1,296 ACT Practice Questions, 3rd Edition (2013)
ACT Practice Test 2
Test 2. Answers and Explanations
TEST 2 ENGLISH ANSWERS
TEST 2 MATH ANSWERS
TEST 2 READING ANSWERS
TEST 2 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 2 ENGLISH EXPLANATIONS
1. A The mother says that the author will be surprised to find that family histories can be very interesting, which implies that the author currently believes the opposite. Choice (A) is the best answer, expressing boredom and disinterest. Choices (B) and (C) are too optimistic, and choice (D) is irrelevant in this paragraph.
2. J Choice (F) creates a fragment because hoping begins an incomplete thought. Choice (G) creates a fragment because there is no subject for the verb hope. Choice (J) is the best answer because it corrects the sentence fragment error by connecting the incomplete thought to the complete one before it with a comma. Choice (H) confuses the meaning of the sentence.
3. D Pictures and letters is a list of only two items, so no commas are needed before the and, eliminating choices (A) and (B). Choice (C) also has an unnecessary comma after letters, interrupting the flow of the sentence.
4. F In EXCEPT/LEAST/NOT questions, the underlined portion of the sentence is correct. Choice (G) has the same structure and meaning as the original, since yet and but are both coordinating conjunctions, which, with a comma, can join two complete ideas. Choice (H) is acceptable because a semicolon is an appropriate punctuation to separate two complete thoughts. Choices (F) and (J) eliminate the need for punctuation by deleting he and making the second half of the sentence incomplete. However, choice (F) uses an incorrect tense and is NOT acceptable.
5. C Choice (C) correctly uses the apostrophe to show possession. An apostrophe after relatives is necessary to indicate more than one relative has the memories, eliminating choices (A) and (B). Memory does not possess into;thus choice (D) is incorrect.
6. H Sentences 1 and 2 continue the narrative by providing a setting and the scanner’s activity. Sentence 4 shows an important shift in the author’s attitude from reluctance to happiness. Sentence 3 offers information that can be figured out from the context and is therefore the least relevant to the telling of the story.
7. B The word belongings refers to the relatives, which is plural, so you can eliminate choices (A) and (C). The correct answer is choice (B), not choice (D); there refers to a place and their is the plural possessive pronoun.
8. J Choice (J) gives the past perfect form of the verb to send; this form is needed because the letters were sent in the distant past. Choices (G) and (H) are in the wrong tense, and choice (F) does not use the proper past participle form of the verb send.
9. B A pause is necessary between kitchen and penning to clarify that the great-grandmother, not the kitchen, was penning the entries, which makes choice (B) better than choice (A). Choices (C) and (D) can also be eliminated because which and that refer to the closest preceding noun, which is kitchen, and create the same error in meaning.
10. J This sentence continues the same attitude about stories that is expressed in the previous sentence, so you can eliminate choice (F) for incorrect direction. Because makes the phrase after incomplete, so choice (G) is incorrect because it creates a sentence fragment. Therefore indicates the correct direction but doesn’t link the ideas in a logical way. The best answer is choice (J).
11. B A comma should precede the last and in a list of 3 or more things, eliminating choices (C) and (D). Choice (A) has an unnecessary comma after the and, so the correct answer is choice (B).
12. J The best answer is (J) because it clearly introduces the paragraph’s focus on the author’s growing interest in her family. Choices (F) and (H) mention the relatives; however, the focus is not on how many names and relatives the writer needs to keep track of. Choice (G) revisits the idea of using the computer to preserve family memories but does not match this paragraph’s main idea.
13. A Paragraph 6 discusses what the writer gained from her experience, and the conclusion should continue that idea. Choice (A) is the best choice because it discusses what the writer plans to do with what she gained and emphasizes the important relationship between grandfather and grandchild seen in this narrative. Choices (B), (C), and (D) digress from the main point of the essay about the significance of the experience.
14. J Paragraph 5 discusses the writer’s positive view of her grandfather’s stories. Her change in attitude is first introduced at the end of Paragraph 3. Paragraph 5 then concludes by introducing the chest of stuff, which explains what the belongings are in the beginning of Paragraph 4. Therefore, the best placement of Paragraph 5 should be between Paragraphs 3 and 4.
15. B The writer concludes the essay by stating how much she appreciates family memories and mementoes after helping her grandfather research their family lineage; thus her purpose has been achieved, eliminating choices (C) and (D). Choice (A) is not true because the computer skills are not the benefit the writer gained from her experience.
16. H The writer is trying to state that she is standing alone; thus the correct pronoun is myself not me, eliminating choices (F) and (G). The phrase after myself is incomplete and cannot be separated by a period, eliminating choice (J). A comma can be used to connect a complete thought to an incomplete thought.
17. B The words new and cold are both adjectives describing bedroom and should be separated by a comma, eliminating choices (C) and (D). A comma after cold is unnecessary and disruptive to the flow of the sentence, eliminating choice (A).
18. F The writer is trying to describe spectacle, which is a noun, so complete should be an adjective, eliminating choices (G) and (H). The correct idiomatic expression is to make a spectacle of, so choice (F) is better than choice (J).
19. C Since the action has never been more than 30 minutes away…refers to only child, the pronoun should be in subject case who, eliminating choices (A) and (B). Choice (D) incorrectly uses the plural verb form, rather than the singular.
20. H The pronoun one’s does not agree with the subject we earlier in the sentence. Only choice (H) uses the correct possessive pronoun of we, which is our.
21. D The sentence is listing two different pairs of breakfast items—milk and juice, eggs and bacon. There should not be a comma after milk because the and is used to connect two nouns, milk and juice, not to list 3 or more items. You can eliminate choices (A) and (B). The comma is necessary between juice and fluffy in order to separate the two different pairs of items.
22. F Choice (F) clearly articulates the angst she feels and clarifies that she misses her old way of life. Choice (G) is incorrect because the different stages of mourning are not described. Although the original sentence is short and concise, it is too literal and does not accurately describe her emotional state. Eliminate Choices (H) and (J).
23. C Because the first half of the sentence is an incomplete thought, the underlined portion must include a subject to make the second half a complete thought, eliminating choices (A) and (D). Choice (C) uses the present tense of the verb, which fits better in the context of the story than the present perfect tense in choice (B).
24. G Choice (G) is correct, because the phrase does clarify why the writer stops crying in the first half of the sentence. There is no evidence to support a strained roommate relationship, so choice (F) is incorrect. Choice (H) is incorrect because the phrase does not show that the writer is right to feel sad. The phrase does give new understanding into what the author is thinking and feeling, so choice (J) is incorrect.
25. D Choices (A), (B), and (C) imply that the writer hears her roommate crying because she is surprised, which is not the intended meaning. The writer is surprised to hear her roommate cry, making choice (D) correct.
26. H The conjunction and is not the correct link between the incomplete thought Curiosity overwhelming me and the complete second half the sentence, eliminating choices (F) and (G). Choice (J) is incorrect because a period cannot come after an incomplete thought.
27. B Choice (B) is the only transition listed that suggests a quick, unexpected reaction from the roommate. Choices (A), (C), and (D) all indicate that some time passes before the roommate responds.
28. F Choice (F) is the only appropriate verb that is consistent in meaning with the description of the roommate as shaken up and surprised by the presence of the writer. Choice (G) means to state confidently, choice (H) means to use another person’s words, and choice (J) means to yell loudly.
29. D Choice (D) both captures the roommate’s emotion and explains why the writer responds by suggesting they adjust to college life together. Choices (A) and (B) are not consistent with the writer’s response. Choice (C) completely disagrees with the emotions of both the writer and the roommate.
30. F The passage is a personal account of the writer, a first-time college student who is worried after moving away from home, and of the writer’s roommate, who feels similar emotions. Thus, choice (F) is the best answer.
31. B Choice (B) is the best answer here because the analogy provides vivid detail. The reasons provided in choices (A), (C), and (D) are not compelling.
32. J The phrase if murky is unnecessary information, so it should be offset by commas. Thus choice (J) is correct. Choice (G) has no pauses to offset this information, which confuses the flow of the sentence. Choices (F) and (H) create sentence fragments.
33. A The phrase clarifies the term anyone by describing the kind of people who should try canyoning, so choice (A) is correct. Choice (B) is incorrect because the paragraph focuses on canyoning, not people. Choice (C) is extreme and not logical. Choice (D) is incorrect because the phrase does not confuse the focus of the sentence in any way.
34. F The word river ends a complete thought, and the word without begins a second complete thought. Choice (F) correctly uses a comma with a coordinating conjunction to link two complete thoughts. Choices (G), (H), and (J) create run-on sentences and do not provide proper punctuation to link two complete thoughts.
35. D Choice (D) is the most concise answer that conveys the correct meaning. Choices (A), (B), and (C) are wordy and unclear.
36. G Because A remarkable activity in its own right is a modifier, the activity—skydiving—must be named immediately after the modifier. Thus, choices (F) and (J) are wrong. Choice (H) omits the sentence’s verb and also treats skydiving as unnecessary information by setting it off with commas. Choice (G) is the answer.
