Chapter 33

Practice Exam 4: Answers and Explanations

ENGLISH TEST

1. C

Read carefully! This question asks for the alternative that would NOT be acceptable. In this case, (C), so that to win 26 World Series championships, cannot work in the context, so (C) is the only possible answer.

2. F

There is STOP punctuation in the answer choices, so use the Vertical Line Test! The idea before the line The Yankees have had many great baseball players is complete, but the idea after the line contribute to the team, but one man stands out for his fortitude and good spirit: Lou Gehrig is not. This eliminates (G). Then, if you can’t cite a reason to use a comma, don’t use one: In this case, no further punctuation or additional words are necessary, making (F) the correct answer.

3. A

Use POE. Choice (B) creates an incomplete idea, so it can be eliminated. Choice (C) switches to the passive voice and makes things unnecessarily wordy. Choice (D) changes the meaning of the sentence to nonsense. Only (A) works in the context.

4. J

Read carefully! This question asks for the alternative that would be LEAST acceptable. In this case, (J), A Yankee scout had seen an intercollegiate game and played Gehrig, changes the meaning, so it would be the LEAST acceptable alternative in this context.

5. B

If you cannot cite a reason to use a comma, don’t use one. The only required comma comes at the end of the underlined portion as it sets off the unnecessary information including those for runs batted in and extra-base hits. Choice (B) is the only answer with the correct number of commas.

6. G

Read the question carefully. It asks for a word that most clearly communicates how positively Gehrig was viewed as a player. The most positive word among the choices is impressed, so (G) must be the correct answer.

7. A

Use a comma after an introductory idea. In this case, Then suddenly provides just such an introductory idea, so there should be a comma after the word suddenly, eliminating (B) and (C). Then, Gehrig’s should be possessive because the stamina belongs to him, making (A) the correct answer.

8. J

Pick the odd man out! The words infer and speculate mean essentially the same thing. The word imply cannot work as it changes the meaning, making (J) the LEAST acceptable alternative to the underlined portion. Infer means to deduce or interpret; imply means to suggest. This sports writer is inferring Gehrig’s illness from Gehrig’s slowed performance, but Gehrig’s slowed performance implies that he is ill.

9. D

The prognosis referred to in Sentence 1 must come after Sentence 3, which previews Gehrig’s illness. Only (D) puts these two sentences in the appropriate order.

10. H

Although would of and would have sound very similar, the correct form is would have, thus eliminating (F) and (G). Then, the past participle of to withdraw is withdrawn. If the word have were not there, withdrew would be acceptable, but this is not an option. The correct answer is therefore (H).

11. C

This entire passage is about Lou Gehrig, and the author’s personal experience does not play a role at all. Therefore, this sentence about the narrator’s experience with his dog does not contribute to the flow of the passage and should be eliminated. Choice (C) correctly states that the sentence should not be added and gives the correct reason it should not.

12. F

The underlined portion refers to the retirement belonging to Gehrig, or Gehrig’s retirement, eliminating (H) and (J). Then, if you can’t cite a reason to use a comma, don’t use one. There’s no reason to use one here, so (G) can be eliminated, and the correct answer is (F).

13. D

Choose the quotation that supports the words in the first part of the sentence, paid tribute to the life-affirming support he’d received from his fans. Choice (D) acknowledges this support, whereas the others discuss other topics.

14. G

The sentence could be rewritten to say his eternal optimism. Whose must therefore be the possessive, not the contraction who’s, which can be expanded to who is. Choice (G) is the only one among the choices that gives the correct possessive form.

15. B

The phrase comes at the beginning of the passage, which discusses the Yankees and the team’s long tradition of success. The inclusion of the year 1913 helps to set the stage for the emergence of Lou Gehrig, who is the main subject of this essay, so the opening phrase should be kept.

16. G

There is no contrast in this sentence, so there is no need for a word that suggests any such contrast. The correct answer is therefore also the shortest, (G).

17. C

Read the question carefully. It asks for a choice that identifies a personal connection the narrator feels to the locations she visits. Choice (C) is the best of the bunch: It has a positive tone and gives the narrator’s personal spin on the places she visits.

18. J

Read the question carefully. It asks for a choice that reinforces…the relationship between the narrator and her grandmother. Choice (J) is the only one among those listed that mentions both people, so it must be the correct answer.

19. D

The narrator is discussing her trips. Nothing belongs to those trips, so there’s no need for an apostrophe. Then, if you can’t cite a reason to use a comma, don’t use one. Choice (D), with no punctuation at all, is the correct answer.

20. G

The description of the cold weather conditions in this phrase helps to explain why the narrator was shivering with George Washington, so it should be kept. The passage as a whole is focused on travel, not history, so (G) gives a better reason the phrase should be kept.

21. A

The second sentence of this paragraph states, This is for you, so some gift or item must be given in the first sentence. Choice (A) is the only one in which such a gift or item is given, so (A) is the only possible answer.

22. F

Use POE on answers that don’t have a clear meaning. Choice (G) is too wordy and changes the intended meaning of the sentence. Choices (H) and (J) don’t make sense in the given context, so the sentence must be correct as written, as (F) suggests.

23. A

If each answer says essentially the same thing, choose the shortest that makes sense in the context. In this case, (B) and (C) add unnecessary words, so they can be eliminated. Without the word and, however, the sentence becomes two complete ideas separated by a comma, which does not work either. Choice (A) is the shortest answer that preserves the grammatical correctness of the sentence.

24. G

As written, the sentence creates a comma splice: a comma separating two complete ideas. The other choices correct this mistake, but only (G) makes sense in the given context.

25. C

Whenever you see STOP punctuation, use the Vertical Line Test! The first idea, I was so excited when the first three were released, is complete, but the second, Delaware, Pennsylvania, and New Jersey, is not. Choice (B), which contains STOP punctuation, cannot work, but there must be some kind of punctuation between these ideas. The best comes in the form of the colon, as in (C), which is appropriate after a complete idea and before a list.

26. J

Note the 3-1 split! Choices (F), (G), and (H) contain STOP punctuation. Choice (J) contains GO punctuation, so the odd man out must be correct. In addition, a comma would NOT be acceptable because the ideas surrounding it are both complete.

27. B

All four answers say essentially the same thing and are grammatically correct, so choose the shortest that makes sense. In this case, the word admiring says everything the other answer choices do, and it does so in a single word, so (B) is the correct answer.

28. H

Choices (F), (G), and (J) all create comma splices in that they separate complete ideas with commas rather than some form of STOP punctuation. Only (H) fixes this error.

29. C

Read the question carefully. It asks for a choice that best makes a connection between the narrator’s view of history and that of her friends. The only answer that mentions both the narrator and her friends is (C). Choice (D) is close, but it doesn’t mention the narrator at all.

30. H

While curious, anxious, and nervous might mean the same thing in some contexts, in this context, nervous doesn’t quite fit. Curious and anxious capture the largely positive tone of the essay, but nervous changes that tone to something negative or ambiguous. Choice (H) would therefore be the LEAST acceptable answer.

31. C

All the answers say essentially the same thing and are grammatically correct, so choose the shortest that makes sense in the context. In this case, (C) contains all the information the other answers do, and it does so in the most concise way.

32. H

Notice the 3-1 split! Choices (F), (G), and (J) all contain STOP punctuation (period, comma + FANBOYS, semicolon). Choice (H) is the only one that does not, so it must be the one that is NOT an acceptable alternative to the original sentence’s STOP punctuation.

33. D

The words cannot be where they currently are in the sentence because one can’t guess about something. The only answer that could work is (D), which changes the end of the sentence to say I shouldn’t be surprised about her request.

34. F

The passage is in the present tense, so (H) and (J) can be eliminated for changing that tense. Then, (F) provides the most concise form of the verb in question, so it is the correct answer.

35. A

Notice the 3-1 split! Choices (B), (C), and (D) all use the adjective appropriate, while (A) uses the adverb appropriately. The adjective is preferable because it modifies the word it; the adverb in (A) would modify the verb believes, which would not make sense, thus making (A) the NOT acceptable alternative.

36. F

There is STOP punctuation in the answer choices, so use the Vertical Line Test! The first idea, I’ll never forget my utter dismay when he taught her to jump off the swing set in our backyard, is complete, but the second idea, pretending she was a pilot and shouting, “Airborne!”, is not, so STOP punctuation is not acceptable, thus eliminating (H) and (J). A comma is acceptable in this situation, however, so (F) is correct. Choice (G) moves the comma to a place where there is no reason to have a comma.

37. C

Each of the answer choices should refer to the daughter, or she, playing house. Choices (A), (B), and (D) all do so, but (C) changes the subject of this part of the sentence to house. Choice (C) creates an odd incomplete idea, so it is the alternative that would NOT be acceptable to the underlined portion.

