Answers and Explanations

English Test

Passage I
C

Difficulty: High

Category: Sentence Structure

Getting to the Answer: At first glance, there may not seem to be anything incorrect here. However, the dash after Aegean Sea alerts you that the writer has chosen to set off the parenthetical phrase describing Acropolis with dashes instead of commas. This means that you have to replace the comma after Acropolis with a dash in order to have a matching pair, making (C) correct. If there were a comma after Aegean Sea, this underlined part of the sentence would not need to be changed. Knowing that you need to “make it all match” will help you score points on ACT English.
G

Difficulty: Medium

Category: Agreement

Getting to the Answer: “To climb . . . is to have beheld” is unparallel. The two verbs should be in the same form: “to climb . . . is to behold.” Choice (G) is correct; it is the only option that offers parallel construction.
D

Difficulty: Low

Category: Conciseness

Getting to the Answer: DELETE the underlined sentence is an option, so check to see if the sentence is either redundant or irrelevant. Athenian cuisine has nothing to do with the subject of the paragraph or the passage, so (D) is correct.
F

Difficulty: Medium

Category: Agreement

Getting to the Answer: This verb is appropriately plural—the subject, generations, is plural—and in the present perfect tense, so (F) is correct. Choices G and H are singular verbs, so they are incorrect. Choice J is incorrect because generations of architects can’t all be proclaiming at the present time.
D

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: The sentence discusses the columns of the temple, which requires the singular possessive form. Choice (D) correctly indicates that one temple had multiple columns. Choice A is missing a necessary apostrophe. Choice B changes the meaning of the sentence by creating a plural possessive word. Choice C includes the necessary apostrophe but creates a new error by changing the plural columns to a singular possessive column’s.
G

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: “Viewed from a distance” is a misplaced modifier that has to be moved to a position where it clearly modifies columns. Choice (G) accomplishes this. Choices F, H, and J each place the modifying phrase in an incorrect location.
D

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: The sentence is incorrect as written because the colon is not introducing a short phrase, quotation, explanation, example, or list. There is no need for a semicolon or any other kind of punctuation mark between of and uprightness, making (D) correct. Don’t place a comma before the first element of a series, C, and don’t place a colon between a preposition and its objects, B.
J

Difficulty: Medium

Category: Organization

Getting to the Answer: The phrase “Because of this” doesn’t make sense here. The optical illusion the architects created is not the reason you’ll get a different impression of the Parthenon from the one the ancient Athenians had; the reason is that the statue of Athena Parthenos isn’t there anymore. The introductory phrase that makes sense won’t suggest conclusion or contrast; it will emphasize the information in the sentence, making (J) correct.
C

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: “Only by standing . . . Golden Age of Athens” is a sentence fragment that has to be connected to the sentence after it to fix the error, so you can eliminate A and D. You can’t use a semicolon to join the two, B, because then the first clause of the new sentence will still be only a fragment. You have to reverse the subject and verb of the second sentence to attach the fragment to it, as (C) does.
J

Difficulty: High

Category: Sentence Structure

Getting to the Answer: What was removed from the temple? The underlined part of the sentence is an introductory modifying phrase that you know describes the statue, but the word statue isn’t anywhere in the sentence. As a result, the sentence doesn’t make sense at all; it’s impossible that “all that remains” in the temple was removed in the fifth century c.e. Choice (J) fixes the error and provides the clearest wording.
D

Difficulty: Medium

Category: Agreement

Getting to the Answer: Quite a few words come between the subject and the verb of this sentence; many is the subject of the sentence, not carvings, walls, or Acropolis. Because many is plural, the verb of the sentence has to be plural as well. Is has to be changed to are, which matches (D).
H

Difficulty: High

Category: Sentence Structure

Getting to the Answer: This sentence is really only a sentence fragment; it has a subject, decision, but no verb. Choice (H) rewords the underlined portion to make Lord Elgin the subject and decided the verb.
C

Difficulty: Medium

Category: Agreement

Getting to the Answer: They is an ambiguous pronoun because it’s not immediately clear what group they refers to. You can figure out from the context that they is the Greeks; no other group could have won independence from the Turks and demanded the carvings back from the British. Choice (C) is correct.
J

Difficulty: Medium

Category: Organization

Getting to the Answer: What could have been destroyed by explosions in the Parthenon? Carvings. The fact that some of the carvings were destroyed during a war is another good reason that many of them can no longer be found in the Parthenon, as Paragraph 4 states. Therefore, the new material belongs in Paragraph 4.
C

Difficulty: Medium

Category: Development

Getting to the Answer: The answer to the question is “No.” The writer did not fulfill the request, because only the second paragraph discusses techniques of construction at all; even then, only one technique, the bulging of the columns, is described in any detail. The author covers several topics in the essay in addition to construction techniques, including the statue of Athena Parthenos and the fate of the carvings, which matches (C).
Passage II
H

Difficulty: Low

Category: Agreement

Getting to the Answer: The previous sentence tells you that “Robin is the hero,” so look for a verb form that matches the present tense is because the sentence continues the discussion of the ballads. In (H), tell is in the right tense. Choice F switches to another tense, the present progressive, which makes it sound as if the ballads were literally speaking. Choice G lacks a main verb, creating a sentence fragment. Choice J has the same tense problem as F and compounds it by adding an extra, unnecessary subject, they.
C

Difficulty: Medium

Category: Agreement

Getting to the Answer: You need a verb that is parallel to robbing and killing, so giving, (C), is the correct choice.
H

Difficulty: Medium

Category: Agreement

Getting to the Answer: The adjective frequent is the correct choice to modify the noun enemy, making (H) correct. Choice F uses both the word most and the suffix -est to indicate the highest degree, or superlative form. Use one or the other, but not both. Likewise, G incorrectly uses more and the suffix -er together. Both of these express the comparative form—but again, you’d use one or the other, not both at once. In J, frequently is an adverb, which can’t describe a noun.
D

Difficulty: High

Category: Development

Getting to the Answer: Eliminate A and B because the proposed sentence discusses a modern adaptation of the King Arthur legend, which does not provide direct support the main focus of the paragraph: the legend of Robin Hood. Choice C is incorrect because even if the sentence included more than one example, it would still be off-topic. Choice (D) is correct; the sentence should not be added because it is irrelevant to the paragraph’s main focus.
F

Difficulty: Medium

Category: Agreement

Getting to the Answer: This is correct as is. Them matches the plural noun it is standing in for: writers. Choices G, him, and H, it, are singular, so they don’t. Choice J is too wordy.
A

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: Choice (A) is correct because the possessive apostrophe is necessary. Choices B and C are incorrect because they are the plural, not the possessive, form of king. Choice D is incorrect because the comma is unnecessary.
J

Difficulty: Medium

Category: Development

Getting to the Answer: Because this passage is aimed at discussing the historical development of the Robin Hood legend, (J) is most in keeping with the subject matter. Choice F goes way off track; you’re asked to add more information on Richard I, not on English history. The main topic of the passage is Robin Hood, not antiquaries, as in G. (Remember, you want the choice that is most relevant to the passage as a whole.) As for H, King Arthur was mentioned earlier in the passage, but then only to make a point about Robin Hood. A discussion of Richard I’s interest in King Arthur would stray from the topic of the passage.
C

Difficulty: Low

Category: Sentence Structure

Getting to the Answer: The shortest answer—(C)— is the best choice because it provides a verb, was, and an article, a. Choices A and D incorrectly imply a comparison between Robin and a nobleman, when the claim was that Robin was a nobleman. Choice B is incoherent.
G

Difficulty: Medium

Category: Agreement

Getting to the Answer: The comparison with a puppy doesn’t match the matter-of-fact tone of this passage; all choices except (G) can be eliminated.
D

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: The only choice that will tie in both parts of the sentence is (D). A dash in this context correctly makes an emphatic pause between love interest and its appositive, Maid Marian. All the rest of the choices have punctuation errors. Semicolons are used between independent clauses, and the part that would follow the semicolon in A isn’t a clause. The plural form of the noun, interests, B, doesn’t agree with the singular article. Choice C can be ruled out because there is no reason to pause in the middle of a name, and so the comma is incorrectly placed.
G

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: The correct verb tense, and the only choice that doesn’t create a sentence fragment, is (G). Choices F, H, and J create fragments.
B

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: The underlined portion includes two commas; check to make sure they are both necessary. Choices A and C are incorrect because the comma after Robin is unnecessary. Choice (B) is correct because the comma after “Britain” separates the dependent clause before the comma from the independent clause after the comma. Choice D eliminates the necessary comma after “Britain,” so it is incorrect.
H

Difficulty: High

Category: Organization

Getting to the Answer: The passage moves to a discussion of a new time period after Point C, so you should begin a new paragraph there, matching (H). Choices F, G, and J are incorrect because they do not offer logical options.
D

Difficulty: Medium

Category: Development

Getting to the Answer: You’re told that the audience is unfamiliar with the story, so it would make sense to include a summary of the Robin Hood legend, (D), something the passage lacks. Choices A and C would do nothing for a reader curious about Robin Hood, because they go off on tangents about other issues. As the passage states that Robin Hood’s existence is questionable (legendary), B doesn’t fit in with the stance of the writer.
J

