And here are the solutions! I’ve detailed my thinking process for solving each of the problems on the ACT practice exam in Step 6. Use the solutions to identify your mistakes and to determine how you should have employed the ACT 36 strategies to solve the problems you had trouble with. Be sure to enter these problems under “Problems to review” in the appropriate section of your 36 Review notebook.
1. C. Since the subject, “Minneapolis and St. Paul,” is plural, the verb must be plural: “are.” The article “a” must be used with the phrase “conjoined metropolis.”
2. J. A comma is necessary, because the clause modifying “settlers” is not a complete sentence. “Who” is correct, because it is the subject of its clause.
3. B. Because the action of growing was completed by a certain time in the past (“within only a few decades”), the past perfect “had” is correct. Answer choice D is incorrect, because the subject, “the city,” is singular.
4. G. Since more than two metropolitan areas are being compared, “largest” is correct. “In” is correct, because “the United States” is considered a single geographical entity.
5. C. The rest of the paragraph addresses the population size of the cities and area. Sentence 2 explains the origin of Minneapolis’s name and is out of place here.
6. F. The second part of the sentence provides an example of the residents’ passion for the outdoors. A semicolon would be used if the sentences were related but equal. A dash would be used to introduce a contrasting idea or exclamation. A period would ignore the relationship between the two sentences.
7. D. Because there are more than two cities, “among” is used instead of “between.”
8. G. Parallel structure is the key; all of the phrases must match the infinitive “(to) visit an opera.” All other answer choices contain at least one verb with an “-ing” ending.
9. C. This is a contraction of “it” and “is.” Without an apostrophe, “its” is a possessive. “Its’” is ungrammatical. “It was almost” is past tense, which doesn’t match the present tense earlier in the sentence.
10. J. Since the subject, “Minneapolis and St. Paul,” is plural, the verb must be plural: “are.” The author is obviously talking about the cities’ current characteristics, so the present tense is correct, eliminating answer choices G and H.
11. C. Although “themselves” is commonly used to refer to “anyone” in everyday language, the pronoun must be singular: “himself or herself.”
12. J. The “if” clause is a sentence fragment, so it must be joined to another clause or a sentence. A period, colon, or dash in this context would incorrectly indicate separation of complete sentences.
13. D. To achieve parallel structure, the verb must be omitted so that only nouns are the objects of the series of prepositions.
14. G. This is a contraction of “there” and “is.” “Theres” and “they’res” are ungrammatical. “Theirs” is a pronoun.
15. D. The essay lists many positive features of the Twin Cities, but nowhere does the author try to convince the reader to live there.
16. G. “The fields” is the object of “brings together”; it would be incorrect to interrupt the predicate with a punctuation mark after “together.” Because two “fields” are involved, “and” is correct.
17. B. Since the subject, “research,” is singular, the verb must be singular: “hopes.” The paragraph addresses the current situation, so a present-tense verb is required, eliminating answer choices C and D.
18. J. To achieve parallel structure, the infinitive “to digest” must be changed to the verb’s “-ing” form to match “producing.” A comma after “biofuels” is incorrect, because both “-ing” phrases are objects of “capable of.”
19. B. “It’s” is a contraction of “it” and “is” and makes no sense in this context. “Its” indicates possession, here referring to the subject of the sentence, “this exciting new field.” Since the subject is singular, “their” is incorrect.
20. H. Since the clause “which was coined in the early 20th century” is unnecessary to the meaning of the sentence, “which” is used and the clause is set off by commas.
21. A. The punctuation mark links two complete and related sentences. A dash would incorrectly introduce a contrasting idea or exclamation. A period would ignore the relationship between the two sentences. It is incorrect to separate two complete sentences with a comma.
22. G. The modifier of “field” should be an adjective, which eliminates “conglomeration.” While “conglomerated” is a past participle acting as an adjective, it makes no sense as a modifier of “field.” “Conglomerater” is not a word.
23. D. Since the subject, “a scientist,” is singular, references to it must be singular: “his or her.” The homonyms of “their”—“they’re” and “there”—make no sense in this context.
24. H. An adverb—not an adjective—modifies a verb, so “well” is used instead of “good.” Since the subject of the main clause, “someone,” is singular, the verb of the dependent “who” clause must also be singular; this eliminates answer choices G and J.
25. B. The transition word introduces a new paragraph that builds on the previous one, so a contrasting transition word, as offered in answer choices A, C, and D, would be inappropriate. “As such” in this context signals that an example will follow.
26. G. The comma sets off “when choosing their classes” as a clause that is unnecessary to the meaning of the sentence. “They’re” is a contraction of “they” and “are” and makes no sense here; “their” is a possessive referring to “undergraduate students.”
27. A. Since the subject, “they,” is plural, the verb must be plural, eliminating answer choices B and C. There are more than two offerings, so “among” is correct.
28. G. The second sentence, “there are … need answers,” serves as an example of “challenges” in the first sentence. This relationship is best expressed by a colon, not by a period or semicolon. A dash would be used to introduce a contrasting idea or exclamation.
29. C. To avoid wordiness and to maximize clarity, the simple present-tense verb “demonstrates” is the best answer choice. “Have demonstrated” is incorrect, because its subject is “backlash,” which is singular.
30. G. “Surrounds” makes the sentence ungrammatical. “Surrounding” conveys the notion that the suspicion continues in a way that “that surrounds” doesn’t. “That will surround” makes no sense in this context.
