McGraw-Hill Education ACT 2017 (2016)
Part II. ACT DIAGNOSTIC ASSESSMENT
DIAGNOSTIC TEST ANSWERS AND EXPLANATIONS
English Test Explanations
1. The best answer is D. To maintain parallel structure within this paragraph, you need to use the past tense of the verb begin. Notice that Sentences 2 and 3 use past tense main verbs. Sentence 4 also has a clause with the main verb began. The verb forms should match tense.
2. The best answer is G. The question asks you to identify the correct punctuation surrounding the phrase, happy and healthy learning to walk and talk. The phrase contains the main clause, she was happy and healthy, and a gerund phrase, learning to walk and talk like her toddler peers. Gerund phrases are set apart with a comma. No other commas should be placed within the main clause or the gerund phrase.
3. The best answer is D. In order to eliminate the redundancy and clearly express the intended idea, omit the underlined portion.
4. The best answer is G. Paragraph 2 illustrates the difficulties faced by both Helen and her parents as they adapted to their new situation. Answer choice G provides the best introduction because it summarizes what is to come while providing enough detail to be complete: Helen is frustrated, and her parents are overwhelmed by her resulting tantrums (they consider sending her to an asylum).
5. The best answer is A. The underlined phrase is part of the infinitive clause, meaning, an infinitive form of a verb has to follow the to. The other choices are simply restatements of the original phrase. The most concise selection is answer choice A.
6. The best answer is G. The possessive Helen’s modifies parents. Therefore, the two words must not be separated by a comma. A comma is placed after the gerund phrase Feeling sorry for their impaired daughter to avoid misunderstanding.
7. The best answer is B. This question requires you to use the correct idiom.
8. The best answer is F. The sentence as it is written is clear, gives all the necessary information, and is most concise.
9. The best answer is A. This question requires you to express the idea clearly and simply. The main idea of the paragraph is Helen’s need for self-discipline. Only the original phrase has that emphasis and is grammatically correct. The other answer choices are awkward.
10. The best answer is J. The rest of the passage is in the past tense, so to maintain parallel construction, you should use the past tense verb form was. Also, the stubbornness in question belongs to a particular person: Helen. Therefore, you should restate the antecedent for the sake of clarity.
11. The best answer is D. This question asks you to identify the correct punctuation surrounding the phrase if channeled. Because it interrupts the sentence between that and the clause beginning it would be…, it should be set apart by commas.
12. The best answer is F. The passive verb construction was given implies that Annie is the one who is acting. The context of the passage clearly indicates that it is Helen’s parents who act; they are the ones who give permission for Annie and Helen to move to a different house. Since Annie receives the action, the verb phrase must be in the passive voice. Only the original phrase is correct.
13. The best answer is D. In this context, Annies should be possessive. Therefore, it requires an apostrophe before the s: Annie’s. Furthermore, the phrase Annie’s efforts ends the first independent clause of the sentence. The second clause, introduced by the conjunction but, should be set apart with a comma.
14. The best answer is H. This sentence continues the idea of the previous sentence chronologically. A contradictory relationship does not exist, as the other answer choices indicate.
15. The best answer is C. This is a main idea question. The essay focuses on Helen’s teacher, Annie Sullivan, and her professional accomplishments in working with Helen.
16. The best answer is H. The phrase for the first time is idiomatic. Answer choice F can be eliminated because it contains redundancy. Answer choices G and J are awkward (not idiomatic) and can be eliminated.
17. The best answer is C. The adverb enthusiastically correctly modifies the verb anticipating. Answer choice A includes the redundant pronoun you, which requires a different verb form.
18. The best answer is H. Notice that the paragraph uses the words begin and buy, both of which are present tense. To maintain parallel structure within this paragraph, you need to use a present tense verb; therefore, answer choices G and J can be eliminated. Answer choice F is in present perfect tense. With a critical part of the holiday as the subject of the sentence, this answer choice does not make sense. Answer choice H is best because it uses is to equate the two noun phrases a critical part of the holiday and shopping for gifts.
19. The best answer is B. The phrase not wanting to be rushed with last-minute purchases is a gerund phrase and needs to be separated from the main clause by a comma.
20. The best answer is F. To maintain parallelism in the paragraph, all of the verb forms must match. The passage states that you “buy” and you “compliment” (present tense). Therefore, you “find” the ghost figurine.
21. The best answer is B. You’re is the contraction of you are. Since the sentence already has a main verb, you’re is grammatically incorrect. The correct form is the possessive pronoun your. Also, in this context the introductory phrase this year could be set off by a comma or left without punctuation; however, it would never be followed by a colon. Therefore, only answer choice B is correct.
22. The best answer is G. This question requires you to express the idea clearly and simply. Only this answer choice is a fully formed clause in standard word order.
23. The best answer is C. This choice eliminates the redundancy.
24. The best answer is J. Semicolons and periods separate complete sentences. While the first half of this sentence could stand on its own, the second half could not. It does not have a subject or a finite verb in the main clause. The comma is used to separate gerund phrases from the clauses they modify.
25. The best answer is B. One way to approach this question is by process of elimination. The sentence as it is written doesn’t include a legitimate verb form. So, eliminate answer choice A. The passage has consistently been in the present tense, which means the sentence requires a present verb form. This eliminates answer choice D. Answer choice C does not have tense, so the sentence would be incomplete. This leaves answer choice B, has become, which is in the present perfect tense.
26. The best answer is F. In this case, the transition is from Paragraph 4 to Paragraph 6. Paragraph 4 ends with the author discovering that she is running out of time to buy gifts and that no one is available to help her. She must solve this problem on her own and act quickly. Answer choice F best captures this sentiment. The choice is supported by the first sentence in Paragraph 6, which emphasizes her frantic shopping.
27. The best answer is D. To maintain parallel structure within this paragraph, you need to use a present tense form of the verb trudge. Notice that the paragraph uses verbs such as dart, give up, and are, all of which are present tense. The verb forms should agree, that is, have the same tense. Finally, answer choice D is more concise than answer choice C, which makes it stylistically the better choice.
28. The best answer is H. To maintain parallel structure within this paragraph, you need to use a present tense form of the verb ask. Because the subject (“your son”) is in the third person singular, the correct form is asks, answer choice H.
29. The best answer is D. The passage as a whole describes one person’s holiday stress building as it gets closer to Christmas. Paragraph 6 has the story’s climax, as the author breaks down as she realizes that she will never finish her tasks in time. A hug from her son helps to remind her of the joy of the season, and she decides to rest instead of doing the next thing on her list. Answer choice D indicates her frustration and her ultimate decision to relax. This best captures the function of Paragraph 6 in relation to the rest of the passage.
30. The best answer is H. Paragraph 5 serves as a temporal marker: it tells the reader that, at this point in the narrative, it’s the beginning of November with six more weeks before Christmas. Logically, it should be placed after Paragraph 2, with its reference to Halloween, and before Paragraph 3, with its reference to Thanksgiving (late November).
31. The best answer is A. The paragraph starts with a reference to “popular opinion.” The next sentence refers back to that by using the phrase beginning with “this same.” That means the sentence needs a subject noun that is a synonym for popular opinion. The word culture captures that sense more accurately than either emotion or specimen.
32. The best answer is G. To answer this question, you should first recognize that physical fitness is a singular noun phrase. In order to maintain parallel structure within the sentence, you should use societal fitness, a singular noun phrase. Eliminate answer choices F and J. The word societal is an adjective, describing the noun fitness, so it should not show possession. Eliminate answer choice H.
