1,296 ACT Practice Questions, 3rd Edition (2013)
ACT Practice Test 1
Test 1. Answers and Explanations
TEST 1 ENGLISH ANSWERS
TEST 1 MATH ANSWERS
TEST 1 READING ANSWERS
TEST 1 SCIENCE ANSWERS
SCORING YOUR PRACTICE EXAM
Count the number of correct answers for each section and record the number in the space provided for your raw score on the Score Conversion Worksheet below.
Using the Score Conversion Chart on the next page, convert your raw scores on each section to scaled scores. Then compute your composite ACT score by averaging the four subject scores. Add them up and divide by four. Don’t worry about the essay score; it is not included in your composite score.
TEST 1 ENGLISH EXPLANATIONS
1. D The phrase left by the delivery man is an unnecessary detail added to the sentence and should be off-set by two commas, making choice (D) the best answer. The semicolon in choices (A) and (C) creates a fragment in the second half of the sentence.
2. F The sentence uses scrawled as an adjective to describe the words, not as a verb, so you can eliminate (G). Choice (H) uses the wrong form of scrawl, and choice (J) is the wrong idiomatic expression.
3. B The phrase my heart skipping a beat (or two) is incomplete and cannot be linked to the complete phrase with and, eliminating choices (A) and (C). When changes the meaning of the sentence, making (B) the best answer.
4. H The two halves of this sentence are both complete, eliminating choice (J). Since the second half already uses the pronoun it to refer to the box, that and which are unnecessary, making choice (C) the best answer.
5. C Since the question asks you to make a contrast, you can eliminate choices (B) and (D). Choice (C) better describes the people for whom the record holds value than choice (A).
6. J The verb should be in past perfect tense to show that he made his living as a musician before marrying, making choice (J) the only possible answer. Choices (F), (G), and (H) all use would, which is the conditional tense of will.
7. D The phrase performing in music hall and local festivals is incomplete and must be linked to the previous thought, eliminating choices (A) and (B). By using which to link the ideas, choice (C) makes it sound as if the grandfather performs the band, rather than the band performing.
8. J The best answer is (J) because it is the most concise of the choices. It is unnecessary to the meaning of the sentence to mention who produced the album.
9. A The phrase after the dash is adding further details to how rare the record truly is, making choice (A) the best answer. Choice (B) is a contrasting transition, and choices (C) and (D) use transition words that confuse the meaning of the sentence.
10. F The verb should be in past perfect tense because it is describing how long one copy had existed before the writer received the record in the mail, eliminating choices (H) and (J). Choice (G) uses the incorrect expression.
11. B The words beg and plead are synonyms, so it is redundant to use both. Choice (B) is the most concise answer.
12. G Since the question asks you to discuss the significance to the writer’s upbringing, you can eliminate choices (F) and (H). Choice (G) is more personal to the writer than choice (J), making it the best answer.
13. C Choice (C) is the only answer that clearly expresses the writer’s intended meaning. Choices (A), (B), and (C) all misplace phrases throughout the sentence, confusing who and what are being described.
14. H The punctuation should separate two complete ideas, eliminating choices (F) and (J). Choice (G) is an unnecessary transition word, because however is already used in the following sentence.
15. B The phrase that he was still with me is an incomplete thought and should be linked to the previous complete thought, eliminating choice (D). Since the sentence explains what the author feels reassured of, punctuation between me and that creates an unnecessary pause, making choice (B) the best answer.
16. F This question requires that you determine whether an apostrophe or additional punctuation mark is required. No apostrophe is needed because the word lives is not possessing anything, so eliminate choices (H) and (J). No pause is required between the words lives and completely, so eliminate choice (G), which interrupts the sentence unnecessarily. The sentence is correct as written, so the best choice is (F).
17. D The question asks for a line that indicates some similarity between the narrator and his friends. Choice (A) discusses only the narrator; choices (B) and (C) contain information that is much too general to discuss only the narrator and his friends. Only choice (D) has all the appropriate elements, particularly as presented in the words palpable likeness.
18. J This question requires that you determine whether an apostrophe or additional punctuation mark is required. No apostrophe is needed because there is no indication that owners are possessing anything (hint: don’t get thrown off by the phrase restaurant’s owners in which the word appears), so you can eliminate choice (H). Only choice (J) has the appropriate comma placement to situate chat with the restaurant’s owners within a list (the other items in this list are sit, drink a cup of coffee, and figure out which new and exciting place we’d be driving to next). A semicolon is inappropriate here because the semicolon is a punctuation mark used to separate two complete ideas, and the context indicates that it is not used to separate the items in this list.
19. B The sentence as written contains the phrase looking forward to it in anticipation, which is redundant, so you can eliminate choice (A). Choices (C) and (D) contain the same error. Only choice (B) preserves the meaning in a concise, non-redundant way. In addition, the word it in choices (A) and (C) is ambiguous.
20. H This question asks whether the writer’s proposed addition would be appropriately placed at the end of this paragraph. If you’re not sure whether to answer Yes or No, look at the reasons. Choice (F) must be eliminated because the proposed addition is too general and is consequently not relevant to other, more personal information in the passage. Choice (G) must be eliminated because it is too general and gives no indication why the narrator should choose a specific diner. Choice (J) suggests that the primary focus of the paragraph up to this point has been driving, which it has not; rather, the primary focus of the paragraph is the stop at the diner and the things the narrator and his friends did there. Accordingly, only choice (H) appropriately recognizes the personal tone of the paragraph and correctly advises not to include the proposed addition.
21. A The first place you should look in this question is to whether that or whom is an appropriate first word. Whom is the objective form of who, which is used to refer only to people. The word here refers back to something, not a person, so eliminate choices (B) and (C). Choice (D) changes the meaning of the sentence to suggest that something is doing the ordering, rather than being ordered. The sentence is correct as written, so NO CHANGE is required.
22. J This question asks you to determine which word would be most appropriately modified by the phrase from childhood. To place the phrase after any of the words in choices (F), (G), or (H) is to break the flow of the sentence and to make the meaning of the sentence unclear. Only choice (J) establishes the proper link between the underlined and non-underlined portions of the sentence in the phrase remembered from childhood.
23. B In an earlier part of the sentence, the narrator refers to the food in the city as too expensive. Only choice (B) supports and modifies this idea. Read the question closely: While the other choices may be true, the best answer will be one that supports and modifies a specific part of the passage.
24. J In EXCEPT/LEAST/NOT questions, the underlined portion of the sentence is correct. Compare your answer choices. What do words like as and when do to the first part of the sentence? They make it an introductory idea and an incomplete thought. When the first part of the sentence is incomplete, the comma after the word could sets this first part off from the complete idea after it. By contrast, if the first part of the sentence is made complete as it is in choice (J), this creates a comma splice, wherein two complete ideas are insufficiently separated by a comma.
25. B Identify the subject of the verb. Although the word restaurants is closest to the verb, it is not the subject; rather, the subject is the word place, a singular subject that requires a singular verb. Since choices (A), (C), and (D) all contain plural verbs, eliminate them. Only choice (B) remains, and the verb was does agree in number with the word place.
26. F We need an idea that will signal the transition between the paragraph above, which is a recollection of the trips, and the paragraph below, which fast forwards to the present and discusses the narrator’s life now. Only choice (F) contains this transition. Choice (G) deals only with the narrator’s friends who are not mentioned in the last paragraph. Choice (H) deals only with the past, and choice (J) deals only with the narrator’s life after graduation. Only choice (F) has both the past and present components it needs to transition from one paragraph to the next.
27. D This question asks you to determine whether you need a transition between the first and second sentences of this last paragraph. Choices (A) and (C) suggest a disagreement between the two ideas where none exists. Choice (B) suggests a cause-and-effect relationship between the two sentences where none exists. Only choice (D) makes sense in the context, where no transition is needed.
28. F In EXCEPT/LEAST/NOT questions, the underlined portion of the sentence is correct. To answer this question, you need to determine which prepositions work idiomatically with the verb drive. Choice (G) contains the same preposition, about, used in the underlined portion, and although not a particularly common usage, drive about is idiomatically correct. The same goes for the more familiar drive around, as it is used in choices (H) and (J). Accordingly, only choice (F) does not work in the context of the sentence because it is incorrect usage to say drive among the town.
29. D All the answer choices mean roughly the same thing; each just presents a different way to say it. In situations such as this one, the most concise answer that preserves the meaning is the best. Accordingly, choices (A), (B), and (C) are all too wordy in comparison with choice (D).
30. F This question too asks you to determine which choice presents the most concise alternative that preserves the meaning of the sentence. Eliminate choices (G) and (J) because each presents an awkward, wordy alternative to the original. Choice (H) is as concise as choice (F), but note the context: Your answer will need to be parallel to other verbs in the sentence. In this case, only came back is parallel with the tense and tone of drove by, making the best choice (F).
31. D In EXCEPT/LEAST/NOT questions, the underlined portion of the sentence is correct. The original sentence uses even though to introduce two contrasting ideas. Choices (A), (B), and (C) are all contrasting transition words and are acceptable. Choice (D) indicates that the ideas are similar and, therefore, is not an acceptable alternative.