31. D. A colon indicates that “a pony” is “the most asked-for present”; a comma doesn’t necessarily signify this. A period would create a sentence fragment, and no punctuation at all would create a run-on sentence.
32. G. To compare more than two items, the suffix “-est” is used instead of “-er.” “Most cutest” is repetitive and ungrammatical.
33. D. An adverb—not an adjective—modifies a verb, so “quickly” is used instead of “quick” to modify “abandoned.” “Soon” could be used in this sentence, but only if it immediately preceded “abandoned.”
34. F. “It’s” is a contraction of “it” and “is”; “its’” is ungrammatical and “its” makes no sense here. Since the opinion is expressed from the viewpoint of the present, present-tense “it’s” is correct, eliminating answer choice J.
35. C. “Fracturing” is correct, since it is the object of the preposition “aside from”; the other answer choices are active or passive verb forms. Reading the choices “aloud” in your mind quickly narrows the choice to C.
36. H. The phrase “never tiring … around” must be placed next to the noun that it modifies, eliminating answer choices F and J. Choice G is incorrect, because “I” should be “me” as the object of the preposition “by.” Choice H, which converts the modifying phrase into a “who” clause, is correct; in addition, unlike choice G, choice H is written in the active voice.
37. C. To achieve parallel structure, “pretending” is correct, because it matches “riding” earlier in the sentence.
38. J. The object of “carry” refers to “picnics” and must therefore be plural. The verb “carried” is incompatible with “would pack.”
39. D. To avoid wordiness, “without fail” should be deleted. The verb “would tolerate” doesn’t match the other verbs in the paragraph; the past-tense verb “tolerated” expresses the idea simply and well.
40. G. “One student” avoids the wordiness of answer choices F and H. “Some student” would compromise specificity.
41. C. Since this pronoun refers to “one student,” it must be singular: “himself or herself.” “His or herself” is ungrammatical, and “theirselves” isn’t a word.
42. F. This sentence introduces the topic of the paragraph; without it, the rest of the sentence wouldn’t make sense.
43. B. This sentence contrasts with the preceding one—the author writes that the pony is “probably enjoying peace and quiet,” but wonders if the pony misses “all the fun we had.” A contrasting transition word is therefore required: “still.”
44. H. “Standing quietly … to see her” lists examples of how Goldilocks was “there for me,” so a colon is correct. A comma would not clearly express this relationship. A period would create a sentence fragment, as would a semicolon.
45. B. Before the last two paragraphs, the essay is written in chronological order. Placing this paragraph about middle school between the paragraph about elementary school and the paragraph about college would preserve chronological integrity.
46. J. “Your,” a possessive, is correct; “you’re” is a contraction of “you” and “are” and makes no sense. Since the subject, “eyes,” is plural, the verb must be plural, eliminating answer choices F and G.
47. B. Since “BANG!” is an exclamation and completely interrupts the flow of the sentence, it should be set off by a pair of dashes. Answer choice C creates a sentence fragment. Since “BANG!” was not spoken, it should not be in quotation marks.
48. J. This paragraph generally uses the present tense. The simple present tense is correct here, as a transition from the present-perfect form “has slammed.”
49. B. An adverb—not an adjective—modifies an adverb, so “alarmingly” is correct, not “alarming.” Answer choice C is wordy.
50. G. “Than” is used in comparisons, not “then.” Since “the recommended 8 hours” refers to a block of time, “less” is correct. If “the recommended 8 hours” were replaced by “8 hours,” “fewer” would be correct, since “8 hours” by itself is countable (see No. 57 below).
51. A. The clause “that one … amount” is necessary to the meaning of the sentence, so it is not set off by commas or dashes.
52. H. To indicate the correct cause-and-effect relationship, the cause (“your sleep debt”) must be placed before the effect (“physical and psychological impairments”). Answer choices G and J are sentence fragments.
53. B. “Include” is never followed by a colon when it introduces a list. Answer choice D would create a sentence fragment.
54. H. “Their” is possessive; “there” and “they’re” make no sense here. Since the possessive refers to “athletes,” which is plural, it must also be plural, eliminating answer choice J.
55. D. “Effects,” a noun, is correct. “Due to,” as opposed to “of,” is wordy.
56. H. To achieve parallel structure, “reduced mental quickness” is correct, since it matches the two other noun phrases in the list (a past participle modifying a noun).
57. C. “Fewer” is correct, since “8 (hours)” is countable. Answer choice B is eliminated, because it uses the passive voice.
58. G. Because the subject, “studies,” is plural, the verb must be plural: “have.” The phrase “conducted … University” is necessary to the meaning of the sentence, so it is not set off by commas.
59. B. Since this is an “if/then” sentence, the “if” clause must be separated from the “then” clause by a comma. A comma after “ahead” is incorrect, because “plan ahead” and “sleep in” are parts of the same concept.
60. J. To achieve parallel structure, “maintaining” matches “succeeding.” Answer choice J reads most smoothly, because it places the verb phrase with two objects (“a student and an athlete”) at the end of the sentence, rather than in the middle, where the syntax might confuse the reader.
61. C. The clause “that ranged there” is critical to the meaning of the sentence, so “that” is used and the clause is not set off by commas.