33. The best answer is D. The writer is setting up a line of reasoning parallel to that of the preceding sentence; physical exercise is compared to social activity. In both cases, the writer argues that if it hurts, don’t do it; you’re probably doing something wrong. Answer choice D best completes the parallel relation.
34. The best answer is H. The author states that pain receptors exist to limit physical injury. Guilt, the writer implies, is a psychological pain receptor that helps us “limit injury to others.” Repeating the phrase limit injury allows the author to emphasize the parallel nature of the processes. The other answer choices either fail to mark the parallel or are too wordy.
35. The best answer is D. The word attempting is modifying the verb turn. In this usage, turn needs to be in the infinitive, that is, the sentence needs to read “attempting to turn.”
36. The best answer is J. The focus of the paragraph is social interaction. Information about the time it takes to stop a car is irrelevant and should be deleted.
37. The best answer is C. This question requires you to correctly punctuate the underlined portion. The pronoun yourself is the object of the verb find, and driving is the verb without tense linked to yourself. Therefore, no commas should separate them.
38. The best answer is G. Because manner describes a behavior, the sentence requires a verb that denotes action (acts), not a state of being (is). Answer choices H and J are wordy and can be eliminated.
39. The best answer is A. This question requires you to express the idea clearly and simply. The phrase legal penalties is concise and complete. Adding detailed descriptions of those penalties would only distract from the focus of the paragraph, social behavior.
40. The best answer is J. The first clause of the sentence begins with although, making it a dependent clause. Therefore, a subject and a verb of the main clause is needed here. Answer choice J is also the most clear, simple option.
41. The best answer is D. The underlined phrase is redundant because it repeats the meaning of insanity. It should be omitted.
42. The best answer is F. The transition word however suggests a contrast between the idea contained in the preceding sentence and the idea contained in this sentence. This is, in fact, the case, so answer choice F is correct.
43. The best answer is A. The paragraph implies that it is human nature to avoid pain, including the pain of guilt. The writer suggests there are two ways to do this: avoid making mistakes and avoid accepting responsibility for mistakes. The first is impossible. That leaves the second. The way to mark this type of logical progression is with the adverb therefore, indicating that one thing is the result of another.
44. The best answer is H. The phrase if improperly managed is an interrupting phrase in the sentence and should be set off by commas. The comma at the beginning of the phrase is a clue to the reader to expect a second comma at the end. A semicolon would require a complete sentence preceding it. Eliminate answer choice F. The relative pronoun which would create a sentence fragment. Eliminate answer choice G. The pronoun it would create a run-on, so eliminate answer choice J.
45. The best answer is C. This question requires you to punctuate the underlined portion correctly. The relative clause that they never move on is one unit and should not be broken up by commas or any other punctuation. Nor should a comma separate the clause from the conjunction that which precedes it.
46. The best answer is F. The sentence as written implies that Kennedy’s public image was of a healthy person and that Kennedy himself was tall and trim, which makes sense in the context of the paragraph. Answer choices G and H would create a run-on. Answer choice J would make the first sentence a fragment.
47. The best answer is C. This question requires you to express the idea clearly and simply. The focus of this paragraph is the contrast between Kennedy’s appearance of health and his actual state of chronic illness. Answer choice C best captures this dynamic. The sentence as written is a run-on, so eliminate answer choice A. Answer choice B has three grammatically correct sentences, but their structure is rigid and plain. It is not the best answer. The word order of answer choice D is awkward, so it can be eliminated.
48. The best answer is J. It is idiomatic to use the phrase “began with” in this context.
49. The best answer is C. The best way to provide more detail is to offer a better description. Paragraph 2 continues from Paragraph 1 by describing in more detail the effects of Addison’s disease on Kennedy. A list of the symptoms of the disease would help the reader gain a more complete understanding of the disease.
50. The best answer is F. The sentence is best as written. The clause has standard subject– verb–object word order. The rest of the information follows in logical order. The prepositional phrase in his back comes immediately after the noun phrase anesthetic injections, which it modifies. The prepositional phrase up to six times a day modifies the whole clause and can be placed at the end.
51. The best answer is D. The information given by the phrases in answer choices A, B, and C is already implied in the verb hide. Therefore, all these answer choices are redundant and can be eliminated.
52. The best answer is J. Always try answer choices that do not contain punctuation. In this case, a dash would be unnecessary, and a semicolon would be incorrect before a fragment. In addition, commas should not be placed before or after conjunctions or unless they link independent clauses or the last two elements in a series of three or more elements.
53. The best answer is B. The subject he is implied in the second half of this compound sentence. Answer choice B is clear, concise, and grammatically correct. As it is written, the sentence contains a comma splice. Both a period and semicolon must be followed by independent clauses, which is not the case in answer choices C and D.
54. The best answer is F. The question requires you to express the idea clearly and simply. The idea that Kennedy was able to “act healthy” is developed by the sentence, which explains exactly what that means: he was able to hide crippling pain from everyone except his doctors and relatives. These three distinct groups (doctors, relatives, and the public) should be kept together in the sentence because they comprise three parts of one audience. In other words, the author implies that Kennedy is trying to fool all of them, but it only works with the public. Answer choice F includes all of that information while also being the most concise choice.
55. The best answer is D. This question requires you to express the idea clearly and simply. Answer choice D is complete and the most concise. The other answer choices are awkward and wordy.
56. The best answer is G. To maintain parallel structure within this paragraph, you need to use the past tense of the verb attribute, which is attributed. Notice the use of the verbs was and looked. The verb forms should agree in tense. Furthermore, Kennedy is deceased, so his actions have past tense.
57. The best answer is C. The last two sentences of this paragraph clarify its focus, which is proving that Kennedy’s illness did not negatively affect his ability to govern. Answer choice C asks the question that the last two sentences answer. Therefore, it is the best response.
58. The best answer is H. Like the positive pairing either … or, neither … nor are usually used together. Therefore, to maintain the parallelism, the underlined portion should be nor the drugs.
59. The best answer is A. The sentence as it stands gives us the most important information first: what he did (“performed”), followed by how he did it (“at the highest level”). This order makes logical sense and is the most concise option.
60. The best answer is H. This question requires you to determine the main idea of the passage. Although the passage does describe Addison’s disease in some detail, its primary focus is the effect of Addison’s disease on President Kennedy. For example, the reader is not told if Kennedy’s experience of the disease is common among Addison’s sufferers. Likewise, the reader is also not told if treatment has changed since the early 1960s. Therefore, the essay would not be a good general description of Addison’s disease and its treatment. Eliminate answer choices F and G. While the essay does describe symptoms of the disease, this is not the main focus, so eliminate answer choice J.
61. The best answer is C. The contraction we’re represents the subject pronoun we and the auxiliary verb are, indicating that the next verb form should be a gerund to form the present progressive tense: We are traveling.
62. The best answer is G. The sentence is awkward as written. A relative pronoun could link the two clauses; where is best because it refers to a place, Southern California.
63. The best answer is A. The author is comparing personal warmth, or genuine friendliness, to the outdoor temperature. She implies that the people of Tromso demonstrate the former. Being helpful is an excellent way to show friendliness. The other answer choices incorrectly refer to literal warmth.
64. The best answer is G. The passage states that Tromso residents are very helpful to foreigners. This best matches answer choice G. While answer choice F describes polite behavior, it is not as strong an example.
65. The best answer is C. The verbs twirling, flipping, and twisting are synonyms of spinning and could replace spinning in the sentence without changing its meaning. The verb throwing does not fit the context, and it is NOT acceptable.