37. A Choice (A) is correct because the statement describes an additional thrilling activity in an exotic location, which is the focus of this paragraph. Choice (B) does not correctly describe the main idea of the paragraph. Choice (C) is incorrect because the locations and activities are different in each scenario, not just this one. Choice (D) is too narrowly focused and strays from the main idea.
38. H The phrase because of which was our most exhilarating adventure yet is intended to describe (modify) canyoning. Thus, the phrase should begin with the word which, as in choice (H). The remaining answer choices are unclear and create fragments.
39. D The word walls ends a complete thought, and the word we begins a second complete thought. Choice (D) correctly uses a comma with a coordinating conjunction to link two complete thoughts. Choices (A), (B), and (C) create run-on sentences and do not provide proper punctuation to link two complete thoughts.
40. G Choice (G) is the most concise answer that conveys the correct meaning, since leaping naturally implies a following descent. Choices (F), (H), and (J) are redundant.
41. C The subject of the sentence is the word danger, so its verb must be singular to agree with it, as with choice (C). Choice (A) contains a plural form of the verb, so it does not agree with the subject. Choice (B) contains a future tense, so it does not agree with the past tense of this sentence and of the passage. Choice (D) uses a gerund form incorrectly.
42. G A clear distinction between water and land activities is made in this paragraph, so choice (G) best clarifies this distinction with its mention of rocky surfaces and chilly water. Choices (F), (H), and (J) do not address the distinction at all.
43. A The word thrills begins a complete thought that switches the direction of the sentence, so an opposite direction conjunction is necessary at the beginning of the thought preceding it. Choice (A) provides the correct conjunction. Choices (C) and (D) are adverbs that indicate the ideas are going in the same direction, so you can eliminate those choices.
44. F The essay focuses on the enjoyment of thrills, so choice (F) is correct. Choices (G) and (H) do not mention thrills at all. Choice (J) mentions thrills but with a tone opposite to that of the entire essay.
45. C The best location for Paragraph 2 is before Paragraph 4, choice (C), because Paragraph 3 introduces the activity of canyoning discussed in the first sentence of Paragraph 2. There is also a logical sequence from the introduction and description of the river in Paragraph 2 to its navigation in the beginning of Paragraph 5.
46. G Note that the subject of this sentence—Mexican-American War—is singular. Don’t be thrown off by the words conflicts and compromises, which, although closer to the verb, are not the main subjects of the sentence. Since Mexican-American War is singular, you can eliminate choices (F) and (H), and (J) creates a sentence fragment. Only choice (G) works.
47. A Two main things are changing in the answer choices here. First, the verb in the sentence changes from the present include to the past included, but this sentence discusses the Mexican-American War as being overlooked in the present (and note the mention of the current shape and culture in the following sentence), so you’ll want to keep include. Moreover, if you’re going to use a colon (:), you must have, at the very least, a complete idea before it, which you do not in this case.
48. J Choices (F) and (H) break the flow of the sentence unnecessarily, so they can be eliminated easily, but to determine whether you need the commas around the phrase to American arts, determine whether the sentence makes sense without this piece of information. As you can see, without this phrase, the word contributions is not clearly defined in the text. Accordingly, to American arts is an essential part of the sentence and should not be set off by commas.
49. D Choices (A), (B), and (C) are all rewriting the same sentence—only choice (D) gives a completely different option. If you check (D) first, you can save yourself a lot of work. In this case, you can DELETE this sentence because it is inappropriately placed in the paragraph. While Mexican-American musicians are mentioned earlier in the paragraph, the previous sentence represents an important transition to the following paragraphs discussing Mexican-American authors.
50. G To determine whether or not a selection should be set off by commas as María Amparo Ruiz de Burton is in this sentence, see if the sentence makes sense without that selection. In this case, it does not make sense to say, A major landmark in early Mexican-American literature came in 1885, when author published her first novel…The author’s name is an essential part of this sentence and so cannot be set off by commas.
51. C Choices (A) and (D) are out, because neither is indicated elsewhere in the passage. (B) is deceptive—the paragraph says this novel was the first to be written in English by an author of Mexican descent, not that it was the first by a Mexican author to be read in the United States. Only choice (C) captures the historical importance of the novel having been the first written in English by an author of Mexican descent.
52. J Since all of these answer choices ultimately say the same thing, pick the most concise answer that preserves the meaning of the original sentence. This definitely eliminates choices (F) and (H), and while choice (G) seems similar in length to choice (J), choice (G) is unclear and awkward in its construction, not least because give a glimpse at is idiomatically incorrect.
53. B Because A family of landed gentry living in San Diego is a modifier, the family—the Alamars—must be named immediately after the modifier. Thus, choices (A), (C), and (D) are wrong, and choice (B) is the answer.
54. F The sentence discusses a single event that took place during the Mexican-American War, so choice (H), which implies that the event was continuous, must be eliminated. Choices (G) and (J) alter the meaning of the sentence and are idiomatically incorrect. Only choice (F) works appropriately.
55. C Choices (A), (B), and (D) all create sentence fragments. Only choice (C) contains a verb, was, that can make this sentence complete.
56. H You need to determine here whether the sentence should be added to or kept out of the paragraph. If you’re not sure whether to answer Yes or No, look at the reasons in each answer choice. Choice (F) can’t work because the sentence discusses individuals of French descent, and there is no indication that the writer is drawing any kind of parallel between individuals of French descent and those of Mexican descent. Choice (G) can’t work because the sentence does not give any indication that it is meant to be connected to The Squatter and the Don. Choice (J) can’t work because the reaction of Mexican-Americans to the Louisiana Purchase is never discussed. Only choice (H) indicates that the sentence does not provide information relevant to this paragraph.
57. D In EXCEPT/LEAST/NOT questions, the underlined portion of the sentence is correct. In this case, the words in choices (A), (B), and (C)—investigate, examine, and look into—are all roughly synonyms for explore. Choice (D), solve, has a meaning different than explore and its synonyms and changes the meaning of the sentence. Thus, choice (D) is the LEAST acceptable solution and the correct answer to this question.
58. H Choices (G) and (J) are both idiomatically incorrect and change the meaning of the sentence, so all you really need to decide is whether to use the relative pronoun that or those. To determine this, find which word or words the pronoun will be replacing. In this case, the word replaced is writings, a plural noun, which can be replaced only by the plural pronoun those.
59. B Sentence 3 introduces other authors for the first time in the passage. Sentences 1 and 2 provide examples of two other authors who are important. Therefore, Sentence 3 must come before Sentence 1. Choice (B) is correct.
60. F Because all four answer choices have the same meaning, select the most clear and concise. Choice (F) is the most clear and concise.
61. D Note the context of this sentence. The underlined portion ends a portion of the sentence that should be set off by commas—typically cited alongside Walter Gropius and Le Corbusier as a pioneer of modern architecture, so you can eliminate choices (A) and (B). The word being, as in choice (C), creates a sentence fragment, so the best answer is choice (D).
62. H Note the other verb in this sentence, sought. Since this is in the past tense, the other verbs in this sentence must be in the past tense. For the underlined portion, only choices (H) and (J) are written in the past tense, and choice (J) creates a sentence fragment with its use of the relative pronoun who.
63. B The easiest answer to eliminate is choice (D), as the semicolon would improperly separate two incomplete ideas. The phrase based on van der Rohe’s designs is a necessary part of the sentence, so it should not be set off by commas. Likewise, it is not part of an introductory clause, so it should not be followed by a comma. Choice (B) correctly omits any commas.
64. J In EXCEPT/LEAST/NOT questions, the underlined portion of the sentence is correct. Choice (J) is NOT acceptable, because it changes the meaning of the sentence by suggesting that something is being made into steel and glass, when in fact the buildings are constructed out of steel and glass.
65. A The phrase that is is an introductory clause and therefore is properly followed by a comma. The part of the sentence after the dash serves to elaborate upon the sentence’s earlier mention of the materials, and that is (an idiomatically shortened form of that is to say) functions in the same way that expressions like for example or in this case might in another sentence.
66. J Of the choices available here, only the colon is appropriate. The latter part of the sentence gives an example of one of the problems mentioned earlier in the passage. Accordingly, only choice (J) can be appropriate. Also note, when using a colon, make sure there is a complete sentence before it as there is in choice (J).
67. C Choices (A) and (B) don’t directly discuss the visual elements of the buildings, merely how long they took to construct or their historical importance. Choice (D) gets closer by mentioning that the buildings are on display in various cities, but only choice (C) really discusses the buildings’ visual appeal in its description of the buildings’ complex beauty.
68. F The easiest answer to eliminate is choice (H), as the semicolon would improperly separate two incomplete ideas. Because the phrase under teacher Peter Behrens’s guidance is unnecessary to the sentence as a whole, it should be set off by commas. Therefore, choice (F) is correct. Choice (J) is wrong because it eliminates the comma needed at the end of an unnecessary phrase and it incorrectly inserts a comma after teacher. Choice (G) is wrong because, while the entire phrase as a whole may be unnecessary, Peter Behrens’s guidance is a necessary part of the phrase, so the comma following teacher is inappropriate.