32. G The best connecting statement should continue the previous idea that Siena has both ancient and modern elements, eliminating choices (F) and (J). The following sentence begins with Another remnant, which means the inserted sentence should already list specific examples and makes choice (G) better than (H).
33. D It is redundant to describe the horse race as biannual and as held twice a year, eliminating choices (A) and (B). Choice (D) is better than choice (C) because it is more concise.
34. H The phrase dreaded right-angle turns describes an obstacle racers must face as they complete each lap, therefore it must immediately follow laps to clarify meaning. Choices (F), (G), and (J) do not provide logical sentences because the phrase does not describe horses, track, or plaza.
35. C Choice (C) correctly agrees with the present tense of the other verb in the sentence. Choices (A), (B), and (D) do not agree in tense and alter the meaning of the sentence.
36. J Because introduces an incomplete thought, so choice (F) creates a sentence fragment. Choice (G) suggests contrasting rather than similar ideas. Choice (H) is incorrect because the preceding sentence has already mentioned financial commitments, so voluntary taxation cannot be considered an additional act by members.
37. A The previous sentence illustrates the enormous cost to hire a jockey, which contrasts with the idea that it is a small price to pay, so the best transition word is choice (A). Choices (B), (C), and (D) all indicate a similar relationship, which is not consistent with the passage.
38. G The phrase even more so than getting married is an unnecessary description within the sentence and should be offset by either two commas or dashes, eliminating choice (F). Since the non-
underlined portion uses a dash before even, the best answer is choice (G) not choice (H). Choice (J) creates a sentence fragment, since a semicolon can separate only complete ideas.
39. C The word throughout begins an incomplete idea, and the phrase cannot stand on its own as a sentence, eliminating choice (A). Choice (C) connects the incomplete phrase to the complete idea before it with the smoothest transition. The comma in choice (D) creates an unnecessary pause. Since a semicolon is generally used to separate two complete sentences, choice (B) is also incorrect.
40. F The word Contrade ends a complete thought, and Contrada begins a second complete thought, so you need a period making choice (F) the best answer. Choices (G), (H), and (J) all create run-on sentences because they do not separate complete ideas.
41. B The phrase from baptisms to food festivals is an unnecessary description within the sentence and should be offset by either two commas or dashes, eliminating choice (A). Since the non-underlined portion uses a comma after festivals, the best answer is choice (B) not choice (D). Choice (C) incorrectly uses a colon, which can be used only after a complete idea.
42. F The correct pronoun is who because members is the subject for the verb become. Choices (G) and (H) use possessive rather than subject case, and choice (J) is object case and does not indicate which noun become describes.
43. D The second half of the sentence is an incomplete idea and must be linked to the complete thought, eliminating choices (A), (B), and (C).
44. G The passage is written in the present tense, eliminating choices (F) and (H). Since the parties are thrown by the locals, you need the passive form for the verb (also called the past participle) not the past tense verb threw.
45. D The best location for Paragraph 3 is before Paragraph 5, choice (D), because Paragraph 4 introduces and defines the contrada discussed in the first sentence of Paragraph 3. There is also a logical sequence from winning the Palio at the end of Paragraph 3 to the celebration in the beginning of Paragraph 5.
46. H As written, the pronoun it in the underlined portion has no clear referent. Choices (G) and (J) do not fix the problem. Only choice (H) replaces the ambiguous pronoun with a clear referent.
47. C The sentence as written is a fragment. Choice (B) is also a fragment. Choices (C) and (D) both fix the sentence fragment, but choice (D) changes the meaning of the sentence.
48. J The sentence as written is incorrect because the adjective tireless cannot modify the verb continued. Choices (G) and (H) do not make sense in the given context. Only choice (J) links the word tireless with its appropriate noun, literary experimentation.
49. B In EXCEPT/LEAST/NOT questions, the underlined portion of the sentence is correct. Since the verbs to seem and to appear are synonyms, look for differences among the answer choices. Note that the original sentence and choices (A), (C), and (D) all contain the present tense, appropriately matched to the word contemporary used earlier in this sentence. Only choice (B) changes the tense to past, making choice (B) the LEAST acceptable substitution.
50. H The sentence as written is idiomatically incorrect. The prepositions until and at, as in choice (G), are incorrectly linked to the phrase take a real step. Only the word toward completes this phrase appropriately to create take a real step toward. Deleting the underlined portion, as in choice (J), makes the sentence unclear and changes its meaning.
51. A Choices (B), (C), and (D) all incorrectly separate the verb fuse from its objects. NO CHANGE is required here because no punctuation is necessary between the verb and its objects.
52. H In EXCEPT/LEAST/NOT questions, the underlined portion of the sentence is correct. Note the similarities between the words. Encouraged, motivated, and emboldened, in choices (F), (G), and (J) are all synonyms for the verb inspired. Only the word forced in choice (H) changes the meaning of the sentence and is thus the LEAST acceptable substitution.
53. A Since the phrase as American writers living abroad were known is a descriptive phrase that plays no essential role in determining the meaning of the sentence, it must be set off by a comma as it is in the sentence as written. Choices (B) and (D) introduce new punctuation that loses the clarity of the original sentence. Choice (C) suggests that the phrase is a portion necessary to preserve the meaning of the sentence and should not be set off from the rest. This is incorrect because as American writers living abroad were known is merely a phrase that clarifies and defines the word before it, expatriates.
54. J For two ideas to be separated by a comma and a coordinating conjunction such as but, the ideas on either side of this punctuation and conjunction must be complete. The sentence as written is incorrect because the phrase limited to those who were able to find copies of the book is not a complete idea. Choice (H) is incorrect because a semicolon is also a punctuation mark that requires that the two ideas on either side of it be complete. Choice (G) creates an unnecessary pause in the sentence. Accordingly, only choice (J), which removes all punctuation marks, maintains the proper flow of the sentence and correctly treats positive but limited to those who were able to find copies of the book as a modifying phrase for the word reception.
55. D The sentence as written discusses the reception of a different book, not the one discussed in the previous sentence. Choice (C) refers to the current reputation of the book, and choice (B) is too general to be said to refer to only the specific book mentioned in this paragraph. Only choice (D) contains the reaction of critics to the appropriate work and the idea that the book was difficult to obtain.
56. F This question asks you to identify which answer best indicates that the novel Beyond Desire had presented something new in American literature. Choice (G) suggests that this book had other influences and does not say whether Anderson was the first to incorporate these influences. Choices (H) and (J) discuss the reactions of critics and readers to the book, not the book itself.
57. A Choice (B) is idiomatically incorrect—the preposition used with the word contributions in this context should be to, rather than from. Choices (C) and (D) are unclear in creating the phrases the 1930s of the various writersand he influenced of the various writers, respectively. Only choice (A) properly links the noun and the proper prepositional phrase in works of the various writers.
58. G To keep the sentence as written is to suggest the word American is not an essential piece of the sentence, but without this information, the words the name are undefined and unclear. Choices (H) and (J) omit the necessary comma before the conjunction and, which, in this case, is separating the items in a list: the troubled relationship, the direct style, and the idea are the main nouns used in this list. Only choice (G) indicates the importance of the word American to the meaning of the sentence and sets this portion of the sentence in a list appropriately.
59. D Pay close attention to the years discussed in each of these paragraphs. Paragraph 2 discusses Anderson’s death in 1941 and his influence today. It should be logically placed after the paragraph discussing the time period most directly before that. Paragraph 5 is appropriate here because it discusses the 1920s and the 1930s, the periods closest to 1941 in this passage.
60. G Pay close attention to the reasons given in each of these answer choices. Choice (F) is too general and does not accurately reflect the content of the passage. Choice (H) erroneously says that the passage is primarily about a difference between two large groups when in fact it is about only a single author and his influence on a group of other authors. Choice (J) suggests that the passage only discusses the 1920s and the 1930s when the years 1919 and 1941 are mentioned explicitly.
61. C Choice (C) is the clearest and most concise option. The verbs retracted and diminished essentially mean the same thing, thus choices (A) and (B) are redundant. Choice (D) is incorrect, because without a verb the sentence is incomplete.
62. J The passage is written in past tense, eliminating choices (G) and (H). The correct past tense form of to begin is began, making choice (J) the best answer. The form begun is used after a helping verb.
63. A These responsibilities refer to the previous sentence, which describes the responsibilities to be traditionally assigned to men. Choice (B), therefore, is redundant. Choice (C) creates a sentence fragment. Choice (D) does not agree in number with the plural responsibilities.
64. J Choice (J) eliminates the word but, fixing the sentence fragment that is created by the pronoun that. Choices (F), (G), and (H) incorrectly add conjunctions that create incomplete sentences.
65. C The two words machinists and making should be separated by a period because the sentence has two complete ideas, making choice (C) the best answer. Choices (A) and (D) create run-on sentences. A comma cannot separate two complete ideas, eliminating choice (B).
66. F The previous sentence already mentions factories and shipyards, making choices (G) and (H) redundant. Choice (J) changes the meaning of the sentence, therefore the best answer is choice (F).