62. F. The introductory phrase “in one tradition of the red men” must be set off from the rest of the sentence by a comma. There is no reason to capitalize the adjective “red.” “These” explicitly identifies the hills being discussed; “the” is not specific.
63. B. The phrase “floundering toward the ocean to bathe” describes the monster that was turned into stone. It is important to note that the monster was floundering, not the stone. For this reason, the sentence reads most smoothly with the transition word “as” (answer choice B), which indicates when the Great Spirit turned the monster into stone. The other choices don’t make this connection clear.
64. H. Since the subject, “the two lakes,” is plural, the verb must be plural: “were.” “It’s” is a contraction of “it” and “is,” which makes no sense here; “its” is a possessive modifying “eyes.”
65. C. Answer choice A is not a complete sentence. There is no reason to capitalize “witch,” so choice D is eliminated. It is unclear in choice B whether “adjusting” modifies “these peaks” or “an Indian witch.” Choice C expresses the relationship between the witch, the peaks, and “adjusting” clearly and succinctly.
66. H. Answer choices F, G, and J are run-on sentences—reading them “aloud” would quickly indicate this. “Holding” (choice H) correctly expresses the relationship between the clause “it was she …” and the remainder of the sentence.
67. C. Don’t be concerned about the streak of C and H answers. Such a sequence happens occasionally on the ACT exam, so don’t start second-guessing yourself. “Into” is the correct preposition, not “in to.” Answer choice D, because it inverts the relationship between “old moons” and “stars,” makes no sense.
68. J. The transition word “for” is required to introduce the result of the residents’ irreverence. Answer choice H, which has no comma before “for,” creates a run-on sentence.
69. D. It is necessary to emphasize the timing of the actions in this sentence; the witch would vanish when the hunters overtook her, not because they overtook her or so that they’d think they had overtaken her.
70. F. Answer choice G creates an incomplete sentence before the comma. Choice H creates an incomplete sentence and makes no sense. The comma in choice J separates the verb “stopped” from “with a shudder,” a prepositional phrase that modifies it. Reading choice F “aloud” shows that it flows well and makes sense.
71. D. Answer choices A and B use the passive voice, while choice D is in the active voice. Choice C incorrectly indicates that the Indians, not Garden Rock, were held in awe.
72. G. Reading answer choices F and J “aloud” shows that the past-tense verb “feared” creates an awkward, ungrammatical sentence. Since the hunter took a gourd, then turned to leave, a contradicting conjunction is required: “but.”
73. A. The revenge belongs to a single witch, so “witches” and “witchs’” are incorrect. The comma in answer choice C incorrectly separates the subject of the sentence from its verb.
74. G. To achieve parallel structure, the past participle “dashed” is used to match “engulfed” and “swept.” Series punctuated with commas use a comma after the second-to-last item, so a comma is placed after “Cove.”
75. C. The second sentence tells the story that led to the creek’s naming and so should be placed first.
Section 2 Mathematics
1. C. Substitute 3 for x in the equation:
Following PEMDAS, 
applies only to values in parentheses. A calculator will facilitate the computations.
2. G. To determine the price per pound of each of the coffees, divide the price by the number of pounds:
3. E. First, sketch a diagram:
Because this is a right triangle, the Pythagorean identity can be used:
4. J. The most efficient way to solve a logic problem is to scan the answer choices and eliminate those that contradict one of the statements or are not directly supported by one of the statements. Choice F is eliminated, because according to the first statement, all tall men play basketball. Choice G is eliminated, because no statement indicates whether Man A is tall or short. Choice H is eliminated, because according to the second statement, Man A does not play basketball. Choice K is eliminated, because the third statement says that Man B is tall. The only remaining choice is J.
5. A. Write an equation using the information given. Since the $20 charge is fixed without regard to the number of recycling pickups, $20 can be a constant in the equation. The number of recycling pickups varies, so a variable is multiplied by $10, the charge for one recycling pickup. These are added to yield $20 + $10x.
6. H. The value of x is determined as follows:
There are two solutions: x = –2 and x = 0.
7. D. Because alternate interior angles are equivalent, angle FEI is equivalent to angle EIH. Because the base angles of an isosceles triangle are equal, angle 
so 
8. K. The least common denominator of 2, 4, 6, and 8 is the smallest number of which all four denominators are factors: 24.
9. A. To reduce this expression, 2x is distributed among the terms in parentheses:
10. K. If you buy 4 tires, you are paying for only 3, so 
Since you are buying 4 tires, however, divide $375 by 4 to determine the price per tire: 
11. D. To solve this equation, expand the expression:
12. J. To find the total number of unique outfits, multiply the number of blouses (10) by the number of skirts (5) by the number of shoes (3): 
13. E. If c2 = 64, c can be either +8 or –8; similarly, d can be either +9 or –9. Thus, the possible values are as follows:
14. G. The total distance between –10 and 22 is 32, so the midpoint can be found by adding the quotient of 
to the smaller number (–10) or subtracting 16 from the larger number (22). Either way, the result is +6.
15. D. To solve this equation, subtract the expression to the left of the equals sign from both sides:
There are two solutions: x = 2 and x = –1.
16. G. Both 3x + 4 and 3x – 4 have a positive slope of 3, so they are parallel. Only answer choice G fulfills both conditions.
17. B. To solve this equation, multiply the terms in parentheses:
The only answer choice that works is x = 3, as (34) = 34.