69. B In the sentence as written, it is unclear what the pronoun This refers to, so to fix this pronoun ambiguity, you’ll need a substitute that is more specific. Choices (C) and (D) are no more specific than is (A); only choice (B) fixes the problem by giving a specific subject.
70. J First, consider whether the last sentence of the paragraph provides a contrast to or a continuation of the prior sentence. Both sentences concern van der Rohe’s development of a new style, so contrasting choices (F) and (G) are wrong. Choice (H) is wrong because it would transform an incomplete sentence followed by a comma and a complete sentence into two complete sentences separated by a comma. Choice (J) is grammatically correct and clear.
71. B Since this sentence refers to an event that occurred in 1937, the sentence must be in the past tense (note, also, that the other sentences in the paragraph are in the past tense). Only choices (A) and (B) satisfy this condition, but (A) creates a sentence fragment by introducing the relative pronoun who.
72. H In EXCEPT/LEAST/NOT questions, the underlined portion of the sentence is correct. Choices (F), (G), and (J) all preserve the meaning of the original sentence. Choice (H) changes the meaning of the sentence and, moreover, contains a pronoun, this, that does not refer to any noun. Choice (H) is thus NOT an acceptable substitution.
73. C Choices (A) and (D) create a misplaced modifier—since van der Rohe comes directly after the introductory phrase, the introductory phrase must properly refer to van der Rohe, and must be modifying this subject in some way. The word while in choice (B) suggests that a contradiction will come later in the sentence, but none does. Only choice (C) functions properly to modify the actions of van der Rohe.
74. F Since all the answer choices are roughly synonymous, choose the most concise that preserves the meaning. Choices (G), (H), and (J) all contain some redundancy and do not contain any essential information beyond the word enthusiastic.
75. B Look for clues in Sentence 3 that might give you some hints as to its proper placement. The main clue is the word there, which suggests that a previous sentence will contain some mention of a place. Sentence 2 discusses the Illinois Institute of Technology, but look closely, the end of Sentence 3 indicates that this is one of the commissions awaiting him there, so we still don’t have a clear idea of what there is. In Sentence 1, however, you see that the architect is discussed as moving from Germany to the United States, so Sentence 3 should clearly be placed after Sentence 1 because the there in this situation clearly refers to the United States.
TEST 2 MATH EXPLANATIONS
1. E Use Process of Elimination aggressively. Since Violet has 10 cherries, she uses three times 10 = 30 blackberries, eliminating choices (A), (B), and (D). Thus, she also uses 30 raspberries and twice 30 = 60 blueberries. Choice (C) lists 2 rather than 2 × 30 for the number of blueberries.
2. H Expand the equation with FOIL (first, outside, inside, last): (3x)(x) + (3x)(2) + (−5)(x) + (−5)(2) = 3x2 + 6x + (−5x) + (−10). Combine the middle terms to get the simplified expression 3x2 + x − 10. Choices (G), (J), and (K) are the results of confusing the signs. Choice (F) only multiplies the first terms and the last terms, which is not the correct way to multiply binomials.
3. B Substitute 8 and 6 for x and y, respectively, into the equation f(x,y), to get f(8,6) = 8 − [(8 × 6) − 6] = 8 − 42 = − 34. Choices (A), (C), (D), and (E) are wrong because they do not distribute the negative correctly.
4. G 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 equation is x×8,000. So, x = 320. Choice (H) is 7××8,000, a common fraction mistake.
5. C When you have numbers in the answer choices and variables in the question, you can plug the answer choices into the variables in the question to find out which answer choice makes the equation true. Start with answer choice (C) when plugging in the answer choices because it is the middle value and will sometimes tell you whether you need a bigger or smaller number if answer choice (C) is not the correct answer. Does 6(3) + 3 = 12 + 3(3), or, 21 = 21? Yes, and you’re done!
6. F First, calculate the difference of the third and second terms: 8 – (−2) = 10. The first term, therefore, is the second term minus the difference: (−2) − 10 = −12. Choices (G) and (K) are variations of the actual common difference, rather than the value of the first term. Choice (H) calculates the first term in a geometric, rather than arithmetic, sequence. Choice (J) incorrectly calculates −2 as the first term, rather than the second.
7. C Probability is equal to . If you find a common denominator between the two probabilities, you can determine the number of unfavorable outcomes. The least common denominator between and is 9. The probability that the jellybean is NOT pink is , so the probability that the jellybean is pink is . Now, multiply by the total number of jellybeans, 72, to find the bag contains 32 pink jellybeans, choice (C).
8. G Because the flat rate of $100 includes the first two months, Bob will be billed $60/month for only 10 months out of the year. The total cost is $100 + $60 (10) = $700, so choice (G) is correct. Choice (F) results if you incorrectly charge $100 for every two-month period. The flat rate applies only for the first two months. Choice (H) calculates the total without the flat rate. Choice (J) incorrectly charges the flat rate twice for the first two months. Choice (K) adds 12, rather than 10, months of service charges to the flat rate.
9. C If one side of the pentagon measures 20 inches, the perimeter of the pentagon is 100 inches (20 × 5). Because the pentagon and the square have the same perimeter, the square also has a perimeter of 100 inches. Each side of the square is then 25 inches (100 ÷ 4). Choice (E) is wrong because it is equal to the perimeter of both the square and the pentagon, which is not what the question asks for. Choices (A), (B), and (D) give a perimeter that is not equal to our target of 100 inches.
10. F Translate the words into an equation, making x the number of bricks. Contractor A charges $1,600 plus $2 times the number of bricks, 1,600 + 2x. Contractor B charges $400 plus $8 times the number of bricks, 400 + 8x. Set the expressions equal to each other to get 1,600 + 2x = 400 + 8x. Choice (G) sets each contractor’s flat rate plus the other contractor’s per brick charge equal. Choice (H) sets the sum of each contractor’s per brick charges and the number of bricks equal. Choices (J) and (K) set the per brick charges equal to Contractor A’s and B’s flat rates, respectively.
11. D Solve for B. Divide both sides of the equation by ACD to get B = .
12. H You need to remember some things about angles and lines: A straight line, in this case WVZ, measures 180°, and XVY measures 90° because it is marked as a right angle. The sum of the measures of WVX and YVZ = 180°− 90° = 90°. Since WVX and YVZ measure 4a and 2a respectively, 6a = 90° so a = 15°. Therefore, YVZ = 30° and XVY = 90° + 30° = 120°. Choice (F) is the value of YVZ. Choice (J) is the sum of WVX and WVY. Choice (K) is too big because we know that VVZ is not a straight line.
13. B First find the temperature of New Orleans in °F by adding 25°F to 70°F to get 95°F. Your answer choices give you different values of °C. You can start with the middle answer choice, 68°C, and substitute this value for C in the equation to see if you get 95°F. Choice (C) gives (68)+32=154 °F. Since this value is too large, you can eliminate choices (C), (D), and (E). Choice (B) gives (35)+32=95°F.
14. G The factored form of the expression is 2(3x + 2y) − 7, so you can substitute 5 for 3x + 2y to get 2(5) − 7 = 3. Choice (F) results if you forget to multiply 3x + 2y by 2, and choice (J) forgets to subtract 7. Choices (H) and (K) incorrectly use the coefficients of x and y to determine the value.
15. B The total amount of beef in pounds would be . This number falls in the range “At least and less than .” Choices (A), (C), (D), and (E) are incorrect because does not fall within those ranges.
16. H Draw a picture. Since Dave went directly east and then directly south, the distance to his house can be found using a right triangle. The distance is d = . Careful not to select choice (K), which is the sum of the two legs of the triangle!
17. B The rate at which the sensor records—1 piece of data every .0000000038 seconds, or —is constant, and therefore the ratio of pieces of data recorded per second will be equal for any given number of pieces of data or seconds. Set equal to the ratio 100,000,000,000 pieces of data every x seconds: . Solve for x by multiplying diagonally across the equation: x × 1 = 100,000,000,000 × .0000000038. x = 380.
18. J Use the answers: Since the width and length are reduced by the same amount, you can eliminate any that do not use the same difference between original and new dimensions, choices (F), (H), and (K). Then, calculate the original area of the photograph: A = l × w = 20 × 30 = 600cm2. The final area of the photo, therefore, equals 600 − 264 = 336 cm2. Choice (G) gives you 12 × 22 = 264 cm2. The correct answer is choice (J), 14 × 24 = 336.
19. C The perimeter is the sum of all 4 side lengths of the quadrilateral. The answer choices give you the length of the shortest side, so you can work backwards by adding the three larger consecutive even numbers to each answer choice. You can immediately eliminate choice (D) because 7 is not an even number. Choice (C) correctly gives you 6 + 8 + 10 + 12 = 36. Choices (A), (B), and (E) do not give you a sum of 36.
20. G Rearrange the equation into the slope-intercept form, y = mx + b. The resulting equation is y = x + 3, with slope m of . Choice (F) confuses the signs. Choice (H) results if you rearrange the equation into “x =” form, which does not indicate slope. Choice (J) is the y-intercept of the line.