38. F

There is a semicolon in the middle of this sentence, so both parts of the sentence must be complete ideas. Choice (H) creates an incomplete idea, and (G) suggests a continuation where none exists. This leaves (F) and (J), which both provide contrasts, though (J) implies some kind of replacement or alternative where none exists.

39. D

When DELETE shows up as an answer choice, there must be some very good reason NOT to pick it. In this case, there is no such reason: Each alternative gives information that is redundant with the word annual, so the phrase as a whole should be deleted, as (D) suggests.

40. G

The sentence would be grammatically correct if the phrase other children her age could be removed, but such a removal would change the meaning of the sentence. The phrase should be kept because it clarifies the narrator’s daughter’s uniqueness among her peer group, as (G) suggests.

41. B

When DELETE shows up as an answer choice, there must be some very good reason NOT to pick it. In this case, there is a reason—the sentence is incomplete without a word where the underlined portion is. The word which cannot be used with people, so that can be eliminated. Then, use the word who where you would use he and whom where you would use him. In this case, you’d say he was mistaken, which means the correct answer must be (B), who.

42. J

Both words in the underlined portion modify the adjective right. Both words should therefore be adverbs, as both are in (J).

43. B

Choices (A), (C), and (D) note the father’s big dreams, but (B) claims those dreams are impossible, of which the passage gives no evidence. Choice (B) is therefore the LEAST acceptable alternative.

44. G

The sentence is incorrect as written (because the subject individual and the verb design do not agree), so (F) can be eliminated. Then, all the remaining answers say essentially the same thing, so choose the shortest that makes sense in the context. In this case, (G) contains all the information the other answers do, and it does so in the most concise way.

45. C

There is no contrast between this sentence and the last, so there is no need for the contrast words that appear in (A), (B), and (D). In this case, the correct answer is also the shortest, (C), which gives the correct meaning and is grammatically sound.

46. J

When DELETE shows up as an answer choice, there must be some very good reason NOT to pick it. In this case, there is no such reason: Each alternative gives information that is redundant with the phrase as a child, so the phrase as a whole should be deleted, as (J) suggests.

47. B

When DELETE shows up as an answer choice, there must be some very good reason NOT to pick it. In this case, there is a reason: If a word is removed from this part of the sentence, this sentence has two complete ideas separated by only a comma. In this context, only (B) can work, as the sentence describes what happened when the author looked into his hands.

48. F

The ideas on either side of the underlined portion are complete. These ideas should therefore be separated with STOP punctuation. Only (F) provides it in giving a comma plus and, one of the FANBOYS.

49. A

There is a comma in the middle of this sentence, and the idea after the comma, they’re not totally certain what it is intended to do, either, is complete. Because the second idea is complete and only a comma separates the two ideas, the first idea must be incomplete. Only (A) makes it incomplete, so it is the only possible answer.

50. J

Because the pronoun refers back to organisms, it should be the plural themselves, eliminating (G) and (H). Then, note the other verbs in this sentence: attract, repulse, and communicate. The verb camouflage should be consistent with those, making (J) the only possible answer.

51. A

The next sentence refers to how the same adaptation can be used to both attract and repulse, so the mention of how the adaptation can repulse predators in the previous sentence should be kept, and it should be kept for the reason that (A) gives. Although (B) may be true, (A) gives the better answer as it relates to the construction of this essay. Remember—this is English, not Science!

52. H

The phrase or land-based is used to clarify the word terrestrial, but it could be removed with no change to the meaning or completeness of the sentence. The unnecessary phrase should therefore be set off with commas, as it is in (H).

53. B

All the answers say essentially the same thing, so choose the shortest that makes sense in the context. In this case, (B) contains all the information the other answers do, and it does so in the most concise way. The mention of the researchers does not contribute anything to the meaning of the sentence and makes things overly wordy.

54. G

The paragraph as a whole discusses the ocean and various sea creatures. The only choice that previews what is to come is (G), which mentions that things are quite different in the ocean.

55. A

The two ideas in this sentence are complete: the most commonly emitted colors are blue and green and red and yellow have also been observed. There should therefore be STOP punctuation between them, eliminating (B) and (D). Choice (C) can also be eliminated because it incorrectly combines a semicolon with a FANBOYS conjunction. Choice (A) provides the correct answer by combining a comma with one of the FANBOYS.

56. J

The underlined portion can be expanded to read It is a veritable rainbow of color, making (J) the only possible answer. Choice (F) gives the possessive form; (G) does not make sense in the context; and (H) is never used.

57. C

The word these suggests that the word organisms will be plural. Therefore, use the plural possessive organisms’, which is contained only in (C).

58. H

Then is used for time or sequence. Than is used for comparison. In this case, one thing is being described as more than another, so (H), which contains than, is the only possible answer.

59. C

Choices (A), (B), and (D) are all synonyms for the underlined word, clarified. Choice (C) does not work in the context and changes the meaning, so it is the LEAST acceptable of the available alternatives.

60. G

This essay describes bioluminescence as it exists in both marine and non-marine habitats, among animals on Earth and those in the ocean. The essay would therefore achieve the stated goal, and it would do so for the reason that (G) outlines.

61. B

This sentence contrasts with the previous sentences, so it should begin with the word yet, thus eliminating (A) and (C). Then, because the idea continues from the ideas in the previous sentences, there is no need to begin a new paragraph, as (B) indicates.

62. J

Whenever you see STOP punctuation in the answer choices, use the Vertical Line Test. In this case, both ideas are incomplete: that is why a group of French physicians and started Doctors Without Borders in 1971. Therefore, STOP punctuation cannot be used, so you can eliminate (H). There is no need for commas, so the correct answer is the one with no punctuation, (J).

63. A

Read the question carefully. It asks for a choice that introduces the basic goal of Doctors Without Borders. The only answer that does this is (A), which gives that basic goal: to reach out to the innocent victims of wars in lesser-developed parts of the world.

64. H

If you cannot cite a reason to use a comma, don’t use one. In this case, no comma is necessary, so choice (H), with no commas, is the correct answer.

65. D

Choices (A), (B), and (C) each provide reasonable similes for the word atrocities. Choice (D) does not; furthermore, the UN and Red Cross are not raising sufficient alarm about these atrocities, though they are not trying to stop these alarms either. Choice (D) is therefore the LEAST acceptable alternative to the underlined portion.

66. G

The sentence in question describes the state of things in Nigeria in the late 1960s and the international community’s dismissive attitude toward it. The sentence provides some basis for why Doctors Without Borders formed when it did and the purpose that motivated that formation. The sentence should therefore be kept and for the reason that (G) states.

67. C

The ideas on both sides of the punctuation are complete: The doctors felt…alleviate the suffering and thus they declared…was on. Because both ideas are complete, there must be STOP punctuation between them. Only (C) contains this type of punctuation.

68. G

None of these introductory words is essential to the meaning of the sentence. There is no contrast, thus eliminating (F). There is no concurrent action, thus eliminating (H), and this is not a concluding thought, thus eliminating (J). Eliminate the introductory words altogether, and choose the most concise answer, (G).

69. A

If the phrase in question were deleted, it would not be clear whom the medical training was being provided to, and readers might believe that Doctors With Borders had founded a medical school in the region. The sentence should therefore be kept and for the reason that (A) states.

70. J

As written, this sentence does not contain a subject, unless the word suffering is the subject, but suffering cannot have felt aid. The only choice that provides an appropriate subject is (J), which completes the subject to be individuals suffering in war-torn regions.

71. A

The word between is used for two things, so this sentence is correct as written. If there were three or more groups being discussed, the correct answer would be (B).

72. H

The underlined word modifies the adjective simple, so it must be an adverb, thus eliminating (F) and (J). Then, because there is no reason to add the word more, the correct answer must be (H).

73. B

First, match the subject in the beginning of the underlined portion to the verb at the end of it. Choice (A) says the effort…have, and (C) says the efforts…has, so both can be eliminated. Then, (D) changes the verb to make it sound like the action being described happened entirely in the past. Because the organization described continues into the present, only (B) can work appropriately in place of the underlined portion.

74. F

Doctors Without Borders is a volunteer organization, and volunteers serve in this organization, making (F) the correct answer. Choices (G), (H), and (J) do not work in this context because they change the meaning, and each verb requires an object that the sentence does not provide.

75. C

Read the question carefully. It asks for the choice that most clearly shows that the self-sacrifice of the doctors deserves praise. Only (C) does so. Although (A) praises Doctors Without Borders, it does not suggest that the doctors deserve praise.

