between 0° and 90°, so X + Y 45°. H. If X + Y = 60°, then Y = 60° – X and sin X = cos(60° – X) sin X = cos 60° cos X + sin 60° sin X sin X = cos X + sin X 1– sin X = cos X = tan X = 2 + , so X = 75°, Y = –15°. But both X and Y must be between 0° and 90°, so X + Y 60°. K. If X + Y = 135°, then Y = 135° – X and sin X = cos(135° – X) sin X = cos 135° cos X + sin 135° sin X sin X = cos X + sin X 1– sin X = cos X = tan X = –( + 1), so X = 112.5°, Y = 22.5°. But both X and Y must be between 0° and 90°, so X + Y 135°. 9. The correct answer is A. The triangle is a 30°-60°-90° triangle so the sides are in the ratio 1: So = , 2 = x , x = 2. :2. B. If x were , then, according to the ratios for 30°-60°-90° triangles, the hypotenuse would be 2 feet long. But this is the length of a leg, and the length of the hypotenuse must be greater than the lengths of the legs. C–E. Since these values all exceed 2 , none can be correct because each would imply that 60° is less than 30°, since the smaller angle must be opposite the smaller side. 10. The correct answer is F. –2x > 4 so – (–2x) < – (4), x < –2 and the graph is all points to the left of –2. G, H, and K are not correct because each includes x = 0; –2(0) = 0 and 0 J is not correct because J includes x = 3; –2(3) = –6 and –6 4. 4. 11. The correct answer is D. Lines parallel to 2x – y = 5 have the same slope as 2x – y = 5. The slope-intercept form for 2x – y = 5 is y = 2x – 5, so the slope is 2. The desired line has slope 2 and passes through (0,0). Its equation is then y = 2x or 2x – y = 0. A. The line with equation –2x + y = 5 does not go through (0,0), since –2(0) + 0 5. B. The line with equation 2x + y = 5 does not go through (0,0), since 2(0) + 0 5. C. The slope of the line with equation x – y = 0 is 1, since the slope-intercept form is y = So the line with equation x – y = 0 is not parallel to the line 2x – y = 5. E. The slope of the line with equation 2x + y = 0 is –2, since the slope-intercept form is y = –2x. So the line with equation 2x + y = 0 is not parallel to the line 2x – y = 5. © 2006 by ACT, Inc. All rights reserved. ACT Corporate Home | Contact Us | Site Index
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