67. C Choice (C) provides the correct verb, was, that agrees with the singular subject of the sentence, presence. Choices (A), (B), and (D) all incorrectly use a plural verb.
68. G Choice (G) is correct because the addition distracts the reader from the topic at hand, which is the changing role of women in the workforce during World War II. Choice (F) is wrong because although it suggests not adding the information, its reasoning is incorrect. The proposed sentence is consistent in style and tone with the rest of the essay. Choices (H) and (J) incorrectly recommend adding a sentence that is irrelevant to the essay.
69. B The rest of the essay is about the women’s baseball league, therefore the best transition is choice (B). Choices (A) and (C) do not reflect the focus of the essay, and choice (D) is too extreme.
70. G Philip K. Wrigley is necessary to clarify who the Founder is and should not be off-set by commas, eliminating choice (J). Choices (F) and (H) have unnecessary pauses due to too many commas; therefore, choice (G) is the clearest answer.
71. A Choice (A) describes a specific visual with pretty smiles and baseball mitts in their hands. Choices (B), (C), and (D) are incorrect because the added information does not qualify as descriptive detail that helps the reader visualize the photographs.
72. J The sentence lists different feminine characteristics but does not make clear where the list ends, usually indicated by and before the last item. The best answer, therefore, is choice (J). Choices (F) and (G) don’t list the items in parallel form. Choice (H) uses the wrong linkage for a list of things.
73. D The following sentence states that the photographs of the female players exemplify the balance between feminine appeal and masculine labor of women during WWII, making choice (D) the best explanation. Choice (A) is incorrect because the previous sentence suggests the physical attractiveness of the players but does not give specific details about what they look like. Choice (B) is incorrect because women’s athleticism is not the focus of the paragraph. Choice (C) is incorrect because the captions of the photographs are never discussed.
74. J Choice (J) is the correct answer because the correct form of the possessive pronoun is its. The correct possessive form of the pronoun does not use apostrophes, eliminating choices (F) and (G). Choice (H) uses the plural pronoun their, which incorrectly replaces the singular antecedent All-American Girls Professional Baseball League.
75. B The essay directly describes various jobs that women held during World War II, all of which were roles traditionally filled by men, eliminating choices (C) and (D). Choice (A)’s reasoning only addresses the All-American Girl’s Baseball League, which is the focus of Paragraph 4 but not the essay as a whole.
TEST 1 MATH EXPLANATIONS
1. A Since is the length of , will be 3 × 24 = 72 kilometers. Since X is the halfway point of the trail, the trail’s entire length will be twice , or 72 × 2 = 144 kilometers.
2. J To find the value of x, first subtract 7 from both sides to get = −1. Next, multiply both sides by 5 to get 4x = − 5. Finally, divide both sides by 4 to give you choice (J). Choice (F) neglects the negative sign. Choice (G) is the reciprocal of the correct answer. Choices (H) and (K) are partial answers.
3. B Determine how many minutes it takes each cyclist to make 9,760 pedal revolutions. Cyclist A takes 9,760 rev ÷ 80 rev/min = 122 minutes. Cyclist B takes 9,760 rev ÷ 61 rev/min = 160 minutes. So, Cyclist B takes 160 − 122 = 38 more minutes than Cyclist A. Notice that Choices (C) and (E) are partial answers. Choice (D) is the sum of each cyclist’s rate, and Choice (A) is the difference of their rates.
4. K The perimeter of a square is 4s, so one side of this square is = 9 inches. The area of the square is s2 = 92 = 81. Choice (F) is the length of one side if the square had an area of 36. Choice (G) is the length of one side rather than the area. Choice (H) is the result of 9 + 9. Choice (J) is the result of 62, rather than 92.
5. D From the figure, you can see that the y-coordinate must be greater than 4, eliminating choice (C), and the x-coordinate must be less than 8, eliminating choice (E). Since the figure is a rectangle, opposite sides must be parallel and thus have the same slope. The slope from (2,0) to (8,3) is 3 units up and 6 units right. You can now calculate the fourth vertex from the point (0,4): (0+6, 4+3), which gives you (6,7). Choices (A) and (B) have an x-coordinate of 4, which is halfway between 0 and 8.
6. H If Carla’s brother has x notebooks, Carla has 5x notebooks, so 5x + x = 42. Since x = 7 and Carla has 5x notebooks, she has 5(7) = 35. You can also use the answer choices to solve this problem: divide the answer choices by 5 to calculate how many notebooks Carla’s brother has and determine when Carla (the answer) and Carla’s brother (the answer ÷ 5) add up to 42. A calculation error of x = 6 leads to choice (F). Choices (J) and (K) add and subtract numbers from the problem without answering the question asked.
7. A A right angle has a measure of 90°; therefore, any angle contained within a right angle must be smaller than 90°, leaving only choice (A).
8. J You have to count the number of different ways Susie can choose her one T-shirt and her one pair of shorts. She has 3 options for her T-shirt and 3 options for her pair of shorts. She can combine any of the T-shirts with any of the pairs of shorts, so there are 3 × 3, or 9, combinations. Choices (F) and (G) do not account for all possible combinations. Choice (H) is 23 rather than 32.
9. C Use the words in the problem to create an equation: percent means “divide by 100,” of means “multiply,” and what number means “use a variable.” The resulting equation is . Solve to find that y = 8. Be careful of choices (B), which is 20% of 20, and (D), which is 50% of 20.
10. H The number of piano players exceeds the number of violin players; thus the number of musicians who play both instruments cannot exceed the number who play violin, eliminating choices (J) and (K). Since all 22 musicians who play the violin could also play the piano, choice (H) gives the maximum possible number.
11. A In order to make m2 (and therefore m) as large as possible, make n2 as small as possible. The square of any real number can’t be negative, so the smallest that n2 can be is 0. This makes m2 = 196, so m equals either −14 or 14. Choices (B), (C), (D), and (E) are based on multiplication, division, or subtraction, not taking a square root.
12. F To solve this problem, break it down into manageable pieces. × $925 = $185, so the sale price of the drum kit is $925 – $185 = $740. Since the sales tax is .05 × $740 = $37, the total owed is $740 + $37 = $777. Phil receives back the amount he gave the sales clerk minus the amount he owes: $800 – $777 = $23. Choice (G) is the amount of tax paid. Choices (H) and (J) resemble numbers from steps within the problem and choice (K) calculates the taxed price without applying the sale discount.
13. D Taking the square root of a negative number yields an imaginary number. If you picked choice (C), be careful—this number is not rationalized, but that does not mean it is not a real number.
14. G The general quadratic expression a2 − b2 equals (a − b)(a + b). In this question, take the square root of 25x4 and the square root of 16y8; thus a = 5x2 and b = 4y4. Choice (F) correctly factors the variables but not the coefficients, introducing an incorrect factor of the coefficients. Choices (H) and (K) incorrectly factor the coefficients. Choice (J) incorrectly factors the variables.
15. D Use the formula Shaded Area = Total Area − Unshaded Area. In this case, the Total Area is the area of the square, which is 42 = 16. To find the Unshaded Area, add up the areas of the 4 unshaded triangles. Starting at the lower left of the figure and going clockwise, those areas are: (1×2)+(2×2)+(2×1)+(1×2)=5. So, the Shaded Area = 16 − 5 = 11.
16. G To find the percent P, substitute 20 for t to calculate −0.001(20)2 + 0.4(20) = 7.6. Choice (F) is the rounded value of 0.076%, which is not equivalent to 7.6%. Choices (H) and (J) result if you don’t pay attention to PEMDAS or distribution of the negative sign. Choice (K) results if t2 and t are switched.
17. A Find the cost per grapefruit at each store by dividing the cost of each bag by the number of grapefruits in each bag. The cost per grapefruit at Fatima’s is $4.40 ÷ 8 = $0.55, while the cost per grapefruit at Ernie’s is $1.86 ÷ 3 = $0.62. Find the difference: $0.62 – $0.55 = $0.07. Choice (B) comes from multiplying $0.07 by the difference in the number of grapefruits (8 − 3 = 5). Choice (C) comes from averaging $0.55 and $0.62. Choice (D) comes from adding $0.55 and $0.62. Choice (E) is the difference in costs of the two bags.
18. G In order to multiply factors, you need to FOIL (First, Outer, Inner, Last). Remember to add exponents when multiplying numbers with the same base and watch your signs carefully: x8 + 4x4 − 4x4 − 16 = x8 − 16. Choice (F) adds rather than multiplies the factors. Choice (J) multiplies the exponents instead of adding them. Choices (H) and (K) confuse the signs.
19. B First, calculate the number of tile pieces laid in the first period of work: × 3.5 hours = 175 pieces. Next, since you are looking for the time Wade spends working after the interruption, you’ll need to figure out how many tile pieces he laid during that time. Subtract 280 pieces − 175 pieces = 105 pieces. Calculate the number of hours he spends in the second work session by dividing = 3 hours. If you chose choice (D), be careful—you may have included the 60 minutes during which Wade is interrupted, but the question is looking for the time it took Wade to complete his work after he was interrupted.