MATHEMATICS TEST

1. D

To find the quotient between terms in the geometric sequence, divide the fourth term by the third to find that 16 ÷ 8 = 2. Then divide the third term by the quotient, 2, to find the second term: 8 ÷ 2 = 4.

2. G

To solve for f(3, 4), substitute 3 into the original equation for a and 4 for b: f(3 ,4) = 2(3)(4) − (3 + 4) = 24 − 7 = 17.

3. D

To find the smallest number of coins Christine could use, start by counting the number of quarters she could use because they have the largest denomination. Because she wants to use exact change, she can only use three quarters, for a total of 75¢. This leaves 99¢ − 75¢ = 24¢. Next, count the number of dimes Christine could use, which is two, for a total of 20¢. The amount left is now 24¢ − 20¢ = 4¢, which must be paid in pennies. The total number of coins she will use is 3 quarters + 2 dimes + 4 pennies = 9 coins.

4. K

The equation for the area of a square is A = s². Plug 8 into the equation for s: A = 8² = 64.

5. A

Plug 3 into the equation for .

6. H

When dealing with NOT questions, eliminate answer choices that work. Use your calculator and try out the answer choices. 1,776 ÷ 12 = 148, and because 12 is a factor of 1,776, you can eliminate (F). The same is true of the numbers in (G), (J), and (K). However, 1,776 ÷ 18 = 98.66, so 18 is NOT a factor of 1,776 and is the correct answer.

7. C

Be careful with the CANNOT and NOT in this problem. Probability equals . In this case, only one person, Lauren, fulfills the requirements. There are 19 total students, but 4 of them cannot be the song leader, so the total number of students who could be the song leader is 19 − 4 = 15. The probability that Lauren will be selected is therefore . If you picked choice (B), you may have forgotten to subtract the 4 seniors from the total students.

8. K

To solve for x, first distribute the 4 on the left side of the equation. Remember to watch your negatives! 4x − 20 + x = 45. Next, combine like terms to get 5x − 20 = 45. Then, add 20 to both sides: 5x = 65, and finally divide both sides by 5 to find that x = 13.

9. B

Read carefully to translate this word problem into a math function. The problem indicates that there is a charge of $0.99 for each mile, which means that the final expression should include the term 0.99m. Eliminate (C), (D), and (E). The problem also states that the rental company charges $112 plus the mileage fee, so the final expression should include addition, which makes (B) correct.

10. K

Find the total amount that Stella would pay according to the finance plan. 4 years of 12 monthly payments per year makes a total of 4 × 12 = 48 payments. 48 payments × $130 = $6,240. The question asks how much more than the purchase price Stella would pay, so find the difference between the total price of the finance plan and the purchase price: $6,240 − $4,800 = $1,440.

11. B

Begin by reducing the number part of the fraction: . Next, remember the exponent rules: When dividing two numbers with exponents, subtract the exponents, so = 5y⁸⁻² = 5y⁶.

12. F

To avoid making a careless error, be sure to write down all the steps in simplifying this fraction. First, do the subtraction in the numerator and the addition in the denominator: . To divide by a fraction, multiply by the reciprocal: .

13. D

Point D could lie either to the right or to the left of point C. To find the point to the right, add the distance between the two points, 8.5, to point C: 8.5 + 3.5 = 12. Eliminate (A), (B), and (C). To find the point to the left, subtract the distance between the points from point C: 3.5 − 8.5 = −5, so (D) is correct.

14. K

To find the mean, or average, of a group of numbers, add the numbers up, and then divide by the number of numbers. This can be written as an equation, . Since you don’t know the total in this case, plug the information you have into the equation: 7 = , then multiply both sides by 4 to find that Total = 28. Add the three numbers you are given to find that 2 + 4 + 10 = 16. To find the value of the unknown number, subtract the total of the three known numbers from the total of all four numbers: 28 − 16 = 12.

15. A

Read carefully! The problem tells you that the net profit increased linearly, which means it increased by the same amount each year. This means that the answer should be the number that is exactly halfway between $1,489,000 and $1,725,000. You can eliminate (C) because it is much too close to $1,725,000 and (D) and (E) because they are bigger than $1,725,000. To solve, first find the difference between the 2009 profit and the 2007 profit: $1,725,000 − $1,489,000 = $236,000. To find the number in the middle, divide the difference by 2: $236,000 ÷ 2 = $118,000, then add that number to the 2007 profit: $1,489,000 + $118,000 = $1,607,000.

16. F

Notice that the dimensions of the picture are given in inches, and the question asks for the dimensions of the finished painting in feet. Start by converting the dimensions of the original picture from inches to feet. To make the conversion, divide each measurement by 12. The width is = 0.67 feet, and the height is = 0.83 feet. Next, set up a proportion of the original measurements to the finished measurements: . To solve for x, which is the width of the finished painting, first cross-multiply: 0.83x = (0.67)(6), or 0.83x = 4.02. Then, divide both sides by 0.83: x = 4.02 ÷ 0.83 = 4.84. The question asks for the approximate width of the finished painting, so round 4.84 to 5.

17. B

Slope-intercept form is y = mx + b, where m is the slope of the line, and b is its y-intercept. To put the given equation in that form, first subtract 5x from both sides: −y = −5x + 2. Next, divide both sides by −1, making sure to divide all three terms: y = 5x − 2. If you picked a different answer choice, you may have made a mistake with the negatives.

18. J

Remember order of operations on this problem. First, do the subtraction within the first absolute value sign to get |−12| − |−25|. Next, apply the absolute value to each term to get 12 − 25, and do the subtraction: 12 − 25 = −13.

19. D

All the angles in a triangle add up to 180°. Because the problem gives a range of possible values for the measure of ∠K, plug in a number that is less than 63°, such as 60°, then solve for ∠L:

37° + 60° + ∠L = 180°

97° + ∠L = 180°

∠L = 83°

Only (D) describes this result.

20. K

First, simplify the given inequality. Start by adding 1 to both sides: 3x > 27. Next, divide both sides by 3: x > 9. Because x must be greater than 9, its smallest possible integer value is 10.

21. E

This diagram of ribbons is essentially just parallel lines intersecting. The question states that the second red ribbon will be parallel to the first, and the two sides of the white ribbon are parallel to each other. The rule with intersecting parallel lines is that all big angles are equal, all small angles are equal, and any big angle plus any small angle equals 180°. The angle in question is a big angle, so to find its measurement, subtract the given small angle measurement from 180°: 180° − 62° = 118°.

22. G

Begin by finding the measurement of PR. If you recognize the side lengths of the triangle as a Pythagorean triple, you know that PR = 6. Otherwise, use the Pythagorean theorem, a² + b² = c², where c is the hypotenuse. Make PR side a:

a² + 8² = 10²

a² + 64 = 100

a² = 36

a = 6

Since the midpoint is the exact center of a line, QR is half the length of PR: QR = 6 ÷ 2 = 3.

23. A

The three marked points on the graph show the weight (which is the given x-coordinate) for books of three different lengths (the y-coordinate gives the number of pages). The weight of a book with 1,056 pages is 107.8 ounces, and the weight of a book with 868 pages is 89.0 ounces. To find how much more the longer book weighs, subtract the two weights: 107.8 − 89 = 18.8.

24. G

Katie’s equation, y = 0.1x + 2.2, is given in the description of the graph. The number of pages is shown on the x-axis of the graph, so substitute 1,338 for x in the equation: y = 0.1(1,338) + 2.2 = 133.8 + 2.2 = 136. This gives you the weight of the book in ounces, but the question asks for its weight in pounds. Notice that the question tells you, in the note, how many ounces are in a pound, in case you don’t know. To find the weight of the book in pounds, divide its weight in ounces by 16: 136 ÷ 16 = 8.5.

25. D

First, divide the shape into smaller rectangles:

In this diagram, the points have been labeled for reference. Use the formula for the area of a rectangle, A = lw, to find the area of each smaller rectangle. Rectangle BCDE has a length of 4. To find its width, note that AC, which is equal to 22, will have the same measurement as JI + HG + ED. The measurements of two of those segments are given, so solve for ED:

4 + 10 + ED = 22

14 + ED = 22

ED = 8

The area of BCDE = 4 × 8 = 32. Next, find the area of IFGH. The width is given, but you need to find the length. AJ plus IH must equal CD plus EG, so fill in the values you know and solve for IH:

10 + IH = 4 + 8

10 + IH = 12

IH = 2

The area of IFGH = 2 × 10 = 20. Now find the area of ABFJ. Its length is given, and the width is JI + IF. Since IF = HG, the width is 4 + 10 = 14, and the area is 10 × 14 = 140. Finally, add up all the individual areas to find the area of the entire figure: 32 + 20 + 140 = 192.

