grubers complete sat guide 2009 phần 9 ppsx

According to the given, S ϭ 3M Also given, R ϭ 18M Dividing by , we get ᎏ R S ᎏ ϭ ᎏ 6 1 ᎏ (Math Refresher 200 and 120) 10. 9 Volume of cube ϭ (side) 3 Thus, the volume of a cube whose edge has length of 1 ϭ 1 3 ϭ 1. The volume of a cube whose edge has the length of 2 ϭ 2 3 ϭ 8. Thus the sum of the volumes of the two cubes ϭ 8 ϩ 1 ϭ 9. (Math Refresher 313) 11. 105 (Use Strategy 11: Use new definitions care- fully. These problems are generally easy.) Given: ΂ ᎏ n 2 ᎏ ΃ ϭ ᎏ n(n 2 Ϫ 1) ᎏ Thus ΂ ᎏ 1 2 5 ᎏ ΃ ϭ ᎏ 15(15 2 Ϫ 1) ᎏ ϭ ᎏ 15( 2 14) ᎏ ϭ 105 (Math Refresher 431) 12. 0 Given: r 2 ϭ 9 s 2 ϭ 25 (Use Strategy 17: Use the given information effectively.) From and , we have r ϭ 3 or Ϫ3 s ϭ 5 or Ϫ5 The greatest possible value of s Ϫ r occurs when s is a maximum and r is a minimum or 5 Ϫ (Ϫ3) ϭ 8 The greatest possible value of r Ϫ s occurs when r is a maximum and s is a minimum or 3 Ϫ (Ϫ5) ϭ 8 The answer to this question is the difference between and : 8 Ϫ 8 ϭ 0 (Math Refresher 430 and Logical Reasoning) 65 6 5 4 3 21 2 1 56 6 5 13. 33 ᎏ 1 3 ᎏ , which translates to 33.3 in “grid” form. (Use Strategy 2: Translate from words to alge- bra.) According to the graph, 4 people had green eyes, 6 people had blue eyes, and 5 had brown eyes, so there were 15 people in the group. The percent- age, x, can be found by setting up the ratio ᎏ 10 x 0 ᎏ ϭ ᎏ 1 5 5 ᎏ ϭ ᎏ 1 3 ᎏ , or x ϭ 33 ᎏ 1 3 ᎏ . 33 ᎏ 1 3 ᎏ % had brown eyes. (Math Refresher 704) 14. 5 N5 LM 385 385 4235 (Use Strategy 17: Use the given information effectively.) From the given problem we see that N5 ϫ M ϭ 385 Use Strategy 7: Use numerical examples: Try N ϭ 1 15 ϫ M ϭ 385 M must be greater than 10, which is incorrect. Try N ϭ 2 25 ϫ M ϭ 385 M must be greater than 10, which is incorrect. Try N ϭ 3 35 ϫ M ϭ 385 M must be greater than 10, which is incorrect. Try N ϭ 4 45 ϫ M ϭ 385 M is not an integer. Try N ϭ 5 55 ϫ M ϭ 385. Thus, M ϭ 7 Therefore, L can be equal to 7 to give: 55 ϫ 77 385 ϩ 385 4235 (Logical Reasoning) ALTERNATE METHOD SAT PRACTICE TEST 3 – SECTION 6 ANSWERS • 833 706-1045.qxd 5/1/08 3:26 PM Page 833 834 • SAT PRACTICE TEST 3 – SECTION 6 ANSWERS The number “N5” can be written as 10N ϩ 5. For example, “25” ϭ 10 ϫ 2 ϩ 5. So we have (10N ϩ 5) ϫ M ϭ 385 in the multiplication example given. (Use Strategy 12: Factor to make problem simpler.) 10N ϩ 5 ϭ 5(2N ϩ 1) So from , 5(2N ϩ 1) ϫ M ϭ 385 Now divide by 5: (2N ϩ 1)M ϭ 77 Because the only two integers that can give us 77 when multiplied are 11 and 7, or 77 and 1, and because N and M are integers, each must be less than 10, 2N ϩ 1 ϭ 11, M ϭ 7. If 2N ϩ 1 ϭ 11, then N ϭ 5. 15. 24 (Use Strategy 11: Use new definitions care- fully.) By definition, the hand of dial Y moves one number for each complete revolution of the hand of dial Z. The hand of Dial Y must move 8 numbers to com- plete one of its own revolutions. Therefore, it must move 24 numbers to complete 3 of its revolutions. From above, 24 numbers on dial Y correspond to 24 complete revolutions on dial Z. (Logical Reasoning) 16. ᎏ 7 8 ᎏ or .875 (Use Strategy 17: Use the given information effectively.) Given: 6 rolls uses ᎏ 1 4 ᎏ pound of powder 6 rolls uses 2 ᎏ 1 2 ᎏ quarts of water Number is not necessary to solve the problem! We need to know how much powder is needed for the same mixture for 21 rolls. Let x ϭ number of pounds for 21 rolls. We set up a proportion: ϭ ᎏ 21 r x olls ᎏ (Use Strategy 10: Know how to use units.) (6 rolls ΋ )x ϭ (21 rolls ΋ ) ϫ ΂ ᎏ 1 4 ᎏ pound ΃ 6x ϭ 21 ϫ ᎏ 1 4 ᎏ pound 3 6 rolls ᎏ ᎏ 1 4 ᎏ pound 2 2 1 1 1 1 1 (Use Strategy 13: Find unknowns by multi- plication.) Multiply by ᎏ 1 6 ᎏ . We get ᎏ 1 6΋ ᎏ ΂ 6΋x ΃ ϭ ᎏ 1 6 ᎏ ΂ 21 ϫ ᎏ 1 4 ᎏ pound ΃ x ϭ ᎏ 1 6 ᎏ ϫ 21 ϫ ᎏ 1 4 ᎏ pound x ϭ ᎏ 2 2 1 4 ᎏ pound x ϭ ᎏ 7 8 ᎏ of a pound (Math Refresher 200, 120, and 406) 17. 