18. K. Rotating about the origin would place the line exactly where it is now, so it would still pass through quadrants I and III.
19. D. The move from B to D is 8 units, from D to C is 4 units, from C to B is 4 units, and from B to D is 8 units: 
20. J. For the matrix, the determinant is 
Entering the values for x and y yields 
21. C. Assume that the larger bottle has a capacity of 1,000 mL and the smaller bottle has a capacity of 500 mL:
22. J. Neither answer choice F nor G is correct, since the number of minutes Amy sets aside for a date depends on how long the date will last, plus the time it takes her to choose an outfit. Choices H and K are also incorrect, since time spent choosing a restaurant and travel time are not included in the equation. Only choice J fits the equation.
23. B. To fly 100,000 miles in 4 hours, Fry would have to be flying 
Going 25,000 mph faster would have him traveling 50,000 mph, so it would have taken him only 2 hours to travel 100,000 miles. Thus, he would save 2 hours (4 – 2 = 2).
24. K. Answer choice F cannot be true, since the > sign doesn’t allow c and d to be equal. Depending on whether c and d are positive or negative (or equal to zero), choices G, H, and J could be true, but are not necessarily true. Choice K remains, which makes sense, since the > sign doesn’t allow c and d to be equal.
25. C. To obtain the slope, solve the equation for y to determine the coefficient of x:
26. H. In exponential form, 2x = 16. Since 
27. D. Because triangles CFH and CGH share three side lengths, they are similar by the side-side-side theorem of triangle similarity. Because the triangles are similar, the smaller angle in triangle CFH is congruent to angle x, so 
, and 
28. H. To solve this problem, distribute the 
power:
29. B. First, sketch a diagram:
The only inequality consistent with our sketch is CF > DF.
30. F. To solve this equation, remember to flip the inequality when multiplying by –1:
31. B. Enter 45 for d. Using a calculator, r = 2.44.
32. K. Square both sides:
33. A. To convert degrees to radians, divide by 180 and multiply by π.
34. J. Use the distance formula:
35. C. Use the formula for the volume of a cylinder:
This is closest to answer choice C.
36. J. To find the weight, multiply the number of gallons by the weight per gallon: (12,000)(7) = 84,000 pounds.
37. A. Calculate the volume of the cylinder using the external dimensions, then subtract the volume using the internal dimensions:
38. H. To find the dimensions of the tent bottom, calculate the base of the right triangle with a height of 4 feet and a hypotenuse of 8 feet, using the Pythagorean identity:
Thus, the width of the tent floor is 
Since the length is given as 12 feet, the tent bottom is 
square feet, or about 166 square feet.
39. B. Because AC is the diameter of the circle, we know that the sum of angle ABD and angle CBD is 180°. Given that angle CBD is 110°:
Since the total angle measure of the circle is 360°, the percentage of the circle’s area that lies within angle ABD can be calculated by dividing the angle measure of ABD by the angle measure of the circle:
40. F. To find the total area of the sheet needed to cover the painting, take into account not only the two-dimensional surface of the painting, but also its depth. Imagine the painting as a rectangular prism. The front of the prism is 3 feet by 3 feet (9 square feet), while each of the prism’s four sides is 6 inches by 3 ft (1.5 square feet). Add the front and four sides:
41. E. To solve this problem, it’s necessary to use the SOHCAHTOA identity. Replace (tan B)(sin A) as follows:
42. J. The best approach to this type of problem (in which a set of statements is given and each of the answer choices offers some combination of those statements) is to independently assess each of the statements and determine whether it is true.
Statement I: If the water coming from the hose increases, the rate at which the pool is filling should increase; therefore, an increase in slope would be expected after event a rather than the line shown.
Statement II: If the water coming from the hose decreases, the rate at which the pool is filling should decrease; therefore, a decrease in slope, as shown, would be expected after event a.
Statement III: If the drain at the bottom of the pool were opened, the rate at which the pool is filling should decrease; therefore, a decrease in slope, as shown, would be expected after event a.
Based on the slope of the line in the diagram, only statements II and III could be true.
43. A. The best approach is to assess each statement separately before selecting an answer choice. The line 4x + 1 is a straight line with a slope of 4 and a y- intercept of 1. Since the line has a positive slope, Statement I is true. Since the line doesn’t have a negative slope, Statement II is false. Since a line parallel to the x- axis would have a slope of 0, Statement III is false. Thus, only Statement I is true.
44. G. Statement I is clearly false: if the parabolas had identical functions, they would overlap at every point, not just at their vertices. Statement II is true, since the parabolas need to be described with different functions if they are to overlap at one point instead of at all points. Statement III is false, since a horizontal line (for example, y = 3) could easily intersect a parabola that opens upward (for example, x2) without touching another parabola that opens downward (for example, –x2). Thus, only Statement II is accurate.
45. D. To calculate the percentage of cable composed of copper wire vs. the weatherproof insulation, calculate and compare the cross-sectional area of the copper to the cross-sectional area of the cable.
46. K. If the ratio of a to b is 4:5, then 5a = 4b. The ratio of b to c is 8:10, which is the same as 4:5, so the ratio of a to c is 
47. A. Because the two endpoints are solid, the inequality must be represented by ≤ or ≥ signs. Since the two endpoints are at 0 and 4, the correct answer is A.
