12.Practice.Tests.for.the.SAT_2015-2016_1128p

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1004 1 12 Practice Tests for the SAT Practice Test Eleven Answers and Explanations Getting to the Answer: 1 0(8) = 80, so the sum must be greater than 80. 12(8) = 96, so the sum must be less than 96. 4. E Difficulty: Medium Strategic Advice: Since Earth makes a complete rotation about its axis in 24 hours, any point on its surface must rotate through 360° in that time. Getting to the Answer: Goannaville rotates 360° in the 24 hours from 1 :00 PM January 2 to 1 :00 PM January 3. In the three hours between l :00 PM and 4:00 PM on January 3, it rotates { 4 (360°) = 45° more. 360° + 45° = 405° 5. c Difficulty: Low Strategic Advice: While questions about sets are more likely to be of low or medium rather than high difficulty, they will, at any difficulty level, assume that you're familiar with some of the basic terminology of sets. With that in mind, begin to absorb a few facts. The things in a set are called elements or members. The union of sets is the set of elements in one or more of the sets being united. Think of the union set as what you get when you merge sets. The symbol for the union of sets is u. The intersection of sets is the set of common elements of the sets being intersected. Think of the intersection as the overlap of sets. The symbol for the intersection of sets is n. Getting to the Answer: To be in SnTnU-that is, the intersection of 5, T, and U-a number would have to be between -3 and 3, inclusive; prime; and positive. Given the sets in question, the only such numbers are 2 and 3. Remember that 1 is not prime; test takers who forget that fad wrongly choose (D). 6. c Difficulty: Medium Strategic Advice: Both a and b can be positive, negative, or equal to zero. The square of a negative or a positive number will be positive. Zero is neither positive nor negative. Getting to the Answer: a+ b can be ruled out because a or b (or both) could be negative or zero. a2 - b2 + 1 O can be ruled out because b2 could be greater than a2 + 10. a2 + b2 + 1 is correct. a2, b2, and 1 are all positive, so their sum must be positive. a3 + b3 + 16 can be ruled out because a orb could be negative, and the cube of a negative number is negative. a4 + b2 + a2 can be ruled out because a and b could both equal zero. 7. D Difficulty: Medium Strategic Advice: Do not assume that the measurements of the angles in this figure resemble the way the figure is drawn. Any figure on the SAT that is not drawn to scale is drawn in such a way as to be deliberately misleading. To find the angles, you will need to use three pieces of information: the sum of the interior angles of a triangle is 1 80°, the sum of te angles along a straight line is 1 80°, and vertical angles-angles pointed toward each other-are equal. Using this information, you can find the measure of every angle in the diagram, as shown below. Any triangle with a 90° angle is a right triangle. Getting to the Answer: 8. E Difficulty: Medium c Strategic Advice: Questions about exponential growth can be quite challenging for many test takers. You'll be the exception if you come to think about such questions in commonsense terms. To double is simply to multiply by 2. The question calls for this doubling to occur 24 times.
12 Practice Tests for the SAT Practice Test Eleven Answers and Explanations I 1005 The mathematical way of expressing "doubling to occur 24 times" is 224. Getting to the Answer: The answer is the total growth that occurs, times the original population. Again, total growth is 224. The original population is p. 9. E Difficulty: Medium Strategic Advice: When you come upon absolute value questions, one great immediate reaction is to think, "Every positive number is the absolute value of two numbers: the number itself and the negative of the number." Getting to the Answer: Call the integer n. If the absolute value of n is between 3 and 6, n must be -5, -4, 4, or 5. Two less than each of these would be (A), (B), (C), and (D), respectively. 10. B Difficulty: Medium Strategic Advice: This problem tests your ability to read instructions and perform calculations carefully. Follow each step of the procedure in order and avoid careless errors to find the answer. Getting to the Answer: 0.62(20) = 12.4 The largest integer less than 12.4 is 12. 12-4=8 11. D Difficulty: Medium Strategic Advice: Follow the steps for the smallest and largest numbers that can be selected in step 1 to find the smallest and largest numbers than can be written in step 5. This range includes all possible numbers you can write down in step 5. Numbers outside that range, therefore, are not correct. Getting to the Answer: Lower bound: 0.5(20) = 10 10 is the largest integer less than or equal to 10. 10-4=6 Upper bound: 0.99(20) = 19.8 19 is the largest integer less than or equal to 1 9.8. 19-4=15 Therefore, the only numbers that could be written in step 5 are the integers between 6 and 15. 0 and 5 are too small, 7.4 is not an integer, and 17 is too large. 12. c Difficulty: Medium Strategic Advice: Think about what is happening at each step. What kind of change does each step make to the number? It may be helpful to pick a few sample numbers to see what happens. Getting to the Answer: It does not matter whether you find the greatest integer less than or equal to the number and then subtract 4 or you subtract 4 from the number and then find the greatest lower integer. Either order produces the same number in step 5. 13. E Difficulty: Medium Strategic Advice: Remember the rules of multiplying exponents and raising numbers with exponents to powers. Plug 33 into each answer choice and see which one equals 38. Getting to the Answer: (E) 9(33)2 = 9(33 x 2) = 9(36 ) = 32(36 ) = 32 + 6 = 3s 14. A Difficulty: High To find the area, add the dimensions of the square and the triangle. First relabel the diagram as follows: 12 12 13 b-x Notice that the value of x can be solved with or without using the Pythagorean theorem. (The group 5-12-13 is a Pythagorean triple.) x2 = 132 - 122 = 169 - 144 = 25, so x = 5 x
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