84 Use Strategy 5: Average ϭ Let x ϭ Total number of students Then .40x ϭ Number of students scoring 100 .10x ϭ Number of students scoring 80 y ϭ Average score of remaining students We know the whole class is 100%. From and we know: 40% ϩ 10% ϭ 50% have been accounted for. (Use Strategy 3: The whole equals the sum of its parts.) Subtracting from , we get remaining stu- dents represent 50% of the class. Using and , we get Number of remaining students ϭ .5x We know Average ϭ Given: Average ϭ 90 Substituting , , , , , and into , we get 90 ϭ Multiply by x. We get 90x ϭ 40x ϩ 8x ϩ .5xy 90x ϭ 48x ϩ .5xy 42x ϭ .5xy 42 ϭ .5y 84 ϭ y (Math Refresher 601, 114, and 406) 18. 5 (Use Strategy 3: The whole equals the sum of its parts.) The sum of the angles in a tri- 11 11 .40x(100) ϩ .10x(80) ϩ .5x(y) ᎏᎏᎏᎏ x 91084321 10 9 Sum of the values ᎏᎏᎏ Total number of values 8 17 7 56 6 32 5 4 3 2 1 Sum of the values ᎏᎏᎏ Total number of values 3 706-1045.qxd 5/1/08 3:26 PM Page 834 Substituting the given and in gives 180 ϭ 10t ϩ 16x Substituting in , we have 180 ϭ 10(10) ϩ 16x 180 ϭ 100 ϩ 16x 80 ϭ 16x 5 ϭ x (Math Refresher 505, 406, and 501) 41 4 32 angle ϭ 180°. Therefore 3t ° ϩ 5t ° ϩ 10t °ϭ 180 18t ϭ 180 t ϭ 10 Since ABC is a line segment, straight angle ABC ϭ 180° (Use Strategy 3: The whole equals the sum of its parts.) ЄABC ϭ ЄABD ϩ ЄDBC 3 2 1 SAT PRACTICE TEST 3 – SECTION 6 ANSWERS • 835 706-1045.qxd 5/1/08 3:26 PM Page 835 836 1. Choice D is correct. The word “degradation” means deterioration, a lowering of position. The sight of a person in such a state would generally bring about a feeling of pity. Choices A, B, C, and E do not make good sense in the sentence. Therefore, these choices are incorrect. See Sentence Completion Strategy 1. 2. Choice B is correct. See Sentence Completion Strategy 4. The key word “although” in this sen- tence indicates that there is opposition or difference between the first part of the sentence and the last part. Since our team knew that the opponents (the Raiders) were “sluggish,” we were stupid—we should have pushed hard instead of being so “easy- going.” The other four choices are incorrect because their word pairs do not make sense in the sentence. 3. Choice C is correct. See Sentence Completion Strategy 2. STEP 1 We first examine the first word of each choice. We then eliminate Choice (A) heroic, Choice (B) respected, and Choice (E) insightful because a prime minister with any of these positive qualities would hardly be expected to cause a downfall of his country. So Choices A, B, and E are incorrect. STEP 2 We now consider the remaining choices. Choice (D) vacillating . . confidential does not make sense in the sentence because we cannot refer to a country as confidential. Therefore, Choice D is also incor- rect. Choice (C) incompetent . . powerful makes sense and is the correct choice. 4. Choice B is correct. See Sentence Completion Strategy 1. The word “aloof ” means withdrawn, distant, uninvolved. A character who is dignified and who is a man of reserve is likely to be aloof. 