48. K. If (x – 6) is a factor, the other factor must be (x + 7), since (–6 + 7) = 1 for the coefficient of x. Thus, k would be (–6)(7) = –42, which is not among the answer choices.
49. B. If the value of a is increased by 2, then b increases by 10(2) = 20, due to the coefficient of a. If c decreases by 1, then b decreases by 2(1) = 2. An increase of 20 and a decrease of 2 results in a net increase of 18 for b.
50. H. Since cubes have three dimensions, a tenfold increase in each dimension results in a volume increase of 103, or 1,000.
51. A. To determine the area of the remaining half of the circle, calculate the area of the entire circle and divide by 2. Be sure to avoid entering 10 for the radius—the diameter is 10, so the radius is 5.
52. G. To compute the average of averages, perform a weighted average by multiplying the average age of men by the number of men, multiplying the average age of women by the number of women, adding the two products, then dividing by the total number of people.
53. A. Each successive discount affects the previous discounted price, so the total discount cannot be calculated simply by adding up the percentages of all discounts and subtracting the total discount from the original price. The discounts must be applied one at a time:
54. G. To solve this problem, multiply the coefficients 
and add the exponents of the x and y terms 
The product is 
55. C. To solve this problem, two pieces of information must be compared: (1) how much the university saves by not paying Professor Fry for 36 days and (2) how much the university pays a substitute teacher for 36 days. The university is paying Professor Fry 
If he takes 36 days off with no pay, the university saves $52.79 × 36 days = $1,900.44. The university pays $104 per day for a substitute teacher: 
Find the difference between the two: 
56. K. To calculate the CO2 level of the lake, divide the amount of dissolved CO2 of the water by its dissolved CO2 capacity:
57. B. An equilateral triangle has three sides of equal length. First, sketch a diagram:
To find the area of a triangle, use the formula A = ½ bh. The length of the triangle’s base is known (220 feet), but its height is not known. Fortunately, the height can be determined by using the Pythagorean identity and knowledge of the properties of an equilateral triangle. Dividing the triangle in half yields a right triangle with the following dimensions:
Use the Pythagorean identity to solve for the unknown height of the triangle:
Now, calculate the area of the farm plot:
58. K. If 
Thus, 
59. B. The key to solving a probability problem is to divide the number of favorable outcomes by the number of possible outcomes. There are 4 white candies, so the numerator is 4; the total number of candies is 
so the denominator is 22. Thus, the probability is 
which can be reduced to 
60. K. Multiply each destination’s packages by the fraction that will be paid for and add the products:
1. C. The author doesn’t approve of the trickery employed by the “subdividers.” It is evident that he regards their sales as a con when he says that “sold” was originally supposed to refer to the lots but came to refer to those who bought them, indicating that the purchasers had been tricked.
2. F. The subdividers “had undertaken to put in” these amenities, but before they could, the money disappeared and they weren’t able to. The promised amenities were never installed, while the other enticements in the answer choices were employed.
3. B. The context of the phrase suggests that Mrs. Groarty is doing something to “support her seven children,” meaning that she is making money from the endeavor. Answer choice B fits the context, while none of the other choices make sense.
4. J. Because of the recent discovery of oil in their area, the Groarty family expected to have many visitors. Not having clothing “suitable for this present occasion”—that is, their entrance into society—Mrs. Groarty bought a dress that would make her look like a member of high society.
5. C. Both the house, with a staircase but no second story, and Mrs. Groarty, who is awkwardly stuffed into an ill-fitting dress that is far more expensive than anyone of her social standing would normally wear, present a façade of luxury that they don’t measure up to. Their appearances suggest more grandeur than either Mrs. Groarty or the house possesses.
6. G. Although “in the back of the room … there was a wooden staircase,” the Groarty house “had a flat roof over its entire extent, and at no part was there any second story.” While answer choices F and H are true, they are not as odd as a staircase that goes nowhere. Choice J is incorrect.
7. D. First, Mrs. Groarty took in washing to support her children, presumably while they were still living at home. Of the more recent events, the first to occur was the oil strike, and as a result of that, Mrs. Groarty bought the satin dress and then the etiquette book.
8. H. Although it can be assumed that Mrs. Groarty has worked hard all her life (for example, she took in washing to support her children), her decision to buy the satin evening gown and the etiquette book indicate that she is very eager to become an “oil-queen,” having been completely swept away by the prospect.
9. D. Although Sinclair doesn’t admire the Groarty couple (in fact, he probably regards them as shallow and unintelligent), he does not condemn them or mock them outright. He comments on their activities in a compassionate way, as if he can understand why they are behaving as they do.
10. G. Answer choices F and H are incorrect: an oil company does not advertise the lots on Los Robles, and the Groartys use anticipated oil wealth to buy luxury items. Choice J is correct, but it summarizes only the first two paragraphs of the passage and doesn’t mention the chief focus of the passage, which is the Groarty family.
11. C. Answer choices A, B, and D contain errors or oversimplifications that make them inappropriate summaries of the main idea.
12. J. The context of the word “consumption” is that men trade the surplus of what they produce and use themselves. Answer choice J accords with this sense of “use.”
13. A. In order for a trade to work, each side must want what the other person has in surplus, which didn’t always happen. The other answer choices may be plausible, but Smith doesn’t discuss them.