21. C To find the area of the trapezoid BCEF, subtract the area of triangle CDE from rectangle BDEF. The area of rectangle BDEF is 36 square feet (9 × 4), and the area of triangle CDE is 10 square feet [(5 × 4) ÷ 2]; therefore, the area of the trapezoid BCEF is 26 square feet (36 − 10). Choice (A) is incorrect because it finds the area of the square with sides BC and BF. Choice (D) is incorrect because it is only solving for the area of the rectangle BDEF.
22. G Make sure you read the given information carefully. You don’t have to do any figuring aside from approximating because all the other values are given to you. Because ≈ 11.7, to find the perimeter, simply add the sides: 11.7 + 10 + 6 + 12 = 39.7. If you chose (F), you may have forgotten to include the diagonal in your calculation. If you chose (J), you did too much work—this is the area!
23. E Use the Pythagorean theorem a2 + b2 = c2. Since = 10 and = 6, (10)2 + (6)2 = , and = . If you chose (B), you may have confused this with a 6:8:10 triangle, but be careful— and are just the legs in this triangle. If this were a 6:8:10 triangle, the longest side would have to be 10. Also note, that because point J shares a y-coordinate with the midpoint of , = .
24. F Since the graph is rotating clockwise, the point will be moving 90° and will have a new point on the x-axis. Any point on the x-axis must have a y-coordinate of 0, so you can eliminate choices (G) and (J) immediately. If you chose choice (K), be careful—you may have rotated the graph in a counterclockwise direction rather than a clockwise direction.
25. C A geometric figure has rotational symmetry if it looks the same after a certain amount of rotation. A geometric figure has reflectional symmetry when one half is the reflection of the other half. Choice (C) is the only figure that has rotational and reflectional symmetry.
26. K Expand the equation with FOIL (first, inside, outside, last) and you will see that only the first term in each polynomial has exponents that add together to become x8: – x4 · 5x4 = −5x8. Choice (F) wrongly assumes the absence of a x8 term. Choice (G) confuses the sign; choice (H) incorrectly adds the coefficients; choice (J) multiplies the wrong terms.
27. D To find the mean, add up all the scores: 66 + 67 + 71 + 72 + 72 + 73 + 75 + 77 + 79 + 82 + 83 + 83 + 87 = 987. Divide this number by the total number of scores, 13, to find ≈ 75.9. If you selected choice (C), be careful—this is the median. If you chose (B), you may have taken the means of the stems and leaves separately and added them together.
28. F To find the probability, determine the number of desirable outcomes divided by the number of total possible outcomes. Since you want a score of exactly 83, go to the stem-and-leaf plot to see that two of the golfers had a score of 83. Since there were 13 total golfers, the probability that an 83 would be selected out of the whole group is . If you chose either choices (J) or (K), be careful—this question is asking about the probability of selecting a certain score; the actual numerical value of that score is not relevant.
29. B First, factor each number. In this problem, the given numbers are all products of 2, 3, a, and b. To find the lowest common multiple of the given values, you need to figure out the maximum number of times each component (2, 3, a, and b) appears in any one of our given values. 8 = 2 × 2 × 2, so the lowest common multiple must have 2 × 2 × 2 as a factor. No value has more than one factor of 3, so our number is only required to have one factor of 3. Finally, our least common multiple must have one a and one b. Multiply the mandatory factors together, 2 × 2 × 2 × 3 × a × b, to get 24ab.
30. J To solve for the function, you need to determine the value of m in December. Since December is 7 months after May and m = 0 in May, m = 7 in December. Substitute 7 for m in the function to get A(7) = 2(7) + 2, so Aleksandra will have 16 model airplanes. Choice (F) is the number of airplanes she had in May. Choices (G), (H), and (K) result if you use the wrong value of m for December.
31. E The midpoint of a line is . Thus, the x-coordinate of the midpoint = = 4, eliminating choices (A), (B), (C), and (D). The only remaining choice is (E), which also has the correct y-coordinate = = −1. Be careful not to subtract x2 from x1, which would give you an x-coordinate of 7. Choices (A) and (B) merely add or subtract the x- and y-coordinates, rather than finding their averages.
32. K Factor the numerator and denominator separately: . The factor (x − 4) on both the top and the bottom of the fraction cancel each other out, so you’re left with choice (K). Choices (F), (G), and (H) are all the result of incorrectly canceling out terms without factoring. Choice (J) cancels both factors from the numerator, which is not possible with only one (x − 4) in the denominator.
33. B If Evan purchased 6 boxes, with 10 bags in each box, and 12 cookies in each bag, he will have purchased 720 cookies (6 × 10 × 12). Dividing 720 by 30 will give us the number of family packs with 30 cookies that he could have purchased instead. 720 ÷ 30 = 24. Choices (A), (B), (C), and (E) are wrong because they do not result in the target amount of total cookies.
34. F If , then s = −2r. Substitute −2r for s in the given expression: 16r4 − (−2r)4 = 16r4 − 16r4 = 0. If you selected choice (H) you may have made a sign error.
35. A Because the nine circles fit into the square “as shown,” quickly estimate the area that remains to eliminate any answer choices that couldn’t possibly be correct. Roughly, it appears that of the square remains. Since the total area of the square is 144 square inches, and 144 ÷ 4 = 36, choices (C), (D), and (E) are out because they are too big. Choice (A) is slightly closer to our estimate than answer choice (B), but if you have time, do the math. Since the circles are identical and are tangent to all adjacent circles and to the edges, the diameter of any circle must be of a 12-inch side, or 4 inches, and the radius of any circle must be 2. The area of each circle is × the radius squared, or 3.14 × 4, or 12.56. Multiply 12.56 square inches by 9 cookie cut-outs to get 113.04 square inches cut out, and 30.96 square inches remaining. You can also make this problem fast if you know that the area of a circle inscribed in a square is always equal to × the area of the square, and can see that the area remaining in each of the small squares is proportional to the area remaining in the big square. 144 − ( × 144) = 30.9.
36. J Use the answer choices and Process of Elimination. Remember that a prime number has only two distinct factors, itself and 1. 63 is divisible by 3, 7, 9, and 21, eliminating choice (F). 91 is divisible by 7 and 13, eliminating choices (G) and (H). 81 is divisible by 3, 9, and 27, eliminating choice (K).
37. C First determine the cost per quarter hour using the rate formula: rate = . Pick two different packages: to find the rate that is $15 per quarter-hour. Now use the 8 quarter-hour package: fixed cost + $15 × 8 = $2000 to find that the fixed cost is $80. Choice (B) finds the rate for the 10-quarter-hour package without a fixed cost. Choice (D) is a partial answer.
38. K Because you know the height of the building opposite the angle and want to find the shadow length adjacent the angle, use SOHCAHTOA: tan(45°) = 1 = , thus x = 100/tan 34° ≈ 100/0.67 ≈ 148. Choices (F), (H), and (J) are the result if you use the wrong trigonometric function. Choice (G) is the result if you incorrectly set up tan θ = .
39. E The general equation for a circle with center (h, k) and radius r, is (x − h)2 + (y − k)2 = r2. Because h = 4, k = −3, and r = 12, the equation for this circle is (x − 4)2 + (y + 3)2 = 144. Choices (A), (B), and (C) are incorrect because they do not square r. Choice (D) is incorrect because it does not distribute the negative in the (y − k)2 term.
40. H Use your calculator to make the comparisons easier:. Now, test the answers. Choice (F) is , which is less than and choice (G) is which makes the two fractions equal. Choice (H) is which makes the inequality true. Choices (J) and (K) also make the inequality true but neither is the least integer that makes the inequality true.
41. E Substitute (a + b) for a. Square the quantity (a + b), distribute the 2 within (a + b) by multiplying a and b both by 2, and add 5.
42. G Since lines and are parallel, NMO ≅ NLP and NOM ≅ NPL. Thus, MNO and LNP are similar triangles with congruent angles and proportional sides. To find the length of , set up a proportion: . Using x for , solve for x:. = 91 feet. Choice (F) gives the length of . Choice (K) is the sum of the three side lengths.
43. C First, convert 2 miles to feet, 2 miles× because height, h, is given in feet in the equation. Now, substitute the answer choices for the value of t to see which choice equals 10,560 feet. Choice (C) gives you: 1,200+32(293)=10,576. The precise answer is 292.5 seconds, but the question asked for the nearest second.
44. J The three angles of a triangle will always equal 180°, so 2x + 3x + 5x = 180. Since C = 5x and x = 18°, C = 5(18°) = 90. Choices (F) and (K) are partial answers. Choices (G) and (H) give the measures for the wrong angles.
45. B If the basketball player made 12 out of his 30 shots, he currently has a free-throw percentage of 40%. Use the answers to calculate the least number of additional free throws he must make. Make sure you add the number to both the numerator and denomination, since any addition free throws are both attempted and made. Choice (B) gives you × 100 = 55%. Choice (A) is the result of adding 5 only to the numerator. Choices (C) and (D) approximate 55% to 56% of 30 free throws. Choice (E) incorrectly raises the percentage by 55% rather than to 55%.