5. Choice C is correct. See Sentence Completion Strategy 2. STEP 1 Let us first examine the first words of each choice. We can then eliminate Choice (A) frequent, Choice (B) heavy, and Choice (E) bland because saying that blood contains frequent or heavy or bland amounts does not make sense. So Choices A, B, and E are incorrect. Section 7: Critical Reading Note: All Reading questions use Reading Comprehension Strategies 1, 2, and 3 (pp. 133–138) as well as other strategies indicated. As you read these Explanatory Answers, refer to “Using Critical Thinking Skills in Verbal Questions” (beginning on page 118) whenever a specific Strategy is referred to in the answer. Of particular importance are the following Master Verbal Strategies: Sentence Completion Master Strategy 1—page 118. Sentence Completion Master Strategy 2—page 119. Reading Comprehension Master Strategy 2—page 136. Explanatory Answers for Practice Test 3 (continued) 706-1045.qxd 5/1/08 3:26 PM Page 836 SAT PRACTICE TEST 3 – SECTION 7 ANSWERS • 837 STEP 2 We now consider the remaining choices. Choice (D) definite . . puzzling does not make sense because blood does not contain puzzling amounts. Therefore, Choice D is also incorrect. Choice (C) minute (pronounced “mine-yute”—meaning excep- tionally small) . . excessive makes sense and is the correct choice. 6. Choice D is correct. See lines 7–9 where it states that many people in our generation were not exposed to classical music. Don’t be lured into the distractor choice A even though there was mention of sales. 7. Choice A is correct. See lines 19–21 where it men- tions that the emotional feeling gradually wears out in time. 8. Choice B is correct. Since the next sentence after the word “evergreen” qualifies that enjoyment lasts only for a short time, “lasting” would be an appro- priate definition of “evergreen” in this context. Be careful of the distractor choice “colorful.” 9. Choice C is correct. Note that only in Passage 1 lines 3–5 is an example of a symphony of Brahms illustrating the point. No specific examples are pre- sented in Passage 2. In Choice A, the time period is addressed in both passages. In Choice B the types of music are presented in both passages (classical in Passage 1 and rock and contemporary in Passage 2). In Choice D, no instrument is addressed in either passage and in Choice E, specific musicians are not mentioned in either passage. 10. Choice B is correct. See lines 25–29: “That was why till he reached bitter despair the man of property could die.” The “well-upholstered hell” constituted the lifestyle that almost caused him to commit suicide. The passage shows no justification for Choices A, C, D, and E. Accordingly, these are incorrect choices. 11. Choice D is correct. Throughout paragraph 3 we see the evidences of the speaker’s happiness as a result of his renouncing the “power, women and money” (lines 22–23) as well as the arrogance and intellec- tuality referred to in line 17. Choices A, B, and C are incorrect because, though the passage discusses these choices, they do not really pinpoint the relation between the third and fourth paragraphs. Choice E is incorrect because paragraph 3 does not generalize about the specific points made in paragraph 2. 12. Choice B is correct. His “complete hopelessness and despair” (lines 3–4) led to Siddhartha’s decision to commit suicide. The passage does not answer the questions expressed in Choices A, C, D, and E. Therefore, these choices are incorrect. 13. Choice C is correct. From the context of the sentence and the one preceding it, we can see that the word “transitory” means short-lived. See also Read- ing Comprehension Strategy 5. 