Difficulty: Low

Category: Development

Getting to the Answer: Rarely are ACT English passages written for authorities or experts; they’re usually written for the general public, as (J) correctly states in this question. If the passage were directed toward experts, F, or authorities, G, much of the basic information it presents would be unnecessary and therefore not included. The passage states that the existence of Robin Hood is legendary, so the passage can’t be aimed at readers craving confirmation that he “was an actual historical personage.” So H is incorrect.
Passage III
A

Difficulty: Low

Category: Conciseness

Getting to the Answer: The shortest answer, (A), is correct. Ten-mile is correctly punctuated: the hyphen makes it an adjective modifying radius. The other answers—B, C, and D—are wordy and awkward.
H

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: You don’t look forward at something. You look forward to something, so F is incorrect. Choice G incorrectly implies that it is the brother who looks forward to the opportunity to show off the narrator’s skills. Choice J incorrectly implies a contrast between the two parts of the sentence. Choice (H) is correct.
D

Difficulty: Medium

Category: Organization

Getting to the Answer: Ever since means from the time the narrator first could read to the present time of the narrative, which makes sense in context, so (D) is correct. If in A signals a hypothetical situation, rather than a period of time. Since in B implies a cause-and-effect relationship that doesn’t make sense in context. Although in C signals a contrast, but there isn’t one.
F

Difficulty: Low

Category: Agreement

Getting to the Answer: It’s true that you use I and me, in G and H, when you’re writing about yourself. However, you can’t say “I always envisioned I” or “I always envisioned me.” Per the rules of grammar, you have to say “I always envisioned myself.”
A

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: Choice (A) is correct because the comma separates the dependent clause “giving me . . . international event” from the rest of the sentence. You don’t need a colon, as in B; colons signal lists or definitions. You don’t need a semicolon, as in C, either—a semicolon should be placed between clauses that could stand alone as sentences, but the second part of this sentence can’t. Choice D creates a sentence with no verb.
G

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: This is an example of a misplaced modifier. Choices F and H make it sound as if it is the airport, and not the pilot, that is filing the flight plan. Choice J is awkward (it uses a passive construction) and is wordy. Choice (G) is concise, and the verbs filed and gave are parallel.
D

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: The colon in the original interrupts the flow of the sentence, so A is incorrect. Colons signal lists or definitions, but nothing needs to be equated in this sentence, so B is incorrect as well. Choice C includes unnecessary commas. The correct answer is (D).
G

Difficulty: Medium

Category: Organization

Getting to the Answer: The sentence should appear after “As we departed Troutdale airport, my Cessna 152 ascended slowly on its way toward Mt. St. Helens,” and before “A few other pilots were also circling around the crater.” Choice (G) is correct. Choices F, H, and J do place the sentence in a logical location within the paragraph.
D

Difficulty: Low

Category: Conciseness

Getting to the Answer: Because speechless and mute mean the same thing, it’s redundant to use both of them. “DELETE the underlined portion,” (D), is correct.
G

Difficulty: Medium

Category: Agreement

Getting to the Answer: Steadying and took should be in parallel form, so F and H are incorrect. This makes (G)—with steadying and taking—correct. The verbs in J are parallel, but they’re in the present tense, which doesn’t fit with the past-tense verbs shot and dictated in the non-underlined part of the sentence.
A

Difficulty: Medium

Category: Development

Getting to the Answer: Jeff and the narrator are circling the mountain, so “a description of Mt. St. Helens,” (A), would be appropriate. Choice B contradicts the information in the passage; we’re told that the plane must stay high enough to avoid smoke and ash. Choice C sounds as if it belongs in a science textbook rather than in a story. Choice D wanders too far from the direct observation of the Mt. St. Helens volcano, which is the paragraph’s focus.
G

Difficulty: Medium

Category: Organization

Getting to the Answer: “Since that time,” (G), is an appropriate transition. It makes clear the time shift between the day at Mt. St. Helens and the present. The other choices contain inappropriate connecting words. However in F and nevertheless in J signal contrasts, but there isn’t one in the passage. Furthermore, H, suggests an elaboration of what came before, but there is no elaboration in the passage.
C

Difficulty: Medium

Category: Development

Getting to the Answer: Because the author is favorably recalling a memorable past experience, nostalgic, (C), is the best choice. The passage is positive in tone. It’s definitely not bitter, B, or exhausted, D. Optimistic, A, is close but incorrect. Optimistic means “hopeful.” The passage focuses on the excitement of the past, not on the good things that might happen.
H

Difficulty: Medium

Category: Development

Getting to the Answer: The use of I is appropriate because this is a firsthand account. First-person narratives are designed to draw the reader in, making the immediacy mentioned in (H) the desired outcome. Choice J is not true, because I is not appropriate in all types of writing. The passage is personal and chatty; it’s not an example of “formal writing.” The passage isn’t focused on volcanoes in general, as G says, but on the Mt. St. Helens eruption, the narrator’s first international story.
B

Difficulty: High

Category: Organization

Getting to the Answer: The passage reads best if the first and second paragraphs are switched. Choices A, C, and D confuse the time sequence of the narrative, which follows the narrator from early dreams of becoming a photojournalist, to the memorable Mt. St. Helens story, to the present experience as a foreign correspondent.
Passage IV
G

Difficulty: Low

Category: Conciseness

Getting to the Answer: The description of Sherlock Holmes as “ingenious and extremely clever” is redundant because ingenious and extremely clever mean the same thing. You need to use only one of the two to get the point across, so (G) is the only possible option.
D

Difficulty: High

Category: Organization

Getting to the Answer: Therefore is supposed to be a signal that the sentence that follows is a logical conclusion based on information from the preceding sentence or sentences. The use of therefore doesn’t make sense here because you can’t conclude that everyone knows the phrase “Elementary, my dear Watson,” just because everyone knows of Holmes’s detective abilities. Choice C is incorrect for the same reason—for this reason and therefore mean the same thing in this context. Although, in B, indicates some sort of contrast; this is incorrect because there is no contrast within this sentence or between this sentence and the previous one. Really, there is no need for a structural signal here at all. Choice (D) is correct.
J

Difficulty: Medium

Category: Development

Getting to the Answer: You must choose the word that best fits the context of the sentence. The essay discusses Holmes’s ability to solve mysteries, which matches (J) since deductions are conclusions reached through reasoning. Choices F, G, and H do not make sense in context; the words tales and stories do not indicate Holmes’s logical reasoning skills, and the word subtractions is illogical in context.
B

Difficulty: Medium

Category: Agreement

Getting to the Answer: He is an ambiguous pronoun because it’s unclear whether he refers to Conan Doyle or to Sherlock Holmes. You know after reading the entire sentence that he is Conan Doyle, so you have to replace he with Conan Doyle for the sake of clarity. This makes (B) correct.
J

Difficulty: Medium

Category: Conciseness

Getting to the Answer: From a grammatical point of view, there is nothing incorrect here; it’s just unnecessarily wordy. “To be remembered,” (J), is the most concise answer and therefore correct.
A

Difficulty: Medium

Category: Organization

Getting to the Answer: In fact is the appropriate signal phrase here, so (A) is correct. Despite this, regardless, and yet would all indicate a contrast between this sentence and the previous one. There is no contrast, however; Conan Doyle did not want to be remembered as the author of the Sherlock Holmes stories, so he killed the detective off (at least for a while).
J

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: A modifying phrase that begins a sentence refers to the noun or pronoun immediately following the phrase. According to that rule, the phrase “having had enough of his famous character by that time” modifies Sherlock Holmes, which doesn’t make sense. The sentence has to be rearranged so that the introductory phrase describes Conan Doyle. Choice (J) is the choice that accomplishes this.
D

Difficulty: Low

Category: Sentence Structure

Getting to the Answer: The phrase eight years and the verb offering are connected with the word and, so they must have a parallel form. Choice (D) changes the verb to a noun, which matches years. Choices A, B, and C are incorrect because they do not offer parallel compounds.
H

Difficulty: Medium

Category: Agreement

Getting to the Answer: The verb is in the incorrect tense. “Has been deeply immersed” is in the present perfect tense, which is used to describe an action that started in the past and continues to the present or that happened a number of times in the past and may happen again in the future. Because Conan Doyle’s immersion in spiritualism is over and done with, you should use the simple past, “was deeply immersed.” This makes (H) correct.
B

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: This is a sentence fragment because there is no subject and verb; all you have is an introductory phrase and a subordinate clause starting with that, so A is incorrect. By omitting that, you can turn the subordinate clause into a main clause, making he lectured the subject and verb, as in (B). Choice C would only work if the sentence began with “so convinced.” Choice D is incorrect because the introductory phrase can’t stand alone as a sentence.
J

Difficulty: Low

Category: Organization

Getting to the Answer: Based on the context, the sentence requires a continuation transition, which matches (J). Choices F and H are incorrect because they are contrast transitions. Choice G is incorrect because it is a sequence transition.
D