66. The best answer is G. This question requires you to express the idea clearly and simply. The current sentence is wordy and redundant (it’s unnecessary to repeat Tromso in this context). Answer choice G sets up a concise contrast between what other towns claim to do and what Tromso actually does.
67. The best answer is A. The paragraph that follows indicates that, instead of working or sitting, the writer spent much of his time hiking. The phrase at all is appropriate here, because it makes a connection between the idea that the writer thought his time in Norway would drag and the fact that his visit was actually very enjoyable.
68. The best answer is G. The best introductory sentence will be one that shows a transition from Paragraph 3 to Paragraph 4. Since Paragraph 3 discusses some of Tromso’s attributes (mild weather and friendly people) it makes sense that Paragraph 4 should start out with another of Tromso’s characteristics. Sentence 2 does this best. Therefore, the correct sequence of sentences will begin with Sentence 2. Furthermore, there is a strong link between Sentences 1 and 5, and only answer choice G places them together.
69. The best answer is D. The sentence introduces the idea of boots and blisters to the paragraph. Since this is not echoed elsewhere, it is irrelevant and should be omitted. Eliminate answer choices B and C for the same reason.
70. The best answer is F. The first part of the sentence indicates that hiking is so popular in Norway, that the government passed regulations allowing anyone to hike across wilderness areas. The question stem says expand hikers’ rights, which mirrors adding designated areas in answer choice F.
71. The best answer is B. Answer choice B is the only one with descriptive adjectives that help create a vivid image of the “many beautiful scenes.” The other answer choices are either too general or contain irrelevant information.
72. The best answer is F. The sentence is complete and concise as it stands. The addition of a transition word or phrase is not necessary, so eliminate answer choices G, H, and J.
73. The best answer is D. The sentence requires the possessive form of Tromso, a singular noun. The correct form adds an apostrophe and an s to create Tromso’s.
74. The best answer is F. This question requires you to express the idea clearly and simply. The phrase a view that has been described as world class is a singular view. This implies that the author is referring to only one vantage point: Mount Storsteinen. This eliminates answer choice G. Answer choices H and J are wordy and awkward, so eliminate them.
75. The best answer is B. As written, it’s is the contraction of it is. A better choice would be the possessive form its. However, the antecedent of its would be unclear. (It is not vista, Mount Storsteinen, northern lights, or midnight sun.) When an antecedent is too distant or unclear, use an expressed noun in possessive form instead, as in answer choice B.
Mathematics Test Explanations
1. The correct answer is A. This is a basic algebra problem that requires you to solve for x. Isolate the variable, x, on one side of the equation, as follows:
4x – 9 = 11
4x = 20
x = 5
2. The correct answer is F. This kind of statement is called a “conditional.” You are told that if the first part is true (XY is 4), then the second part (YZ is 7) will certainly be true. Since the second part is NOT true, you can conclude logically that the first part is also NOT true. Therefore, answer choice F is correct. If XY were equal to 4, then, according to the given statement, YZ would have to be 7. Remember that some ACT mathematics problems require only logic and no computations.
3. The correct answer is D. To solve this problem, first set up an equation, as follows, to find the given number (x):
0.6x = 9
x = 15
The given number is 15. Next, calculate 25% of 15, as follows:
0.25x = 15
x = 3.75
4. The correct answer is G. The first step in solving this problem is to calculate the amount of fuel needed for each vehicle for the trip, as follows:
Vehicle A: 1,120 total miles ÷ 16 miles per gallon = 70 gallons
Vehicle B: 1,120 total miles ÷ 35 miles per gallon = 32 gallons
Next, find the difference between the gallons required for Vehicles A and B:
70 – 32 = 38
5. The correct answer is A. To solve this problem, set up an equation, as follows:
(x – 3) + (x – 2) + (x – 1) + x + (x + 1) = 390
Next, simplify the equation and solve for x:
5x – 5 = 390
5x = 395
x = 79
6. The correct answer is H. This problem requires you to substitute the values given for P and Q into the equation P – Q. The problem states that P = 5a and Q = 3b – 2a. Set up the equation as follows, and remember to keep track of the negative sign as you simplify the expression:
P – Q
= 5a – (3b – 2a)
= 5a – (–2a) –3b
= 5a + 2a – 3b
= 7a – 3b
7. The correct answer is E. The figure in the problem represents 2 parallel lines cut by 2 parallel transversals. The angles created as a result have special properties. Where each of the parallel lines is cut by a transversal, there are 2 pairs of vertical, or opposite, angles. Each angle in the pair is congruent to, or equal to, the other angle in the pair. Therefore, where l3 intersects l1 and also where it intersects l2, two 100° angles are formed; in addition, two 80° angles are formed that are adjacent to the 100° angles, since a straight line measures 180°. The same angles are created where l4 intersects l1 and l2. This means that angle z must equal 80°
8. The correct answer is H. Simply plug 2 in for x wherever x appears in the equation and solve the equation. Don’t forget to keep track of the negative signs!
–(22) + 4(2)–3
= –(4) + 8 – 3
= 8 – 4 – 3 = 1
9. The correct answer is B. If the average of 8 numbers is 6.5, then the total of the 8 numbers is 8 · 6.5, or 52. If each of the 8 numbers is decreased by 3, then the total of the 8 new numbers is 52 – 8(3), or 52 – 24, which is 28. To find the average, divide 28 by 8, to get 3.5.
10. The correct answer is J. This question tests your ability to recognize and apply the distributive property of multiplication. According to the distributive property, for any numbers a, b, and c, c(a + b) = ca + cb. In this problem, c is 5 so you can factor the expression 5a + 5b into 5(a + b):
11. The correct answer is D. To solve this problem, first subtract $40 from $375 (375 – 40 = 335). Because $40 is a flat fee, it will not figure in the calculations for the number of hours. Set the number of hours to x, multiply by the hourly rate, and solve:
25x = 335
x = 13.4
12. The correct answer is K. The easiest way to solve this problem is to plug the answer choices into the inequality and solve. Because the question asks you for the largest possible value of x, start with the largest answer choice (note that the answer choices are in ascending order):
This satisfies the inequality, so answer choice K, because it is the largest, must be correct.
13. The correct answer is C. In order to solve this problem you must know that there are 360° in a circle, and that the clock shown is divided into 12 segments, 1 for each hour in the day. To calculate the number of degrees that the hour hand moves from 1:00 P.M. to 8:00 P.M. perform the following operations:
360° ÷ 12 = 30°. Each hour in the day is equivalent to 30°.
30° × 7 (the number of hours between 1:00 P.M. and 8:00 P.M.) = 210°
14. The correct answer is J. The first step in choosing the correct answer is to locate point R in the coordinate plane. You will see that it is located in the upper-right quadrant, which means that both of the coordinates must be positive. Eliminate answer choices H and K because they both include negative coordinates. You can also eliminate answer choices F and G, because neither of the coordinates of point R is zero. That leaves answer choice J as the only possible correct answer.
15. The correct answer is A. This problem requires you to find the Greatest Common Factor. The Greatest Common Factor is 3xy, because each term has at least 1 factor of 3, 1 factor of x, and 1 factor of y. When you factor 3xyout of 3x3y3 you are left with x2y2, and when you factor 3xy out of 3xy, you are left with 1. Therefore, when factored, 3x3y3 + 3xy = 3xy(x2y2 + 1).