14. Choice E is correct. The unhappiness that may result from wealth and power are brought out clearly throughout the second paragraph. In con- trast, peace and quiet are likely to assure a happy life. The last paragraph demonstrates this conclu- sively. Although Choices A, B, C, and D are vital points, none of the choices is sufficiently inclusive to be considered the main idea of the passage. References to these choices follow. Choice A—lines 13–21: “He had been full of arrogance brought him salvation.” Choice B—lines 5–8: “Was it not his Self filled him with fear?” Choice C—lines 10–11: “Too much knowledge had hindered him.” Choice D—lines 19–21: “Now he understood brought him salvation.” 15. Choice E is correct. The word “Self” as it is used in this passage means one’s own interests, welfare, or advantage; self-love. By an extension of these defi- nitions, “Self” may be considered selfishness. See lines 5–8: “Was it not his Self filled him with fear?” Accordingly, Choices A, B, C, and D are incorrect. 16. Choice E is correct. See lines 21–22: “All human beings have at least four types of intelligence.” Choice A is incorrect. See lines 50–52: “Per- sistence kept Einstein looking for the solution to the question of the relationship between the law of gravity and his special theory of relativity.” Isaac Newton (1642–1727) formulated the law of gravita- tion. Choice B is incorrect. The passage simply states: “The idea for a self-starting electric motor came to Nikola Tesla one evening as he was recit- ing a poem by Goethe and watching a sunset” (lines 30–32). Choice C is incorrect. The author indicates a span of time when he states: “The dis- coveries made by scientific geniuses, from Archimedes through Einstein . . .” (lines 1–2). Archimedes was an ancient Greek mathematician, physicist, and inventor (287–212 B.C.), whereas Einstein was, of course, a modern scientist (1879–1955). Choice D is incorrect. The passage states: “. . . while an IQ above a certain point— about 120—is very helpful for a scientist, [it] is not crucial for producing a work of genius” (lines 18–21). The passage does not specifically say that most scientists have IQ scores above 120. 706-1045.qxd 5/1/08 3:26 PM Page 837 838 • SAT PRACTICE TEST 3 – SECTION 7 ANSWERS 17. Choice D is correct. See lines 42–44: “The scientist solves a problem by shifting from one intelligence to another, although the logical-mathematical intel- ligence is dominant.” Accordingly, Choices A, B, C, and E are incorrect. 18. Choice B is correct. When the author describes the work experiences of Einstein and Tesla, he refers to their use of one or more of the four types of intelligence. Moreover, lines 26–28 state: “Some corroboration of these [four intelligence] cate- gories comes from the reports of scientists who describe thought processes centered around images, sensations, or words.” Choices A, C, D, and E are incorrect because the author does not refer to these choices in the passage. 19. Choice C is correct. The author indicates that great scientists use to advantage four intelligences— logical-mathematical, spatial, linguistic, and bodily- kinesthetic. See lines 22–25: “The great scientist possesses the ability to move back and forth among them—the logical-mathematical, the spatial which includes visual perception, the linguistic, and the bodily-kinesthetic.” Choices B and D are brought out in the passage but not at any length. Therefore, Choices B and D are incorrect. Choice A is incorrect because the author nowhere compares the thinking of the average individual and that of the great scien- tist. Choice E is incorrect because though the con- cepts are mentioned, they are certainly not clarified in the passage. 