Difficulty: High

Category: Organization

Getting to the Answer: Sentence 2 refers to “these experiences,” so it should come directly after the sentence that describes the paranormal experiences Conan Doyle seemed to have had. Sentence 4 is the one that talks about materialized hands and heavy articles swimming through the air, so Sentence 2 should come after Sentence 4, making (D) correct.
H

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: There are two problems with the underlined portion of the sentence: the colon does not belong there, and the pronoun they is ambiguous because it doesn’t refer to anything in particular in the previous sentence. Choice (H) fixes of both of these problems by omitting the colon and by explaining the pronoun.
B

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: Here, you just have to pick the choice that makes sense. Sherlock Holmes is only a fictional character, so A, C, and D are incorrect; Holmes could not possibly have said anything about Conan Doyle’s spiritualism, nor will he ever. You can still wonder, however, what the esteemed detective would have said, if he were real. This is the idea behind the last sentence, so since (B) matches that language, it is the correct answer.
G

Difficulty: High

Category: Development

Getting to the Answer: The passage contrasts the logical, deductive thinking used by Conan Doyle’s fictional character, Sherlock Holmes, with Conan Doyle’s own exploration of the paranormal. An appropriate subtitle will reflect this contrast. Choice (G) is the only choice that does.
Passage V
C

Difficulty: Medium

Category: Development

Getting to the Answer: The question provides four words, and you must choose the word that best fits the context of the sentence. The essay indicates that emphasizing auditory, visual, and experiential learning is not a new concept. Choice (C), groundbreaking, reflects this idea. Choices A, B, and D do not make sense in context; fashionable and popular do not refer to how old or new a concept is, and illustrious means well-known and respected, which is the opposite of the writer’s opinion.
J

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: The phrase “from corporate management to consulting” is a nonessential phrase that must be properly punctuated. The phrase can be set off from the rest of the sentence with two commas or two dashes, but not a mix of one comma and one dash. Choice (J) fixes the error by changing the comma to a dash. Choices G and H do not fix the issue presented in F.
D

Difficulty: Medium

Category: Agreement

Getting to the Answer: A pronoun and a verb are underlined, so check to make sure they are both correct. The antecedent is these slides, which is plural, so the singular pronoun it is incorrect. In addition, the verb must also be plural: was should be were. Eliminate A and B because they include the singular verb was. Choice C is incorrect because the apostrophe makes the word slides plural possessive. Choice (D) is the only option that includes a plural pronoun and verb, so it is correct.
H

Difficulty: High

Category: Sentence Structure

Getting to the Answer: There are several ways to join independent clauses, but only one choice will do so without introducing additional errors. As written, the sentence is a run-on, so F is incorrect. Choice (H) correctly inserts as to make the first clause dependent. Choice G does not address the error. Choice J creates a grammatically incorrect sentence.
A

Difficulty: Medium

Category: Organization

Getting to the Answer: When two answer choices have transitions that convey the same meaning and create grammatically correct sentences, you can eliminate both choices because they can’t both be right. This sentence is correct as written. Choices B and D use transitions, indicating a contrast, but the idea that people are working on improving visual presentation style does not contrast with the idea that “less cluttered” aids work better than “denser ones.” Choice C uses the transition similarly, but the second sentence is an example supporting the first.
J

Difficulty: Low

Category: Conciseness

Getting to the Answer: When the underlined selection consists of two words joined by and or or, consider whether the two words mean essentially the same thing. If they do, the correct answer choice will eliminate one of them. Enhance and improve, in this context, mean the same thing, so F is incorrect. Choice (J) omits the redundancy. Choice G is unnecessarily wordy. Choice H does not address the error.
A

Difficulty: Low

Category: Sentence Structure

Getting to the Answer: Items in a list must be separated with commas, so the sentence is correct as written. Choices B, C, and D omit one or more necessary commas.
J

Difficulty: Medium

Category: Development

Getting to the Answer: In questions like this one, first answer the “yes” or “no” part of the question; you’ll be able to eliminate at least one answer choice, and usually more. This paragraph focuses solely on how “visual presentation style” is being refined. The topic sentence of the paragraph doesn’t discuss audio aids, nor does any other sentence in the paragraph. Therefore, the sentence should NOT be added; (J) is correct.
B

Difficulty: High

Category: Sentence Structure

Getting to the Answer: When you need to determine the correct order of words in a long sentence like this one, start by focusing on the correct placement of descriptive phrases and then eliminate your way to the correct answer. “In respected journals” needs to follow the verb phrase “have been published.” This eliminates C. “In listeners” belongs with “improve comprehension,” which eliminates A and D. Choice (B) is correct.
G

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: The passive voice will not always be incorrect on the ACT, but passive constructions are generally wordier than active ones, so check for an active version of any underlined passives. “It has been determined by researchers” is a wordy and indirect way of saying “Researchers have determined,” so (G) is the best choice here. Choice H is a sentence fragment with no independent clause. Choice J uses incorrect grammatical structure.
A

Difficulty: Medium

Category: Sentence Structure

Getting to the Answer: The end of one sentence and the beginning of the next are underlined, so determine if the sentences should be combined. None of the answer choices offers an option for correctly joining two independent clauses; NO CHANGE is needed, so (A) is correct. Choice B creates a run-on sentence. Choices C and D leave the meaning of the second clause incomplete.
J

Difficulty: Medium

Category: Agreement

Getting to the Answer: When a pronoun is underlined, check that it agrees with its antecedent—the noun it replaces. The underlined pronoun refers back to the audience members, so the third-person plural pronoun them, as shown in (J), is correct. Choices F and G use singular pronouns, which don’t agree with the plural noun audience members. Choice H uses the second-person pronoun you, but the writer is not directly addressing the reader.
D

Difficulty: Medium

Category: Conciseness

Getting to the Answer: Check underlined selections for words that are redundant. Recently and of late mean essentially the same thing, so using them together is redundant. Only (D) eliminates all redundant language.
G

Difficulty: High

Category: Organization

Getting to the Answer: You need to pick the best supporting material to link Sentences 1 and 2, so read Sentence 2 before going to the answer choices. Sentence 2 discusses the importance of body language in presentations; the most effective link to this sentence will introduce this topic. Only (G) mentions body language. Choice F is much more general than (G), repeating ideas that have already been stated in the passage. Choice H focuses on visual images, which were discussed in the previous paragraph, not Sentence 2 of this paragraph. Choice J is unnecessarily wordy, using the passive voice and redundant language.
B

Difficulty: Medium

Category: Development

Getting to the Answer: Read the question stems carefully. Frequently, more than one answer choice will be both relevant and consistent, but only one will meet the specific criteria of the question. The writer wants to show how the theory about body language has “influenced” the education and public speaking experts who are the subject of the sentence. Choice (B) explains a specific way these experts have been influenced; they now focus on teaching presenters how to effectively use body language. Choices A and C are both too general; neither shows the specific influence of the body language theory. Choice D is out of scope; audience size isn’t discussed in the passage.

Mathematics Test

D

Difficulty: Low

Category: Number and Quantity

Getting to the Answer: When you’re converting units, writing out the units will help you determine if you’ve made a mistake. Arrange the conversion factor in whichever format will allow you to cancel the units you are trying to do away with. Here, “a rod is equivalent to 5.5 yards” can be written as or :
J

Difficulty: Low

Category: Number and Quantity

Getting to the Answer: Instead of finding the increase and adding it to the original cost, you can do the computation in one step by adding 100% to the percent increase. When the cost of the pizza is raised by 22%, the new cost will be 122% of the original cost, so multiply the original price by 1.22 to get $20 · 1.22 = $24.40, (J).
B

Difficulty: Low

Category: Statistics and Probability

Getting to the Answer: Phrases like “average increase” may sound a little complicated, but there’s nothing difficult going on here. The chart shows increases, so you just need to find the average to get the “average increase.” Remember, the average of a set of terms is the sum of the terms divided by the number of terms, so the average here is:

Choice (B) is correct.
G

Difficulty: Low

Category: Number and Quantity

Getting to the Answer: Recall the DIRT formula: Distance is rate × time. Use this formula to calculate each train’s distance and then subtract the results. Convert the mixed number to a decimal to make it easier to enter into your calculator. Train A travels 50 × 3 = 150 miles. Train B travels 70 × 2.5 = 175 miles. The difference is 175 − 150, which is 25 miles, or (G).
B

Difficulty: Low

Category: Algebra

Getting to the Answer: When a factored product equals 0, one of the factors must be 0.

Only one of these, 3, appears in the answers, so (B) is correct.
J

Difficulty: Low

Category: Geometry

Getting to the Answer: Because ABCD is a square, each side has the same length, which means the base and height of triangle BCD both equal 6 centimeters. Substitute these numbers in the formula for the area of a triangle:

The area of triangle BCD is 18 cm², which is (J).
C

Difficulty: Medium

Category: Number and Quantity

Getting to the Answer: When a question tests your knowledge of a number property (even/odd, prime/composite, positive/negative, etc.), the easiest way to answer it is to Pick Numbers. Because u is an integer, pick some integers for u. Start with easy numbers (but not 1 because the number 1 has special properties).

If u = 2:
(u – 3)² + 5 = (2 – 3)² + 5 = (–1)² + 5 = 1 + 5 = 6
This eliminates B, D, and E.