16. The correct answer is K. To find the total number of seats in the entire classroom, you must multiply the number of rows, (r + s), by the number of seats in each row, t, using the Distributive Property:
(r + s) · t = (r · t) + (s · t)
17. The correct answer is D. The first step in selecting the correct answer to this problem is to recognize that x cannot be less than 16. This means that answer choices A and B can be eliminated. If you look at answer choice C, you should notice that 16 is , or 50% of 32, not 20% of 32, so answer choice C can be eliminated. It does not make sense that 20% of 800 would be 16, so by a simple process of elimination you can arrive at the correct answer, which is answer choice D. To solve this problem mathematically, follow these steps:
16 is to x as 20% is to 100%.
; cross-multiply and solve for x.
20x = 1,600
x = 80
18. The correct answer is H. To solve this problem quickly, notice that the slowest time (24 : 04) is just over 24 minutes and the fastest time (19 : 53) is just under 20 minutes. Therefore, the difference between the two times will be around 4 minutes. You can eliminate answer choices F and G because they are too small, and answer choice K because it is too big. Next, convert the times to seconds, as follows:
Slowest time: 24(60) + 4 = 1,444 seconds
Fastest time: 19(60) + 53 = 1,193 seconds
Now subtract to find the difference in seconds: 1,444 – 1,193 = 251. Finally, convert 251 seconds to minutes and seconds: 251 ÷ 60 = 4, remainder 11.
19. The correct answer is E. In order to solve this problem you must first calculate the total cost of the watch, including tax. Since the sales tax is 6%, multiply the price of the watch ($12.99) by 0.06, the decimal equivalent of 6%:
$12.99 × 0.06 = $0.7794
$0.7794 rounded to the nearest cent is $0.78.
Now, add the sales tax to the price of the watch:
$12.99 + $0.78 = $13.77
Based on these calculations, you will need $0.77 in exact change.
20. The correct answer is G. An expression is undefined when the denominator equals 0. Set the denominator equal to 0 and solve for x:
16 – x2 = 0
16 = x2
4 = x
21. The correct answer is C. To solve this problem, you can use your calculator to determine the square root of 99:
Clearly, 10 is the smallest integer greater than the square root of 99: 10 > 9.9498. You could also have figured that is slightly less than , which is 10, making 10 the smallest integer greater than the square root of 99.
22. The correct answer is K. The key to solving this problem is to recognize that the box has a top and a bottom, plus 4 sides. Because the tape must go completely around all 4 sides of the box, you must account for the sides as follows:
2(40 cm) = 80 cm (top and bottom, length)
2(13 cm) = 26 cm (top and bottom, width)
4(20 cm) = 80 cm (four sides, height)
80 + 26 + 80 = 186 cm
23. The correct answer is A. The first step in solving this problem is to calculate the value of Kahla’s inventory at each price point, as follows:
Next, find the total value: $5,000 + $8,000 + $12,000 = $25,000.
24. The correct answer is G. To find the solutions of the expression x2 + 2x = 8, first put it in the correct quadratic form by subtracting 8 from both sides: x2 + 2x 8 = 0. Now you can factor the polynomial x2 + 2x – 8:
(x +__)(x – __) = 0
Find 2 factors of –8 that, when added together give you 2, and plug them into the solution sets:
(x + 4)(x – 2) = 0
Now, solve for x:
(x + 4) = 0, so x = – 4
(x – 2) = 0, so x = 2
The solutions of x2 + 2x = 8 are –4 and 2.
25. The correct answer is C. The key to solving this problem is to recognize that if (f + g)2 = 81, then f + g must equal 9, because 92 equals 81. Now, since you are given that fg = 20, you need to find 2 numbers that, when added together give you 9, and, when multiplied together give you 20. The only 2 numbers that will satisfy both equations are 4 and 5. Substitute 4 for f and 5 for g in the final equation: f2 + g2 = 42 + 52 = 16 + 25 = 41.
26. The correct answer is J. When exponents are raised to an exponential power, the rules state that you must multiply the exponents by the power to which they are raised. In this problem, x is raised to the (4a – 3) power. This exponent is then squared, so you should multiply 4a – 3 by 2: 2(4a – 3) = 8a – 6. You now have the equation x8a – 6 = x10. Since the coefficients equal (x), the exponents must also be equal, so 8a –6 = 10. Solve for a:
8a – 6 = 10
8a = 16
a = 2
27. The correct answer is E. The first step in solving this problem is to determine the value of i6 and 3i4. Even though this problem contains a complex number, it is actually a relatively simple exponent problem. You are given that i2 = –1, which means that i6 = (i2)(i2)(i2) = (–1)(–1)(–1), which equals –1. By the same token, 3i4 = 3(i2)(i2) = 3(–1)(–1), which equals 3. Therefore, the value of i6 + 3i4 is –1 + 3, or 2.
28. The correct answer is G. The slope-intercept form for the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Put the given equation in the standard form as follows:
5x – 4y = 7
–4y = –5x + 7
Based on this solution, b, the y-intercept, is equal to
29. The correct answer is D. A circle centered at (a, b) with a radius r has the equation (x – a)2 + (y – b)2 = r2. Based on this definition, a circle with the equation (x + 3)2 + (y – 2)2 = 10 would have a radius of . If r2 = 10, then r = .
30. The correct answer is F. The sine of any acute angle is calculated by dividing the length of the side opposite the acute angle by the length of the hypotenuse In this problem, the length of the side opposite angle βis l, and the length of the hypotenuse is n. Therefore, the sin of angle β is
31. The correct answer is E. You should think of this problem as a basic fraction, where (4a3b) × (—5a5b3) is the numerator and (10a4b2) is the denominator. The first step is to multiply together the 2 elements in the numerator, as follows:
When multiplying exponents, the rules state that you should add exponents with like coefficients, so (4a3b)(–5a5b3) = –20a8b4.
To solve a fraction, you simply divide the numerator by the denominator.
When dividing exponents, the rules state that you should subtract exponents of the same coefficients in the denominator from the exponents of the same coefficients in the numerator, so –20a8b4 ÷ 10a4b2 = –2a4b2.
32. The correct answer is G. Because the 3 lines are parallel, the distances between the points of intersection of each of the transversals are directly proportional. So, the distance from point E to point C (6″) is directly proportional to the distance from point A to point C (2″), and the distance from point F to point D (8″) is proportional to the distance from point D to point B (x″). Set up the following proportion and solve for x:
6 : 2 as 8 : x
which can be simplified to
33. The correct answer is D. A square is a parallelogram with 4 right angles and 4 sides of the same length. The perimeter of a square is the distance around the square, or the sum of all 4 sides. Since the perimeter is given as 28, the length of each side of the square must be 28 ÷ 4, or 7. This means that radii and are both equal to 7. The area of a circle is calculated using the formula A = πr2. Plug 7 in for r and solve:
A = πr2 = π(7)2
A = π49, or 49π
34. The correct answer is K. According to the graph shown, the number 2 is included, but the number 4 is not included. This means that x must be less than or equal to 2 (x ≤ 2) and/or x must be greater than 4 (x > 4). You can eliminate answer choices F and G, which both indicate that x is greater than or equal to 4 (x ≥ 4). You can also eliminate answer choice H, which says that x is less than but not equal to 2 (x < 2). Now you must decide whether to use and or to use or. Since the sets do not overlap on the graph, the correct answer is x ≥ 2 or x > 4.
