AccelePrep for the ACT Test 2nd Edition Student Text

116 • S URGE TO S UCCESS ! M ATH T EST P REP

1. You should be able to answer this item with just a quick glance. The “big” angle is the supplement to the angle which measures 42.5°. And the “big” angle is certainly greater than 90°, probably greater than 120°. So only (D) is a possible answer. 2. The angles opposite equal sides of a triangle are also equal. This is possible for the given triangle only if each of the three angles equals 60°. Therefore, the triangle is an equilateral triangle and each side is 3 units long. The perimeter of the triangle is: 3 3 3 9 ǡ ȋ ȌǤ If you aren’t able to make this deduction to determine the unknown length, assume the drawing is approximately accurate: all three sides seem to be equal in length, so the perimeter must be approximately 3 3 9 : . 3. If you cannot see that the answer is (B), place the corner of a piece of paper next to the angle in question and fold back the corner: The angle seems to be about half of the right angle formed by the page, so x 45 . To be sure, the answer sheet does not have marked inches or centimeters, but then again, you won’t need them. Relative ‡ƒ•—”‡‡–•Ȅ„ƒ•‡† ‘ Ž‡‰–Š• ’”‘˜‹†‡† ‹ –Š‡ ϐ‹‰—”‡ accompanying an item stem—will be enough to draw basic conclusions regarding lengths. 4. The Dz‘ˆϐ‹…‹ƒŽdz ™ƒ› –‘ •‘Ž˜‡ –Š‹• ’”‘„Ž‡ ‹• –‘ —•‡ –Š‡ ›–Šƒ‰‘”‡ƒ theorem. The vertical line from the center of the circle, O , and perpendicular to the chord of length 16 bisects the chord. So you have a right triangle with sides of 6, 8, and r . You can use the Pythagorean –Š‡‘”‡ –‘ ϐ‹† r : 6 8 2 2 2 So what do you do if that insight escapes you? Measure r . No, you don’t have a ruler, but you do have an answer sheet. And your answer sheet can be used as a straight-edge. Using very light tics, mark off the length of r on your answer sheet. Compare it to the length of the chord: r is a bit more than half the chord and so a bit more than 8, roughly 10, choice (B). r r r 100 10

Answers

Return to the pages below to review each item:

1. p. 113 2. p. 113 3. p. 113 4. p. 114 5. p. 114 6. p. 115 7. p. 115