20. Choice E is correct. As a football star, he would certainly have to have a high level of (a) spatial intelligence [II], which involves space sensitivity as well as visual perception, and (b) bodily-kinesthetic intelligence [IV], which involves the movement of muscles, tendons, and joints. As a literature major, he would certainly have to have a high level of linguistic intelligence [III], which involves the abil- ity to read, write, speak, and listen. Whether he would have logical-mathematical intelligence to a high degree is questionable. It follows that Choices A, B, C, and D are incorrect. 21. Choice E is correct. According to what is stated in lines 50–56, persistence is an important character- istic of the scientist. Thus the author would proba- bly not agree with the statement in Choice E. The author would agree with the statement in Choice A: See lines 4–5. Note that although the author may not agree that IQ is what makes the scientist bril- liant, he believes that most people feel that way. The author would agree with the statement in Choice B. See lines 30–32 and lines 56–60. The author would agree with the statement in Choice C. See lines 15–16 in the context with the rest of the passage. The author would probably not disagree with the statement in Choice D since the author does not appear to distinguish artists from scientists in their thinking process even though the passage is pri- marily about the scientists: See lines 9–14. 22. Choice C is correct. See lines 52–54. Note that although “persistence” is mentioned in lines 47–52, the passage states that fluid thinking may be con- nected to persistence, not defined as persistence. Thus Choice A is incorrect. See also Reading Comprehension Strategy 5. 23. Choice B is correct. Given the context in lines 47–54, the word “paradoxically” means seemingly contradictory. See also Reading Comprehension Strategy 5. 24. Choice A is correct. It can be seen in the passage that the author is intrigued by and interested in the way the scientist thinks but at the same time reports the findings very objectively. 706-1045.qxd 5/1/08 3:26 PM Page 838 1. Choice B is correct. (Use Strategy 2: Know the definition of percent.) Percent of Caramels ϭ ϫ 100 Given: Weight of Caramels ϭ 0.6 pound Weight of Coconuts ϭ 3.6 pounds Adding and , we get Total Weight ϭ 0.6 pounds ϩ 3.6 pounds Total Weight ϭ 4.2 pounds Substituting and into , we have Percent of Caramels ϭ ᎏ 0 4 . . 6 2 p p o o u u n n d d s ΋ s ΋ ᎏ ϫ 100 ϭ ᎏ 4 .6 .2 ᎏ ϫ 100 ϭ ᎏ 4 6 2 ᎏ ϫ 100 ϭ ᎏ 6 4 0 2 0 ᎏ ϭ ᎏ 3 2 0 1 0 ᎏ ϭ Percent of Caramels ϭ 14 ᎏ 2 7 ᎏ (Math Refresher 106 and 107) 2. Choice B is correct. Notice that $25,000 is one- fourth of $100,000 (the total funds). (Use Strategy 17: Use the given information effectively.) That is, ᎏ 1 2 0 5 0 ,0 ,0 0 0 0 0 ᎏ ϭ ᎏ 1 4 ᎏ . So look for the piece or part of the circle that is closest to ᎏ 1 4 ᎏ of the whole circle. ᎏ 1 4 ᎏ of the whole circle (360°) is 90°. Lincoln H.S. represents about ᎏ 1 4 ᎏ of the whole circle or 90°. (Math Refresher 705) 3. Choice A is correct. Given: y ϭ r Ϫ 6 z ϭ r ϩ 5 (Use Strategy 13: Find unknown expressions by addition of equations.) Adding and , we get y ϩ z ϭ 2r Ϫ 1 y ϩ z ϩ 1 ϭ 2r ᎏ y ϩ 2 z ϩ 1 ᎏ ϭ r (Math Refresher 407) 21 2 1 142 4 32 3 2 1 Weight of Caramels ᎏᎏᎏ Total Weight Explanatory Answers for Practice Test 3 (continued) As you read these solutions, do two things if you answered the Math question incor- rectly: 1. When a specific Strategy is referred to in the solution, study that strategy, which you will find in “Using Critical Thinking Skills in Math Questions” (beginning on page 69). 