26. F

To find the average speed of essay grading, divide the total essays graded by the number of days it took to grade them. This can be written as an equation, . If Mr. Baylor averaged 178 essays per day for the first 3 days, you can find the total number of essays he graded in those three days:

Total = 178 × 3 = 534

In his last 3 days, he then had 996 − 534 = 462 essays left to grade. Use the equation to find the average speed for the last 3 days: Average = = 154

27. C

To correctly multiply, each term in the second set of parentheses must be multiplied by both terms in the first set of parentheses. To ensure you don’t miss something, write out all six terms, then combine like terms. Multiply each term in the second set of parentheses first by y, then by 1: (y + 1)(y² − 3y + 2) = y³ + y² − 3y² − 3y + 2y + 2. Count to be sure you have six terms before proceeding! Combine like terms to get y³ − 2y² − y + 2. If you picked another answer, you may have either forgotten a term or made a mistake with your negatives.

28. H

Use SOHCAHTOA to solve this problem. Because 5, the number in the denominator, is the hypotenuse of the triangle, the answer to the question must be one of the trig functions that has H in the denominator (that is, sine or cosine), so you can eliminate (G), (J), and (K). 4, the number in the numerator, is the side adjacent to ∠D. Since cos θ = , (H) is correct.

29. A

Plug In The Answers! If Shawn bought 7 contemporary songs, he must have bought 15 classical songs because he bought 22 in all. This means that Shawn spent 7($0.95) + 15($0.75) on songs altogether. These numbers add up to $17.90, which is the number we want, making (A) the correct answer.

30. G

To find the value of (−3)#(−7), substitute −3 for x and −7 for y throughout the equation:

31. C

A fraction is a relationship, so create a fraction with the amount of pineapple juice in the numerator and the total amount of punch in the denominator, then simplify:

32. G

Label the figure first: You know that XZ = 8. Because O is the center of the circle, XO = 4, so XY is also 4. Any triangle formed with two vertices at the ends of the diameter of a circle and the third vertex also on the circle is a right triangle. Because the hypotenuse (XZ) of triangle XYZ is twice as long as the short leg (XY), this is a special 30-60-90 triangle, so the long side (YZ) measures 4 feet. If you forget this triangle, you can always use the Pythagorean theorem. The formula for the area of a triangle is A = bh. Use XY and YZ as the base and height to find that A = (4)(4) = 2(4) = 8.

33. C

The roots of a quadratic equation are the same as the solutions. Begin by subtracting 7 from both sides to set the equation equal to zero: y² − 4y − 12 = 0. Now you can factor. Since the y² coefficient is 1, each factor will begin with y, like this: (y )(y ) = 0. Next, look for two numbers whose sum is −4 and whose product is −12. Those numbers are −6 and 2, so add them to your factors: (y − 6)(y + 2) = 0. To find the solutions for y, set each factor equal to zero and solve for y:

y − 6 = 0	y + 2 = 0
y = 6	y = −2

You could also plug in the answer choices into the original equation for y. You will find that only (C) makes the equation work.

34. G

Start by finding the volume of the rectangular portion of the model house. The formula for volume of a rectangular prism is V = lwh, so the volume is V = (20)(20)(16) = 6,400. Next, use the formula given in the note to find the volume of the right pyramid: Finally, add the two volumes together to find the total volume of the model house: 6,400 + 1,600 = 8,000.

35. B

The formula for the area of a trapezoid is Plug the numbers you know into the formula, then solve for height:

36. J

The formula for slope is slope = . Plug the values from the given points into the formula:

37. D

Draw the figure. Collinear means “in line with,” so point Z is on the same line as points X and Y.

The problem states that ΔWXY is both a right triangle and isosceles, so ∠XYW = 45°. Angles on a straight line must add up to 180°, so to find ∠WYZ, subtract ∠XYW from 180°: 180° − 45° = 135°.

38. H

Look for a pattern. This decimal repeats in 6-digit pattern. That means that the 6th digit is 5, and so is the 12th digit, the 18th digit, the 24th digit, and so on. Because 96 is a multiple of 6, the 96th digit is also 5. The 97th digit is therefore 3, the 98th is 8, and the 99th is 4.

39. B

In unit vector notation, i represents the change in the x value, and j represents the change in the y value. To find the sum u + v, you need to add the i values and the j values: u + v = (a + 2)i + (5 + b)j. The question states the u + v = 4i − 3j, so (a + 2)i + (5 + b)j = 4i − 3j. Look at the i terms first: (a + 2)i = 4i, so (a + 2) = 4, and a = 2. Eliminate (A), (D), and (E). Now, look at the j terms: (5 + b)j = −3j, so 5 + b = −3, and b = −8. The ordered pair (a,b) is (2, −8). The correct answer is (B).

40. H

An asymptote is a line that a function approaches but never reaches. A rational function has a vertical asymptote anywhere that the function is undefined, which occurs when the denominator is zero. Set the denominator equal to zero and solve for x: 2x − 6 = 0, so 2x = 6, and x = 3.

41. D

Because JM and KN are parallel, you know something about the angles in this figure, but you are given no information about the lengths of any line segments. Therefore, you can eliminate any answer choices that have to do with the lengths of line segments rather than angles. ∠KJM ≅ ∠JMN and ∠JKN ≅ ∠KNM because they are opposite interior angles of a line that intersects parallel lines. ∠JLK ≅ ∠NLM because they are opposite angles of two intersecting lines. Therefore, (D) must be true because similar triangles have congruent angles. Choice (C) is incorrect because for the triangles to be congruent the sides would also have to be equal, and the problem does not include the measurements for any line segments.

42. H

The printing cost of each cap is $3.50, and caps are sold for $5.00 each, so the profit on each cap is $5.00 − $3.50 = $1.50. The rental fee is $23.00, so to find the number of caps that must be sold to cover that fee, divide by the profit made on each cap: 23.00 ÷ 1.50 = 15.33. Be careful! If the athletic department only sells 15 caps, they won’t quite cover the $23.00 rental charge, so round up to 16.

43. A

Work this problem in bite-sized pieces. First, find the number of adult tickets sold by translating 60% of 540 into math: (450) = 324. If the price of each ticket had been $2.00 more, the department would have earned an additional (324)($2.00) = $648.00. The budget deficit is $3,000.00, so the final step is to find what percent $648.00 is of $3,000.00. Translate into math, then solve:

The question asks for the approximate percent, so round up to 22.

44. J

The printing cost of each T-shirt is $2.25, and T-shirts are sold for $4.00 each, so the profit on each shirt is $4.00 − $2.25 = $1.75. Try out the answers to find the number of shirts that will cover the budget gap. If the athletic department sells 1,726 shirts, as in (J), it will make 1,726 × $1.75 = $3,020.25, enough to cover the budget gap. Choice (H) is too small, and while (K) would cover the gap, the question asks for the minimum number of shirts, so (J) is correct.

45. C

The formula for the area of a triangle is A = bh. Make DE the base of the triangle. Count the hash marks on the graph to find that DE = 4. The height of the triangle is the perpendicular distance from point O to DE, which in this case is along the x-axis. Again, count the hash marks on the graph to find that h = 4. Now plug the numbers into the area formula: A = (4)(4) = 8

46. K

Since this is not a right triangle, you will need the law of sines to solve this question. The law of sines states that in triangle ABC with side lengths a, b, and c opposite ∠A, ∠B, and ∠C, respectively, . Because you know the length of XY, designate that as side a, and make YZ side b: To find b, first cross multiply: (b)(sin 53°) = (12)(sin 68°). Next, substitute the decimal values given in the second note for the sine expressions, then solve:

47. C

Factor the expression under the radical: = = . The imaginary number i is equal to , so 4c = 4ci. Substitute 4ci into the original equation for to find that 3 ± = 3 ± 4ci.

48. J

Draw two radii of the circle from the center to points C and D. Because the measure of an arc is proportional to the measure of the central angle it makes in a circle, ∠COD = 60°. Because OC and OD are both radii of the circle and therefore equal, ∠C must also equal ∠D. All angles of a triangle add up to 180°, so you can find the measurements of ∠C and ∠D:

∠C + ∠D + 60° = 180°

∠C + ∠D = 120°

∠C = ∠D = 60°

Since all three angles are equal, triangle OCD is equilateral. That means that all three sides, as well as the radius of the circle, are equal to 12. The diameter of a circle is twice the radius, so D = (2)(12) = 24. If you picked (F), you picked the radius instead of the diameter!