46. H Pick a number in the provided range and try out the answers. If y = −2, choices (F), (G), and (J) yield positive results. Choice (H) is approximately −, which is less than the result of choice (K), −.
47. C Draw five placeholders for the positions of each of the 5 groomsmen: __________________. How many groomsmen could possibly walk in the first position? Five. Write a 5 in the 1st position. Next, if one groomsman takes the first position, how many possible groomsmen are left to take the second position? Four. Write a 4 in the second position, and multiply the 5 possibilities for the first position by the 4 possibilities for the second position (each of the 5 possible groomsmen in the 1st position could be with 4 different other groomsmen in the 2nd position). After another of the groomsmen is chosen for the 2nd position, there are 3 possible groomsmen for the 3rd position, then 2 possible groomsmen for the 4th position, and finally only 1 possible groomsman for the 5th position. 5 × 4 × 3 × 2 × 1 = 120 total possible orderings.
48. J As with all circle problems, it is helpful to first calculate and draw the radius. Given the area of the circle is 169π square inches, use the area formula: A = 169π = πr2, so r = 13. Radii and form two right triangles with chord , so you can use the Pythagorean theorem to find the length of the two missing legs: 52 + b2 = 132, so b = 12. The length of the chord is 2 × 12 = 24 inches. Choice (F) gives only half the length of the chord. Choices (G) and (K) give the radius and diameter of the circle, rather than the chord. Choice (H) is the sum of 5 and 13, which is not the correct operation to calculate lengths of a right triangle.
49. A The x-intercept occurs where y = 0, eliminating choices (B), (C), and (D). Next, find the slope of the line: , or −. The line to the x-intercept must have the same slope. The slope between choice (A) and (−3,7) is . Careful not to select choice (C), which is the y-intercept.
50. G Intercepting the x axis at x = 7 means the equation must satisfy the coordinate (7,0). The only equation that does this is choice (G). Choices (F) and (H) incorrectly give x-intercepts at (−7,0). Choice (J) gives the y-intercept at y = 7, and choice (K) gives the y-intercept at (0,−7).
51. A If the tan θ = , the side opposite to θ is 2, and the side adjacent is 9. Therefore the hypotenuse is , so cos θ = and sin θ = . cos θ + sin θ = .
52. G Triangle OAB is equilateral since OA and OB are both radii of the circle and OA = AB. The formula for the area of a triangle is A=bh. The base of OAB is 8. To find the height of OAB, draw a line from A that is perpendicular to OB, creating two 30°-60°-90° triangles. Using the relationship a:a, the height of OAB is 4. So, A=(8)(4)=16. Choice (F) uses 4 for the base. If you chose (J), you probably forgot the in the area formula. Choice (H) uses 8 for both the base and the height of the triangle.
53. C Use the formula given and replace variables with values from the diagram. You will also need to find the degree measure of angle Z, since the problem asks for the length of the side opposite Z. Given that there are 180° in a triangle, subtract 105° and 40° from 180° to get 35° for angle Z. Now Plug In all of the information in the equation: . Solve for z by multiplying both sides by z and by 30 to get: z sin 40° = 30 sin 35°. Divide both sides by sin 40°.
54. G To find arc length, use a ratio of . Since the radius is 9 ft., the circumference is C = 2π(9) = 18π. Now, fill known values into the ratio: . Cross-multiply and solve to find the length of the arc is 6π. Choice (J) is a partial answer that gives the circumference rather than arc length. Choice (K) is the sector’s area, rather than arc length.
55. C In order to subtract these matrices, you must combine the corresponding elements from each matrix. That is, you subtract the first row, first column numbers in the second and third matrices from the first row, first column number in the first matrix. Thus, the matrix , choice (C), is the best answer. Choices (A), (B), and (E) all improperly subtract fractions and integers. Choice (D) uses multiplication rather than subtraction.
56. K To deal with compound functions, the trick is to work inside out. First, determine the value of the inside f(1) = −2(1)3 = −2. The value of f(1) becomes the new x-value for the outside f function, so determine f(−2) = −2(−2)3 = −2(−8) = 16. Remember that a negative number raised to an odd integer stays negative; thus choices (F) and (G) are wrong because they confuse the signs. Choice (H) is the value of –x3, rather than –2x3. Choice (H) is the result of multiplying f(x) by f(x), which is not the same operation as compound functions.
57. A If a function y varies directly with x, this means that as x increases, y increases proportionally, eliminating choices (B) and (D). This proportionality means that the function must be a straight line, eliminating choice (E), with the equation y = kx, where k is a constant. This line must then pass through the origin, because if x = 0, then y = 0. Choices (C) is incorrect because it does not pass through the origin.
58. K If the quiz scores are listed from lowest to highest, the middle score, the median, is 9. The two highest scores are both 10. Since the only mode of the quiz scores is 10, the remaining two scores must be distinct integers. The mean of the 5 scores is 8, so the sum of the five scores is 8 × 5 = 40. The sum of the two lowest scores must be 40 − (9 + 10 + 10) = 11. Choices (F), (G) and (H) could be true because the quiz scores could be (3, 8, 9, 10, 10), (4, 7, 9, 10, 10), or (5, 6, 9, 10, 10). Choice (J) is the number of scores multiplied by the mode.
59. E First, draw a picture and fill in as much information as you can from the problem. Two opposite sides of the cardboard are 60 inches, and two opposite sides are 40 inches. Since you’re looking for the height of the table and the answer choices are numbers, not variables, representing the height of the table, use the answer choices to fill in the diagram further. Try labeling the height of the table starting with choice (C), the middle value. Given that the width of the cardboard is 40 inches, a height of 25 inches on either side of the tabletop is not possible—50 inches is greater than the size of the paper. Try the next smallest number, 20 inches, in choice (D). 20 inches is too big: If the paper table were 20 inches tall on either side, the top of the table would be a line. Choice (E), 10 inches, must be the correct answer.
60. H To find the area of a triangle, use the formula Abase × height. You already know the base is 10, but you need to find the height. Draw a line from point B that is perpendicular to line . Use SOHCAHTOA: sin 35° = , so the height of this triangle is 10sin 35°. The area is A = (10)(10sin 35°) = 50 sin 35°. Choices (F), (G), and (H) use the wrong trigonometric functions. Choice (K) does not take the product of and .
TEST 2 READING EXPLANATIONS
1. A The use of the word stultifying refers to the boy’s experience of life on his family’s farm; later in the sentence, the passage tells us that the boy felt landlocked by this life, so something like trapped would fit well. Therefore, you can eliminate choices (B) and (C), because strengthening and welcoming don’t match this description. Choice (D) is incorrect because nothing in the passage implies productivity.
2. G Line 20 shows that the boy had only heard about but never seen fireworks. Line 7 shows that the boy has companions who lead him through the jungle, so choice (F) is incorrect; line 55 implies that the boy respects the captain’s knowledge, so Choice (H) can be eliminated. Line 25 shows that memories of the storm often intruded in the boy’s thoughts, so choice (J) doesn’t work.
3. D Line 30 refers to the boy’s second home on the ocean, the idea presented in choice (D). Line 3 refers to the jungle as inhospitable and mentions the snarling vines in the jungle, making choice (A) incorrect; choice (B) is incorrect because the passage portrays the boy’s mother only as frail and worn-looking (line 35), not frightening; and choice (C) is incorrect because the passage doesn’t note that the boy feels positive about any aspect of farm life.
4. F This choice is correct because the passage about the boy leaving the farm is a flashback, as shown in line 44. Choice (G) is incorrect because the boy is remembering his past life while he continues to walk through the jungle; choice (H) doesn’t work because the boy meets the captain and sets sail before the captain is killed and the ship is destroyed in the wreck; choice (J) is incorrect because his parents create a home for him (line 36) on the farm, before he goes off to sea.
5. C This choice is correct because the boy follows his question about what the phrase means with an acknowledgment that he can’t distinguish the captain from the other men in his mind (lines 63−67). Choice (A) is incorrect because the passage up to this point has shown the boy wondering about the meaning behind the captain’s words, implying that the captain hadn’t explained the phrase previously; choice (B) is incorrect because, although the boy wonders what the dead can do earlier in the passage, his thoughts here are focused on the captain; choice (D) is incorrect because there is no indication that the boy’s experiences will lead him to a better life.
6. J Choice (J) is correct because the boy was eager to learn about navigation from the captain, as seen in lines 52−55, and the passage shows us the captain’s dislike of ignorance, which he sees as dangerous (line 51). Choice (F) is incorrect because the boy wonders what the words mean at the beginning and end of the passage (lines 60−70); choice (G) is incorrect because the passage contains no evidence that the captain even knew the boy’s father was worn down; choice (H) is incorrect because the passage contains no evidence about the captain’s view of life at sea.
