Victory for the ACT Student Text 15e

M ATH T EST M ECHANICS • 197 A thought-reverser is any word, such as “not,” “except,” or “but,” that turns a question inside out. As shown, below, make sure you mark the thought-reverser so that you do not forget it as you work the problem. Example: A. 0 B. 2 C. 12 D. 132 E. 144 Since 1 is the square of 1, and 144 is the square of 12, there are a total of 12 integers in the set of integers from 1 to 144, inclusive, that are a square of an integer ( 1 2 , 2 2 , 3 2 , 4 2 , 5 2 , 6 2 , 7 2 , 8 2 , 9 2 , 10 2 , 11 2 , 12 2 ). Therefore, there are a total of 144 1 132 − = integers in the •‡– –Šƒ– ƒ”‡ ƒ •“—ƒ”‡ ‘ˆ ƒ ‹–‡‰‡”Ǥ In the Math Lessons, you will learn some very powerful test-taking strategies that use the multiple-choice answers to test items to help solve the items. For now, there are two simple suggestions to keep in mind. Sometimes, the array of answers will include choices that, taken at face value, seem to be plausible, but when examined more carefully, must be incorrect. Example:  –Š‡ ϐ‹‰—”‡ ƒ„‘˜‡ǡ ƒ…‹”…Ž‡ ™‹–Š…‡–‡” O and a radius of 2 is inscribed in a square. What is the area of the •Šƒ†‡† ’‘”–‹‘ ‘ˆ –Š‡ ϐ‹‰—”‡ǫ F. 2 r G. 4 2 r H. 16 2 r J. 16 4 r K. 16 6 r The shaded area is equal to the area of the square minus the area of the circle. Since the radius of the circle is 2, the side of the square is 4 and its area is 4 4 16 ] g . The area of the circle is (2) 4 2 r r . Therefore, the shaded area is 16 4 r . ‘–‹…‡ –Šƒ– ™‹–Š‘—– even solving the item, you can eliminate answer choices. Take a closer look at (F), (G), and (K). Since r is approximately 3.14, (F), (G), and (K) are negative. Area, however, cannot be a negative number, so (F), (G), and (K) must be wrong, and you …ƒ ‡Ž‹‹ƒ–‡ –Š‡ ™‹–Š‘—– †‘‹‰ ƒ› ‘–Š‡” ™‘”Ǥ ‘™ǡ ‹ˆ ›‘— Šƒ† –‘ǡ ›‘—…ƒ ƒ‡ ƒ educated guess from the remaining choices and the odds of guessing correctly are 50/50. ȋ ‘–‡ –Šƒ– ‡˜‡ ‹ˆ ›‘— ƒ”‡ —ƒ„Ž‡ –‘ ‡Ž‹‹ƒ–‡ ƒ•™‡”…Š‘‹…‡•ǡ ›‘— •–‹ŽŽ •Š‘—Ž† ‰—‡••ǡ since the ACT test does not penalize for wrong answers.)

Pay Attention to Thought-Reversers

Use the Answer Choices

Eliminate Answer Choices That Cannot Be Correct