If u = 3:
(u – 3)² + 5 = (3 – 3)² + 5 = 0 + 5 = 5
This eliminates A, leaving (C) as the correct answer.
G

Difficulty: Low

Category: Algebra

Getting to the Answer: If you forget the rules of exponents, try writing out an example and canceling. For example, . When you’re dividing, you subtract the exponents when the bases are the same.

This matches (G).
A

Difficulty: Medium

Category: Geometry

Getting to the Answer: Whenever you see parallel lines, look for corresponding angles and alternate interior angles. They’re most obvious when you’re given just two parallel lines and a transversal, so questions that include parallel lines as parts of shapes like triangles or parallelograms can be a little tricky. Because is parallel to , by corresponding angles, has the same measure as , so add the measure (40°) to the figure:

Using the fact that the angles of ∆PXQ sum to 180 degrees, you find that:

Choice (A) is correct.
J

Difficulty: Medium

Category: Number and Quantity

Getting to the Answer: Scientific notation is defined as a number between 1 and 10 (not including 10) multiplied by a power of 10, so you can eliminate K right away. Use your calculator (or jot the numbers down quickly) to add the numbers: 740,000,000 + 800,000,000 = 1,540,000,000. Now move the decimal point (which is to the right of the last 0) until it is between the 1 and the 5. To determine the power of 10, count the number of times you moved the decimal, 9 times. The sum, 1,540,000,000, is a very large number, so the exponent on 10 must be positive, making (J) correct. (Some people forget whether moving the decimal point left or right results in positive powers of 10. It’s easier to remember that negative powers of 10 produce tiny decimal numbers, while positive powers produce very large numbers.)
A

Difficulty: Low

Category: Number and Quantity

Getting to the Answer: This question is really testing whether you pay attention to detail and work carefully. First, find the number of participants who were undecided: 1,250 − 800 − 150 = 300. Now find the percent: , which is (A).
K

Difficulty: Medium

Category: Number and Quantity

Getting to the Answer: The greatest common factor (GCF) is the largest factor that the two numbers share. The least common multiple (LCM) is the smallest number that is a multiple of both numbers. Start with the GCF and choice F: 15 is not a factor of 9 or 25, so these numbers can’t have a GCF of 15. On to G: 15 is not a factor of 27, so these numbers can’t have a GCF of 15. Choice H: 15 is not a factor of 25, so these numbers can’t have a GCF of 15. To choose between the remaining pairs of numbers, try factoring the numbers. Choice J: 30 = 15 · 2 and 45 = 15 · 3, so 15 is the GCF here; 30 = 3 · 5 · 2 and 45 = 3 · 5 · 3, so the LCM must be 2 · 3 · 3 · 5 = 90 (not 225). Choice (K) must be correct: 45 = 15 · 3 and 75 = 15 · 5, so 15 is the GCF here. Finally, 45 = 3 · 5 · 3 and 75 = 5 · 5 · 3, so the LCM is 5 · 5 · 3 · 3 = 225.
D

Difficulty: Medium

Category: Algebra

Getting to the Answer: This is a straight substitution question. Remember that if you raise a negative number to an odd power, the result is negative. (If the power is even, the result is positive.) Any question that involves negative numbers will require extra attention. It’s very easy to lose track of negative signs.

Choice (D) is correct.
F

Difficulty: Medium

Category: Geometry

Getting to the Answer: The first step is to recall the definition of perimeter—the distance around the sides of a figure. For a square, the perimeter is four times the length of a side, which means a side is one-fourth the perimeter. Be careful to divide both terms in the expression by 4 to get , which is (F).
A

Difficulty: Medium

Category: Algebra

Getting to the Answer: Memorizing the three classic quadratics will save you valuable time on questions like this. Remember, (x − y)² = x² − 2xy + y². You could multiply out the squared binomial (using FOIL), or better yet, write down the formula from memory: (x − k)² = x² − 2kx + k², which you’re told in the question stem is equal to x² − 26x + k². Because the coefficient of x must be the same in both equations, −2k = −26, which yields k = 13. Choice (A) is correct.
K

Difficulty: Medium

Category: Algebra

Getting to the Answer: As with every question involving negative numbers, be careful with the negative signs. Also pay attention to the location of the parentheses. Here you need to cube both the −2 and the x⁵ because both are inside the parentheses: (−2x⁵)³ = (−2)³(x⁵)³ = −8x¹⁵. Choice (K) is therefore correct.
B

Difficulty: Medium

Category: Number and Quantity

Getting to the Answer: If the labels are missing on a number line, you can find the length of each interval by finding the difference in the endpoints (how much the total interval is) and dividing by the number of subintervals. The unmarked interval goes from 2.7 to 2.8, so it must be 0.1 units long. It’s divided into 10 equally spaced subintervals, each of which must be = 0.01 units long.

The number e has an approximate value of 2.718, so you want a point between 2.71 and 2.72. Choice (B) is the closest.
H

Difficulty: Medium

Category: Functions

Getting to the Answer: You don’t have to find the solutions to the equation, just the number of solutions. As long as you know the technique you would use to solve it, you can eyeball the answer in seconds. The graph of a function crosses the x-axis when y = 0, so set the equation equal to 0: (x + 1)(x + 2)(x − 3)(x + 4)(x + 5) = 0. There are 5 distinct factors, any of which could equal 0 (for example, if x = −1, then x + 1 = 0), so there will be 5 x-intercepts, which is (H). Specifically, they are −1, −2, 3, −4, and −5, but you don’t need to know that to answer the question. If you have a graphing calculator, you could also use it to graph the equation and see how many times the graph intersects the x-axis.
A

Difficulty: Medium

Category: Algebra

Getting to the Answer: To reduce a rational expression, you must factor out the same number from the top and the bottom, then cancel. You cannot only reduce the 4, neglecting the 8x (or vice versa).

This matches (A).
G

Difficulty: Low

Category: Number and Quantity

Getting to the Answer: This is a very straightforward question, so don’t make careless errors. If 5 people buy 5 tickets for $95, each pays . Because the individual rate is $21.50, this represents a savings of $21.50 − $19 = $2.50 per person, which is (G).
C

Difficulty: Low

Category: Algebra

Getting to the Answer: Small mistakes will add up quickly—keep yourself focused! The key to this one is that x²y and 2xy² are NOT like terms. Like terms must have the same exponent on each variable. Combine only the first terms from each expression to get: (−2x²y² + 3x²y²) + x²y + 2xy² = x²y² + x²y + 2xy², which matches (C).
H

Difficulty: Low

Category: Geometry

Getting to the Answer: Use SOHCAHTOA to help you remember which trig function involves which sides of the triangle: tan θ = which is (H). Note: When answering sine and cosine questions, you can eliminate any answers that are not between −1 and 1, but remember that tangent can get very large or very small.
E

Difficulty: Medium

Category: Algebra

Getting to the Answer: If you’re not sure which operation is appropriate, try Picking Numbers. If Yuri was 10 years old 15 years ago, then he’s 25 today. In another 7 years, he will be 32. Plug x = 10 into each answer choice to see which one equals 32:

A: 10 + 7 = 17 Eliminate.
B: (10 − 15) + 7 = –5 + 7 = 2 Eliminate.
C: (10 + 15) − 7 = 25 – 7 = 18 Eliminate.
D: (10 − 15) − 7 = –5 – 7 = −12 Eliminate.
(E): (10 + 15) + 7 = 25 + 7 = 32 Correct.

The key to answering this question algebraically is to realize that if Yuri was x years old 15 years ago, he is now (x + 15) years old, not (x − 15) years old. Seven years from now, he’ll be another 7 years older, so the expression is (x + 15) + 7, which is (E).
K

Difficulty: Medium

Category: Algebra

Getting to the Answer: Before factoring a quadratic expression, look for common factors that you can pull out first. Here, you should begin by factoring out a 2 to get 2x² − 8x − 24 = 2(x² − 4x − 12). To factor the simplified quadratic, you need two numbers that multiply to −12 and sum to −4; those numbers are −6 and +2, so 2x² − 8x − 24 = 2(x − 6)(x + 2). The latter factor is (K).

D

Difficulty: Medium

Category: Geometry

Getting to the Answer: When using the Pythagorean theorem, a² + b² = c², remember that a and b are the legs and c is the hypotenuse. Wrong answer choices may come from plugging numbers into the wrong part of the formula.

Choice (D) is correct.

G

Difficulty: High

Category: Number and Quantity

Getting to the Answer: You add fractions that contain radicals the same way you add regular fractions—find a common denominator and multiply each fraction by whatever it takes to get that denominator. Here, the common denominator is .

This matches (G). Note that you could also use your calculator to find the decimal equivalent of the given expression (which is approximately 3.9831) and each of the answer choices until you find a match, but you must enter the expressions very carefully.

C

Difficulty: Medium

Category: Number and Quantity

Getting to the Answer: Don’t worry when you see an unfamiliar term like “relative atomic mass.” The test makers don’t expect you to be familiar with such terms (including ones they just made up), so they’ll tell you everything that you need to know. Use the definition provided to write a ratio in the form of . The result is = 2.5, which is (C).

