ACT Elite 36 by Princeton Review

Author:Princeton Review [Review, The Princeton]
Language: eng
Format: epub
ISBN: 978-0-8041-2556-7
Publisher: Random House Children's Books
Published: 2015-01-27T05:00:00+00:00

Continue in this manner, crossing off the same numbers of scores from the front and back ends of the list, until the middle of the list is reached.

If there were an odd number of scores on the list, the single score in the middle would be the median. With an even number of scores, the median is the average of the middle two scores. In this case, the middle two numbers are 72 and 74. The average of these two numbers is 73, so (G) is the credited response.

53. E The question gives the measure of Angle R in radians, but the answers contain degree measures. Start by converting π radians into degrees. The unit circle is 2π radians and a circle has 360°, so 2π = 360° and π = 180°. Therefore, π radians = (180°) = 1,575°. “Coterminal,” or having the same terminal angle, means that the angle measures are equivalent on the unit circle. From a measure of 1,575°, it is necessary to go down to the much smaller measures in the answer choices. So subtract 360° from 1,575° as many times as is needed to hit one of the answer choices. 1,575° − 360° = 1,215° − 360° = 855° − 360° = 495° − 360° = 135°. Therefore, 1,575° and 135° are coterminal, so (E) is the credited response.

54. H This looks ugly, but there are pairs of numbers in parentheses. That indicates that it is possible to use FOIL (First, Outer, Inner, Last) to multiply the binomials together. The result is 4 + 3i − 20i − 15i2. The middle two terms can be combined to get 4 + (3 − 20)i −15i2. At this point, (G) and (J) can be eliminated because they do not contain 4. Choice (F) does not contain (3 − 20)i, so it can be eliminated as well. Neither (H) nor (J) match the equation exactly, but now there is a 50-50 chance of choosing the right answer. To get the exact answer, however, it is necessary to know that i2 is equal to −1, so 15i2 equals −15. Most calculators also include a button for i, so calculating i2 on a calculator can help if this rule doesn’t come to mind. This changes the equation into 4+ (3− 20)i −(−15) or 4 + (3− 20)i + 15, which makes (H) the credited response.

55. B If y = 2 is a solution to the equation, that means to plug in 2 for y to solve the equation for c. The equation becomes 22 + c(2) − 8 = 0, which simplifies to 4 + 2c − 8 = 0 or 2c − 4 = 0. Add 4 to both sides of the equation to get 2c = 4, so c = 2. Plug this value for c into the original equation to get y2 + 2y − 8 = 0. Now use FOIL to determine the two factors of this equation. The factors are (y − 2) and (y + 4).

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