20. H To find the midpoint of a line, you must take the average of the x-coordinates, , and the average of the y-coordinates of the endpoints, . Choices (F), (G), and (K) incorrectly average the x-coordinates. Choice (J) incorrectly averages the y-coordinates.
21. B You might want to draw a picture to see what is happening. Add the lengths of the two short sides of the backyard and one long side: 16 + 16 + 22 = 54. Choice (C) is the sum of two long sides and one short side. Choice (D) is the perimeter of the backyard but the problem says the fencing is needed only on 3 sides. Choice (E) is the area of the backyard.
22. F One way to solve this problem is to rewrite the equation in the slope-intercept form, y = mx + b, by subtracting 7x and dividing by −3 on both sides. The resulting equation is y = x − 7, where −7 is the value of b, the y-intercept. Another way to solve this problem is to remember that the y- intercept occurs at x = 0 and calculate 7(0) − 3y = 21. Choice (H) is the slope of the line, and the other choices do not modify the equation correctly.
23. C Find the flower’s growth rate by dividing the total growth by the number of days. This is the same thing as finding the slope: cm per day. You want to know when the flower was 16.5 cm tall, which means it has grown 16.5 − 15.0 = 1.5 cm: 1.5 cm ÷ 0.3 cm/day = 5 days after April 8th, which is April 13th.
24. K To subtract, you must first distribute −3 to each term in the second parentheses. You get 2x3 – x − 1 − 3x4 − 6x3 + 6x2 + 3x − 9. Combine like terms to get −3x4 − 4x3 + 6x2 + 2x − 10. Choices (H) and (J) incorrectly distribute the −3. Choices (F) and (G) incorrectly combine terms and exponents.
25. B The slide makes a right triangle, as shown in the picture. Use the Pythagorean Theorem (a2 + b2 = c2) to solve 72 = 62 + x2. 49 = 36 + x2, x2 = 13, x ≈ 3.61, which rounds to 4. Choice (A) is too small, and choice (C) is too large.
26. F You’re looking for a set in which the mean (average), median (“middle” value), and mode (number that appears most often) all equal 8. All five answer choices have a median of 8, but you can eliminate (G) and (K), because their modes are not 8. You can then eliminate (H) and (J) by calculating their means—8.6 and 9, respectively. That leaves you with (F).
27. C The easiest approach to this problem is to test out the answer choices. For choice (C), if the 2nd term is 18, then the 3rd term is (18 + 2) × 3 = 60, and the 4th term is (60 + 2) × 3 = 186. You could also work backwards: if the 4th term is 186, then the 3rd term is (186 ÷ 3) − 2 = 60, and the 2nd term is (60 ÷ 3) − 2 = 18. Be sure to read the problem carefully. Choices (B) and (D) are the 1st and 3rd terms of the sequence, respectively.
28. J The easiest approach to this problem is to test all the answer choices. |9 − 3| ≥ 12 is false; thus the correct answer is choice (J). You could also solve algebraically by solving the equation where (x − 3) ≥ 12 and − (x − 3) ≥ 12. The other choices solve the inequality with wrong direction of signs, choice (K), or confusion of positive/negative values within the absolute value.
29. B Given that v is larger than s, then t + u + v must be larger than s + t + u, since t + u are equal in both expressions. Because s + t + u = 29, t + u + v must be larger than 29. Choices (A), (C), (D), and (E) are not necessarily true, because you don’t know anything about the relationships of t, u, and v. Another way to approach this question is to make up your own numbers for the variables: for example, let s = 20, t = 5, u = 4, and v = 21. Using these numbers, choices (A), (C), and (D) are false. Now make up different numbers: s = 5, t = 4, u = 20, and v = 6. Choice (B) is still true (30 > 29), but choice (E) is now false (15 > 29).
30. H You can eliminate choices (J) and (K) immediately since CBD is clearly less than 90° in the figure. Since is a straight line, CDE + BDC = 180°, BDC = 180° − 155° = 25°. and are opposite sides of a rectangle, so the line segments are parallel. Extend line segments , , and to reveal that the two parallel lines are crossed by a transversal, which means BDC and ABD are congruent. Thus, ABD = 25°. ABDand CBD make up one of the right angles of rectangle ABCD; thus CBD = 90° − 25° = 65°. Choices (F), (J), and (K) are all angles within the figure, but do not answer the question.
31. E Test the prime numbers from the answer choices in the equation. Since all the numbers in the equation a – b = c must be positive prime numbers, the only possible result for c can be 2 (e.g., 13 − 11 = 7 − 5 = 2). The only exceptions to c = 2 are 5 − 2 = 3, 13 − 2 = 11, and 7 − 2 = 5. Even so, the only number common to all of these equations is 2, answer choice (E).
32. H You can determine Pierre’s average speed, in miles per hour, by dividing his total mileage by his total time. The total number of miles he covers is the distance from starting point S to finish line F, which is SF. You can eliminate choices (F), (G), and (J) because they don’t include the entire length of the racecourse. The total elapsed time from point S to point F is tF. You can eliminate choices (F), (G), and (K) because they don’t use the elapsed time clocked at the end of the race.
33. A Since you know the hypotenuse of the triangle and need to find the adjacent side of ABC, use SOHCAHTOA: = cos (70°). So, = 13 cos (70°) ≈ 4.4. Choices (D) and (E) are the answers that you would get if you used either the sine or the tangent functions in the equation above. If you chose either choice (B) or (C), you might have assumed that the triangle was a 5:12:13 right triangle.
34. J When x = −3 and y = −4, then . Choices (F), (G) and (J) all confuse the signs. Choice (K) switches x and y.
35. C The ramp forms a 30°-60°-90° triangle with side lengths in a ratio of 1::2. Since the shortest leg measures 4, the other leg of the triangle will be times the short side: = 6.92 ≈ 7. Choice (D) gives the length of the ramp itself, not the horizontal length.
36. J BCD is equilateral, so CBD is 60°. ABD must be larger than 60°, eliminating choices (F) and (G). Choice (J) would mean ABC is 96° − 60° = 36°. Since ABC is half the measure of BAC and BAC = BCA, each base angle of the isosceles triangle would be (180° − 36°) ÷ 2 = 72°, which works within ABC: 36° + 72° + 72° = 180. Choice (K) mistakenly calculates ABC to be twice, rather than half, the measure of BAC.
37. D Use the standard slope formula with points (8,0) and (0,−4):m = . If you selected choice (E), you may have flipped the x and the y when you calculated the slope. If you selected choice (A), you may have confused some of the negative signs.
38. J Find the hypotenuse with the Pythagorean theorem: a2 + b2 = c2. With the values given in the figure, this becomes (8)2 + (4)2 = c2, and c2 = 80, so c ≈ 8.9. Accordingly, the sides of this triangle have lengths of 4, 8, and 8.9. To find the perimeter, add these sides together to get 20.9.
39. B The formula for cosine is as follows: . Since you are dealing with MNO, the adjacent side will be 4, and the hypotenuse (the same whether you’re dealing with sine or cosine) is . Accordingly, the cosine is . Choice (A) gives the sine of MNO, and choice (C) gives the tangent.
40. F The fraction is equal to . If there are m students in the class, m must be the denominator, so you can eliminate choices (G), (H), and (J). The number of students who received a passing grade is calculated by subtracting the number who didn’t pass the last exam, n, from the total number of students, m. Choice (K) would give a negative fraction, which is not possible.
41. A To solve the inequality, distribute the 2 on the right side of the inequality: 5x + 9 ≥ 6x + 8 + 7. Then combine like terms to get: –x ≥ 6. Remember to flip the sign when you divide by −1 for x to give you the range x ≤−6. Choice (B) forgets to flip the sign. Choices (C) and (D) are the result if you forget to distribute 2 to the 4 in the first step. Choice (E) results if you missed a negative sign.
42. K The tiles must equal the surface area of the box, which is the sum of the areas of all 6 faces. There are three sets of faces: front/back, top/bottom, and the two sides: 2 (4 × 9) + 2 (3 × 9) + 2 (3 × 4) = 24 + 72 + 54 = 150. Because each tile covers 1 cm2, the artist must have 150 cm2 ÷ 1 cm2 = 150, choice (K). Choice (F) finds the area of only three faces, and choices (G) and (J) account for only two of the three pairs of faces. Choice (H) finds the volume of the box.
43. C Draw in , which is parallel to both and , to find BAD. The interior angles of two parallel lines add up to 180°, so you can subtract ABC (130°) from 180° to yield BAD = 50°. Subtract BAE from the larger angle BAD to get EAD = 50° − 22° = 28°. Since AEF and EAD are also interior angles of two parallel lines, subtract: 180° − EAD = 180° − 28° = 152° = AEF. You could also extend to and find the third angle of the triangle. The same rule will apply—the third angle of this triangle will be equal to AEF because and are parallel.
44. G To find the area of a trapezoid, multiply the height by the average of the bases. The bases are 6 and 14, so their average is 10. Don’t confuse the height of the trapezoid with the length of one of the slanted sides, which would give you choice (J). Choices (F) and (H) are the results when you multiply the length of only one of the bases by the height. You can also solve this problem by breaking the trapezoid apart into one central rectangle and right triangles on either side.