7. A Choice (A) is correct because lines 61−63 show the crewmates urging the boy (and finally pulling him) away from the scene of the wreck, showing his reluctance to leave. Choice (B) is incorrect because lines 6−7 shows the boy continuing to walk with his companions—no running away here; choice (C) is incorrect because, although lines 10−12 say that unpleasant memories of the storm often filled his thoughts, there is nothing in the passage that describes his reaction to loud noises; choice (D) is incorrect because the passage contains no evidence that the crewmates know about the boy’s feelings about life on the farm.
8. H This choice is correct because the passage shows the captain teaching the boy about navigation (lines 49−51). Choice (F) is incorrect because the passage never describes the captain scolding the boy for stowing away; choice (G) is incorrect because the boy wonders what the phrase means even at the end of the story, as shown in lines 68−70; choice (J) is incorrect because lines 48−56 show the captain paying attention to the boy by teaching him navigation.
9. D This choice is correct because the passage does not mention hail. Thunder is described in lines 20−22, the walls of water are mentioned in line 22, and lightning is described in lines 19−20, making choices (A), (B), and (C) incorrect.
10. F This choice is correct because lines 13−15 shows the unexpectedness of the storm. Choice (G) is incorrect because the passage does not mention the time at which the storm arrived; choice (H) is incorrect because the passage does not mention how the crew responded to the storm; choice (J) is incorrect because the passage does not contain any reference to the boy’s father mentioning a storm.
11. A The however at the beginning of this sentence tells you that Thorne’s comment is in direct contrast to the paragraph that came before, which identified the typical understanding of slang as something that is said in defiant opposition of authority. Choice (A) is most relevant to undermining that generalization. Choices (B) and (C) do not relate to defying authority, and rather they represent Thorne’s attempts to provide counterexamples to the claim that all slang is intended to be against the status quo. Choice (D) is unsupportable anywhere in the passage; it is a trap answer based on the normal association of the contrast between accusing someone of guilt and his/her innocence.
12. G The final paragraph establishes the need to compile a slang dictionary so that people of future eras will have a way to understand our current forms of communication. The details regarding how Thorne’s dictionary will explain each term and the analogy to modern attempts to decipher Shakespearean slang support choice (G). There is nothing critical in tone in this paragraph to support choice (F). The passage does not say that Thorne uses Shakespearean slang in his dictionary as choice (H) states. While the author does agree that a dictionary of slang would be useful to future generations, he does not argue that the project of compiling such a dictionary is the primary goal of modern linguistics as choice (J) states.
13. B Choice (B) is correct because college professors, while possibly involved in the study of slang, are never mentioned in the passage. Choices (A), (C), and (D) are all mentioned in the passage.
14. F The quotation marks around common man highlight the fact that this is a questionable term that is being applied by someone else’s point of view. This paragraph discusses how a word becomes viewed as slang based on a very subjective assessment of the people who use that word. The parallelism of the two sentences tells you that common man must be the opposite of the respectable people mentioned in the previous sentence. Choice (F) correctly relates the derogatory classification of slang to its less respected users. Choice (G) is not supported anywhere in the passage. Choice (H) incorrectly identifies a point of view held by intellectuals who would categorically denounce slang as the author’s own. Choice (J), while related to this paragraph, is too extreme in wording and does not answer the question of the intended effect of adding quotation marks around a certain term.
15. C The context of this sentence tells you that slang is viewed condescendingly and as a signal of intellectual laziness. Choice (C) reinforces these ideas by identifying vulgar speech as containing something (slang) that sophisticated speech would not include. Choices (A), (B), and (D) are all correctly negative in tone but to an unfairly severe and specific degree. Certain uses of slang may be sickening, malicious, or profane, but this sentence is concerned with the way linguists view ALL slang as being uneducated in tone.
16. F According to the final paragraph, Thorne believes that in order for future generations or civilization to be able to decode the meaning contained in all our written artifacts, we need to provide them with a way of understanding our usage of slang. Choice (F) correctly identifies this purpose. Choice (G) suggests the purpose is for foreign language learners, choice (H) suggests the purpose is to write the first-ever slang dictionary, and choice (J) suggests the purpose is to provide a current how-to-use manual of slang. All three are unsupported and do not address the stated need for this sort of resource.
17. C The quote from Whitman describes slang as an attempt to escape from bald literalism, meaning an attempt to find more colorful ways of saying what one means, and as humanity’s attempt to express itself illimitably, meaning to have limitless expression. Choice (C) is a fair paraphrase of those ideas. Choice (A) is irrelevant and unsupportable. Choices (B) and (D) are stated elsewhere in the passage as reasons for slang but not attributable to Whitman or related to his quote.
18. H The first paragraph attempts to make a contrast between unscholarly sounding words and a man of great academic distinction. The rhetorical question at the end of the paragraph attempts to invite the reader’s curiosity as to why these two things would go together. Choice (H) effectively ties the first paragraph’s anecdote to the purpose of the passage as a whole, discussing the academic treatment of slang. Choices (F) and (J) are too narrow in scope, failing to explain the first paragraph’s relation to the passage as a whole. Choice (G) has an extreme claim that British scholars are the leaders, which is unsupported by the passage.
19. C The parallelism of this sentence indicates that while most modern slang comes from groups like corporate office workers, students, and computer users, previously most slang came from groups like the military. In describing groups such as the military as hotbeds of slang, the author is saying that such groups are likely inventors of slang. Choice (C) correctly matches this concept. Choice (A) means to predict the future, which is not supported by the passage. Choices (B) and (D) are unsupportable and make use of the trap language association between traditionally and old-fashioned as well as the military and strict.
20. J The passage indicates that most intellectuals do not completely reject slang because they realize almost all slang initially involves as much inherent creativity as the admired word play of poetry. Choice (J) addresses this detail. Choices (F), (G), and (H) are not supported anywhere in the passage.
21. D The author says his genius is and will continue to be undisputed (lines 93−94), so she does not think it is an overstatement or inadequate to suggest Gaudi’s work is genius, eliminating choices (A) and (B). It is reasonable to assume that the author views the description of Gaudi’s work as freakish genius as a correct interpretation of how current critics and viewers understand his contributions to architecture (choice (D)). Choice (C) is wrong because it is directed only at first-time viewers and is only a suggestion.
22. G The harsh images of Gaudi begging on the street suggest that the 1900s (choice (G)) were a time of great need, and when funders were least likely to fund construction. The passage also says, financial contributions for the church’s construction fizzled out completely around the turn of the century. Choice (F) is incorrect because Gaudi began construction in the 1880s and there was “significant funding.” The progress of the 1950s, choice (H) is due to increases in funding and construction picked up in the 1980s because of steady donations to fund that work, choice (J).
23. A The passage says that the Sagrada Familia stands apart from the rest of the world’s cathedrals because of its unique and startling design (line 4), supporting the claim that it is more remarkable because of its unique appearance and design, choice (A). Choice (B) is incorrect because the passage does not indicate that the Sagrada Familia compares unfavorably to other cathedrals. There is no information in the passage to support choices (C) or (D), and neither is mentioned in comparison to other great cathedrals.
24. F The primary objective of the third paragraph is to tell the reader about Gaudi’s childhood and show that he caused controversy from an early age choice (F). The reference to his family is not the primary point of the paragraph, choice (G). The education of the day was boring and unsatisfying because he was looking for more creativity, so choice (H) and choice (J) take excerpts of the paragraph out of context.
25. A The passage says that Guell funded a wide array of structures, including a mansion, park, and crypt, meaning a wide range choice (B), a broad selection choice (C) or large variety choice (D). Arrangement choice (A) does not capture a similar idea.
26. G In context of the sentence, grumblings refers to the reasons the finished Sagrada Familia may receive criticism, thus choice (G) is the best answer. Choices (F) and (J) are more literal, common usages of the word.
27. A When compared to his contemporaries and artists since his time, Gaudi used controversial methods, developed unique designs, and pioneered his own techniques like trencadis (line 47). Therefore Gaudi was less inhibited, eliminating choice (B), and other contemporaries were more reserved, making choice (A) the best answer. The passage never compares Gaudi’s focus on architectural techniques to that of his peers. Eliminate choices (C) and (D).
28. F The passage says that politicians and architects agreed that the plans Gaudi had left behind were sufficient to achieve his vision and that, therefore, they would continue with the construction (choice (F)). There is no evidence to suggest that viewing the Sagrada Familia in person (choice (G)), the impending civil war (choice (H)), or the popularity of Gaudi’s design (choice (J)) influenced their decision.
29. B The passage says that even at this early age, he engendered controversy (lines 23−24), which supports choice (B). While it is true that Gaudi was able to withstand harsh criticisms (choice (A)), he was unable to complete the Sagrada Familia. His inspiration from Nature also influenced his work (choice (C)), but it not clear when he started using natural inspiration. Moreover, there is no support in the passage that his creations ever blurred the distinction between art and nature—no one mistook his buildings for nature itself. There is also no evidence in the passage to suggest that Gaudi changed his building’s design (choice (D)) according to surroundings or other people’s desires.
30. H In the passage, the discussion of the architecture-as-art includes the statement that functional designs dominated the architectural world for years, suggesting that the most recent generations preferred pragmatic designs, supporting choice (H). There is no mention of historical architecture or modern unconventional designs in the passage, eliminating choices (F) and (G). Choice (J) is also weaker than choice (H), since the passage mentioned functional designs.