K

Difficulty: Medium

Category: Algebra

Getting to the Answer: Don’t stop until you’re sure you’ve answered the question asked. It’s tempting to bubble in the value of x and move on, but that’s not what this question is asking for—instead, you need to use the equation to find the value of x and then substitute that value into the other expression:

Choice (K) is correct.

D

Difficulty: Medium

Category: Algebra

Getting to the Answer: Inequalities work exactly like equalities, except that the direction of the symbol changes if you multiply or divide by a negative number. To save a bit of time here, think about dividing by 8 at the appropriate time rather than distributing it:

The inequality now reads “x is less than –4.” The numbers less than −4 on a number line are to the left of –4, which means the correct graph is (D).

K

Difficulty: Medium

Category: Number and Quantity

Getting to the Answer: Break the question into steps. First, find how long it took the employee to collect samples from one house, and then use that amount to find how long it should take the employee to collect samples from all of the houses.

The employee started the 1st house at 8:00 and started the 6th house at 9:05, so it took him 1 hour and 5 minutes, or 65 minutes, to collect samples from 5 houses (not 6 houses because he didn’t finish the 6th house at 9:05). This gives a unit rate of 65 ÷ 5 = 13 minutes per house. Multiply the unit rate by the number of houses in the subdivision (40) to get a total of 13 × 40 = 520 minutes to collect samples from all the houses. The answers are given in hours and minutes, so convert 520 minutes to hours and minutes by dividing by 60. The correct answer is hours, or 8 hours and 40 minutes, making (K) the correct answer.

D

Difficulty: High

Category: Functions

Getting to the Answer: You can make abstract questions like this one easier to handle by Picking Numbers. Be sure the numbers you pick obey any restrictions in the question stem. Try k = 2 and x = 4. (These numbers will make the radical in E easy to calculate.) The question involves a composition of h and g, so start with the inner function, g(x):

A:

B:

C:

(D):

E:

The largest value for g(x) is (D). When this is plugged into h(g(x)) = 5^g(x), the largest value of g(x) will produce the largest value of h(g(x)). For the values of k and x allowed in this question, (D) is always the largest, so it is correct.

H

Difficulty: Medium

Category: Functions

Getting to the Answer: Some questions look tougher than they really are, especially when you are asked to interpret a graph. The question asks for total vertical distance, which is the total change in altitude both while the hiker is ascending the mountain and while she is descending. At 8:00 AM, the hiker is at 4,500 feet of altitude. After 8:00 AM, she ascends 500 feet without descending. After reaching her highest point at 11:00 AM, she descends 1,000 feet by 1:00 PM. Therefore, the total vertical distance traveled is 500 feet + 1,000 feet = 1,500 feet, which is (H).

E

Difficulty: Medium

Category: Functions

Getting to the Answer: This question requires no math, but rather an interpretation of the graph. Beginning at 9:00 AM, the hiker had just finished an ascent and did not travel up or down the mountain. Thus, her altitude remained the same. Therefore, either A or (E) is correct. From 10:00 AM to 11:00 AM, she ascended 250 vertical feet. Between 11:00 AM to 12:00 PM, after having reached her highest point, she descended 250 vertical feet at the same rate as during the previous one-hour interval. Choice (E) best describes this progression.

F

Difficulty: Medium

Category: Geometry

Getting to the Answer: Even if a question talks about rounding, the correct answer may require no rounding whatsoever. The distance from a point to a line is measured perpendicular to the line, so you can be sure that the triangle shown is a right triangle. Because this distance is perpendicular and measured from the center, it bisects the chord, which means the base of the triangle is 15. Use the Pythagorean theorem to find the length of the hypotenuse, r:

Choice (F) is correct.

D

Difficulty: Medium

Category: Algebra

Getting to the Answer: Understanding slope-intercept form of a line, y = mx + b, is essential on the ACT. When a linear equation is written in the form y = mx + b, the slope is the coefficient of x. Rewrite the first equation in this form, y = 3x, to find that its slope is 3. In the second equation, the slope is a. To be parallel, the two equations must have the same slope, so a = 3, which is (D).

J

Difficulty: Medium

Category: Statistics and Probability

Getting to the Answer: The average of a set of terms is the sum of the terms divided by the number of terms. Even if you’re not sure what to do on an averages question, plugging the given information into this formula can help you figure out where to go.

For the first four numbers:

When you include the fifth number, x, the new sum will be 56 + x. The new average is:

The fifth number is 24, which is (J). Don’t forget to divide by 5 (not 4) in the second equation, because there are now five numbers.

A

Difficulty: Medium

Category: Algebra

Getting to the Answer: If a system of linear equations has infinitely many solutions, then both equations describe the same line. When two equations represent the same line, one is an exact multiple of the other. Look for a multiple. Because 3 · 4 = 12 and 27 · 4 = 108, you can get the first equation by multiplying the second by 4:

Therefore, 4k = –20, or k = –5. This means (A) is correct.

J

Difficulty: High

Category: Algebra

Getting to the Answer: Sometimes on the ACT, you will need to put together several pieces of information in the right way to get the answer. Because each extra inch adds approximately 10 pounds, a 72-inch person should weigh about 40 pounds more than a 68-inch person, for a total of 190 pounds. Now use the formula:

Choice (J) is correct.

A

Difficulty: Low

Category: Statistics and Probability

Getting to the Answer: It’s easy to get confused on “counting” questions. Drawing a Venn Diagram will help you visualize the scenario:

Using the diagram, you can see that 45 + 25 + 21 = 91 students are signed up for either the sack race, the balloon toss, or both. This means that 100 – 91 = 9 of the students who signed up to participate in a sporting event at the festival are not signed up for either the sack race or the balloon toss. This makes (A) correct.

H

Difficulty: Medium

Category: Geometry

Getting to the Answer: Always be on the lookout for special right triangles. What kind of triangles are formed when a perpendicular bisector is added to an equilateral triangle?

Because ∆ABC is equilateral, each of its angles is 60°. Angle BDA is 90° because is perpendicular to . Then each half of ABC is a 30°-60°-90° triangle, with side ratios of . The side opposite the 60° angle is units long, so x = 4. The hypotenuse, , is 2x = 8 units long, which is (H).

C

Difficulty: Medium

Category: Geometry

Getting to the Answer: To find the perimeter of a composite figure like this one, it can be easy to leave out some sides. Try marking each side as you add it so that you don’t accidentally forget any or add any twice. First find the missing lengths:

The small horizontal side must be the same length as the small horizontal side above it (7 m), because all the angles are right angles. The interior vertical side must be 22 − (10 + 3) = 9 meters long, because the total vertical distance on each side of the figure must be the same. Now add the length of each side to find the perimeter: 16 + 22 + 16 + 10 + 7 + 9 + 7 + 3 = 90, or (C).

J

Difficulty: Medium

Category: Statistics and Probability

Getting to the Answer: Permutations are sequences, so order matters. Any of the 5 books could be placed in the first spot on the shelf. Any of the remaining 4 books could be placed in the second spot, any of the remaining 3 books could be placed in the third spot, and so on until there is only 1 remaining book for the fifth spot. You can represent this visually by drawing a line representing each of the shelf’s 5 spots, then writing in how many book choices there are for each spot:

Therefore, the number of possible arrangements is 5 × 4 × 3 × 2 × 1 = 120, or (J).

E

Difficulty: Medium

Category: Geometry

Getting to the Answer: If your answer doesn’t look quite like any of the answer choices, rearrange it so that it does. Don’t just pick an answer that looks similar; make sure it actually means the same thing. Parentheses make a big difference, so you should carefully consider where they should be! The outer circle has area πr² = π(12²). The inner circle has area πr² = π(4²). The shaded area is π(12²) − π(4²) = π(12² − 4²), which is (E).

J

Difficulty: Low

Category: Number and Quantity

Getting to the Answer: The temperature of the container of liquid nitrogen is lower than the temperature of the room, so it must rise to match the room’s temperature. Eliminate F and G, which indicate that a drop in temperature is needed. To find the positive difference, subtract:

72°F − (−330°F) = 72°F + 330°F = +402°F,

Therefore, (J) is correct.

E

Difficulty: Medium

Category: Geometry

length = 17 feet
width = 2(17) − 21 = 34 − 21 = 13 feet
area = 17(13) = 221 square feet

This still isn’t big enough, so (E) must be correct:

length = 19 feet
width = 2(19) − 21 = 38 − 21 = 17 feet
area = 19(17) = 323 square feet
Perfect!

You could also solve algebraically:

An equation for the width (W) in terms of the length (L) is W = 2L − 21.

Length must be positive, so the length is 19, matching (E).

G

Difficulty: Medium

Category: Geometry

Getting to the Answer: Picking Numbers can make a theoretical question much more concrete. Say the original radius was 1. Then the area of the circle would be πr² = π(1²) = π. Twice this area would be 2π. Find the radius of a circle with area 2π:

The new radius is times the old radius of 1, so (G) is correct.