45. D First, raise both sides of the equation to the fifth power to get rid of the fifth root: becomes x2 + 4x = 32. Then, subtract 32 from both sides to get a standard quadratic form: x2 + 4x − 32 = 0. Factor the quadratic to get (x + 8)(x − 4) = 0. So, x = −8 or x = 4. You could also test the answers until you find all the numbers that satisfy the equation. Choice (A) gives only one of the possible values for x. Choice (C) reverses the signs. Be careful of choice (E)—that’s what you get if you only square the 2 and use the quadratic formula!
46. J Since you know the length of the hypotenuse (the ramp) and are solving for the height opposite the angle of 32°, use SOHCAHTOA: . By process of elimination, you can get rid of choices (F), (H), and (K). If , the height h is 10 sin 32°.
47. C Since average is , the sum of j + j + k + n must equal 0 to make the average equal 0. Combining like terms gives you 2j + k + n = 0. Subtracting 2j from both sides, you get k + n = −2j. Choices (A) and (B) are not necessarily true (for example, if j = −3, k could equal 4 and n could equal 2). Choices (D) and (E) are only true when j is equal to 0.
48. J In the composite function f(g(x)), the value of g(x) is the input x value in f(x); therefore f(x) is taking the square root of g(x). When g(x) = 4x2 − 5, its square root is . Choices (G) and (K) make errors in taking the square root of 4x2 − 5. Choices (F) and (G) reverse the composite and use g(f(x)).
49. C Start with the rate formula: d = rt. In this problem, t = 150 s, and you’ll want to set up equations for as much as you can. If rr is Rusty’s rate and dr is Rusty’s distance, the equation will be dr = rrt. When the two cars meet, their combined distances will equal the length of the entire track, 6,000 m. Therefore, you can use the relationships given in the problem to set up an equation as follows: 6000 ft = rrt + (rr − 8 ft/s)(t). Since t is constant at 150 s throughout this problem, substitute it into the equation to get 6000 ft = (150 s)(rr) + (150 s)(rr − 8). The (150 s) is common to both terms so you can factor it out and divide both sides by 150 s to get this: =rr+rr−8 and 40 ft / s = 2rr − 8 ft / s. Manipulate the equation to isolate and find rr = = 24 ft / s. If you selected choice (A), be careful—this is Dale’s rate!
50. K Since Rusty drives the first 7 laps at an average time of 180 s, you can multiply these values together to find that he drives the first 7 laps in a total time of 1,260 s. Complete the same operation for the second set of numbers: since Rusty drives 8 laps at an average time of 190 s, multiply these values together to find that he drives all 8 laps in a total time of 1,520 s. Since you know the two total times, you can simply find the difference between them to find the time of the last lap: 1,520 s − 1,260 s = 260 s. If you selected choice (H), be careful—this is the average of 180 and 190, but it doesn’t take into account that Rusty drives 7 laps at an average of 180 s and only one lap at an average of 190 s.
51. D Dale drives 6 laps, each of which is 6,000 ft, for a total of 36,000 ft in 90 minutes. The question asks for this value in feet per hour, so convert the 90 minutes to 1.5 hours. 36,000 ft ÷ 1.5 hrs = 24,000 ft/hr. If you selected choice (A), you may have forgotten to change the 90 minutes to 1.5 hours.
52. G The equation of a circle is (x − h)2 + (y − k)2 = r2, where (h, k) is the center of the circle and r is the radius. Thus, circle B has its center at (−4,2) with a radius of 3. If you draw a diagram, you’ll find that point (−2,2) lies outside circle A and inside circle B.
53. B The perimeter is the distance of the shape’s outline. There are two straight lines: from (0,0) to (0,4) and from (0,0) to (4,0), each with a length of 4. The straight lines total 8, eliminating choices (A), (D), and (E). The curved parts are two semicircles and two semicircles make one complete circle, so find the circumference of one circle with radius 2: C = 2πr = 2π(2) = 4π. Eliminate choice (C) and pick choice (B). If you picked choice (D), you may have found the area instead of the perimeter.
54. F An even function is defined in the question as a function for which the value of f(x) = f(−x). This means that f(x) has the same value for both x and −x. If you fold the graph of an even function along the f(x) axis, the two sides of the graph will be mirror reflections of each other. Choices (G), (J), and (K) are odd functions, in which f(−x) = −f(x) for all values of x. Odd functions rotate 180° about the point (0, 0). Choice (H) is not a function, because it does not pass the vertical line test; the same x value yields two values for f(x).
55. B Use the distance formula: . .
56. F In a right triangle with angle A, . In this triangle, and . Since RST is a right triangle, use the Pythagorean Theorem to determine that r2 + s2 = t2. You’re left with .
57. C Trapezoid DECA is isosceles because ABC is isosceles and, since , line segments and have equal lengths. Since the trapezoid is isosceles, the diagonals are congruent. Thus, DFE and AFC are similar. Set up a proportion to find the missing side: . So, = 18. Choice (A) is the short side of DFE multiplied by 2. Choice (B) is 9 + 6. Choice (D) is 27 + 6 and choice (E) is 27 + 9. Remember that hard problems typically require more work than just adding together some of the numbers from the problem!
58. F The dimensions of a matrix product are determined by the number of rows in the first matrix and the number of columns in the second matrix, in this case 2 × 1. Thus, choices (H), (J), and (K) have the wrong dimensions. To find the product value, multiply rows by columns and add the products of one row-column: (4 × 0) + (−2 × 2) = −4 and (3 × 0) + (−6 × 2) = −12.
59. D An ! symbol denotes a factorial, which is the product of decreasing consecutive integers starting from the integer in front of the ! sign. (For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.) You can simplify this expression if you separate the two largest factors in the numerator; in other words, write (n + 1)! as (n + 1) × (n) × (n − 1)! Canceling (n − 1)! from numerator and denominator leaves you with (n + 1)(n). So (n + 1)(n) = 20, which means that n + 1 = 5 and n = 4. Finally, the question asks for n! = 4! = 4 × 3 × 2 × 1 = 24. Choice (A) is 3! Choice (B) is half of 20. Choice (C) is half of 24. Choice (E) is 5!
60. K To simplify this abstract problem, substitute a value in for the circle’s radius. If the radius is 3, the circumference is . Choice (F) gives the ratio of the circumference to the radius. Choices (H) and (J) work with the diameter instead of the radius, and choice (G) finds the ratio of the diameter to the radius.
TEST 1 READING EXPLANATIONS
1. C Choice (C) points to the portion of the passage in which the narrator says that his grandmother had gained considerable stature in Robertson County and, more importantly, refers to information concerning the story’s principal character. The main topic of the passage is Ruby and her diner, so you can safely assume there will be a connection between the main topic and the correct answer. Choice (A) focuses on information that occurs only in the beginning of the story and choices (B) and (D) are too general and not directly supported by information in the passage.
2. J The second paragraph begins by introducing the character of Ruby Sanders, the narrator’s grandmother. This indicates that the paragraph will explain who she is and why she is important. Choices (F) and (G) point out topics in the beginning of the passage, but they do not serve to cover the character of Ruby. Finally, choice (H) is an overstatement, so we have to dismiss it as a viable choice in light of choice (J).
3. B Only choice (B) contains an answer that refers correctly to a part of the text—If the diner were a sort of cell, then my grandmother was its nucleus; without the nucleus, the cell would surely perish. The other answer choices contain words from the passage as well, but the things stated in those answer choices are either untrue or not supported by the passage.
4. H Choice (H) should be selected in this instance because the question asks you to make an inference, and inferences must always be supported by the facts within the area in question. The end of the paragraph directly states that the narrator was glad that he didn’t know that he wouldn’t return to the diner after his last summer there. Choices (F), (G), and (J) force us to make unfounded assumptions as to how the narrator would feel.
5. B Locate where the author talks about working at the diner (paragraph 8). The narrator mentions that the work was hard but never dull. Therefore, you should select choice (B). Although each of the others contains individual characteristics that may be true, both characteristics listed in the correct answer must be true.
6. F Note the sentence at the end of the second paragraph: It didn’t take long before my grandmother was a person of considerable stature in and around Robertson County, just like the restaurant that bore her name. From this sentence, you can easily infer that both Ruby and her restaurant were popular in and around the community. If you chose one of the other answers, be careful—these refer to either Ruby or the restaurant, but never to both.
7. A The lines in question provide the introduction to this paragraph, which details the ways in which Ruby’s was significant to the community in ways other than as a restaurant—choice (A). Choice (B) is not supported in the text, and choice (D) gives a too literal interpretation of the lines referred to in the passage and misreads the word expect. Choice (C) is deceptive—the passage does suggest that Ruby herself had risen to prominence, but it does not mention anyone else in this regard.
8. G The author speaks of choices (F), (H), and (J) in the sixth paragraph. He mentions football leagues in the last paragraph, but as something he had to forego to continue to work at the restaurant. Accordingly, the passage mentions all of the things as being available at the diner EXCEPT the football leagues, choice (G).