14. H. Smith’s exact words are “a certain quantity of one commodity or the other, such as he imagined few people would be likely to refuse in exchange for the produce of their industry”—meaning that it’s a good idea to carry something that almost everyone wants, and thereby increase the likelihood of a trade.
15. B. Coins are not mentioned until the final paragraph of the essay. It is important to base your answer on the portion of the passage that the question refers to, and not on the passage in general.
16. G. Smith devotes the fifth paragraph to a discussion of metals as the favored medium of commerce, explaining their advantages in detail, so answer choice F can be eliminated. There is no evidence that he feels a “sentimental attachment” to quaint instruments of commerce (choice H), and the issues of weighing and assaying metal bars (choice J) don’t negate the advantages of metal, since they can be overcome by using coins.
17. A. In both paragraphs, Smith lists the media used without offering an explanation as to why each might have been used in a particular place; this eliminates answer choices B and C. Choice D is incorrect, because the first description explicitly states that each of the media was used in a different region, presumably by a different culture.
18. J. This is the point of view of an economist (which Smith was, in fact). In the passage, Smith examined the history of the current economic system; he wasn’t writing from the other points of view, none of which matches the writing style or information presented in the passage.
19. A. Here are the line numbers at which the items, in order of appearance, can be found: I (8–11), IV (30–42), II (43–54), III (82–90).
20. H. The passage explains how the division of labor resulted in the adoption of commerce, which led to the need for a common medium of commerce, which led to the use of metals, which resulted in the adoption of coins. Answer choice F is incorrect, because everyday life is not discussed in the passage. Choice G is not supported by the passage, which doesn’t account for regional differences. Choice J is incorrect, because its focus excludes the transition to a commerce-based economy discussed at the beginning of the passage.
21. D. The author agrees that many farmers contribute to the negative stereotype, but he doesn’t believe the stereotype to be entirely true, and would thus be likely to disagree with the blanket statement in answer choice D.
22. G. In this paragraph, Allen says that farmwork may be rough and unclean, but this does not mean that the farmer doesn’t know how to maintain neatness and even elegance in his household. Answer choice J expresses a similar idea, but includes the assertion that farmers are lazy and uncouth, which is certainly not supported by the second paragraph.
23. A. A house cannot be fickle (answer choice B). A house can be furnished (choice C), but this is irrelevant in the context of the sentence. The word seems to have a negative connotation, and “fastidious,” which means excessively particular about small details, fits the context better than “fancy.”
24. H. The author uses simile in the form “A is to B as C is to D.” He claims that a farmer wearing tattered clothing is to a rundown farmhouse as a farmer wearing fancy, tailored clothing is to a palatial farmhouse—both are absurd and inappropriate to the farmer’s occupation.
25. B. The paragraph states, “It is an arrangement … that costs little or nothing in the attainment … and … is a source of gratification through life.” This directly supports answer choice B. There is no support for choice A or choice D in the fifth paragraph. Allen speaks to the moral obligation of mankind to improve the world (choice C), but this isn’t the strongest reason he provides.
26. J. Line 64 states that older farmhouses “have been ruled out as antiquated.” The other answer choices may be plausible, but none is supported by the passage.
27. A. The author establishes a hypothetical situation in the very first sentence; this is not an example from real life. The purpose of the paragraph is to show how a well-meaning farmer can end up doing more harm than good by abandoning traditional ways and adopting new and unnatural architectural methods.
28. H. Although the author provides examples of mistakes farmers have made, he generally regards them in a friendly and respectful light, trying to convince the reader that they are not rough and uncouth, as the stereotype suggests. The author would certainly not agree with answer choices F, G, and J, all of which suggest that farmers lack intelligence and culture.
29. D. It is important not to confuse the order in which these events appear in the paragraph with the order in which they actually occurred. While the farmer is reported as prosperous before his childhood is mentioned, his childhood occurred before he achieved prosperity. The correct sequence of events is that the farmer was cold as a youth, he finds himself prosperous, he builds an airtight house, and his family gets sick.
30. G. Allen’s tone throughout the passage is respectful but concerned for farmers. While he understands their motivation for doing what they do, as he illustrates in the final paragraph, he believes that they are often misguided and wants the best for them. In this way, his tone is paternal. He certainly isn’t mocking them (answer choice F); in fact, he defends them against negative stereotypes. He isn’t condescending (choice H) or reverent (choice J) toward them, since he neither looks down on them nor looks up to them.
31. C. This sentence is the best summary of the paragraph’s main idea. The other sentences merely provide evidence or examples to support the claim of this topic sentence.
32. F. Although the author states that the majority of people use leaf character (shape) to distinguish types of trees, he goes on to explain the flaw of using this method (most trees are leafless for a good part of the year). He would thus be less likely to use this method himself than any of the other characteristics, which he lists as alternatives to leaf shape.
33. D. Answer choices A, B, and C are technically correct, but none of them describes a contradiction. Choice D contains a conflict: the author advises against using leaves to tell trees apart in the first paragraph, then does just that in the second paragraph.
34. J. Lines 21–22 state that there are only 80 distinct species of pine, although there are over 600 varieties. The other answer choices are correct.
35. C. “Character” cannot mean “personality” (answer choice A) in this context. Since “size and character” are specific “characteristics” (choice B) of the needles, replacing “character” with “characteristics” would increase the level of generality. “Length” (choice D) and “size” mean nearly the same thing with regard to pine needles, so “shape” (choice C) is the only satisfactory replacement for “character” in this context.