2. When the solution directs you to the “Math Refresher” (beginning on page 191)—for example, Math Refresher #305—study the 305 Math principle to get a clear idea of the Math operation that was necessary for you to know in order to answer the ques- tion correctly. Section 8: Math 706-1045.qxd 5/1/08 3:26 PM Page 839 840 • SAT PRACTICE TEST 3 – SECTION 8 ANSWERS Rate AC ϫ 8 ϭ 2D Rate AC ϭ ᎏ 2 8 D ᎏ Rate AC ϭ ᎏ D 4 ᎏ We are asked to find the ratio Substituting and into , we have ϭ ϭ ` ᎏ D 3 ᎏ Ϭ ᎏ D 4 ᎏ ϭ ᎏ D ΋ 3 ᎏ ϫ ᎏ D ΋ 4 ᎏ ϭ ᎏ 4 3 ᎏ ϭ 4 : 3 (Math Refresher 201, 202, and 120) 6. Choice C is correct. (Use Strategy 7: Use num- ber examples.) If a ϭ ᎏ 2 3 ᎏ , b ϭ ᎏ 4 3 ᎏ , and x ϭ ᎏ 3 2 ᎏ Then, substituting from , we get ax ϭ ᎏ 2΋ 3΋ ᎏ ΂ ᎏ 3΋ 2΋ ᎏ ΃ bx ϭ ᎏ 4 3΋ ᎏ ΂ ᎏ 3΋ 2 ᎏ ΃ ϭ ᎏ 4 2 ᎏ ax ϭ 1 bx ϭ 2 Neither a nor b nor x are integers, but both ax and bx are integers. Thus, Choices B, D, and E are eliminated. (Use Strategy 13: Find unknown expressions by addition of equations.) Adding ax to bx, we get ax ϩ bx ϭ (a ϩ b)x Since ax and bx are integers, is an integer. Thus, Choice C is correct. (Math Refresher 431) 2 2 1 1 ᎏ D 3 ᎏ ᎏ ᎏ D 4 ᎏ Average Speed from A to B ᎏᎏᎏᎏ Average Speed from A to C 11106 11 Average Speed from A to B ᎏᎏᎏᎏ Average Speed from A to C 10 4. Choice E is correct. (Use Strategy 2: Translate from words to algebra.) Given: The 3 polygons have equal perimeters, gives us 6a ϭ 3b 8c ϭ 6a Dividing by 6, we get a ϭ ᎏ 3 6 ᎏ b ϭ ᎏ 1 2 ᎏ b Thus, a Ͻ b Dividing by 8, we get c ϭ ᎏ 6 8 ᎏ a ϭ ᎏ 3 4 ᎏ a Thus, c Ͻ a (Use Strategy 6: Know how to use inequali- ties.) Using the Transitive Property of Inequality with and , we have c Ͻ a Ͻ b. (Math Refresher 304, 306, and 406) 5. Choice B is correct. (Use Strategy 9: Know the formula for rate, time, and distance.) Rate ϫ Time ϭ Distance Given: Time from A to B ϭ 3 hours Time from B to C ϭ 5 hours Distance from A to B ϭ Distance from B to C Using , let Distance from A to B ϭ Distance from B to C ϭ D Substituting and into , we get Rate AB ϫ 3 ϭ D Rate AB ϭ ᎏ D 3 ᎏ Substituting and into , we get Rate BC ϫ 5 ϭ D Rate BC ϭ ᎏ D 5 ᎏ From we get whole distance from A to C ϭ 2D From and we get time for whole trip ϭ 3 ϩ 5 ϭ 8 Substituting and into , we get 198 9 32 8 5 7 153 6 152 5 4 4 3 2 1 43 4 2 3 1 2 1 706-1045.qxd 5/1/08 3:26 PM Page 840 7. Choice C is correct. For line q, y ϭmx ϩ b 1 . Since the line q crosses the origin where x ϭ 0 and y ϭ0, b 1 must ϭ 0. Thus for line q, y ϭmx. Now since (4,3) is on line q, this means when x ϭ 4, y ϭ3, so if y ϭ mx, 3ϭ m(4) and mϭ 3/4. Now let’s look at line p. For this line, yϭ Mxϩ b. Since the lines p and q are perpendicular, the slope of one is nega- tive reciprocal of the other. Thus m ϭϪ1/M. Since m ϭ 3/4, 3/4 ϭϪ1/M and so M ϭϪ4/3. Thus for line p, y ϭϪ(4/3)xϩ b. The point (4,3) is also on line p so substituting x ϭ 4 and y ϭ 3 in the equation y ϭϪ(4/3)xϩ b, we get: 3ϭϪ(4/3)(4) ϩ b. We get 3 ϭϪ16/3 ϩ b, and thus 3ϩ 16/3 ϭ b and b ϭ 25/3. Thus for line p, y ϭϪ(4/3)x ϩ25/3. If (3,a) is on line p, then substituting x ϭ 3 and y ϭ a, we get a ϭϪ(4/3)3ϩ 25/3ϭϪ4 ϩ 25/3ϭ 13/3 ϭ 4 ᎏ 1 3 ᎏ . (Math Refresher 414) 8. Choice C is correct. The function f(x) is not defined when the denominator is 