35. The correct answer is D. To solve this problem, substitute the given dimensions into the equation, as follows:
Surface area = 2π(5)2 + 2π(5)(10)
= 2π(25) + 2π(50)
= 50π + 100π
36. The correct answer is G. Because a negative number cannot have a real square root, the value under a square root sign must be positive. In this problem, the value under the square root sign is Choose values for the answer choices and eliminate those choices that would give you a negative value under the square root sign:
If y is negative, then 3y will be negative, so the value under the square root sign could also be negative. Eliminate answer choice F.
If y is positive, then 3y will be positive. Since the square of a negative number is also positive, even if x is negative, as long as y is positive the value under the square root sign will be positive. Answer choice G will work.
Answer choices H and J are not true, because you have just determined that y must be positive, which means that, while y could be either 4 or , it could also be some other positive value.
Answer choice K does not work, because y must be a positive number. By process of elimination, you are left with answer choice G.
37. The correct answer is B. To solve this problem, first list all of the distinct factors of 96: 96, 48, 32, 24, 16, 12, 8, 6, 4, 3, 2, 1. All of these numbers divide evenly into 96. Next, list all of the distinct factors of 64: 64, 32, 16, 8, 4, 2, 1. All of these numbers divide evenly into 64. The only factors that both 96 and 64 have in common are 1, 2, 4, 8, 16, and 32. Since you are told that c is NOT a factor of either 16 or 20, you can eliminate 1, 2, 4, 8, and 16, which factor evenly into either 16 or 20. This leaves you with a value for c of 32. When you add the digits (3 + 2) you get 5.
38. The correct answer is J. The slope of a line is defined as the change in the y-values over the change in the x-values in the standard (x, y) coordinate plane. Slope can be calculated by using the following formula: . Any line parallel to the y-axis is a vertical line: The x-values do not change (see diagram).
The slope of a vertical line is undefined, answer choice J, because there is no change in x, which means that the denominator (x1 – x2) is zero.
39. The correct answer is D. If the coordinates of point J are nonzero and have the same sign, they must both either be positive ( +,+ ) or negative (–,–). Therefore, they must be located in either Quadrant I, or Quadrant III, as shown below:
40. The correct answer is F. The first step in solving this problem is to calculate the sine and the cosine for both angle a and angle b. The sine of any acute angle is calculated by dividing the length of the side opposite the acute angle by the length of the hypotenuse The cosine of any acute angle is calculated by dividing the length of the side adjacent to the acute angle by the hypotenuse In this problem, the sin of angle a is which reduces to and the cos of angle a is reduces to The sin of angle b is or and the cos of angle b is or Now you can plug these values into the equation given in the problem and solve for sin(a – b):
41. The correct answer is D. This problem can be solved by first converting the fraction and the percent to their decimal equivalents: 1/100 = (0.01) and 10% = (0.10). Now, multiply the decimal values: 0.01 × 0.10 = 0.001.
42. The correct answer is K. The best approach to this problem is to pick some numbers for n, plug them into the answer choices, and eliminate the answer choices that do not always yield an odd number.
If n = 1, then 4n2 = 4(1)2 = 4, which is not odd. Eliminate answer choice F.
If n = 1, then 3n2 + 1 = 3(1)2+1 = 3 + 1 = 4, which is not odd. Eliminate answer choice G.
If n = 1, then 6n2 = 6(1)2 = 6, which is not odd. Eliminate answer choice H.
If n = 1, then n2 – 1 = (1)2 – 1 = 0, which is not odd. Eliminate answer choice J.
If n = 1, then 4n2 – 1 = 4(1)2 – 1 = 4 – 1 = 3, which is odd. Try another number: n = 2, then 4n2 – 1 = 4(2)2 – 1 = 16 – 1 = 15, which is also odd. Answer choice K will work.
Answer choice K is the only one that will give you an odd number for any value of n.
43. The correct answer is D. The area of a triangle is calculated using the formula A = (bh), where b is the length of the base, and h is the height. Based on the measures of the angles given, you can draw triangle ABC as shown below:
You are given that , the hypotenuse, is 8 units long. Because this is a 30–60–90 triangle, you can calculate the lengths of the base and the height The relationship between the sides of a 30–60–90 triangle is as follows: The side opposite the 30° angle is equal to of the length of the hypotenuse, and the side opposite the 60° angle is equal to of the length of the hypotenuse times . Calculate the lengths of the sides:
Now you can plug these values into the formula for the area of a triangle:
44. The correct answer is J. The best approach to solving this problem is to draw a picture like the one shown below:
Extend line through point X to an imaginary point A that is below point Z. Then, when you draw line , you create a special right triangle (WAZ) with sides of length 3, 4, and 5. Use your knowledge of the special 3–4–5 right triangle to determine = 5.
45. The correct answer is C. The area of a rectangle is calculated by multiplying the length by the width (A = w × l). Calculate the area of the first rectangle as follows:
Set the width equal to x, and the length equal to 4x.
A = x(4x)= 4x2
Now calculate the area of the second rectangle:
The length and width are tripled, so the width = 3x and the length = 12x
A =(3x)(12x)= 36x2
The area of the second rectangle is 36x2, which is 9 times greater than the area of the first rectangle (4x2).
46. The correct answer is G. Systems of equations will have infinite solutions when the equations are equal to each other. The first step in solving this problem is to recognize that the second equation is exactly twice the value of the first equation: 6x = 2(3x), 8y = 2(4y), so 7b must equal 2(14). Solve for b:
47. The correct answer is D. Logarithms are used to indicate exponents of certain numbers called bases. This problem tells you that log to the base 3 of x equals 2. By definition, loga b = c if ac = b. Therefore, log3 x = 2 if 32 = x. Since 32 = 9, answer choice D is correct.
48. The correct answer is K. The first step in solving this problem is to recognize that the distance from the point on the ground to the telephone pole is equal to the length of the side adjacent to the 37° angle, and that the height of the telephone pole is equal to the length of the side opposite the 37° angle. The length of the side opposite to any given angle divided by the length of the side adjacent to any given angle is the tangent of that angle. So, in this problem, tan Solve for the distance:
By definition, cotangent is so the distance is equal to 24 cot 37°.
49. The correct answer is C. The area of a parallelogram is calculated by using the formula A = (b × h), where b is the base and h is the height. The length of the sides, is not relevant in calculating the area. Plug the given values into the formula:
50. The correct answer is H. The easiest way to solve this problem is to draw a line and place the given points on the line, as follows:
Based on the line above, one possible length of is 27. Eliminate answer choices F, J, and K. Since you are left with answer choices G and H, you need to determine if could also be 3 meters long. Draw another line, and change the order of the points:
Based on this line, another possible length of is 3, so answer choice H is correct.
51. The correct answer is B. Given that both figures have the same area, Therefore, a2 = 3b2; taking the square root of both sides results in or
52. The correct answer is G. In this problem, the quantity 6a4b3 is less than zero, which means it must be negative. Since 6 is positive, and a4will always be positive, b3 must be negative. By definition, if you cube a negative number, the result will be negative. Therefore, if b3 is negative, then b must be negative, or less than zero. This means that b CANNOT be greater than zero, so answer choice G is correct.
53. The correct answer is C. In a geometric sequence, the quotient of any 2 successive members or terms of the sequence is a constant. This means that the exponent is 1 larger in each successive element of the progression, because you multiply by the same number each time you move to the next element in the sequence. Here, the second term of the sequence will have an exponent of 1 (sp), the third term of the sequence will have an exponent of 2 (s2p), the fourth term will have an exponent of 3 (s3p), and so on. You can see that the exponent of any given term is 1 less than the number of the term. Therefore, the exponent of s of the 734th term must be 733, (s733p).