36. H. Lines 53–54 state that “the bark of the white ash is darker in color than the black ash.” The other answer choices are false.
37. B. Answer choices A, C, and D are described as contributing to the instability of the Carolina poplar. The passage blames its large roots for upsetting sidewalks and preventing the growth of other plants, but not for its instability.
38. J. While the passage explains why relying on leaves for tree identification can be troublesome, this is not the purpose of the passage as a whole, so answer choice F can be eliminated. Choice G is not entirely correct, since no information is given about biome or geographical range. Although the passage provides helpful pointers in distinguishing certain types of trees, it is not meant to serve as a quick-reference field guide (choice H)—its organization is not conducive to rapid reading. The purpose of the passage is to introduce the reader to tree identification and provide a variety of examples (choice J).
39. B. The author of the passage clearly has an expert’s knowledge of tree identification and forestry, which eliminates answer choice A. The passage says nothing about conservation and logging, which eliminates choice C. The passage is not a travelogue, which eliminates choice D.
40. J. The tone is characteristic of an academic style, in which the goal is to convey information, not to convince the reader of any particular point of view. No emotion is expressed in the passage, which reads like a detached reporting of facts.
Section 4 Science
1. B. Student 1 missed only 3 symbols overall, while Student 2 missed 9 and Student 3 missed 8.
2. H. In comparing the number of correct identifications in Experiment 1 to those in Experiment 2, it is clear that each of the students performed better in Experiment 2. The only false statement among the answer choices is “All students accurately identified fewer symbols in Experiment 2 than Experiment 1”—in fact, the opposite is true.
3. D. The eye chart contains letters (both vowels and consonants) and numbers, which eliminates answer choices A, B, and C. They are all symbols, however. (Note that the chart elements are referred to as “symbols” in previous questions and in the experiment description.)
4. H. To determine the average percentage, divide (4 + 1 + 2) by (4 + 4 + 4); the result is 7 ÷ 12, which is 58%.
5. A. The students were shown the eye chart up close along with a copy of their responses and were allowed to compare the two; in this way, they could figure out which symbols they misidentified in Experiment 1 and could try to memorize what symbol they needed to guess in Experiment 2. They were still required to stand at a distance from the eye chart, however, and they had not been given an extra incentive.
6. G. Although answer choice J is technically correct, it is not the best choice. The mechanism described in choice G is likely to cause a difference in scores, beyond random chance. Choice F is incorrect, because the same subjects benefited from exposure to the results of Experiment 1 in a way that different subjects could not. Choice H is incorrect, since there is no way to assess the eyesight abilities of either group of subjects.
7. D. Because the gases are at the same temperature, pressure, and volume, they are in equilibrium and won’t move at all. This question requires some knowledge of basic chemistry.
8. F. At a higher temperature, the molecules of Gas 1 will be moving more rapidly than those of Gas 2, causing an increase in pressure. Thus, when the valve is opened, the greater pressure of Gas 1 will force it to enter Gas 2’s side of the chamber.
9. C. An increase in temperature with no possibility of increasing volume will result in an increase in pressure; the two are directly proportional.
10. F. Just as an increase in temperature increases pressure, a decrease in temperature decreases pressure. Thus, if Gas 1 is cooled, its pressure will be less than that of Gas 2, and when the valve is opened, Gas 2 will rush into Gas 1’s side of the chamber.
11. D. Because both the volume of the side of the chamber and the volume of Gas 1 have been doubled, the pressure of the gases will be equal, and the gases will be at equilibrium. If the valve is opened, both gases will remain in their respective sides of the chamber.
12. F. The description of Boyle’s law at the beginning of the passage states that “the pressure and volume … are inversely proportional, provided that the temperature remains unchanged.” Thus, temperature must remain constant.
13. A. According to Table 1, molasses has the highest viscosity by a large margin. As explained in the paragraph, the higher the viscosity, the more resistant a liquid is to deformation.
14. G. The graph shows that the wave height for molasses is greatest, followed by that of cold water, and then by that of hot water. Table 1 shows that molasses is the most viscous, followed by cold water, and then hot water. Thus, as viscosity increases, so does wave height. Answer choice J is clearly not correct, since the wave height for molasses, as shown in the graph, is not 800 times greater than that of hot water.
15. B. As water is heated from 40°F to 100°F, the viscosity decreases (from 10 to 8, according to Table 1). Thus, it can reasonably be assumed that the viscosity of molasses would decrease as its temperature increases.
16. G. Peak refers to the highest point on the graph; for each of the liquids, this point is the time period from 0.4 to 0.5 seconds. Since 0.5 seconds is not among the answer choices, choice G is correct.
17. D. The wave height of both samples of water returns to 0 at 1.0 seconds, but the graph does not show when the wave height of molasses returns to 0. Thus, there is not enough data to answer the question.
18. F. The thermal conductivity of glycol is 0.025, compared to 0.025 for nitrogen and 0.026 for air. Hydrogen and helium have much higher thermal conductivities.
19. A. Divide the conductivity of mercury by that of water: 8.3 ÷ 0.67 = 12.4 times more conductive.
20. J. The most conductive material in both tables is clearly diamond, with a conductivity of 1,000–2,500; the material with the next highest conductivity is silver, at 429.