A

Difficulty: Medium

Category: Functions

Getting to the Answer: On some questions, you won’t be able to depend on your calculator. You simply have to know the formula or rule. Here, the rule you want is that log_b y = x translates to b^x = y. Use this to rewrite the given logarithmic equation using an exponent: x³ = 64. If you’re not sure what number raised to the third power will give you 64, you can always Backsolve. You’ll find that 4³ = 64, which means (A) is correct.

K

Difficulty: Medium

Category: Number and Quantity

Getting to the Answer: Some things in math actually work like you expect them to. To subtract two matrices, just subtract the elements that are in the same position. After you’ve subtracted one position, eliminate the answer choices that don’t have the correct number in that position. You may be able to get away with only subtracting one or two positions before you eliminate all the wrong answer choices.

So (K) is correct.

C

Difficulty: Medium

Category: Number and Quantity

Getting to the Answer: When you’re Picking Numbers for a question with few limits, don’t forget to try both positive and negative integers and fractions. Try a = 1 and b = −2. This immediately eliminates B. Using these values, a² = 1 and b² = 4, which eliminates E. Now try a = 2 and b = 1. This eliminates A. Using these new values, a² = 4 and b² = 1, which eliminates D. Choice (C) must be correct because the square of a number cannot be negative. No matter what b is, b² will be greater than or equal to zero.

G

Difficulty: Medium

Category: Geometry

Getting to the Answer: On Geometry questions, it usually helps to draw the triangle. Use SOHCAHTOA to remember which trig function involves which sides of the triangle.

The smallest angle is the one opposite the shortest side. Here, the smallest angle is marked θ. Based on the diagram, cos θ =, which is (G).

C

Difficulty: High

Category: Functions

Getting to the Answer: A graphing calculator can be a good backup, but understanding the math will always be faster. You could plug this equation into your graphing calculator, find the highest and lowest y-values, find their difference, and divide by 2. Alternatively, you could use algebra and what you know about transformations. Rewrite the equation as y = 5 cos(4θ) + 2. The +2 at the end moves the entire graph up 2 units; it doesn’t affect the difference between the largest and smallest values. The 4 inside the parentheses affects how often the function repeats itself in the same space on the x-axis. It’s the 5 in front that multiplies the y-values and makes the extreme values of the function higher and lower. Cosine usually goes from −1 to 1, so if you multiply all the values by 5, it will go from −5 to 5. The difference is 10, and half of the difference is 5. So the amplitude is 5, or (C).

H

Difficulty: Medium

Category: Statistics and Probability

Getting to the Answer: According to the graph, Angus has been paying down his debt at a rate of $500 per month. To reach 25% utilization, he needs to get down to $10,000 × 0.25 = $2,500, which means he needs to pay off $10,000 – $2,500 = $7,500. To do this, it would take $7,500 ÷ $500 = 15 months, making (H) the correct answer.

E

Difficulty: Medium

Category: Geometry

Getting to the Answer: The wording of this question is a giveaway. One of the angles is a “vertex angle” and the other two are “base angles.” This will allow you to solve the question even if you forgot what an isosceles triangle is! The angles sum to 180 degrees, so:

Base angle = 3x + 18 = 3(22) + 18 = 84, making choice (E) correct.

Notice that A and B are the answers to other questions; they are, respectively, the measure of the vertex angle and the value of x. Be sure to solve for the right thing.

H

Difficulty: Medium

Category: Number and Quantity

Getting to the Answer: If you don’t take the time to read carefully, you’ll lose a lot of points on careless mistakes. One set of potholders requires: (6 · 8) + (5 · 12) + (2 · 18) = 48 + 60 + 36 = 144 inches of fabric. This is . Each yard costs $1.95, so one set of potholders costs 4($1.95) = $7.80. Margot is making 5 sets of potholders, so the total cost is 5($7.80) = $39, which is (H).

A

Difficulty: High

Category: Statistics and Probability

Getting to the Answer: Don’t neglect the 50% at the beginning of the question just because it is presented in a different form. Instead, convert 50% to a fraction and then think logically—the final probability is of of . In math, of means multiply, so the probability of randomly choosing a vehicle that is a car with an automatic transmission and a GPS system is . This means (A) is correct.

H

Difficulty: High

Category: Statistics and Probability

Getting to the Answer: The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order. When there is an even number of terms, the median is the average of the two middle values. Here, there is an even number of terms with a and b in the middle, and you’re given that the median is 4, so it must be that . This is equivalent to a + b = 8. Thus, the product of a and b must be the product of two numbers that add up to 8. The possible pairs of values for a and b are 1 and 7, 2 and 6, 3 and 5, and 4 and 4, which means the possible products are 7, 12, 15, and 16. Only (H) matches one of these products.

C

Difficulty: High

Category: Functions

Getting to the Answer: If you can tell at a glance that a question is going to take several minutes, save it until you’ve done all the easier questions. In the equation of an ellipse, , the center is at (h,k), the length of the horizontal axis is 2a, and the length of the vertical axis is 2b. This particular ellipse is shown here:

The largest circle possible is dotted on the diagram. Notice that it has the same center as the ellipse and has radius 2 (the shortest dimension of the ellipse). In the equation of a circle, (x − h)² + (y − k)² = r², (h,k) is the center and r is the radius. Plug this information into the formula to find this circle’s equation: (x − 4)² + y² = 4, which is (C).

F

Difficulty: Medium

Category: Functions

Getting to the Answer: The highest power in the equation determines the general shape. The graph of y = x³ will always have the general shape of the graph in F. Adding a constant C will move it up by C units (if C is positive—if C is negative the graph will move down). If you’re not familiar with the shape of the graph y = x³, you could either plug it into a graphing calculator or plot a few points. Don’t worry too much about specific values. As soon as you realize that when x is negative, y will also be negative, you can eliminate all the graphs except (F).

C

Difficulty: High

Category: Statistics and Probability

Getting to the Answer: Try not to overthink a question like this—instead, use what you know about finding an average and see where that takes you. The average of a set of terms is the sum of the terms divided by the number of terms. Use this definition along with the average given in the question (10) to solve for x:

Now, substituting 5 for x in each of the expressions, you get: 5, 2(5) – 3, 2(5) + 1, 3(5) – 4, and 3(5) + 1, which gives the numbers 5, 7, 11, 11, and 16. The mode of a data set is the number that occurs most often, which in this case is 11. This means (C) is correct.

J

Difficulty: High

Category: Statistics and Probability

Getting to the Answer: ACT probability questions are simple enough that you can write out all the possible outcomes if you need to. Remember that probability is the number of desired outcomes over the number of possible outcomes. The easiest way to think about this question is to look at it backwards. If there are 3 heads, how many tails are there? In 4 coin tosses, if there are 3 heads there must be exactly 1 tail. That tail could be the first, second, third, or fourth toss, so there are 4 ways to get 1 tail and 3 heads. This means the number of desired outcomes is 4. There are 2 possible positions for each coin (heads or tails), so the total number of possible arrangements of heads and tails in 4 tosses is 2 · 2 · 2 · 2 = 16. Therefore, the probability that in 4 tosses, there will be exactly 3 heads is . Choice (J) is correct.

If you’re in doubt, write it out! All the possible arrangements of 4 coins are as follows:

HHHH THHH HTTH THTT

HHHT HHTT THTH TTHT

HHTH HTHT TTHH TTTH

HTHH THHT HTTT TTTT

The ones with 3 heads are in bold type. There are 4 arrangements with exactly 3 heads and 16 total possible arrangements. Again, the probability of getting exactly 3 heads is , so (J) is correct.

HHHH	THHH	HTTH	THTT
HHHT	HHTT	THTH	TTHT
HHTH	HTHT	TTHH	TTTH
HTHH	THHT	HTTT	TTTT

Reading Test

Suggested Passage Map notes:

¶1: Rosemary (R) - 87 yrs old

¶2: R’s youngest grandson V seems lazy

¶3: R appalled by V’s explanation of “gut” class

¶4-9: R’s father had forbidden her to go to school, wonders what could have been

A

Difficulty: Low

Category: Inference

Getting to the Answer: The author writes that Rosemary “had decided long ago that growing old was like slowly turning to stone; you couldn’t take anything for granted,”(lines 16–18), that the memory of her childhood was “still painful as an open wound,” (line 54), and that she “wondered what life would have been like if her father had not been waiting at the bottom of the stairs that day” (lines 76–78). The writer indicates sympathy for an elderly woman whose life had not gone as she had wished, a match for (A). Choice B is opposite of the information; the author does not use any words that indicate anger at Rosemary. Rosemary may be disappointed by her nephew’s “gut” classes, but that’s not the same as the author being disappointed in Rosemary, C, and there is no suggestion that the author is confused, as in D, by the narrator.

H

Difficulty: Medium

Category: Inference

Getting to the Answer: Rosemary’s unease with Victor’s behavior is broadly in response to what she perceives as his laziness, but laziness isn’t an answer choice. Choice J may be tempting, but Victor isn’t unable to get out of bed, he’s unwilling to. The third paragraph does specifically talk about something he had said that had “disturbed” her—his willingness to take an easy class, which matches (H). There is no evidence that Victor plans to drop out, so F is not correct, and her upbringing is never discussed with him, so G is incorrect.