9. C In the seventh paragraph, the author vividly describes the physical details of the restaurant. In this paragraph, he gives a detailed description of the grounds, down to the furniture and the locations of some minor items. Choices (A), (B), and (D) use words from the passage, but the information in these choices is not supported.
10. J In the last paragraph, the narrator says, After all, the woman who built Ruby’s was strong enough to make me forget those things, if only for the summer. It can therefore be inferred that the narrator is impressed by his grandmother’s strength. None of the other answer choices are supported by evidence in the passage.
11. B The passage is about studies on several different factors that contribute to happiness. According to the second paragraph, Tellegen and Lykken state that genes play a part in happiness, but no specific genes have been found that cause hedonic adaptation, eliminating choice (A). Although an account of Lyubomirsky and Sheldon’s studies indicates that there may be ways to improve happiness levels (lines 70−80), there is no discussion of the cure for depression mentioned in choice (C). No scientist in the passage disagrees that genes have an influence on happiness levels, eliminating choice (D).
12. H All the studies in the passage involve subjects telling researchers how happy they are, which is the same as subjective well-being as defined in lines 8−11. Only Lyubomirsky and Sheldon’s study made specific note of studying their subjects’ levels of happiness over time (lines 64−67), eliminating choice (F), or involved subjects engaging in acts of kindness (line 75), eliminating choice (G). Only Tellegen and Lykken’s study mentioned using identical twins (lines 13−14), eliminating choice (J).
13. D Tellegen and Lykken’s study of twins that had been separated and raised in different families (line 15) does not indicate whether separated twins were less happy. The question presented by choice (A) can be answered by the statistic on line 52, which says 10 percent is influenced by circumstances. Descriptions of Lyubomirsky and Sheldon’s studies suggest that people who varied their acts of kindness (line 75) and who wrote a list of things to be grateful for (line 78) can improve their subjective well-being, which answers the question posed in choice (B). In lines 43−44, Sheldon explains that scientific literature suggests that behaviors such as choosing the right goals provide only a temporary increase in subjective well-being, answering the question in choice (C).
14. F Lyubomirsky hopes to show how conscious strategies counteract genetic forces (lines 63−64)—in other words help people to overcome their genetic predispositions. You can eliminate choice (J) because the passage never indicates that hedonic adaptation can be eliminated entirely. Sheldon and Lyubomirsky also agree that 50 percent of subjective well-being is predetermined by the genetic set point (lines 50−51), which confirms, rather than contradicts, Tellegen and Lykken’s study, eliminating choice (G). Determining which intentional act is more effective is not the primary purpose of their research, eliminating choice (H).
15. D The statistics cited in the last sentence of the passage best support choice (D). Though the passage indicates that some psychologists’ emphasis caused them to suspect that overall levels of subjective well-being are low (line 85), this does not summarize the University of Chicago studies, so eliminate choice (A). Though Americans are mostly happy people, this does not mean that depression is uncommon, as choice (B) states. You can also eliminate choice (C), because it suggests that happiness levels are actually harmed by attempts to improve them.
16. H The Lykken and Tellegen study is discussed in paragraph two. Choice (H) is correct, as the passage clearly states that only some of the twins were raised together, not all of them. The paragraph states that the members of the study were both fraternal and identical twins and that researchers compared the scores of the twins, making choice (F) true. Choice (G) is true because the study compared the twins’ subjective well-being, which is described as our self-reported level of happiness in the first sentence. Choice (J) is found in the final sentence of the paragraph, which states that most of the difference in people’s levels of happiness are determined by differences in genetic makeup.
17. A Hedonic adaptation is useful because it benefits people who experience adverse conditions in their lives (line 25). Although these adverse conditions may include permanent disability or sudden loss of income (lines 26−27), hedonic adaptation does not cause people to forget about these problems, as indicated in choice (B). It is not useful to adjust to the higher level of happiness caused by winning the lottery, eliminating choice (C). Hedonic adaptation helps people to adjust their levels of happiness back to their own genetic set point, not to identify better with family members, eliminating choice (D).
18. G If you deleted the first paragraph, you wouldn’t get a detailed story about a particular person whose life shows that happiness and life events, in this case the Holocaust, are not necessarily correlated, as in choice (G). The passage mentions in the third paragraph that circumstances are not a large contributor to happiness, so eliminate choice (F). The first paragraph includes an example that is relevant to establishing the main idea of the passage, eliminating choice (H). Lines 26−27 mention permanent disability or sudden loss of income as specific examples of adverse conditions people may experience, so you can eliminate choice (J).
19. C The topic sentence of the last paragraph suggests that its purpose is to focus on people’s generally positive assessment of their own happiness. The researchers mentioned in the paragraph had an incorrect suspicion, which is different from making many errors, so you can eliminate choice (A). Choice (B) can be eliminated because Ross’s anecdote in the first paragraph is not meant to suggest that Americans are unhappy. Lyubomirsky and Sheldon’s findings that certain behaviors may improve happiness are still valid even if people are already generally happy, eliminating choice (D).
20. H Lines 64−65 state that Lyubomirsky and Sheldon are currently expanding their study. Though it is possible that the researchers mentioned in choices (F), (G), and (J) may still collaborate, the passage never explicitly gives this information, making choice (H) the best answer.
21. C This question asks what the author has learned. Since the author ended the passage by explaining her new theory of the connectedness of fiction and biography, you want something that agrees with that, which choice (C) does nicely. Choices (A) and (D) both use deceptive language from the passage but do not reflect what the author has learned. Choice (B) is extreme.
22. H The passage states that studying literature in college involved scouring personal letters for hints of relationship problems, familial tragedies, or even fond memories that seemed reminiscent of storylines. Since the prior part of the sentence discussed the intensive research that the author did, scouring is being used to mean something like researching. Choice (F), purifying, is not supported. The author is studying, so choice (G), obliterating, is not supported. Choice (J), cleansing, is one meaning for scouring, but it is not supported in this context.
23. A The author states, since I’ve been a Nathaniel Hawthorne fan since junior high, a side trip to the building that had inspired one of his greatest works seemed to be in order. While the passage states that the author was visiting Salem’s tourist attractions, choice (A) is better supported by the text than choice (B). The author had not originally sought to learn the personal details of Hawthorne’s life, making choice (C) incorrect. Choice (D) is deceptive, since there is no proof that Hawthorne lived during the Salem Witch Trials.
24. F While the college professors are mentioned in line 21, we do not learn until the last paragraph that the author has finally understood that when we weave the threads of the author’s life around that base, we are able to see the interactions between text and author, as they join to create a pattern more complete than either would be on its own. The passage does not state that one is more necessary than the other, as choices (G) and (J) do. Choice (H) is too strong, since the professors are referring to understanding, not enjoyment.
25. B The passage tells us that the author opted to major in literature, assuming that this would involve reading scores of wonderful books. Although the author disagrees with her professors, there is no evidence that she chose her field of study in order to disprove their theories, as stated in choice (C), and choices (A) and (D) incorrectly state that she agrees with the professors’ approach.
26. H The author’s ultimate conclusion regarding the purpose of literary studies is most clearly outlined in the final paragraph, as quoted in choice (J), but that does not answer this question. Choice (F) refers to her earlier aim when reading, and choice (G) refers to what she gleaned in inspired moments. Choice (H) correctly refers to what the author experienced more often and thus was the most likely result of completing her professors’ assignments.
27. B The House of the Seven Gables is discussed mainly in the fourth and fifth paragraphs. The passage does not state precisely who lived there, just that Nathaniel Hawthorne did not, eliminating choice (A). Although it may have been an important historical site, the passage does not tell us if anything actually took place there, as choice (C) states. The garden is described as desolate due to the season but there is no evidence that the house is in poor repair, as in choice (D). Since the author must buy tickets and take part in a tour in order to visit the house, it is reasonable to infer that it is now a tourist attraction, as in choice (B).
28. J The passage closes with the statement that The work itself is indeed the frame, but when we weave the threads of the author’s life around that base…In this context, the frame is referring to the novel, which the author believes is the base of our understanding. Choice (F) incorrectly states that the novel is the isolated goal. Choice (G) likewise treats the novel as the purpose as opposed to the base. Choice (H) refers to the novel as extra, or auxiliary, information. Choice (J) correctly identifies the novel as the focal, or central, point.
29. C Choice (C) most closely matches the author’s final opinion of studying authors’ lives as discussed in the final paragraph, where she states that we are able to see their interactions, as they join to become something more complete than either would be on its own. Choice (A) does not address the author’s ultimate conclusion that this study can be worthwhile. Neither timidity, choice (B), nor frustration, choice (D), is supported by the passage.
30. F The third paragraph tells us what happened after the author finished school, connecting the second paragraph, which details her childhood and schooling, to the fourth paragraph, which brings us back to the visit to Salem. The reasons for her trip, choice (G), are mentioned in the first paragraph. The study of literature, choice (H), was discussed in the second paragraph as well as the third, and the evidence for the author’s final conclusion, choice (J), is found in the last paragraph.
31. A Although the passage mentions that the frogs’ calls concern mating behavior, it doesn’t specify how often they mate, so choice (A) is the best answer. Choice (B) is addressed in line 17, choice (C) is answered in lines 29−43, and choice (D) is answered in lines 54−57.