49. E

Draw a picture:

Use SOHCAHTOA. The distance between the pole and where the cord touches the ground is the side adjacent to the 19° angle, and you know the length of the hypotenuse, so use cos θ = :

cos19° =

x = 25cos19°

50. F

The formula for the graph of a circle is (x − h)² + (y − k)² = r², where (h,k) is the center of the circle, and r is the radius. If you multiply out the x and y expressions on the left side of the equation, you get an equation with two quadratics:

(x − h)(x − h) + (y − k)(y − k) = r²

x² − 2hx + h² + y² − 2ky + k² = r²

To find the center of the circle with the given equation, you need to put the equation into the standard format, which you do by completing the square for the two quadratics, then factoring. Start by subtracting 8 from both sides, and leave a space to complete each square: x² + 8x + y² − 2y = −8. Next, look at the x terms. 8x is equivalent to the middle term in the first quadratic in the example above:

8x = −2hx

h = −4

Since you need to add h², add (−4)² = 16 to the equation. Remember to add it to both sides: x² + 8x + 16 + y² − 2y = −8 + 16. Now repeat the process with the y terms:

−2y = −2ky

k = 1

Add k² = 1² = 1 to both sides of the equation: x² + 8x + 16 + y² − 2y + 1 = 8 + 1. Now you can factor:

(x + 4)(x + 4) + (y − 1)(y − 1) = 9

(x + 4)² + (y − 1)² = 9

The center of the circle is (−4, 1).

51. C

Read carefully, and work the problem in bite-sized pieces. When working with a series on the ACT, formulas are usually not necessary; just list out the terms. The question asks how long it took for the pool to be less than half full, so first calculate that half full is 13,000 ÷ 2 = 6,500. Note that Day 1 is the day after the pool was filled. The day the pool was filled it held 13,000 gallons of water. On Day 1, 10% of the water had evaporated, so it had 13,000 − (13,000)(0.1) = 11,700 gallons. On Day 2, another 10% had evaporated, so the pool had 11,700 − (11,700)(0.1) = 10,530 gallons of water. Keep repeating the process until you get under 6,500 gallons:

Day 3: 10,530 − (10,530)(0.1) = 9,477

Day 4: 9,477 − (9,477)(0.1) = 8,529

Day 5: 8,529 − (8,529)(0.1) = 7,676

Day 6: 7,676 − (7,676)(0.1) = 6,909

Day 7: 6,909 − (6,909)(0.1) = 6,218

52. H

Given a matrix , the determinant can be calculated as ad − bc. Plug in the appropriate values and evaluate: ad − bc = (3)(9) − (−4)(−5) = 27 − 20 = 7. The correct answer is (H).

53. D

The length of one side of the square is equivalent to the diameter of two circles:

24 = 2d

d = 12

Next, find the radius:

d = 2r = 12

r = 6

The formula for the area of a circle is A = πr², so A = π(6²) = 36π.

54. F

Read carefully, and work the problem in bite-sized pieces. First, calculate how much Andy paid for the 30 comic books: ($28.95)(30) = $868.50. The problem states that he will sell them when the combined value is $600 more than he paid for them, which means he will sell them when they are worth $868.50 + $600 = $1,468.50. To find how much each comic book will be worth when he sells them, divide the combined value by the number of comic books: $1,468.50 ÷ 30 = $48.95. To find how much more the value of each book will have risen when he sells them, subtract the current value per comic book from the value at sale time: $48.95 − $34.35 = $14.60.

55. B

AC is a diameter of circle G, so it has the same measurement as BJ, which is also a diameter. If the total length of BJ is 18, then BH = 18 − 3 = 15. Similarly, CE is a diameter of circle K and therefore has the same measurement as HD. If HD = 10, then JD = 10 − 3 = 7. To find the length of BD, add up BH, HJ, and JD: 15 + 3 + 7 = 25.

56. J

Draw the figure. First plot the two points you are given, and draw in the axis of symmetry.

The parabola must be a mirror image across the line of symmetry, so you know it will open to the right, and must cross the y-axis below the line of symmetry at the same distance from it as the given y-intercept. You can then eliminate (F). Because the given y-intercept is 3 units above the line of symmetry at y = −2, the other y-intercept will be 3 units below y = −2, as specified in (J). You can also plot the points given in the answer choices, and you will find that only (J) comes close to being in the right position.

57. E

The denominator of the second term in the expression is the common quadratic x² − y², which can be factored as (x + y)(x − y). So z² − 16 = (z + 4)(z − 4). Start by multiplying the first term by to make the z in the denominator positive: . Next, multiply the first term by to get a common denominator, then add the fractions:

= = .

You could also try plugging in a number for z. If you make z = 2, then

= = .

Plug z = 2 into the answer choices, and you will find that only (E) gives you the correct answer:

= .

58. H

If you are great at trigonometric functions, you may know that the tangent function has a fundamental period of π, so the value of tan (π + θ) would be equal to tan θ. Otherwise, sketching it out is a good way to tackle this question. Use the concept of a unit circle. A radian degree measure of π represents half a revolution along the unit circle, so the angle π + θ is in Quadrant III, as shown below.

It’s worth keeping in mind that tangent is always positive in Quadrants I and III, so (G) and (J) can be eliminated. The angle π + θ is a reflection of the original angle across y = −x, so the coordinates will be (−a, −b). The tangent identity is tan θ = , which, in the provided figure, would equate to the vertical length, −b, divided by the horizontal length, −a, or .

59. A

Start by subtracting a_n from both sides to isolate the terms containing d: a_n − a₁ = dn − d. Now, factor d out of the right side of the equation: a_n − a₁ = d(n − 1). Finally, divide both sides by (n − 1):

You could also Plug In. If you use the arithmetic sequence 2, 4, 6, 8, 10,…, then a₁ = 2. Make n = 5, and then a_n = 10. Because d = 2, the correct answer will be equal to 2 when you substitute those numbers in. Only (A) works: = 2.

60. H

Probability is defined as . In order to determine the total number of possible outcomes, set this problem up like a combination problem. Draw 5 spaces for the five cards she will draw. The first card could be any of the 54 cards, so put a 54 in the first spot. Since she does not replace the card that she just drew, the second card will be any of the remaining 53 cards, so place a 53 in the second spot. Using the same logic, the third space should be 52, the fourth should be 51, and the fifth should be 50. To determine the total number of possible outcomes, multiply these numbers together: there are 54 × 53 × 52 × 51 × 50 possible outcomes. Now that you have the total number of possible outcomes, you need to find the number of outcomes that match what the question “wants.” At this point you may realize that there are only four possible favorable outcomes: she could draw this combination and order of cards in any of the four suits. If necessary, though, you can calculate the numerator by setting up another combination problem. Draw 5 spaces for the five cards. In the first space there are 4 possible 10s that she could draw: one of each suit. Once she has drawn a 10 though, there is only one possible jack of that suit, so put a 1 in the second space. The third space must be the queen of the same suit, so there is also only one possibility. The same idea applies to the spaces for the king and ace. Therefore, the number of possible ways in which she could draw a 10, jack, queen, king, ace of the same suit, in that order, is 4 × 1 × 1 × 1 × 1 = 4. There are four outcomes that you “want,” so the probability becomes .

READING TEST

1. B

Choice (B) is correct because the fourth paragraph states that Rebecca had felt the draw of the fields. According to the first paragraph, she also enjoys the noises and smells of the field and can almost feel the atmosphere. Choice (A) may be tempting, but it is incorrect because Rebecca is not concerned with land ownership in those lines.

2. J

Choice (J) is correct because the fourth paragraph mentions that Rebecca had [k]nown how the land had turned on her parents, who had left the farm and worked elsewhere as a result. Additionally, the paragraph mentions consecutive bad years of farming, so that must refer to poor farming conditions. Choices (F), (G), and (H) can all be eliminated because they do not address farming conditions.

3. A

Choice (A) is correct because the fourth paragraph states that Rebecca wanted to reclaim her family’s heritage. The paragraph also explains that her great-grandparents had claimed the land as their own and passed it down to Rebecca’s parents. It may seem that (B) and (D) describe the land, but there is no support for the idea that the land is beyond the control of anyone or that it is filled with creatures.

4. G

This question asks the reader to identify which aspect of Rebecca’s surroundings is NOT mentioned within the first four paragraphs. Choice (G) is correct because there is no mention of how Earth feels. Choice (F) is incorrect because the scents are described in the second paragraph as Rebecca inhales the fresh and savory scent of almost-ripe wheat and the smell of Earth. Choice (H) is incorrect because the fourth paragraph states that the land had turned on her parents and driven them far from the only home they knew. Choice (J) is incorrect because the best time to visit the fields alone is described in the third paragraph.