D

Difficulty: Medium

Category: Inference

Getting to the Answer: The answer is strongly implied in the passage. The third paragraph notes that Rosemary wanted to go to high school after finishing grammar school. Her father would not permit her to go, so she had to spend time “with animals and rough farmhands for company instead of people her own age,” (D). Choice B is flatly contradicted by the third paragraph, which indicates that Rosemary wanted to go to high school, not college. Choices A and C make inferences that are not supported by the passage.

G

Difficulty: Medium

Category: Inference

Getting to the Answer: Lines 16–17 say that Rosemary “had decided long ago that growing old was like slowly turning to stone.” This sentiment suggests that she is resigned to the physical problems that accompany old age. Acceptance, (G), therefore, is correct. Sadness, F, and resentment, H, are too negative in tone, while optimism, J, is too positive. Rosemary, in short, isn’t at all emotional about the aging process.

A

Difficulty: Low

Category: Detail

Getting to the Answer: Rosemary’s interest in crossword puzzles is discussed in the opening sentences of the first paragraph. She does them for two reasons: to pass the time and to keep her mind active, (A). The other choices distort details in the first and second paragraphs. Choice B plays on Rosemary’s happiness at still being able to write at age 87, C plays on her need to consult an atlas to look up the Swiss river, and D plays on her experience of “an expanded sense of time” as she grows older.

G

Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: The second paragraph describes, among other things, Rosemary’s ability to keep “present and past tense intermingling in her mind,” which the author infers is a function of her old age. As it is used in the paragraph, expanded means “made more extensive,” which matches (G). Since expanded doesn’t necessarily mean “better,” F is out of scope. An unfurled flag is certainly expanded, but doesn’t make sense in the passage, making choice H incorrect. Choice J is opposite; to abridge means to shorten or restrict.

B

Difficulty: High

Category: Function

Getting to the Answer: In the lines that precede the mention of Victor’s “shiny new car,” Rosemary considers his easy upbringing and that her “grandson behaved as if he had never done a chore in his life” (lines 38–39). In other words, Victor’s car is a symbol of his generation, which has had a much easier time getting through life than did Rosemary’s. This contrast is exactly what (B) states. Choice A is incorrect on two counts: Rosemary’s parents—her father anyway—can’t be described as generous, and her parents have nothing to do with Victor’s car, which was a gift from Victor’s parents. Similarly, while Rosemary seems to feel that Victor’s future prospects are bright, C, and that his life lacks hardship, D, neither has anything to do with his car.

G

Difficulty: Medium

Category: Detail

Getting to the Answer: Paragraph 3 says that Rosemary is disturbed by Victor’s dismissive attitude toward his education. She doesn’t like the idea that his only reason for taking a course is that he can pass it. In contrast to Victor’s attitude, Rosemary, in her youth, was eager to continue her education, (G). Choices F and J refer to details from the wrong paragraphs, while H introduces an issue that the passage never tackles.

C

Difficulty: Medium

Category: Function

Getting to the Answer: A few lines before Rosemary recalls what it was like growing up on the farm, the passage says that “Rosemary often experienced an expanded sense of time, with present and past tense intermingling in her mind,” (C). Choice D, on the other hand, alludes to recollections from the wrong paragraphs. Choices A and B distort details in Paragraph 2.

F

Difficulty: Low

Category: Function

Getting to the Answer: The reference to Victor’s bright future comes at the end of Paragraph 2, which precedes Rosemary’s opinion: “if he (Victor) ever got out of bed.” It’s clear from the text that it’s Rosemary, (F), who thinks that he has a good future. The passage never says what Victor thought about his own future, G, nor does it say what his parents thought about his future, H. And it’s extremely unlikely that Victor and Rosemary’s father, J, were even alive at the same time.

Passage II

Passage A

¶1: Sherman Antitrust Act (SAA) 1st to fight econ. monopolies

¶2: many politicians felt gov’t should stay out of econ.

¶3: by late 1800s, SAA needed to protect consumers

Passage B

¶1: author believes altering gov’t = positive reform

¶2: FDR is example of modern liberal econ reg.

¶3: gov’t must adapt to changing needs

B

Difficulty: High

Category: Detail

Getting to the Answer: Use evidence in the passage and your own common sense to form a prediction before looking at the answer choices. The passage states that these revisions were written by “pro-business Eastern senators,” and that these revisions worked to weaken the effectiveness of the Act. Choice (B) is correct; the pro-business senators resisted the purpose of the bill. Choice A is a misused detail; Social Darwinism is not discussed until the next paragraph, and the author makes no direct connection between it and the revisions. Choice C is a distortion; there is evidence of “debate,” because the bill got rewritten, but there is no evidence that the debate took a long time. Choice D is extreme; the author is only discussing this bill, not the nature of all Congressional legislation at that time.

H

Difficulty: High

Category: Function

Getting to the Answer: Remember to keep straight the opinion of the author and other opinions cited in the passage. The trust leaders used the theory of Social Darwinism to explain why it was natural for them to have monopolies. The author must have included this in order to explain how some people justified the existence of monopolies. Choice (H) is correct; this matches your prediction. Choice F is a distortion; this is what the monopolists thought, not what the author thinks. Choice G is out of scope; the author is not exploring what kind of corporations survived, except to the extent that monopolists artificially stifled competition. Choice J is out of scope; the author is discussing a specific instance, not exploring the general “influence” of science on policy.

B

Difficulty: Medium

Category: Inference

Getting to the Answer: When a question stem refers you to a section of the passage but does not provide enough information to make a prediction, it is often helpful to take a quick scan through the passage before looking at the answer choices. The third paragraph states that laissez-faire policies created monopolies that had many negative effects. Many people objected to this, which eventually led to the Sherman Antitrust Act and other similar measures. Choice (B) fits with the description of the many negative effects of the trusts. Choice A is extreme; there is not enough evidence in the passage to use the word all. Choice C is a misused detail; this idea comes from Passage B. The author of Passage A never states that it was necessary; maybe there were other ways to handle the situation. Choice D is a distortion; the author would argue that all businesses, even big trusts like Standard Oil, could compete freely after the act.

J

Difficulty: Medium

Category: Function

Getting to the Answer: Because the answer is in the passage, you should be able to move quickly through Detail questions, saving time for those you find more difficult. Read in the immediate vicinity of the given reference. The prior sentence states that Roosevelt used “government funds for the first time” in “intentional deficit spending.” The sentence after the reference points out that this “ushered in the modern era of liberal economic regulation . . . ” The Act is an example of active manipulation of the economy by the government, which matches (J). Choice F is a misused detail; Passage A, not Passage B, refers to antitrust acts. Choice G is opposite; the passage states that “this act signaled the end of the laissez-faire economics era . . . ” Choice H is opposite; the author says that the Agricultural Adjustment Act helped boost the nation out of the Great Depression.

B

Difficulty: Medium

Category: Detail

Getting to the Answer: The author discusses Franklin D. Roosevelt in the second and third paragraphs. The author quotes Roosevelt as saying that he must “’reform democracy in order to save it’“ (lines 82–83), then describes Roosevelt taking action to end the Depression by instituting deficit spending and “deliberate manipulation of the national economy” (line 99), including paying farmers to produce less. This information matches (B). Choice A is not only opposite but also relevant only to Passage A. Choice C is out of scope, since Passage B has no reference to the Sherman Antitrust Act (and even if it did, it can be assumed that Roosevelt would favor it.) Choice D is also opposite; Roosevelt abandoned the traditional idea of a balanced budget to pour government monies into the economy as a way of relieving the Great Depression.

H

Difficulty: Medium

Category: Function

Getting to the Answer: Opposite choices can be tricky if you do not take the time to read carefully. Many people, including the “conservative capitalist economists,” felt that the economy would naturally rise and fall and that the government should not interfere in that process. The author then goes on to state that Roosevelt felt the economy would not naturally recover, and so he instituted policies and spent money to fix it. The author feels that Roosevelt was right to do so. (The author says that Roosevelt’s success was “undeniable.”) The author explains the viewpoint of the “conservative capitalist economists” in order to then argue that they were wrong and that Roosevelt was right in working to change the economy. Choice (H) fits nicely with the sentiments of the author. Choice F is opposite; Roosevelt took the opposite view from the “conservative capitalist economists.” Choice G is opposite; the viewpoint of the “conservative capitalist economists” was in direct contradiction to policies like the Agricultural Adjustment Act. Choice J is a misused detail; this does not come up until the final paragraph.

B

Difficulty: Medium

Category: Detail

Getting to the Answer: Watch out for choices that only apply to one of the Paired Passages. Both passages refer to economic reform. Passage A talks about preventing monopolies and trusts, and Passage B speaks in more general terms about spending money to pull the nation out of the Great Depression. Look for something that deals with government intervention in the economy. Choice (B) is mentioned in both passages. Choice A is opposite; both authors seem to agree that some degree of governmental control is necessary. Choice C is a misused detail; this only appears in Passage A. Choice D is a misused detail; this only appears in Passage B.