31. A Frank Drake is primarily discussed in the first paragraph and briefly mentioned during the conclusion. He is described as the person in charge of Project Ozma, which is in turn called the first organized attempt to detect alien life by way of radio. The correct answer, choice (A), correctly summarizes this information. The project was unsuccessful in its search for alien life, making choice (B) incorrect. Choice (C) confuses Project Ozma with Project Phoenix, which is not mentioned in connection with Drake. The passage does not explicitly state Drake’s education or position, as in choice (D).
32. G Project Ozma is discussed in the second paragraph, immediately after the description of Frank Drake’s experiment. The passage tells us that the project was a failure in the sense that it failed to find signs of intelligent life but a success in terms of leading to other similar programs. Therefore, choice (G) is the best answer. Choice (F) is incorrect because the project was not a success. The passage does not call Drake’s goals unrealistic, as in choice (H), nor does it discuss NASA at this time, as in choice (J).
33. C The word august is used to describe two colleges, the University of California at Berkeley and the University of Western Sydney. Those programs are then described as having reputations that draw respected scientists from around the world. Therefore, a good word to replace august would be respected. Choice (C), esteemed, is a good synonym for respected. Choice (A), summery, might sound like it’s related to august, but it doesn’t mean respected.
34. H The author concludes the passage by stating that Perhaps someday Frank Drake’s dream of a message from outer space will come true once we know where to look for it. This implies a certain hopefulness about the search while acknowledging that there are difficulties yet to be overcome. Therefore, the best answer is choice (H). There is no evidence that the author is ironic, as in choice (F), or angry, as in choice (G). Choice (J) goes too far, since the author is inclined to be hopeful, not fearful.
35. A The passage describes scientists in this field in the third paragraph. They are described as esteemed academics, typically specializing in the areas of physics, astronomy, and engineering. Choice (A), the best answer, is a good paraphrase of this information. Choice (B) includes words from the passage, but goes against the information given. Choice (C) mentions specific places of employment. Although the passage does mention such institutions, it does not discuss these researchers as specifically employed there. Choice (D) incorrectly focuses on radio mechanics, instead of interstellar research.
36. J The fourth paragraph serves as a bridge between the introductory paragraphs, which discuss the search for extraterrestrial life in general terms, and the rest of the passage, which goes into greater detail about two of the relevant factors in determining various planets’ habitability. Choice (J) is the best answer because it correctly identifies the shift to the two factors as the primary point of the paragraph. Choice (F) incorrectly identifies a minor point in the first sentence as the main idea. Liquid water is not discussed until paragraph five, ruling out choice (G). Goldilocks Zones are not mentioned until paragraph six, ruling out choice (H).
37. D The term hospitable planets is used in the fifth paragraph, during the discussion of temperature and liquid water. The sentence states that hospitable planets must be located within a certain distance of their respective suns.This sentence falls in the middle of the discussion of what conditions will allow for life, so a good phrase to replace hospitable planets with would be life-supporting or, to use another term introduced in the passage, life-sustaining. Choice (D) is the best answer, since it is the best match for life-supporting. Choice (A) refers to cultures, which are not within the scope of this passage. Choice (B) incorrectly focuses on distance from the sun, which does not necessarily mean life-supporting. Choice (C) goes against the information in the passage.
38. H Saturn is mentioned in paragraph five, as an example of a planet that is too far from the sun to have temperatures conducive to life. Choice (H) correctly connects this statement to the earlier statement that planets too far away from the sun cannot sustain liquid water, making it the best answer. Choice (F) incorrectly states that Saturn is too close to the sun. Choice (G) incorrectly associates distance from the sun with a heavy atmosphere, a link not discussed in this passage. Choice (J) mentions gas giants, which the passage does not discuss until the following paragraph, and not in connection with Saturn.
39. D This question asks you to find a situation analogous to that of Venus. The passage mentions Venus in the fifth paragraph, as an example of a planet that is too close to the sun, and thus too hot, to support life. Later in the passage, the author also notes that the size of a planet may alter this rule, since smaller planets retain less heat and can thus be closer to the sun. The correct answer, choice (D), correctly connects these facts. The passage never describes Venus as a gas giant, as in choice (A), nor does it state that Venus lacks a gravitational field, as in choice (B). Choice (C) incorrectly identifies Venus as having an unstable orbit.
40. F Goldilocks Planets are discussed in the fifth paragraph and are described as planets that fall within the range of appropriate temperatures. Therefore, choice (F) is the best answer. Choice (G) incorrectly discusses atmospheres, while choice (H) has the opposite information as the passage. Choice (J) incorrectly mentions hydrogen gases, which are not mentioned in this part of the passage.
TEST 2 SCIENCE EXPLANATIONS
1. D In Table 1, when the current doubles, the velocity of the train also doubles. Therefore, a current of 500 A must be associated with a train velocity of 2 × 200 m/s = 400 m/s.
2. F Table 2 shows that the current consistently increases as the length of the magnetic rods increases, so choice (F) is the best answer.
3. C When B = 9.84 × 10-4 T, I = 500 A, and when B = 1.05 × 10-3 T, I = 600 A. Therefore, I = 570 A would be produced by a magnetic field with a values in between these two B values. Choice (C) is the only option that fits.
4. J The question suggests that an increasing electrical current results from an increasing voltage. Of the options listed, Trial 14 has the greatest electrical current, so it must also have the greatest voltage.
5. B Study 4 stands out because all of the values for electrical current are negative. Therefore, choice (B) is the correct answer.
6. G In Study 3, both current (I) and magnetic field (B) increase with a direct relationship. Choice (G) shows this direct increasing linear relationship.
7. D Using Figure 1, determine the features of a Pipistrellus hesperus starting at Step 8 and work backwards. Step 8 describes it to have a forearm length < 40 mm. Step 7 describes it to have a tragus < 6 mm and curved. Step 5 describes it to have a uropatagium not heavily furred, and Step 1 describes it to have ears shorter than 25 mm. Only choice (D) refers to a feature of Bat IV, uropatagium heavily furred, that differs from those of Pipistrellus hesperus found using the above method. Alternatively, you could use the features of bat IV from Table 1 and find the point on Figure 1 where the result differs from the path necessary to get to Pipistrellus hesperus.
8. G Follow Figure 1 step by step using the descriptions for bats I and II from Table 1 until you find the last step with the same result. Starting at Step 1, both bats have ears shorter than 25 mm making Step 5 next. Therefore, choice (F) must be wrong. Both bats have a uropatagium that is not heavily furred, making Step 7 next. Bat I has a 4 mm, curved tragus, and Bat II has a 7 mm, straight tragus. Therefore, the results of Step 7 differ making choices (H) and (J) wrong. This leaves choice (G), Step 5, as the last point where the bats had similar traits. Note that the obvious fringe of fur on the uropatagium of Bat II does not come into play until Step 9 of Figure 1.
9. A All of the choices are in the kingdom Animalia and phylum Chordata. Vesper bats, like all bats, belong to the class Mammalia. Mammals are vertebrates with sweat glands, hair, and similar middle ear structures that give birth to live young (except monotremes which lay eggs).
10. G Both species are found at Step 6 in Figure 1. Step 6 can only be reached from having heavily furred uropatagium in Step 5, eliminating choice (H). Step 5 can only be reached from having shorter than 25 mm ears in Step 1, eliminating choice (J). Choice (F) refers to Step 3 which is not part of the path for either species, meaning it may or may not be a common trait. Choice (G) is more definitive because it refers to the only feature that neither species can have according to Figure 1. It is not possible to get to Step 6 if the ears are greater than 25 mm long.
11. D Using the features listed in Table 1 for Bat II, follow the steps in Figure 1. Bat II’s 18 mm long ears lead from Step 1 to Step 5 in Figure 1. The uropatagium overall is not heavily furred, which then leads to Step 7. The tragus is 7 mm and straight, leading next to Step 9. Since there is an obvious fringe of fur on the edge of the uropatgium, bat II is Myotis thysanodes. Choice (D), Myotis volans, is most likely the closest genetic relative because it is in the same genus, has very similar features, and is adjacent on Figure 1.
12. J Looking at Figure 2, the 0°C setting is the lowest curve, represented by triangles. At 200 min. the saltwater temperature is about 8°C, and at 250 min. the temperature is about 5°C. Therefore, at 220 min., you should expect the temperature to be between 5°C and 8°C.
13. B Since we are asked about a heater and a 37°C trial, Figure 1 will be the relevant chart. At 8 min. the air temperature is about 27°C, and at 10 min. the temperature is about 31°C. If the air changes 4°C in 2 minutes, divide 4 by 2 to get the answer: 2°C/min.
14. F For every temperature setting in each figure, the temperature changes fastest in the beginning and slower as time progresses. The 0°C cooling trial is no different: from 0−100 min. the saltwater temperature goes from 50°C to about 22°C, a change of 28°C, a much greater change than those recorded in any of the other 100-minute intervals listed in the answer choices.