5. A

Choice (A) is correct because the question asks for Rebecca’s impression of the land, and according to the fourth paragraph, she felt the draw of the fields. Later in the fourth paragraph, she is trying to reclaim the family’s heritage. Choice (B) is incorrect because her family does not give up its claim on the land; rather, the fourth paragraph states that even when her parents left, they had claimed the land as their own. Choice (C) may seem plausible for a short story like this one, but there are not enough literary devices to believe the true meaning of the story lies beyond its narration. Choice (D) is incorrect because, though the passage briefly mentions why the family had to leave the land, (D) does not answer the question regarding Rebecca’s impressions.

6. H

The question asks what the lines Without the former, she could never face the latter refer to. In paragraph six, the author states this moment was for enjoying the sheer bounty of life, not for fears and numbers, so the former is enjoying life, while the latter is fears and numbers. Choice (H) mentions both of these and is the correct answer.

7. C

Choice (C) is correct because in the last two paragraphs, Rebecca ponders loans, mortgage payments, and a bad crop ruining all her plans. However, she also focuses on the warm reality of owning the land. Choice (D) may be tempting because a story can do this, but there is no such parallel is drawn in the passage.

8. F

This passage is narrated in the third person by an omniscient narrator, immediately eliminating (H) and (J). The narrator presents Rebecca’s thoughts but does not judge them, eliminating (G). Thus (F) is correct because throughout the passage, the narrator explains what she liked best of all, that she had felt the draw to return to her land, and that she knew that in her bones.

9. C

Choice (C) is correct because the fourth paragraph states that Rebecca’s grandparents turned the wild prairie into productive fields of wheat and corn. Therefore, “wild” must mean fields not producing crops, which matches (C). The other choices offer synonyms for the word wild, but none of them work in this particular context.

10. J

Choice (J) is correct because the fifth paragraph describes how as soon as the bee landed on her cheek, Rebecca first flinched a little bit and then let it explore her face. Be careful with the other choices—these may state what most of us would do if a bee landed on our faces, but the correct answer needs textual support!

11. C

Choice (C) is correct because in the first paragraph, the author states that, Petrarch coined the name Dark Ages and that the name stuck. The other people are mentioned throughout the passage, but none of these is authors is described as having contributed to the popularity of the term as directly as Petrarch.

12. G

Choice (G) is correct because the sixth paragraph states that architects from the Middle Ages developed some of the most intricate stonework ever seen before or since. Choices (F) and (H) are certainly old arts that flourished at some time, but the author states that both were either disappearing or uncommon in the Middle Ages.

13. A

Choice (A) is correct because the last paragraph says that the Middle Ages are studied as a transition into the modern era. Make sure you are answering the right question! Choices (C) and (D) describe the beliefs of some, but this question asks about “scholars today.”

14. F

The question asks how the author believes an accurate picture of the Middle Ages will develop in the future. The author states in the last paragraph that medievalists will continue studying the evidence to try to understand the era. In the sixth paragraph, he also advises that historians look at what was actually created. These pieces of advice align best with (F), and the other choices are not quite sufficient.

15. D

The question asks the reader to identify which answer was NOT characteristic of people during the Middle Ages. Choice (D) is correct because in the fifth paragraph, the author writes that, while there is a myth that people thought Earth was flat, he states that they didn’t believe that idea. Choice (A) is incorrect because the third paragraph states that Few written records exist, so there were some written documents. Choice (B) is incorrect because the fifth paragraph states that mathematics was not abandoned in this time period. Choice (C) is incorrect because the sixth paragraph mentions the intricate stonework achieved in the Middle Ages.

16. J

Choice (J) is correct because the first paragraph introduces The period that began with the fall of the Roman Empire and goes on to call it the Medieval Period and the Dark Ages. Choice (G) overstates how many terms are given and narrows the field too much. Choice (H) is incorrect because, while the first paragraph did mention that some referred to the Middle Ages as a cultural wasteland, that was not the main point of the paragraph.

17. C

Choice (C) is correct because the sixth paragraph states that three-dimensional, realistic art certainly became less common and the ability to build a self-sustaining dome was lost for hundreds of years. Choices (A), (B), and (D) each refer to areas of study that developed or flourished, but this question asks for those that “truly did go into decline.”

18. F

Choice (F) is correct because the first paragraph states that Petrarch wanted to connect his studies with those of antiquity, or the classical era. Choice (J) may be tempting, but it is incorrect because the paragraph states that Petrarch related his studies to older times, not newer times.

19. D

Choice (D) is correct because the paragraph gives some of the different names for the Middle Ages and states that Petrarch coined one of the terms. Therefore, coined must mean something like came up with or invented. Choice (D) fits this description. Choices (A) and (C) employ different meanings of the word coin, but those meanings do not apply in this context.

20. F

The question asks for how people viewed education in the Middle Ages before Numbers and Lindberg. The fifth paragraph states that scholars refer to the decline in learning that they believed was characteristic of this era. Choice (F) fits this description. The other choices are mentioned in the passage, but they are mentioned as coming after Numbers and Lindberg rather than before.

21. B

The question asks for the primary reason the critics and scholars in Passage A doubt the identity of Shakespeare, and the passage states that Shakespeare couldn’t have had the education, aristocratic sensibility, or the familiarity with the royal court necessary to have authored all the titles attributed to him because of his humble origins. Eliminate (A) as it doesn’t directly address Shakespeare. Eliminate (C) as the medium (novel vs. play) is not in question. Choice (D) is also out as the 19th century is well outside of the timeline. Choice (B) is the correct answer.

22. H

The question asks why critics think Queen Elizabeth may have written Shakespeare’s plays, who is mentioned in regards to Shakespeare’s oceanic grasp of the totality of Elizabethan England. Since there’s no mention of strong female characters, eliminate (F). There is also no mention of natural sciences, so (G) is out. And, though the plays may have been popular with royals of the time, that is not used as evidence of why Elizabeth herself might be their author. Only (H) addressed the depth of knowledge.

23. A

The author of the passage uses the phrase average townsman to show how unlikely it is that someone “average” would create the extraordinary works that have been attributed to Shakespeare. There is no mention of “civic affairs,” so eliminate (B). There is also no indication that Shakespeare was well-liked by his neighbors or otherwise, so (C) is gone as well. Choice (D) brings up the thought that Shakespeare was in disguise, another topic not mentioned in the passage. The correct answer is (A).

24. J

Try scratching oceanic out and replacing it with a word that makes sense in its place. Something like “vast” or “thorough” might work. Neither “natural” nor “informal” match with “vast” or “thorough,” so eliminate (F) and (G). And while the ocean might be “salty,” this choice does not work in any other sense, so (H) is out as well. Select the correct answer, (J).

25. C

The question asks for the main reason that the author of Passage B believes that Shakespeare is the sole author of works attributed to him. While she concedes that it’s not reasonable, she counters that that is the nature of genius. Eliminate (A) as this author does believe Shakespeare to be the solo author of works attributed to Shakespeare. Eliminate (B) as there is no question of when these plays appeared or their significance as “serious works of art.” There is no mention of disapproval of one way of life or another, so (D) is out. Choice (C) is the correct answer.

26. G

The author makes her argument by offering the point that the most intelligent students may not necessarily also be the wealthiest, as is assumed by the anti-Stratfordians according to the author. Eliminate (F) as it offers the anti-Stratfordian’s point of view, not Truelove’s. There is no indication that the Anti-Stratfordians “disapprove” of any of the students, nor any mention of how much was earned from Shakespeare’s plays, so eliminate (H) and (J), and select the correct answer, (G).

27. C

As it’s used in Passage A, the “rhetoric of accumulation” refers to researchers seek[ing] to decode Shakespeare’s texts for hints as to the author’s true identity. This includes finding “parallels” in the language found in other writer’s works. Truelove uses the example of modern tech terms such as “app” and “iPhone” being accessible to non-tech people as evidence that those using a “rhetoric of accumulation” may be misguided. This is not about using the wrong texts, as (A) suggests. There’s also no mention of economics, nor an argument for one more likely alternate “Shakespeare” over another, so eliminate (B) and (D). Choice (C) is the correct answer.

28. J Watch out for what this question is asking: though the authors of both passages are mentioned, we’re looking for the author of Passage A’s point of view to start our answer choice, i.e. one which is skeptical that Shakespeare wrote the works attributed to him. Choice (F) indicates that Thompson prefers one theory over the other, while he presents both points of view without espousing either. Thompson doesn’t overtly criticize either of the groups he describes, so eliminate (G). And (H) is out, as Thompson does not explicitly state any doubt of the anti-Stratfordian claims. Choice (J) is the correct answer.