0. So if 2x ϩ4 ϭ 0, 2x ϭϪ4 and x ϭϪ2. Thus only III is the case where the function is not defined. (Math Refresher 616) 9. Choice E is correct. (Use Strategy 17: Use the given information effectively.) Clearly, we can see from the picture above that the diameter of the sphere has the same length as a side of the cube. We know Volume of cube ϭ (length of side) 3 We are given Volume of cube ϭ 64 Substituting into , 64 ϭ (length of side) 3 Thus, length of side ϭ 4 ϭ diameter of sphere (Math Refresher 313 and 315) 1 2 2 1 10. Choice A is correct. Given: ᎏ m n ᎏ ϭ ᎏ m x ᎏ (Use Strategy 13: Find unknowns by multipli- cation.) Multiplying by m, we have m ΂ ᎏ m n ᎏ ΃ ϭ ΂ ᎏ m ΋ x ᎏ ΃ m ΋ ᎏ m n 2 ᎏ ϭ x (Math Refresher 406) 11. Choice B is correct. (Use Strategy 17: Use the given information effectively.) We are given CD ϭ ᎏ 3 4 ᎏ AC CF ϭ ᎏ 2 7 ᎏ BC We want to find We know that the Area of rectangle CDEF ϭ (CD)(CF) and Area of ΔABC ϭ ᎏ 1 2 ᎏ (AC)(BC) Substituting and into , Area of rectangle CDEF ϭ ΂ ᎏ 3 4 ᎏ AC ΃΂ ᎏ 2 7 ᎏ BC ΃ ϭ ᎏ 1 3 4 ᎏ (AC)(BC) Substituting and into the unknown expres- sion, ϭ ϭ ᎏ 1 2 ᎏ ϫ ᎏ 1 3 4 ᎏ ϭ ᎏ 1 6 4 ᎏ ϭ ᎏ 7 3 ᎏ (Answer) (Math Refresher 304, 306, 431, and 120) ᎏ 1 2 ᎏ (AC ΋ )(BC ΋ ) ᎏᎏ ᎏ 1 3 4 ᎏ (AC ΋ )(BC ΋ ) Area of ΔABC ᎏᎏᎏ Area of rectangle CDEF 54 5 321 4 3 Area of ΔABC ᎏᎏᎏ Area of Rectangle CDEF 2 1 1 1 SAT PRACTICE TEST 3 – SECTION 8 ANSWERS • 841 706-1045.qxd 5/1/08 3:26 PM Page 841 842 • SAT PRACTICE TEST 3 – SECTION 8 ANSWERS 12. Choice C is correct. (Use Strategy 2: Translate from words to algebra.) Let b ϭ number of boys g ϭ number of girls We are given b ϭ g ϩ 7 b ϭ ᎏ 5 4 ᎏ g (Use Strategy 13: Find unknowns by multi- plication.) Multiplying by ᎏ 4 5 ᎏ , ᎏ 4 5 ᎏ b ϭ g Substituting into , b ϭ ᎏ 4 5 ᎏ b ϩ 7 Multiplying by 5, 5b ϭ 4b ϩ 35 or b ϭ 35 (Math Refresher 200 and 406) 13. Choice A is correct. (Use Strategy 2: Translate words to algebra to find percent increase.) Percent increase ϭ Amount of increase is given as 100 per year Substituting into , we get % increase ϭ ᎏ Origin 1 al 00 amount ᎏ (Use Strategy 12: Try not to make tedious calculations.) The greatest % increase will occur when the original amount is least. Since the population is increasing by 100 every year, it is least at the beginning, in 1999. Thus will be greatest from 1999–2000. (Math Refresher 114 and 118) 3 3 12 2 1 Amount of increase ᎏᎏᎏ Original amount 4 4 13 3 2 2 1 14. Choice D is correct. (Use Strategy 14: Draw lines where appropri- ate.) Given: AB ϭ BD ϭ AD ϭ 6 C can be any point on arc BE, not just where it appears in the drawing above. For any point C on arc BE CD ϭ 6 because CD ϭ radius of the arc. (Use Strategy 3: The whole equals the sum of its parts.) We want to find P ϭ perimeter of ABCD ϭ AB ϩ BC ϩ CD ϩ AD Substituting and into , P ϭ 18 ϩ BC We cannot find BC, but we can find the highest and lowest possible values for BC. Clearly, since BC is a side of an quadrilateral, BC Ͼ 0 By looking at the diagram, we see that the high- est possible value of BC occurs when C coincides with E. BC р BE must be true. BE can easily be found. ΔEDB is similar to one of the standard triangles discussed before. (Use Strategy 18: Remember special right triangles.) 6 5 4 312 3 2 1 706-1045.qxd 5/1/08 3:26 PM Page 842 [...]