54. The correct answer is J. If a system of 2 linear equations in 2 variables has no solution, that means that the lines do not cross each other anywhere in the (x, y) coordinate plane. If the lines do not cross each other, then they must be parallel. Parallel lines have the same slope. The line shown has a positive slope, so you can eliminate answer choice F, which has a slope of zero, and answer choices G and H which have negative slopes. Parallel lines cannot have the same y-intercept, so eliminate answer choice K.
55. The correct answer is A. Because angle x is less than 90°, it is an acute angle. The tangent of any acute angle is calculated by dividing the length of the side opposite of the acute angle by the length of the side adjacent to the acute angle This means that the length of the side opposite angle x is 15, and the length of the side adjacent to angle x is 8. The cosine of any acute angle is calculated by dividing the length of the side adjacent to the acute angle by the hypotenuse Since you know the lengths of 2 of the sides, you can calculate the hypotenuse by using the Pythagorean Theorem:
Pythagorean Theorem: a2 + b2 = c2, where c is the hypotenuse.
The hypotenuse is 17, which means that the cos of angle x is
56. The correct answer is F. To solve this problem, first look at the answer choices. You can eliminate answer choice J, because if either L, M, or N were 0, then LMN would equal 0; you are given that LMN = 1. Answer choice F must be correct, because LM = 1/N is true when LMN = 1 (divide both sides by N). The remaining answer choices could be true, but you can find at least one instance where they do not have to be true.
57. The correct answer is D. A number is rational when it can be written as a fraction. Additionally, any square root that is not a perfect root is an irrational number. Only answer choice D can be simplified such that it is a rational number:
58. The correct answer is H. In order to determine the volume of water to remove from the aquarium, you must first calculate the total amount of water that the aquarium holds. Volume is calculated by multiplying the length (24 inches) by the width (12 inches) by the height/depth (10 inches):
24 × 12 × 10 = 2,880
The total volume of the aquarium is 2,880 cubic inches. Since Rana must remove half of that volume to clean the aquarium, divide 2,880 by 2:
2,880 ÷ 2 = 1,440
Rana must remove 1,440 cubic inches of water.
59. The correct answer is B. The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept. Parallel lines have the same slope. Since line p has a slope of 3, line q must also have a slope of 3. Eliminate answer choices A and C because the slope is not 3. Now you need to determine the y-intercept. Line q intercepts the y-axis below the origin (0, 0), which means that the y-intercept must be negative. Eliminate answer choice E, which has a positive y-intercept. This leaves answer choices B and D. The distance between lines p and q is 3, as shown in the figure. If you draw a perpendicular line from the origin to line q, you will create a right triangle, with the y-axis as the hypotenuse. Since the hypotenuse is longer than either of the sides, which equal 3, the y-intercept of line q will be greater than 3, so answer choice B must be correct.
60. The correct answer is F. If 2 numbers, x and y, differ by 12, that means that x – y = 12. Multiplying the 2 numbers, (x)(y), will yield the product. Solve the first equation for x, then substitute the result for x in the second equation, as follows:
Since one of the answer choices must be the solution to that equation, plug in the answer choices, starting with the smallest value (–36) (note that the answer choices are in ascending order):
Now, substitute –6 for y in the first equation and solve for x:
Both equations are satisfied, and –36 is the smallest value among the answer choices, so the smallest possible value for the product of 2 real numbers that differ by 12 is –36.
Reading Test Explanations
1. The best answer is D. Eui Thi’s longing for Laos is triggered by the crowding of thousands of other refugees in Thailand. The vast number implies an uncomfortable chaos in the refugee camp. Answer choice D captures Eui Thi’s feeling of distress. Furthermore, the paragraph emphasizes the continuing political instability and danger in Laos. The author reinforces that emphasis in line 18 by putting the word stability in quotation marks to show she is using the term ironically. This eliminates answer choices A and B. Earthquakes aren’t mentioned in the passage, which eliminates answer choice C.
2. The best answer is J. The previous paragraph ends with a description of Eui Thi’s hopeful excitement at the idea of living in America and going to a new school. This emotion fades when she realizes the difficulties she will face. The word enthusiasm is the best replacement for zeal to capture her initial excitement.
3. The best answer is D. According to the passage, “Although Eui Thi was born in Laos, her family never truly belonged there.” The final sentence of the passage shows that Eui Thi doesn’t feel like she belongs in America either. These statements best support answer choice D.
4. The best answer is F. The description of Eui Thi’s parents’ “late-night whispers” is immediately followed by the military situation in Vietnam. The American army has left the Vietnamese capital, and her parents fear the influence of the communists. This information supports answer choice F.
5. The best answer is B. The passage states that Eui Thi’s family was given a house in America (lines 37–39). None of the other answer choices are stated in the passage as something Eui Thi’s family received in America.
6. The best answer is J. Lines 21–25 describe Eui Thi’s hopes for life in America. She would not be an outsider, meaning she would feel like she belonged there. She would have room to run. And she would have enough to eat so she wouldn’t be hungry all of the time. This covers Roman numerals I, II, and IV.
7. The best answer is B. According to the passage, “America was all Eui Thi had hoped it would be—and more.” At this point, Eui Thi believes that her dreams have come true and that living in America will be a positive experience.
8. The best answer is H. The passage indicates that Eui Thi “did her best to dress and act like the other girls” and that she was able to “approximate … charms … hairstyles, and even, eventually, American slang.” But, she “was from a different world,” and would always be an outsider. This best supports answer choice H.
9. The best answer is C. Lines 70–74 tell the reader that the dancing at Eui Thi’s school dance is completely different from the Tai-Dam dancing she was used to. This supports answer choice C. The author doesn’t describe the specific differences, which eliminates the other answer choices.
10. The best answer is H. In lines 39–40, Eui Thi’s sponsors walk her from her house to her new school. This information best matches answer choice H.
11. The best answer is C. Passage A describes the flexibility and plasticity of the American legal system, which makes answer choice C the best option.
12. The best answer is G. According to Passage A, “American law is an outward expression of the morals and values of the people; this flexibility gives judges the power to adapt the law to the needs and desires of the community. Many have praised the American judicial system because it embodies the idea that the law should do the will of the people.” This information best supports answer choice G.
13. The best answer is A. The context of Passage A shows that the American legal system is flexible and, thereby, able to be altered.
14. The best answer is G. Because the passage states that the efficiency of Western European law “cuts down on the number of frivolous lawsuits,” the author is indicating that such efficiency is a positive attribute of this type of legal system.
15. The best answer is B. According to Passage B, “It is useless for an individual to attempt a case if he knows in advance that the law is not in his favor.” This information best supports answer choice B.
16. The best answer is J. The context of the last sentence in Passage B indicates that, due to the predictability of law in Western Europe, citizens are afforded greater protection under the law.
17. The best answer is A. Passage A suggests that, even though the flexibility of American law can be seen as beneficial, there is still a downside. Likewise, Passage B states that “the Western European format is far from perfect.”
18. The best answer is H. Only answer choice H is a question that is addressed in both passages. The other answer choices are either beyond the scope of the passages, or only a tenet in one passage and not the other.
19. The best answer is B. Because both passages mention potential flaws in the legal systems, it is most likely that the authors would agree that no legal system will serve the needs of every citizen flawlessly.
20. The best answer is J. Each of the passages discusses a different kind of legal system found around the world. Therefore, answer choice J is the best option.