29. B

This question asks how Truelove disagrees with the theories Thompson presents. She directly counters the points made by Thompson by taking the critiques and offering evidence to the contrary that could allow for Shakespeare to have written the works attributed to him himself. There is no “personal attack” or “righteous anger,” so eliminate (A) and (C). While “historical data and archival research” can be assumed, they are not used to disagree with the theories presented in Passage A, so eliminate (D). Choice (B) is the correct answer.

30. J

We know from our previous work that Passage A promotes the possibility of multiple and/or alternate authors of Shakespeare’s works, while Passage B opts to show that it could be possible for Shakespeare to have written those works on his own. Again, neither passage makes its sole argument on economics, so (F) is out. Both passages include elements of criticism, so eliminate (G). Both “wrongheaded fool” and “serious thinker” could be used to describe the authors (though judgmentally), not their relationships to the theories described, so eliminate (H).

31. C

Choice (C) is correct because the third paragraph states that forming lasting romantic bonds is one of the primary proofs given in support of free will. Choices (A), (B), and (D) give examples of things that contradict or complicate the idea of free will.

32. G

Choice (G) is correct because the fifth paragraph states some scientists believe that electrical impulses become chemical impulses, or neurotransmitters, which eventually trigger biological impulses. The third paragraph describes the biological motivations that people have. Therefore, (G) is supported by the link between the two paragraphs. Choice (F) is incorrect because electro-chemical theory supports the third paragraph; the third paragraph does not support electro-chemical theory. Choice (H) is incorrect because the third paragraph does not undermine electro-chemical theory.

33. D

Choice (D) is correct because the last paragraph states that the scientific contributions can help solve the cases, which fits with (D)’s “helpful.” The paragraph also indicates that incorporating the scientific methodologies into police work is increasing and is one example of convergence. This information, combined with the rest of the passage, fits with (D)’s “new.” The other choices may be partially correct, but they have a negative or dismissive tone where no such tone exists in the passage.

34. F

Choice (F) is correct because the fifth paragraph states that electrical impulses become chemical impulses, or neurotransmitters, which eventually trigger biological impulses. The fifth paragraph uses this theory to suggest a link between humans and particles, as both respond to these electrical impulses with biological impulses.

35. B

Choice (B) is correct because the fifth paragraph states that all matter is made up of protons, neutrons, and electrons, each of which reacts to electrical impulses. Choices (A) and (C) are incorrect because electrical impulses are in all types of matter and in human interaction.

36. J

Choice (J) is correct because the fifth paragraph states that electrical impulses become chemical impulses, which eventually trigger biological impulses. Choice (H) is incorrect because it reverses this information. Choices (F) and (G) cannot work because these chemists do not focus on free will.

37. C

Choice (C) is correct because the paragraph addresses pair-bonding, which is typically seen as an example of free will. However, lines 26–30 and earlier indicate that pair-bonding has many evolutionary advantages that may signify its true motivation or origin. Choice (B) takes this mention of evolutionary advantages too literally.

38. F

Choice (F) is correct because the sixth paragraph mentions a practical example of the convergence of scientific theory and human practice. The paragraph describes police departments using these theories to solve crimes.

39. D

Choice (D) is correct because the third paragraph indicates that evolutionary biologists uncovered evidence that suggests that working as a pair has many evolutionary advantages. Pair-bonding had before been considered evidence of free will, because it does not seem to have a natural cause. This supports (D). Choice (C) misunderstands the role of pair-bonding: It was not used to redefine free will but to support an accepted definition of it.

40. G

Choice (G) is correct because the paragraph states that scientists are beginning to question previous ideas. The paragraph then asks How separate are humans…from the rest of the natural world? These questions show the uncertainty in the scientific world. Choices (F), (H), and (J) may describe other scientists, but these scientists are characterized by their uncertainty.

SCIENCE TEST

1. C

Use what you know from biology—mitosis refers to the splitting of a cell into two equal parts. If you weren’t sure of this, use the blurb as a hint—it refers to the dividing cell cycle. This question is asking for the picture of what happens as mitosis nears completion, or in other words, the picture that shows the closest thing to two separate entities, which the picture for Cell 3 does.

2. J

The graph shows a direct relationship between toxin concentration and AI, the apoptotic index. Therefore, if the AI is approximately 0.007 (or 0.7%) at 80 ppm, it must be greater than that value at 90 ppm, making (J) the only possible answer.

3. D

As the actively dividing cell cycle progresses, the cell gets larger before its two halves split into equal parts. The first stage must therefore show the smallest and least divided picture, as (D), Cell 4, does.

4. G

According to Figure 2, there were 225 cells in cycle stage G₂, and there were 75 cells in stage S. There were therefore 3 times as many cells in cycle stage G₂ as there were in stage S, as (G) indicates.

5. A

The text above the graph indicates that the graph charts one thousand actively dividing fibroblast cells. There were just over 525 cells in cycle stage G₁. Therefore, the proportion of all the cells that were in cycle stage G₁ was approximately 525 of 1,000, or (A).

6. H

Use the provided equation. . Refer to Figure 1 to determine that the AI at a toxin concentration of 30 ppm is 0.005. Plug these values into the equation to get which can be rearranged to get 0.005(100,000) = number of cells undergoing apoptosis.

7. B

This question is a reasoning question that requires you to synthesize data from several sources, so this question is best done as a Later question after you have answered some of the other questions on this passage. Use POE. If you have already answered question 11, then you can use this answer to help you out. Patient P most closely resembles Patient 2, so the correct answer needs to either include both I and II or exclude both I and II. Eliminate (A) and (C). Choice (D) includes both Patient P and Patient 2, but it also includes Patient 4. Based on Figure 1, Patient 4 differs from Patients P and 2. Eliminate (D) and choose (B).

8. F

If you’re unsure whether to answer Yes or No, use the reasons. Choices (G) and (J) can be eliminated because Patient 4 and Patient P do have the same blood-smear findings according to Table 1. Judging from Table 1 alone, we have all the necessary evidence to say that Patient 4 and Patient P are the same, thus making (F) the correct answer.

9. C

This question requires a bit of outside knowledge, unless you use POE aggressively! First, choice (A) suggests that hemoglobin breaks down at a pH of 8.6, but this experiment is measuring hemoglobin, so the scientists would not want it broken down. Always give special consideration to opposites—in this case, (C) and (D). Then, the scientists likely used this pH level because the process they were observing occurs best at this level, making (C) the correct answer.

10. F

Use POE. If individuals with sickle cell traits carry resistance to malaria, one of the most deadly mosquito borne illnesses, then they would be better suited to environments with high incidence of mosquito borne illness. Eliminate (H) and (J). Eliminate (G) because it doesn’t make sense that an increase in likelihood of passing sickle cell traits on to offspring would lead to a lower incidence of sickle cell anemia.

11. B

Match the peaks in the various lines. Patient P’s single peak most closely resembles that of Patient 2, thus making (B) the only possible answer.

12. J

The figure shows a positive electrode on the left side and a negative electrode on the right. Similar charge characteristics must therefore be similar positions relative to given electrodes. Of the choices listed, peaks X and Z seem to be a similar distance from the positive electrode, making (J) the correct answer. Peaks W and Y are also similarly positioned, but no answer choice indicates this pair.

13. A

Use POE. Opposite charges attract each other, eliminating (B) and (D). In addition, “the left” refers to the side of the positive electrode. Because opposite charges attract each other, the peaks closest to the positive electrode must be negative, as (A) indicates.

14. H

This is technically an outside knowledge question, but you should be able to get to the answer using POE even without any chemistry background. It wouldn’t be logical for propionic acid to be neutralized by another acid, so eliminate (G) and (J). Now, if you do not know whether bases accept or donate protons, check the passage to see if this information is provided. The second sentence states that “molecules are acidic since they are able to donate protons in solution.” Eliminate (F) because this describes an acid. The correct answer is (H).

15. C

Freezing point is the temperature at which a liquid turns to a solid. Melting point is the temperature at which a solid turns to a liquid. Freezing point and melting point therefore occur at the same temperature. According to Table 1, acetic acid has the highest freezing point, so it must also have the highest melting point, as (C) indicates.

16. G

According to Figure 2, the vapor pressure of formic acid in a 0.5 mole fraction of water is approximately 11mm Hg. Draw a line straight across to see that formic acid has a solid vapor pressure at a 0.8 mole fraction of water, thus making (G) the correct answer.

17. A

According to Figure 2, the vapor pressure of acetic acid starts around 12.5 mm Hg, decreases to approximately 5 mm Hg, then increases again to approximately 15 mm Hg. It therefore decreases then increases, as (A) suggests.