21. C. While the thermal conductivities of diamond, gold, and silver are relatively high, the thermal conductivity of ice is very low; the ice would probably melt rapidly when exposed to heat, making it an extremely ineffective insulator.
22. J. The size of the salmon run has to do with the number of fish, so only the first graph needs to be examined. The peak was clearly in 2005, when 650 million salmon were counted.
23. C. To find the proportion of salmon harvested in a single year, divide the number harvested by the number in the salmon run. Answer choice C has the highest proportion: 148/180, or about 82%. The next highest proportion is 156/200, about 78% (choice A).
24. H. The data don’t support the group’s claim that increasing salmon harvesting has a deleterious effect on the salmon population in the following years. On the contrary, it appears that there is a positive correlation between the size of the harvest and the size of the run in the following years.
25. D. There is no data in the second graph for the number harvested in 1945, so the proportion cannot be calculated. Furthermore, the proportion, as stated on the graph, is in terms of the number of fish, while the proportion in answer choices A, B, and C are in terms of the number of tons.
26. J. One would ordinarily expect that the size of the harvest would be inversely proportional to the size of the salmon run in the following years, but the opposite appears to be true.
27. C. As the temperature increased from 15°C to 25°C, the number of successful germinations went from 5 to 10 to 2, which is an increase followed by a decrease.
28. F. Although the highest success rate was for seeds stored at 0°C, this is not one of the answer choices. For seeds stored at the other temperatures, those stored at 5°C had the highest success rate.
29. A. In Study 1, the time of storage was varied; in Study 2, the storage temperature was varied. Storage time and germination time shouldn’t be confused: germination time is the 30 days that the bean seeds were left in the pots, and that was unchanged in both studies.
30. J. Table 1 shows that the least successful storage time was 0 weeks, and Table 2 shows that the least successful storage temperature was 15°C. Combining the two would likely result in no successful sprouts.
31. C. In Study 1, the temperature whose results most closely mimicked those presented was 25°C, when only 5 total seeds sprouted. Since 25°C had the lowest number of successful sprouts, there is enough information to draw this conclusion.
32. G. Unlike the rest of the variables, which should definitely be held constant to minimize variation in the trials, the person who does the watering is unlikely to have an impact on the plants, as long as the same amount of water is applied by all team members.
33. C. Although the success rate of the sprouts increased as storage time increased, it is uncertain whether this pattern will continue indefinitely or there will be a point at which a longer storage time is no longer favorable. Obtaining more data simply to have more data (answer choice D) is not consistent with the principles of science—scientific investigations should always have an objective.
34. H. The first sentence of the passage states, “The Big Bang is the leading scientific model of the early development of the universe.”
35. A. The first paragraph indicates that the term “Big Bang” is used because the universe was “very small and very dense” and “expanded in volume” extremely rapidly.
36. G. The answer is found at the end of each paragraph. Scientist 1 states that “other evidence validates the theory just as thoroughly,” while Scientist 2 states that “cosmic background radiation is clearly the most compelling evidence to date.”
37. D. Scientist 2 explains that “Within 25 years, further experiments confirmed that such radiation existed at both the frequency and distribution predicted.”
38. F. According to Scientist 1, the speed at which a galaxy is moving away from the earth can be determined by Hubble’s law (v = H0D). A distant galaxy would have a higher value for D, and thus a higher velocity.
39. D. It is important not to invent support for tempting answer choices. The entire passage must be examined for a definitive reason for the Big Bang, and none is found.
40. H. D is defined as comoving distance.
Section 5 Writing
To score your essay, use the guidelines in the box “ACT Writing score sheet” at the beginning of Step 5.
There are three types of ACT scores:
The raw score is the number of questions that you answered correctly on each of the four multiple-choice sections of the exam.
The scaled score, which is calculated from the raw score, is your score for each section of the exam, with a maximum of 36. If you take the optional Writing test, your English scaled score is combined with your Writing score to yield an English/Writing scaled score.
The composite score is the average of all of your scaled scores.
You will have four raw scores, one for each of the multiple-choice sections of the exam. To determine your raw score for each section, use the number of questions you answered correctly:
The total possible points for the Writing test is 12; this number is not included in your raw scores.
You will have four scaled scores, one for each of the multiple-choice sections of the exam (or if you take the optional Writing test, a combination English/Writing scaled score).
A scaled score is computed by multiplying the raw score for a section by 36, dividing by the total points possible on the section, and adding or subtracting a correction factor. (The correction factor varies by section and is based on the average scores on several recent ACT exams; it is intended to equalize scores across several administrations of the exam. The factors used in the chart below approximate the factors currently applied by the ACT.)
Scaled scores, which range from 1 to 36, are rounded to the nearest whole number; for example, a score of 33.4 is rounded to 33 and a score of 33.5 is rounded to 34.
The combination of your English scaled score and your Writing test score (out of 12 possible points) yields your English/Writing scaled score. Using the table on the following page, find your English scaled score in the leftmost column and your Writing test score in the top row, then locate the score where the row and column meet; this is your English/Writing scaled score.
Your composite score is the average of your scaled scores. It is computed by adding the four scaled scores and dividing by 4. The composite score, which ranges from 1 to 36, is rounded to the nearest whole number; for example, a score of 33.4 is rounded to 33 and a score of 33.5 is rounded to 34.
Table for ACT English/Writing scaled score