32. F Lines 15−16 state that the coqui faces almost no ecological competition because there are no other native amphibians; thus, choice (F) is the best answer. Choice (G) is contradicted in lines 58−62.
33. C Paragraph 4 (lines 29−43) states that the volume of the frog’s call is compounded by two other factors, one of which is the wall of sound produced by overlapping calls, making choice (C) the best answer. Choice (A) is contradicted by lines 4−5. Choices (B) and (D) refer to facts that aren’t supported by the passage.
34. H This paragraph states that the coqui thrives because it doesn’t need as much water as it would if it were born a tadpole. The end of the paragraph also implies that the coqui faces little predatorial threat before it has matured. The paragraph does describe the environmental conditions in Hawaii, but description of the habitat isn’t the primary purpose of the paragraph, eliminating choices (F) and (G). Choice (J) is not the primary purpose of the paragraph, nor does it accurately describe the coqui.
35. B The first paragraph is a descriptive, evocative passage that attempts to capture the sound of the frog calls in the night. By contrast, the sixth paragraph explains specifically how scientists believe these frogs could endanger the local environment, so choice (B) is the best description of the change in the language’s tone. Nothing in the passage suggests the author’s opinion, so choice (A) doesn’t fit. The sixth paragraph talks about the frogs as a potential threat, so you wouldn’t select choice (C) or (D) as the best option.
36. G Earlier in the sentence, the coqui populations are described as threatening the survival of arthropods, which indicates that the arthropod population is struggling, eliminating choices (H) and (J). The word pursuit doesn’t fit as well as extinction, making choice (G) the best answer.
37. D The last sentence of the fifth paragraph (lines 54−57) begins with the phrase Ornithologists fear, which means that the potential outcome hasn’t happened yet. Choice (A) is stated as factual information in lines 33−34, choice (B) in lines 71−73, and choice (C) in lines 81−82.
38. F The passage states that nematodes and other types of vertebrate parasites could be transported with coquis and infect indigenous fauna, making choice (F) the best answer. Choices (G) and (H) refer to the frogs’ food sources, not parasites; arachnids in choice (J) aren’t mentioned specifically in the passage, although they are a member of the arthropod class.
39. B The fifth paragraph states that another quieter genus of the frog—the greenhouse frog—represents an equal threat to the biodiversity of the island, which is best summarized by choice (B). Choice (C) incorrectly states that the greenhouse frog is less, rather than equally, dangerous. It is true that the greenhouse frog is relatively quiet, but that characteristic isn’t necessarily what makes the frog hard to eliminate, eliminating choice (D). Although the name greenhouse frog points to an indoor habitat, the passage doesn’t support that assumption, so you can rule out choice (A).
40. J The last paragraph mentions 1,000 acres in the first sentence and continues in the next sentence to describe the land as the habitat in which the coqui has adopted as its home in Hawaii, making choice (J) the best answer. There is no evidence in the passage to support choices (F), (G), and (H).
TEST 1 SCIENCE EXPLANATIONS
1. A The data in Table 3 indicate that for every increase of 25°C, there is a corresponding increase in θ of approximately 3.5 degrees. A temperature of 62.5°C falls halfway between 50°C and 75°C, so the corresponding angle should fall halfway between 25.4 and 29.0 degrees. Only choice (A) has a value anywhere within this range.
2. F According to Table 1, the object made of brick required the largest ramp angle θ before any movement took place. Therefore, it is the most resistant to movement. Raising the angle of the ramp accomplishes the same thing as applying increasing force to the object to eventually overcome friction.
3. D In Experiments 1 and 4, the angle θ where the wooden object starts to move stays the same, no matter how many objects are stacked on top of each other. Since any change to this angle will signal a change to the coefficient of static friction, you can confidently say that if the angle doesn’t change, the coefficient of friction will not change.
4. G The interaction of interest is between the various objects and the polymer coating of the ramp. The polymer coating is what comes into contact with the objects, while the underlying plastic board is not participating, eliminating choice (F). Objects of different material are not brought into contact during the experiment, eliminating choice (H). Objects are not stacked until Experiment 4, eliminating choice (J).
5. D The object with the largest angle θ is the object that is most resistant to movement. According to Table 1, this is brick. Only choice (D) ranks brick as the most resistant to movement, eliminating all other answer choices.
6. G The data in Table 3 indicate that when temperature increases, the corresponding θ increases. The passage states that the tangent of this angle represents the coefficient of static friction between the object and the polymer surface. The experiment is not exploring the interaction between wood and wood, eliminating choice (F). The mass of the object is constant, eliminating choice (H). Only wooden objects are used in Experiment 3, eliminating choice (J).
7. B The transition from April to May shows a small increase in the number of reported polio infections, and the transition from November to December shows a decrease, so neither choices (C) nor (D) would be the correct answer. There are large increases in the number of reported cases from January to February and from February to March, but upon close inspection, the transition from February to March is larger. Therefore, choice (B) is the best answer.
8. J In June 2004, 80 cases of polio infection were reported, so 80 × 200 = 16,000 people would have been at risk for contraction of the infection.
9. A In all the Indian cities, there are more reported cases of polio virus infections in August than in June. Choices (B) and (D) are consistent with decreases, not increases, in the reported polio cases. The study described by Figure 2 only covers the dry summer and rainy monsoon season, not the autumn or winter, so the explanation given in choice (C) is unsupported. Choice (A) is the best answer because the month of August is expected to have more rainfall, and therefore is more likely to feature water contamination.
10. H Figure 2 presents findings that are applicable only to India, not Nigeria, so (F) is incorrect. The findings only present information on reported infections during June and August 2007, not on unreported infections (choice (G) is wrong) nor on winter months (choice (J) is wrong). The findings do, however, show a stark contrast between the small number of reported cases in the cities in western and southern India (Mumbai, Chennai, and Hyderabad) and the large number of cases in the northern cities (New Delhi and Kolkata), making (H) the best answer.
11. D The passage states that the polio virus is most often transmitted through water contaminated with human waste and makes no mention of the role (or the lack thereof) that other life forms play in the transmission of the virus. The answer that summarizes this is choice (D).
12. H In June 2007, there were between 10 and 15 reported polio infections in Kolkata, while in August 2007, there were between 20 and 25 reported polio infections. This is an approximate doubling of the number of reported infections, so choice (H) is the best answer.
13. D The solution with the least osmotic pressure will have the smallest value from Figure 1. The pressure for choice (A) is 85 atm; choice (B) is 70 atm; choice (C) is 90 atm; choice (D) is 50 atm. Therefore, a 2.0 M sucrose solution has the least osmotic pressure.
14. J The introduction states that higher van’t Hoff factors correlate with greater dissociation or ionization. According to Table 1, FeCl3 exhibits the greatest van’t Hoff factor, which means the highest degree of ionization.
15. C Examine the equation given in the introduction: Π = iMRT. Since the values of R and T remain constant among all the answer choices as seen in the question, osmotic pressure is determined by the product of M and i. The product of concentration of solute particles and van’t Hoff factor for a 1.5 M NaCl solution is 1.5 × 1.9 = 2.85. The product for the solution in choice (A) is 1.0 × 1.9 = 1.9; choice (B) is 2.0 × 1.9 = 3.8; choice (C) is 2.9 × 1.0 = 2.9; choice (D) is 3.5 × 1.0 = 3.5. Choice (C) has the closest product to 2.85.
16. G The pressure required to maintain solvent equilibrium across a membrane is the solution’s osmotic pressure, as discussed in the introduction. Figure 1 shows a linear relationship between solute concentration and osmotic, eliminating choices (H) and (J). As concentration of solute decreases, the osmotic pressure will also decrease, eliminating choice (F).
17. D Comparing different solutes in Figure 1 at a given concentration greater than M = 0, you will determine that FeCl3 always has greater osmotic pressure than sucrose, eliminating choices (B) and (C). The trend in Figure 1predicts that a substance with i = 3.8 would have a greater osmotic pressure than FeCl3, which does not support the scientist’s findings.
18. H Examine the relationship between the line for Sample 1 and the line for Sample 4. Between the 30−60-cm depth range and the 60−90-cm depth range, the line for Sample 1 crosses over to become higher than the line for Sample 4. Choices (F) and (G) suggest that the lines would never cross over, while choice (J) incorrectly states that Sample 4’s shallower sodium concentrations were lower than Sample 1’s.
19. B On the line for Sample 3 in Figure 2, the second data point most closely matches 17%. Choice (A) would describe the earliest data point for Sample 3, from a soil depth of 0−30 cm; choices (C) and (D) describe Samples 4 and 5 at this depth, respectively.
20. J Use Sample 4, because the question asks you for soil 40 m away from the river. Remember the definitions given for EC and ESP: EC is the total electrical conductivity of the soil, while ESP is the percentage of that amount which is due to sodium ions. To find the total EC due to sodium ions, you would need to multiply the total EC by the percentage due to sodium. Since the total EC for Sample 4 is significantly less at the 90−120 cm depth than at the 60−90 cm depth, while the ESP is roughly the same, (H) is incorrect; similarly, the low total EC at the 0−30 cm depth rules out the possibility of it having the greatest total EC due to sodium ions. Since the EC at the 0−30 cm depth and 30−60 cm depth are nearly the same, the much lower ESP at the 0−30 cm depth makes (J) the correct answer.