... BOXES ABOVE THE CIRCLES 10 9 / / / / / 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 9 9 9 0 0 1 1 1 1 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 / / 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 0 1 1 1 2 2 2 2 3 3... Student-Produced Responses 10 9 / / / / / 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 9 9 9 0 0 0 0 1 1 1 1 2 2 2 2 1 1 1 1 2 2 2 3 3 3 3 2 3 3 3 3 3 4 4 4 4 5 5 5 5 4 4 4 4 4 4 5 5 5 5 5 6 6 6 6 5 6 6 6 6 6 6 7 7 7 7 6 7 7 7 7 7 7 7 7 8 8 8 8 9 9 9 9 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 / / 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 2 2 2 2 3... Student-Produced Responses 10 9 / / / / / 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 9 9 9 0 0 1 1 1 1 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 / / 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 0 1 1 1 2 2 2 2 3 3... 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 9 9 9 18 17 16 / / 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 1 2 2 2 2 3 3 3 4 4 5 5 6 0 0 0 0 0 / 0 ... 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 9 9 9 / / 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 1 2 2 2 2 3 3 3 4 4 5 5 6 0 0 0 0 0 / 0 0 0... 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 9 9 9 / / 0 0 0 1 1 1 1 2 2 2 2 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 5 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 0 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 7 7 7 8 8 8 8 9 9 9 9 1 1 1 1 2 2 2 2 3 3 3 4 4 5 5 6 0 0 0 0 0 / 0 0 0... 3 3 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 1 2 1 0 1 / / 0 0 1 0 / / 1 1 0 0 0 1 1 5 2 6 6 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 2 3 3 3 4 4 4 2 2 2 3 3 3 3 4 4 Note: You may start your answers in any column, space permitting Columns not needed should be left blank 6 7 9 6 2 ● Mark no more than one oval in any column ● Because the answer sheet will be machinescored, you will receive credit... Page 843 SAT PRACTICE TEST 3 – SECTION 8 ANSWERS • 843 (Use Strategy 13: Find unknown by division of equations.) Divide 1 by 2 We get ϬϬ x9 ϭ 4 9 x7 y2 y2 x2 ϭ 4 ϫ ᎏᎏ 9 4 x2 ϭ ᎏᎏ y2 9 Corresponding sides of similar triangles are proportional, so that ͙2 ෆ BE ᎏᎏ ϭ ᎏᎏ 1 6 or ෆ BE ϭ 6͙2 7 ෆ BC р 6͙2 8 Comparing 4 and 8 , ෆ P ϭ 18 ϩ BC р 18 ϩ 6͙2 9 Comparing 4 and 5 , P ϭ 18 ϩ BC Ͼ 18 10 From 9 and 10... 37 A B C D E B C D E 18 A B C D E 28 A B C D E 38 A B C D E B C D E 19 A B C D E 29 A B C D E 39 A B C D E B C D E 20 A B C D E 30 A B C D E 40 A B C D E B C D E 11 A B C D E 21 A B C D E 31 A B C D E B C D E 12 A B C D E 22 A B C D E 32 A B C D E 3 A 4 A 10 A 12 1 A 2 A SECTION 11 E 9 A 10 A 9 E D 3 A 4 A SECTION D C 1 A 2 A 8 C B 9 A 10 A SECTION B B C D E 13 A B C D E 23 A B C D E 33 A B C D E B... E 26 A B C D E 36 A B C D E 7 A 8 A B C D E 17 A B C D E 27 A B C D E 37 A B C D E B C D E 18 A B C D E 28 A B C D E 38 A B C D E 9 A 10 A B C D E 19 A B C D E 29 A B C D E 39 A B C D E B C D E 20 A B C D E 30 A B C D E 40 A B C D E 706-1045.qxd 5/1/08 3:26 PM Page 857 SAT PRACTICE TEST 4 706-1045.qxd 5/1/08 3:26 PM Page 858 SECTION 1 Time: 25 Minutes — Turn to page 851 of your answer sheet to write . population is increasing by 100 every year, it is least at the beginning, in 199 9. Thus will be greatest from 199 9–2000. (Math Refresher 114 and 118) 3 3 12 2 1 Amount of increase ᎏᎏᎏ Original. together, 18 Ͻ P р 18 ϩ 6͙2 ෆ (Math Refresher 431, 507, 5 09, and 510) 15. Choice B is correct. Given: x 9 ϭ 4 x 7 ϭ ᎏ y 9 2 ᎏ x Ͼ 0 and y Ͼ 0 2 1 1 09 10 54 9 84 8 67 7 (Use Strategy 13: Find unknown by. students ϭ .5x We know Average ϭ Given: Average ϭ 90 Substituting , , , , , and into , we get 90 ϭ Multiply by x. We get 90 x ϭ 40x ϩ 8x ϩ .5xy 90 x ϭ 48x ϩ .5xy 42x ϭ .5xy 42 ϭ .5y 84 ϭ y (Math