21. The best answer is B. Answer choice B captures the descriptive tone of the passage (unlike choice A). The passage focuses on all aspects of Cassidy’s career from its beginning to the present day, and never mentions the author’s own singing career.
22. The best answer is F. While the passage highlights the author’s childhood interests, it does not discuss Shaun Cassidy’s childhood. However, his singing career, acting career, and television writing career are described respectively in the first, second, and third parts of the passage. This supports answer choice F.
23. The best answer is D. The last paragraph discusses Shaun Cassidy’s realization that he enjoyed writing, and now primarily spends his time writing and producing, as opposed to acting, which he did when he was younger.
24. The best answer is G. The phrases “youthful admiration” and “shallow” suggest that the author’s feelings were appropriate for a child, or that they were “childlike.” The contrasting phrase “but his talent was real” suggests that the author’s initial view was inaccurate or oversimplified. These clues support answer choice G.
25. The best answer is A. Paragraph 4 describes the author’s infatuation with Shaun Cassidy. Most of her description involves his physical attractiveness. This supports answer choice A.
26. The best answer is H. The sentence states that most teen pop stars have short careers. This supports answer choice H.
27. The best answer is D. Option I is covered in lines 34–35 (where the author’s crush is described as “long since passed,” or chronologically prior). Option II is covered in lines 37–38, while option III is covered in lines 1–3. So these events happen in the order III, I, II, or answer choice D.
28. The best answer is J. Lines 15–16 describe the author’s immediate reaction to reading about Cassidy for the first time. Her enthusiasm and adolescent crush support answer choice J. No mention is made of envy (answer choice F) or a general interest in entertainment careers (answer choice G)—her interest is definitely focused on Cassidy.
29. The best answer is A. Although the passage mentions that Cassidy had occasional questions for the camera crew, it does not indicate that operating a camera was one of Cassidy’s achievements.
30. The best answer is G. The passage states that the author followed Shaun Cassidy’s career and “learned of each of his accomplishments.” According to the passage, Shaun Cassidy was both curious about and fascinated with “the production end of the entertainment industry.” These details and the positive tone of the passage support answer choice G.
31. The best answer is D. Lines 34–39 tell the reader that our species, Homo sapiens sapiens, is not related to Homo neanderthalensis. While the last paragraph states that human beings were better able to compete for scarce resources, this does not imply that they actively killed off the Neanderthals (answer choice C). Therefore, the passage supports answer choice D.
32. The best answer is G. Lines 66–68 tell the reader that the Neanderthals needed more food to survive in colder weather.
33. The best answer is A. Lines 38–39 state that humans share few genes at all with Neanderthals. This evidence supports the conclusion that Neanderthals are extinct and did not pass on their genetic heritage. Therefore, A is the best answer choice.
34. The best answer is G. The passage indicates that Neanderthals “were an evolutionary dead end,” and that they became extinct thousands of years ago.
35. The best answer is A. Lines 44–47 list data from radiometric dating (answer choice B), sediment cores (answer choice C), and climate models (answer choice D). Comparative femur measurements is the only one NOT mentioned; therefore, A is the best answer.
36. The best answer is G. Lines 10–12 state that the last evidence of Neanderthals is from about 30,000 years ago.
37. The best answer is D. The following lines list the types of innovations that helped humans survive the ice age. The wide range, from clothing to weaponry, supports answer choice D.
38. The best answer is H. Although line 78 mentions nets, the passage doesn’t specify the type. All of the other answer choices are specifically mentioned in the passage.
39. The best answer is B. Cro-Magnons are defined as an early example of modern humans. While the last paragraph states that human beings were better able to compete for scarce resources, this does not imply that they actively killed off the Neanderthals. Therefore, the best answer is B.
40. The best answer is F. According to the passage, “Neanderthals lacked the innovation skills necessary to survive in a changing world.” The other answer choices are contradicted in the passage.
Science Test Explanations
1. The correct answer is C. The results of Experiment 2 are shown in Table 2. While all of the plants grew during each time period, the amount of growth declined after week 6. Therefore, the time frame during which all of the plants began to experience a decline in growth rate was the 6–9 week period, answer choice C.
2. The correct answer is G. Based on the passage, an aphid is not a plant, but an insect.
3. The correct answer is C. The results of Experiments 1 and 2 are shown in Tables 1 and 2. If you look at the total growth for weeks 6–9, you will see that Yaupon experienced the most growth during weeks 6–9 in both studies.
4. The correct answer is F. Based on the results of the experiments, all of the plants experienced the least amount of growth during the time that foreign insects were present in the greenhouse. Table 3 indicates that the mosquito, the grasshopper, and the aphid are all indigenous, or native, insects. Therefore, the mantid, a foreign insect, would have the greatest effect on limiting plant growth.
5. The correct answer is B. The results of Experiment 1 show that all of the plants experienced more growth when native insects were present. Therefore, based on these results, you can conclude that, under some circumstances, native insects can help to increase growth in some plants, answer choice B.
6. The correct answer is F. According to Scientist 2, predictive measures can be developed “once enough information has been derived from past hurricanes.” This suggests that Scientist 2 believes that present-day predictive tools are not based on enough past data to be accurate, answer choice F.
7. The correct answer is A. Scientist 1 claims, “Animals are sometimes seen exhibiting strange behavior as far ahead as weeks before the hurricane makes landfall.” An article stating that animal behavior is useful in predicting hurricanes would support the views of Scientist 1. Scientist 2 does not make any mention of animals, and therefore, this article would not support Scientist 2’s view.
8. The correct answer is J. According to the passage, Scientist 1 believes that hurricanes making their way across the ocean cause ground vibrations. These vibrations can be detected by seismographs. It makes sense that, if seismic activity has been recorded, Scientist 1 would agree that a hurricane could be moving across the ocean, answer choice J.
9. The correct answer is A. Since both scientists agree that historical data is a useful and accurate predictor of hurricanes, it makes sense that both scientists’ viewpoints would be supported by the fact that historical hurricane data has recently been used to predict the path of a hurricane. The other answer choices may support one viewpoint or the other, but not both.
10. The correct answer is F. Scientist 2 believes that past hurricane data is an accurate way to predict when and where a hurricane will occur. Therefore, comparing current data with past data would be a good way to test whether Scientist 2’s claims are realistic. The other answer choices are not supported by the discussion of Scientist 2.
11. The correct answer is A. According to the passage, Scientist 1 believes that certain events, such as shifts in wind direction and wind speed, can be used to predict hurricanes. Because tropical storms are often accompanied by increased winds and later classified as hurricanes, Scientist 1’s viewpoint is strengthened.
12. The correct answer is J. Scientist 1 believes that an increase in tidal volume signals the arrival of a hurricane. Scientist 2 believes that tidal volume can increase for other reasons, so an increase in tidal volume is not a good predictor of hurricanes. According to Scientist 2, then, one major flaw in Scientist 1’s viewpoint is the assumption that tidal volume increases only before or during hurricanes, answer choice J.
13. The correct answer is C. To answer this question, look at Figure 2. Find 65 meters on the x-axis, which is depth, and follow it up until you reach the line. Follow that point on the line over to the left until you reach the y-axis, which is pressure. The point on the y-axis is 6.0 atm, which means that at a depth of 65 meters below the surface, the pressure is 6.0 atm, answer choice C.