21. C This question is essentially asking you to convert one set of data points on a line graph into a bar graph. Choice (C) does this correctly, while choice (A) inverts the values, making small values large and large values small. Choice (B) measures the wrong data point—it would be accurate for a sample depth of 60−90 cm, not 90−120 cm. Choice (D) is very close, but mixes up the values for Sample 4 and Sample 1.
22. G Compare all five samples in Figure 1 using a common depth such as 30−60 cm. In Sample 1, the EC is approximately 1 mS/cm; 20 mS/cm in Sample 2; 1 mS/cm in Sample 3; 0.5 mS/cm in Sample 4; 8 mS/cm in Sample 5. Thus, there is no consistent trend in the electrical conductivity, which means salinity does not increase with consistency with distance from the river, eliminating choices (H) and (J). The explanation in choice (F) is also not supported by passage.
23. B Examine the conditions associated with each group in Table 1. Group 6 is the only group which does not include data from an area affected by habitat loss or declines in prey population. It therefore allows the researchers to compare areas affected by these factors to one unaffected by them. Choices (A), (C), and (D) suggest that Group 6 provides information to the researchers that is not included in the passage.
24. F Examine the conditions associated with Group 2. These areas have additional seaweed which is consumed by marine mammals, the likely prey of the primarily carnivorous polar bear. Choice (G) implies that polar bears may prefer to eat seaweed, but there is nothing in the passage to support this statement. Choice (H) is eliminated because the study does not directly measure the population density of prey animals. Choice (J) would require additional information which links the population of prey animals to Arctic sea ice.
25. C A greater average population density ratio for a certain group indicates that more polar bears are living in areas that are a part of that group. Choice (C) correctly lists the groups by average population density ratio as given in Figure 1.
26. G Group 1 exhibits declines in the number of marine mammals consumed by polar bears. Choices (F) and (H) are not mammals so they are eliminated. Choice (J) is eliminated because the population of polar bears is the outcome being studied as a result of some other environmental change, and there is nothing in the passage to suggest that polar bears consume other polar bears. Only choice (G) is a marine mammal that is likely consumed by a polar bear.
27. D You can use the process of elimination with the definitions in Table 1 to find the correct answer for this problem. Choice (A) includes Groups 1 and 2; these are likely to cause effects in opposite directions, not the same direction. Choices (B) and (C) each include Group 4; as Group 4 is simply a combination of Groups 1 and 3, the researchers are never directly comparing the effects of Group 4 conditions to any other conditions. Choice (D) lists Groups 1 and 3, both groups where there have been conditions likely to make it difficult for polar bears to survive. This is confirmed by data in Figure 1.
28. H Choices (F) and (J) are both true. As seen in Figure 1, average polar bear population ratios for both Groups 1 and 3 are not equal to 1. If they were equal to 1, this would indicate that there is no difference between those areas with the conditions listed and those without. Choice (H) reverses the relationship between Groups 1 and 3 in Figure 1, which means it is not supported. Choice (G) states the relationship from (H) correctly, which means (G) is supported and therefore not the correct answer.
29. D Scientist 2 says “the ·OH generated by Reactions 1 and 4 will react rapidly with any H2CO,” indicating that she does agree those reactions occur; the dispute is what formaldehyde decomposes to after Reaction 3. So according to both scientists, O3 leads to the formation of ·OH (Reaction 1), and OH leads to the formation of ·CH3 (Reaction 2).
30. F As methane (CH4) levels increase, CH3 levels will increase (Reaction 2). As ·CH3 levels increase, H2CO levels will increase (Reaction 3). Therefore the correct graph should show low levels of H2CO when methane levels are low, and high levels of H2CO when methane levels are high. Choice (F) is the only graph that reflects this direct relationship.
31. C Remember: reactants on the left; products on the right. From that you can eliminate answer choices (B) and (D). For choice (A), it is true that H2CO is composed of atoms (it is a molecule); however, composition is not mentioned in the question. Since there are no other reactants, the mass of H2CO (the reactant) must be exactly the mass of the products (H2 and CO). Therefore, the molecular mass of each of the products must be less than that of H2CO.
32. H According to Scientist 1, the first step in the production of formaldehyde requires ozone (O3). Follow the reactions: if O3 levels decrease, ·OH levels would decrease (Reaction 1), leading to a decrease in ·CH3 levels (Reaction 2), which in turn would lead to a decrease in H2CO levels (Reaction 3). Thus, both ·CH3 and H2CO levels would decrease.
33. D Scientist 2 says Reactions 1−4 do occur, which support choices (A) and (C). Choice (B) is Scientist 2’s central argument: that the ·OH produced by Reactions 1 and 4 can react with H2CO to form CO (Reaction 6). While Scientist 2 does say that some H2CO may form from CH4 and O3, she says that “H2CO quickly decomposes” and that the chain reaction of Reactions 2−4 is inhibited. Thus, she would not expect an increase in CH4 levels to cause levels of H2CO to rise dramatically.
34. G If Reaction 4 were inhibited, the amount of H2CO generated would be reduced, and therefore, according to Scientist 2, the amount of CO generated would be reduced, not increased, so choice (F) is incorrect. ·OH can react with H2CO to form CO, but there is no evidence of HO2 reacting with H2CO, as in choice (H). O2 is not involved in the generation of CO, so choice (J) cannot be correct. Answer choice (G) is Scientist 2’s hypothesis: the H2CO generated in Reaction 3 will react in Reactions 5 and 6 to produce CO.
35. B Reaction 6 shows ·OH reacting with H2CO in the atmosphere, which weakens Scientist 1’s hypothesis in 2 ways: it reduces the level of H2CO, which Scientist 1 says is increasing in the atmosphere, and consumes ·OH, inhibiting the chain reaction (Reactions 2−4), which is central to Scientist 1’s hypothesis. Thus, choice (B) is the best explanation. The ·OH produced in Reaction 4 reacts with CH4 (in Reaction 2) agrees with Scientist 1’s argument, so choice (A) is incorrect. The H2O produced in Reaction 6 may react with light and O3, as in Reaction 1, but again, does not weaken Scientist 1’s argument, so choice (C) is incorrect. For choice (D), ·OH is not produced in Reaction 6, it is a reactant.
36. G To solve this problem, you must be sure to read the question carefully: you are looking at the section of the graph where V is decreasing from its largest value. First, find the largest value of V; this is the point on the curve that is furthest to the right, since V increases left to right. Once you are looking in the right place, you just draw a line up from 1.5 mL on the V-axis to where it meets the curve, then draw a line over to the P-axis to get your answer: 30 Pa, choice (G).
37. C From the passage and Figures 1 and 2, you know that both ends of the second half of the curve must meet the ends of the first half to complete the cycle, so P must be higher on the left side than on the right side. Choices (A) and (B) cannot be correct because P is higher on the right side than on the left side. Choice (D) is simply the wrong shape to complete the cycle, so it cannot be correct. Choice (C) has P higher on the left side than on the right side, so it must be correct.
38. H Looking at Figure 1, all you need to do is find the lowest point on the curve, then draw a line down to the V-axis. Choice (H), 3.5 mL is the closest answer.
39. B To solve this question, you must first locate the approximate lowest and highest values of V on Figure 2. The lowest value is about 0.75 mL and the highest value is about 2.25 mL, so the lowest value is about 1/3 times the highest value, choice (B). Another way to solve this problem is to check the answer choices against the graph. Choice (A) cannot be correct because there are no negative numbers on the graph. Choice (C) doesn’t really make sense because if the lowest value were 1 times the highest value, it would have to be the same number as the highest value, and then there wouldn’t be a highest or lowest. Choice (D) doesn’t make sense either because if the lowest value were 2 times the highest value, the lowest value would have to be higher than the highest value. Choice (B) is the only choice which could work because it is the only choice which is not negative and would make the lowest value actually lower than the highest value.
40. F This question is actually just an easy question with tricky wording. All it asks is this: What is the value of V when P is at its highest value? Find the highest value of P, and then find the value of V: 1.0 mL, choice (F).
1. The Introduction
○ start with a topic sentence that paraphrases or restates the prompt?
○ clearly state your position on the issue?
2. Body Paragraph 1
○ start with a transition/topic sentence that discusses the opposing side of the argument?
○ give an example of a reason that one might agree with the opposing side of the argument?
○ clearly state that the opposing side of the argument is wrong or flawed?
○ show what is wrong with the opposing side’s example or position?
3. Body Paragraphs 2 and 3
○ start with a transition/topic sentence that discusses your position on the prompt?
○ give one example or reason to support your position?
○ show the grader how your example supports your position?
○ end the paragraph by restating your thesis?
○ restate your position on the issue?
○ end with a flourish?
○ write neatly?
○ avoid multiple spelling and grammar mistakes?
○ try to vary your sentence structure?
○ use a few impressive-sounding words?