18. G

Note the long molecular formulas in Table 1. Follow the coefficients: Butyric acid has subscripts 3, 2, and 2. Valeric acid has subscripts 3, 2, 3. As the final number increases, the boiling point increases as well, each time by approximately 20°C. Therefore, since the new formula given in the problem has subscripts 3, 2, 4, it should have a boiling point approximately 20°C higher than that of valeric acid, or approximately 206°C. This number is contained in the range given in (G).

19. C

According to Figure 1, the vapor pressures for formic acid are uniformly higher than those for acetic acid at various temperatures. It can therefore be inferred that acetic acid is more resistant to these increases in vapor pressure, making (C) the correct answer. On questions like this one, if you are unsure how to answer, always use POE aggressively: It may reveal trends that you hadn’t seen before. POE can also help to narrow down the choices: (A) and (D) can be eliminated right away, for instance, because they do not match the information in the graph.

20. J

According to Table 3, as the solenoid length of XY decreases, the weight increases. The text above the graph indicates that these weights were found at a voltage of 8.00 V. In Experiment 1, the weight at a voltage of 8.00 V is 5.0095 N, which is less than any given in Table 3. Because this weight is less, the solenoid coil in Experiment 1 must have had a greater length than any of those listed in Experiment 3, or greater than 9.50 cm, as (J) suggests.

21. B

Experiment 2 inverts the orientation of the bar magnet in Experiment 1. This variation caused a different trend. In Table 1, as voltage increased, weight increased. In Table 2, as voltage increased, weight decreased. The direction of the force must therefore have been different, as (B) suggests.

22. J

According to Table 3, as the solenoid length of XY decreases, the weight increases. The voltage is not be altered, thus eliminating (F) and (G). Choice (J) accurately describes the trends in the graph.

23. C

Experiment 3’s data is taken at 8.00 V. Compare the 8.00 V values in Experiments 1 and 2. In Experiment 1, the weight at 8.00 V is 5.0095 N, and in Experiment 2, the weight at 8.00 V is 4.9905 N. This is a decrease of approximately 0.02 N. Therefore, if the orientation of the magnet matches that of Experiment 2 rather than Experiment 1, the weight should be approximately 0.02 N less than the 5.0105 N value given in the chart. Choice (C) offers the closest value.

24. J

According to the text above Experiment 1, before the start of each trial, the scale read 4.7 N. Then, the scale was adjusted to read 5.0000 N. The scale was therefore adjusted upward by approximately 0.3 N, as (J) suggests.

25. B

According to Table 3, as the solenoid length of XY decreases, the weight increases. Choices (A) and (D) can be eliminated because they show direct relationships rather than inverse ones. Then, the weights in Table 3 are closer to 5.0200 N than they are to 0 N, so the data shown in (B) is more accurate.

26. J

In Experiment 1, as voltage increases, the weight increases. Since weight is a measure of force, the increase in weight represents the force that the magnet exerts. For example, at a voltage of 8.00, the force that the solenoid exerts on the magnet is 5.0095 − 5.0 = 0.0095 N. Eliminate (F) because (H) will exert a larger force. Experiment 2 differs from Experiment 1 in the direction of the force, but the magnitudes of the forces in Experiment 2 are the same as those in Experiment 1. At a voltage of 8.00 in Experiment 2, the force exerted by the solenoid is 4.9905 − 5.00 = −0.0095 N. Since magnitude is independent of direction, the magnitude of this force is still 0.0095 N. Therefore, only factor to consider in this question is the voltage; the largest voltage will exert the largest force. The correct answer is (J).

27. C

Use POE! Scientist 2 draws heavily on Figure 2, and his basic argument is that rises and falls in the global average sea level occurred many times in the last 150,000 years. He would not say that the temperature has remained constant, eliminating (A), nor would he attribute global temperature change only to industrial activity, eliminating (B). Later in the passage, Scientist 2 states, In general, global average sea level rises and falls with global average temperature, which is paraphrased in (C).

28. J

According to Figure 1, the change in average global sea level in 2000 was approximately 0.05 m. According to Scientist 1, Since 2000 the change in global average sea level has increased at a rate of 2% per year. Since you don’t have a calculator, make the math easier for yourself—instead of 0.05 m, use 500. If the change in 2000 was 500, in 2001 it was 510, in 2002 it was approximately 520, and in 2003 it was approximately 530. Translate this back into the numbers you started with to find a change of approximately 0.053 m, (J). Even if you found this math a little tricky, you can certainly eliminate (F) and (G) because they are smaller, and you may have ballparked to see that (H) would not be quite high enough.

29. A

If you’re unsure how to answer the question, use POE on the reasons. Figure 1 shows data from the years 1500 to 2000. This eliminates (B) and (D). Then, because it is clear that Figure 1 does not address climate changes from 150,000 years ago, Figure 1 cannot be said to provide sufficient support Scientist 1’s claim, making (A) the correct answer.

30. J

According to Figure 2, 100,000 years ago, the change in average sea level from present was approximately −60 m. If the present location is fixed 90 m above a fixed landmark, then the level 100,000 years ago would be 60 m less than that or 30 m, (J).

31. C

There are two major peaks in average global sea level according to Figure 2. One occurred recently, and the other occurred approximately 115,000 years ago. Scientist 2 would therefore cite the 115,000-year figure as evidence that sea levels have risen to present levels before. Choice (C) is therefore the correct answer. If you chose (D), be careful! You may have been looking at the axis for air temperature rather than the one for global sea level.

32. F

According to Figure 1, the change in average global sea level hovered between −0.15 m and −0.10 m from 1500 to 1800. Scientist 1 would likely consider this a negligible change, and because Scientist 1 sees a direct correlation between rising sea levels and rising temperatures, he would likely consider the rise in temperature to be negligible as well, as (F) suggests. Scientist 1’s bigger point is that temperatures followed a natural course until 1800, when they began to rise dramatically.

33. A

According to Scientist 1, Between 1950 and 2000, global average sea level rose by 0.1 m. Choices (B), (C), and (D) show a general decrease in sea level, so all three can be eliminated. A jump 100 times more than 0.1 m would be approximately 10, and only (A) shows an appropriately large jump in the sea level.

34. H

Use POE to tackle this question. Eliminate (F) because if the unknown ion solution were more dilute, then the water would have moved across the membrane into the glucose solution. Eliminate (G) because the passage states that the glucose molecules are larger than the water molecules, so a membrane that allows glucose through it would have to also allow water molecules to pass through it. Finally, eliminate (J) because the pressure would have to be higher than the osmotic pressure in order to prevent water from flowing from a region of high to low water concentration. The answer is (H); if the water concentration on both sides of the membrane is equal, then water level will not change on either side.

35. D

Use POE. If albumin molecules do not pass through the selectively permeable membrane, the albumin solution on the left side will not pass through to the right, meaning the solution levels on the left cannot fall, eliminating (A) and (C). Then, because there is no glucose-cupric combination, there is no reason for there to be a red solution, eliminating (B). Only (D) remains and is the correct answer.

36. F

In Experiment 1, the cupric solution is able to pass through the membrane to produce a red color with the glucose solution. In Experiment 2, the cupric solution is able to pass through the membrane to form a blue-colored solution with the pure water. It can be inferred, then, that cupric was able to pass through the membrane in both experiments and into both glucose and pure water, as (F) suggests.

37. C

Read the first lines of each experiment. Experiment 2 states that Cupric ion solution is poured in the left, and Experiment 3 states that Glucose solution is poured in the left. These statements match with the information in (C).

38. G

Because mixing glucose and cupric ions results in a red solution, a membrane that allows all solutions to pass through would result in the mixing of all solutions. In Experiment 1, glucose is poured in the left and cupric in the right. With a membrane that allows both these solutions to pass through, the solutions will mix throughout the tube, creating a red solution in all parts of the tube.

39. A

Because the solution on the left becomes red, cupric ions must be able to pass through the membrane, and because the water levels change, water must be passing through the membrane as well. If glucose were able to pass through the membrane, both sides of the tube would be filled with red-colored solution. Therefore, it can be inferred that glucose is larger than both cupric and pure water, but it is not possible to determine the relative sizes of cupric and pure water, as (A) suggests.

40. G

Experiment 1 states, cupric ion solution is poured on the right. The information above Experiment 1 states, Water and glucose solutions are colorless while cupric ion solutions are blue. Therefore, before the experiment begins, the right side, containing only cupric ion solution, must have been blue, as (G) suggests.

SCORING YOUR PRACTICE EXAM

Step A

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.

Step B

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.

Score Conversion Worksheet
Section	Raw Score	Scaled Score
1	______/75	_____
2	______/60	_____
3	______/40	_____
4	______/40	_____