14. The correct answer is F. The passage states the volume of gas in your lungs is inversely related to the pressure. As a diver moves closer to the surface, the pressure on the air spaces in the body is decreased, meaning that the space inside the lungs increases. Since the volume of a gas, like air, is dependent on the space that contains it, then the volume of air inside the lungs will increase when the space inside the lungs increases, answer choice F.
15. The correct answer is A. According to the question, gases have a higher compressibility because of their lower densities. The second paragraph of the passage states that gases have low density and high compressibility, whereas solids have high density and low compressibility.
16. The correct answer is H. Compressibility is the ability of pressure to alter the volume of matter. Answer H is the only choice that could be a hazard of scuba diving. The remaining answer choices are all false based on the information given in the passage.
17. The correct answer is D. According to the passage, portions of the line where large changes in pressure result in only minimal changes in volume signify low compressibility. Therefore, when the change in pressure is greater than the change in volume, compressibility is low, answer choice D.
18. The correct answer is J. The y-axis indicates the percent of salamanders that survive to adulthood. To determine which species of salamanders is most likely to survive to adulthood, find the tallest bar on the graph—the one that is closest to 100%. Species G is most likely to survive to adulthood, answer choice J.
19. The correct answer is B. According to Figure 1, the light-gray bars represent the percent that survive to adulthood when acid rain is present, and the dark-gray bars represent the percent that survive to adulthood when acid rain is not present. To answer the question, find the species that has the biggest difference between the height of the light-gray bar and the dark-gray bar. Species B shows a difference of about 20 percentage points; Species C shows a difference of about 30 percentage points; Species E shows a difference of about 20 percentage points. Species G shows a difference of about 10 percentage points. Therefore, the species with the greatest difference is Species C, answer choice B.
20. The correct answer is H. Common sense tells you that, if a species of salamander burrows into the ground, it should be pretty well protected from potentially harmful rain. Table 1 compares the weather protective behavior with the species’ ability to avoid acid rain damage. It is unlikely that burrowing into the ground would provide more protection than seeking cover inside a building, so the relative ability to avoid skin damage will probably not be greater than 1.5. Eliminate answer choice J. In addition, burrowing would certainly be better protection than remaining in the open, so eliminate answer choices F and G. Based on the data in Table 1, it makes the most sense that this species would have a relative ability to avoid skin damage of 0.5, answer choice H.
21. The correct answer is B. Information in Table 1 shows that high levels of exposure to acid rain correspond with low relative ability to avoid skin damage. This supports answer choice B.
22. The correct answer is J. The first step in answering this question is to look at Figure 1 and notice that Species A has the lowest percentage of survival to adulthood. Next, look at Table 1 and see that Species A does not seek protection, answer choice J.
23. The correct answer is A. To answer this question, locate 13 km on the “Distance along mountain range” horizontal axis of Figure 1. Then, look at the peak section composition. According to this information, at 13 km along the mountain range, the peak is composed of both igneous rock and limestone, answer choice A.
24. The correct answer is G. To answer this question, locate 20 meters on the “peak height” axis of Figure 1. Then, notice that, wherever the peak height is 20 meters, the net change in SCLL is somewhere between –10 and –30, answer choice G.
25. The correct answer is C. The data in Table 1 shows that for every increase of 5 meters in height, exposure to snow melt erosion is increased by about 8%. This means that at a height of 40–45 meters, the peak would be exposed about 8% more during the year than if it had a height of 35–40 meters. Based on Table 1, at 35–40 meters, the peak is exposed about 70% of the year. So, at 40–45 meters, it would be exposed approximately 78% of the year, answer choice C.
26. The correct answer is J. Figure 1 shows a direct relationship between net SCLL and peak height. At lower heights, the net SCLL is lower; at greater heights, the net SCLL is higher. This information supports answer choice J.
27. The correct answer is A. Table 1 shows a direct relationship between the peak section height and the percentage of the year that the peak is exposed to snow melt erosion. As the height goes up, the exposure time goes up. The graph in answer choice A represents this direct relationship.
28. The correct answer is G. The results of Experiment 1 are shown in Table 1. Based on the data in Table 1, as pH levels increase, defecation output also increases, answer choice G. Take care with tables and trends. In this case, the data are arranged by rat number, not defecation output or pH level.
29. The correct answer is A. According to information in the passage, the rats in Experiment 2 were given a dose of gut flora (microbes) 1 hour into the experiment. No such dose was administered to the rats in Experiment 1. Normal diets were followed by rats in both experiments, so answer choice B can be eliminated. Answer choices C and D contain information that contradicts information given in the passage, so they should be eliminated.
30. The correct answer is G. The results of Experiment 2 are shown in Table 2. While you don’t know what the pH levels were at the start of the experiment, you can see that the levels were higher after 5 hours than they were after 1 hour. Therefore, based on the results of Experiment 2, you can say that, if all gut flora are eliminated (as was done at the start of the experiment) and then reintroduced (as was done 1 hour into the experiment), the pH level will increase over time, answer choice G.
31. The correct answer is D. According to Table 1, Rat 5 had a pH level of 6.5 at 5 hours. This is the same pH level that Rat 11 had at 1 hour, before the gut flora were reintroduced. If Rat 5 were administered the gut flora after 1 hour, it is likely that its pH level would be the same as Rat 11’s pH level at 5 hours. Table 2 shows that this level was 8.0, answer choice D.
32. The correct answer is H. Table 1 shows defecation output, as measured by number of pellets. The rat with the highest defecation output was Rat 8, which had a defecation output level of 12.
33. The correct answer is C. The passage states that, “the higher the defecation output, the healthier the digestive tract.” Table 1 shows that rats with a higher defecation output also had pH levels around 8.0 to 8.5. Table 2shows that after bacteria were reintroduced to the digestive tract, the pH levels increased to around 7.5 to 8.5. These results support the conclusion that bacteria are necessary to the normal functioning of a healthy digestive tract, answer choice C.
34. The correct answer is G. The results of Study 3 are shown in Table 3. Look at each answer choice and calculate the differences in Total Time:
(1) Trial 1, Tennis ball and Golf ball: 0 seconds
(2) Trial 2, Tennis ball and Feather: 5 seconds
(3) Trial 2, Golf ball and Paper: 2 seconds
(4) Trial 3, Tennis ball and Feather: 3 seconds
The objects which differed most in Total Time were the tennis ball and feather during Trial 2, answer choice G.
35. The correct answer is A. Based on the passage, the only difference between Study 2 and Study 3 was the direction that the wind was blowing. This would affect the fall times.
36. The correct answer is F. Common sense tells you that dropping an object from a lower height would most likely result in a shorter fall time. Since the objects were dropped from a height of 20 feet, dropping them from a height of 10 feet would most likely produce shorter fall times for all of the objects, answer choice F.
37. The correct answer is B. Greater wind resistance is likely to lead to greater fall times. According to data in Table 2, paper consistently took the longest to fall, and therefore, registered the greatest fall times. It is most likely, then, that paper consistently exhibited the most wind resistance.
38. The correct answer is F. Since during Study 2 the fan was blowing up at a constant rate, and the paper took longer than the feather to fall, it makes sense that the paper was affected more by the wind from the fan (had greater wind resistance).
39. The correct answer is C. In both Study 1 and Study 3, the feather had the longest fall times compared to all other objects. Even though in Study 2 the paper had slightly longer fall times than the feather, overall, the feather took longer to fall over the course of all three studies.
40. The correct answer is G. Because there is no measurable resistance of any kind acting on the objects, they will fall at a nearly identical rate. In a vacuum, any object—from a mouse to an elephant—will fall at exactly the same rate.