15. A Average kinetic energy is directly proportional to temperature. That is, when temperature is high, average kinetic energy is high, and when temperature is low, average kinetic energy is low. Choice (A) corresponds to the highest temperature. However, you don’t need to know what kinetic energy is to answer the question. Choices (B), (C), and (D) all yield the same temperature (25°C), and since there is no other variable in either figure to which average kinetic energy could be related, if one of them were correct, they would all have to be correct. Therefore, by process of elimination, choice (A) is the only possibility.
16. F The lower the cooling device’s temperature setting, the longer it takes for the saltwater to reach that temperature. It takes the cooling device about 300 min. to reach the 25°C setting; about 350 min. to reach the 10°C setting, and about 400 min. to reach the 0°C. Therefore, you should expect the cooler to take more than 400 min. to reach an even lower setting, such as −10°C.
17. C Pepsin is described as an enzyme that is involved with protein breakdown, and that is active in an acidic environment. Of the choices listed, only choice (C) is a component of the digestive system, which is responsible for the breakdown of nutrients. Also, the stomach is an organ with a highly acidic environment.
18. F Note where the Pepsin Activity in Table 2 is High. There is no evidence on the table that Pepsin activity is high at any pH higher than 3.5, so you can only be sure of choice (F).
19. C Pepsin is capable of high activity in the absence of anserine in Trial 4, thus choice (A) cannot be correct. Pepsin activity is also high in the presence of anserine in Trial 3, thus choice (B) cannot be correct. Casein is described as a protein that can be digested by pepsin, so choice (D) cannot be correct. This leaves choice (C) as the only possible answer. Another way to approach this problem is to notice that what makes Trial 5 different from Trials 3 and 4 is that it does not contain casein. If no pepsin activity is seen when casein is absent, it would follow that casein is a substance that can be digested by pepsin, supporting choice (C).
20. H In order for casein to remain undigested, casein must first be present in the solution. Trials 5 and 6 do not contain casein, so choices (G) and (J) can be eliminated. Choice (H) is a better choice than choice (F) because the high pepsin activity in Trials 3 and 4 would break casein down into the smaller peptides.
21. A Trial 3 in Experiment 1 is conducted at a pH of 3.0 and at a temperature of 40°C. While all of answer choices feature Experiment 2 trials conducted at a temperature of 40°C, only Trial 9 is conducted at a similar pH of 3.0. Therefore, choice (A) is the best answer.
22. G The results from Experiment 1 show high activity of pepsin, meaning a fast rate of protein digestion by pepsin, at a temperature of 40°C, which excludes choices (C) and (D). The results from Experiment 2 show high activity of pepsin at pH values that are less than 4.0, so choice (B) is the best answer.
23. C Read the vertical axes in all 3 figures when T = 0°C. The only fluid whose viscosity is less than 1.0 cP is diethyl ether, eliminating choices (B) and (D). Ethanol, water, mercury, and nitrobenzene are all found in both Figures 1 and 2, so the correct answer is choice (C).
24. F The nitrobenzene line in Figure 2 has a sharp initial decrease and then plateaus. Thus, choice (F) has the greatest decrease in viscosity of approximately 1.1 cP. Choice (G) has only a decrease of approximately 0.25 cP. Choices (H) and (J) both decreases less than 0.1 cP.
25. C Figure 1 shows that the viscosity of water at 70°C is approximately 0.4 cP. Although choices (A), (B), and (D) provide values that are represented in the figure, they are all values for temperatures other than the specified 70°C.
26. G Figure 2 demonstrates that viscosity decreased with an increase in temperature, eliminating choices (F) and (H). The introduction states that the greater the viscosity, the greater the resistance to flow, thus the greater time it would take for a fluid to move out of its container. Given Figure 2 shows decreasing viscosity, the time for the fluids to leave their containers would also decrease. Thus, choice (G) is the correct answer.
27. D To assess the hypothesis, you would require values for viscosity at 60°C for nitrobenzene with Additive A and untreated diethyl ether. Although Figure 2 provides the viscosity for nitrobenzene treated with Additive B, no figure shows the viscosity value for nitrobenzene blended with chemical additive A. Figure 1 shows that nitrobenzene has a viscosity higher than that of diethyl ether, and Figures 2 and 3 show that Additive A lowers the viscosity of both ethanol and diethyl ether; however, you cannot assume that treatment of nitrobenzene with Additive A would lower its viscosity below 0.07cP. Thus, choice (D) is the best option.
28. G Examine Figure 3 along the x-axis. Notice how the farther you go to the right along the x-axis, the weaker the wave type becomes. Only choice (G) accurately describes this phenomenon.
29. B First, examine Figures 3 and 4 closely. In both figures, the transition lines show that at densities between 1,000 and 2,000 kg/m3, strong waves appear always to begin to propagate at shorter distances from the epicenter than moderate waves. Thus, choices (C) and (D) may be eliminated. Since the maximum distance from the epicenter is less for strong waves than moderate waves, choice (A) may also be eliminated.
30. J Look at the passage closely, the passage states that ground density and propagation duration were controlled in the experiment. Thus, answer choices (G) and (H) may be eliminated. Choice (F) may be eliminated because in each experiment, the sound intensity was controlled. The wave type formed in the experiments was not controlled as it varied with distance and density.
31. D Examine Figure 1 closely. A wavelength constitutes the distance from one hump to the next. The moderate wave is approximately 150 cm, and the weak wave is approximately 500 cm. Subsequently, neither wave type exhibits a wave length of less than 100 cm.
32. J From the passage, Studies 1 and 2 were conducted using sound intensities of 60 and 80 dB, respectively. Accordingly, the resulting waveform plot of study using 70 dB should exhibit wave types reminiscent of Figures 2 and 3. Both figures exhibit all three types of waves; therefore choice (J) is the best answer. The waveform plot of Study 3 does not include weak waves, but its sound intensity was set to 100 dB, well above the sound intensity of 70 dB given in this question.
33. A Use the range of sound intensities given in the passage to determine which waveform plot you need to use. Since this range is 75 dB to 85 dB, you can confidently use the waveform plot from Study 2, which has as its sound intensity 80 dB. Using Figure 3 (Study 2), therefore, note the range of distances from the epicenter for strong waves: roughly 0 m to 2.3 m. Accordingly, any distance from the epicenter for strong waves between sound intensities of 75 dB and 85 dB can be reasonably expected to have a distance shorter than 2.5 m.
34. G The information in Table 1 indicates that Solution 4 contained three dissolved particles, where Solution 2 contained only one dissolved particle. Solution 4 thus had more dissolved particles, enabling you to eliminate choices (F) and (H). Now compare the respective freezing point of each solution. The freezing point of Solution 2 was −1.9°C while the freezing point of Solution 4 was lower at −5.7°C. Be careful here—a large negative number is smaller than a small one!
35. A Scientist 2 states that the change in freezing point is NOT related to the identity or properties of the solute dissolved. The observation that a solute with no charge such as naphthalene can still lower the freezing point of a solvent does not contradict Scientist 2’s viewpoint, so choices (C) and (D) are incorrect. Scientist 1 specifically states that a change in freezing point only occurs with solutes that form charged particles in solution. Therefore, the fact that naphthalene causes a change in the freezing point of benzene directly contradicts Scientist 1’s viewpoint as stated in choice (A).
36. F Use process of elimination. Scientist 2 argues that any increase in the concentration of a solution will lower its freezing point, so you can eliminate choices (G) and (J). Scientist 1 argues that only charged solvents can have an influence on the freezing point, so you can eliminate choice (H) as well. This leaves you only with choice (F), which agrees with the hypotheses of both scientists.
37. A Scientist 2 states that only the concentration of a solution can change its freezing point, and since the concentration here is held constant, choices (B) and (C) are not the best answers. Scientist 1 states that the decrease in freezing point is related only to the charge of the solute particles, a hypothesis which is supported by the observations in the question.
38. G Scientist 1 states that solute molecules are attracted to the solvent molecules by intermolecular forces and interfere with the orderly arrangement of solvent molecules. Choices (F) and (J) are eliminated because they do not depict attraction between solute and solvent molecules, and both show a very orderly arrangement of solvent molecules. Choice (G) and choice (H) demonstrate attraction between solute and solvent, but only choice (G) illustrates interference with non-orderly arrangement of solvent molecules.
39. A Only Scientist 1 states that the physical properties (charge) of the solute have an impact on changing the freezing point of a solvent. This eliminates choices (B) and (D). Scientist 2 states that the physical properties of the solute do not have an effect on freezing point depression. Therefore, choice (C) is eliminated and choice (A) is correct.
40. J Scientist 2 states that the decrease in temperature is in direct proportion with the van ’t Hoff factor. Choices (F) and (H) show the decrease in temperature and the van ’t Hoff factor in an inverse proportion, so they can be eliminated. Choice (G) can also be eliminated because there is no indication that the van ’t Hoff factor should be squared in the proportion. Only choice (J) shows decrease in temperature (T) and the van ’t Hoff factor (i) in direction proportion with one another.
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?