G

Difficulty: Medium

Category: Inference

Getting to the Answer: When you are trying to infer how one author would react to an idea in another passage, look for a concept that the author specifically addresses. The author of Passage B argues that it is often a good idea for the government to intervene in the economy. Therefore, he would probably not accept the argument that something should continue to exist simply because it is the most natural state of affairs. Choice (G) is correct; this fits with Author B’s view of laissez-faire economic policy. Choice F is out of scope; we do not know how the author of Passage B feels about the theory of Social Darwinism. Choice H is opposite; this viewpoint is what Author B is arguing against. Choice J is a distortion; Author B never mentions monopolies.

B

Difficulty: Low

Category: Detail

Getting to the Answer: Use the passages to research your answer. It is tough to make a specific prediction here, so jump into the answer choices and compare each one against the passages. Choice (B) is correct; Passage B mentions Roosevelt’s plan to “pump-prime” the depressed American economy through government deficit spending. Choice A is opposite; this appears in Passage A but not Passage B. Choice C is opposite; this is from Passage A, not Passage B. Choice D is opposite; this appears in both passages.

J

Difficulty: High

Category: Detail

Getting to the Answer: In the third paragraph of Passage A, the author cites many negative consequences of laissez-faire policies and the trusts and monopolies that arose from these policies. In the third paragraph of Passage B, the author states that the Agricultural Adjustment Act “signaled the end of the laissez-faire economics era.” These details match (J). Choice F is opposite; Passage A describes how laissez-faire policies negatively affected consumers, and Passage B states that the laissez-faire era ended by the end of the 19th century. Choice G includes misused details that are mentioned in each passage but do not address the question. Choice H is out of scope; Roosevelt’s presidential legacy is not discussed.

Suggested Passage Map notes:

¶1: philosophes = Enlightenment ideas

¶2: influenced by Newton, Locke, English inst.

¶3: Newton: reason and nature compatible

¶4: Locke: human beings malleable

¶5: English inst.: individual freedom

¶6: philosophe Voltaire = ex. of Enlightenment ideas

C

Difficulty: Medium

Category: Inference

Getting to the Answer: This question asks for a description of the philosophes, so it’s back to the first two paragraphs. Lines 13–15 say that they took the ideas of others and popularized them. The first sentence of the second paragraph (lines 20–23) goes on to state that they “developed the philosophy of the Enlightenment and spread it to much of the educated elite in Western Europe (and the American colonies).” Thus, (C) is correct. Choices B and D are contradicted by information in the first paragraph, which states that the philosophes were generally neither professors nor scientists. Choice A, on the other hand, is too narrow in scope: true, the philosophes were influenced by Locke, but they were also influenced by Newton and English institutions.

F

Difficulty: Medium

Category: Inference

Getting to the Answer: This author says the philosophes “were rightly considered philosophers,” (line 5), that they were intellectuals, and that they “developed the philosophy of the Enlightenment and spread it to much of the educated elite in Western Europe (and the American colonies)” (lines 20–23). The author seems to admire these people and acknowledge their influence on the educated world, matching (F). Choice G is the opposite of the author’s opinion, and H seems to criticize the philosophes for basing their thinking on the previous ideas of “Newton, Locke, and English institutions” (lines 26–27). Choice J is contradicted by the statement that the philosophes “were rightly considered philosophers” (line 5).

D

Difficulty: Medium

Category: Detail

Getting to the Answer: The answer to a question that contains a line reference is found in the lines around that reference. Locke’s idea that “schools and social institutions could . . . play a great role in molding the individual” comes up right after his belief that humans are shaped by their experiences, (D). Choice A is contradicted by lines 44–47, while B and C distort details in the fourth paragraph.

H

Difficulty: High

Category: Inference

Getting to the Answer: Your passage map should have pointed you to the third paragraph, where Newton is discussed. This paragraph says that Newton believed that “the universe [was]…originally set in motion by God,” Option I, and that “the universe operates in a mechanical and orderly fashion,” Option III. However, this paragraph doesn’t say that Newton believed that “human reason is insufficient to understand the laws of nature,” Option II; if anything, it implies just the opposite. Choice (H), Options I and III only, is correct.

D

Difficulty: Medium

Category: Detail

Getting to the Answer: Lines 54–56 reveal that it was Locke who questioned the notion that “revelation was a reliable source of truth.” Thus, you’re looking for a work written by him, so you can immediately eliminate A, Letters on the English, and C, Elements of the Philosophy of Newton, both of which were authored by Voltaire. The remaining two works, Second Treatise of Civil Government, B, and Essay Concerning Human Understanding, (D), were both written by Locke; but Second Treatise of Civil Government, B, is a political, not a philosophical, work, so it can be eliminated as well. That leaves (D) as the correct answer.

G

Difficulty: Medium

Category: Inference

Getting to the Answer: The first sentence of Paragraph 4 states that Locke “agreed with Newton but went further.” Specifically, Locke also thought that the human mind was subject to “the mechanical laws of the material universe” (lines 41–43), (G). The other choices distort details in the third and fourth paragraphs.

D

Difficulty: Medium

Category: Detail

Getting to the Answer: The philosophes—as the fifth paragraph shows—were greatly influenced by an England that allowed more individual freedom, was more tolerant of religious differences, and was freer of traditional political institutions than other countries, particularly France. Indeed, the philosophes wanted other countries to adopt the English model. Thus (D), Options I, II, and III, is correct.

G

Difficulty: High

Category: Inference

Getting to the Answer: This question also asks about England, so refer back to the fifth paragraph. In the second-to-last sentence of the paragraph, the philosophes cite England’s political stability and prosperity as evidence that England’s system worked. The last sentence of the paragraph goes on to say that the philosophes “wanted to see in their own countries much of what England already seemed to have” (lines 74–75). Choice (G), therefore, is correct. Choice F, on the other hand, flatly contradicts the gist of the fifth paragraph. Finally, H and J distort details from the wrong part of the passage.

D

Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: Mordant is a word the author uses to describe Voltaire’s humor in the sixth paragraph. Think about the other words the author uses to describe Voltaire: versatile, sparkling, outspoken. Consider also that Voltaire was imprisoned, then exiled because of his criticism of church and state. Now go back to the phrase “mordant wit.” Given the context, this must mean something about a sarcastic, critical humor. Biting, choice (D), is another word with the same meaning, and it is correct. Choice A is opposite. The author states that Voltaire offended both church and state, so there were specific, not random targets. Choice B confuses the word intelligentsia (highly educated people) with Voltaire’s intelligence, and C is opposite of the correct meaning.

J

Difficulty: Medium

Category: Function

Getting to the Answer: The notion that the philosophes were “more literary than scientific” appears in the middle of the first paragraph. A few lines further down, the paragraph furnishes a list of the types of literary works produced by the philosophes, so (J) is correct. The passage never mentions any “political change,” F, nor does it compare the literary outputs of Newton and Voltaire, G. Finally, H is out because the philosophes were not scientists.

Suggested Passage Map notes:

¶1: 65 mil yrs ago - mass extinction

¶2: 1980 - Alverezes’ asteroid theory

¶3: research supports theory + additional meteor strikes

¶4: moon surface info also supports theory

¶5: trad. bio/geo resisted theory

D

Difficulty: Low

Category: Detail

Getting to the Answer: This question emphasizes the importance of reading all the choices before selecting one. The second paragraph tells us that the Alvarezes believe conditions created by the impact of a meteorite led to mass extinctions, making (D) correct. The impact of the asteroid, A, caused great damage, but it didn’t do “most of the harm”—see the third sentence. Processes like B and C are the explanations of the traditional scientists.

H

Difficulty: High

Category: Inference

Getting to the Answer: To fully accept the validity of a theory, scientists require verifiable and repeatable evidence. Until that is available, scientists are correct in continuing to challenge the theory and pursuing their own research into it. This makes choice (H) correct. Keep in mind that the question is about traditionalists, meaning that the alternative view must be that of the Alvarezes. The traditionalists’ arguments are given only briefly, and the author clearly believes the Alvarezes have added something valuable to the study of mass extinctions, but the traditional view has not been proven wrong conclusively, as in F. And as the last paragraph indicates, traditionalists have produced their own theories to account for new evidence, such as iridium’s reaching the Earth’s surface via volcanic activity, as in J. Choice G is a distortion; the traditionalists were not skeptical about iridium itself, but of the Alvarezes’ explanation of its origin.

C

Difficulty: Medium

Category: Vocab-in-Context

Getting to the Answer: As it is used in the sentence, enrichment means “increase in amount.” It wouldn’t make sense for the Earth to have wealth, A, improvement, B, or reward, D, of iridium.

F

Difficulty: Low

Category: Global

Getting to the Answer: The arguments of Alvarez-theory opponents are given in the last paragraph: no crater, iridium comes from the Earth’s core, and the Alvarezes are only physicists. If sufficient iridium deposits come from the Earth’s core in lava flows, (F), Alvarez supporters can’t rely on them as evidence of meteorite impact. The Alvarezes didn’t say extinctions never occurred without asteroid impacts, G, or that all meteorites contain iridium, H. Choice J contradicts one of the arguments against the Alvarezes, not their opponents.

D

Difficulty: Medium

Category: Inference

Getting to the Answer: In the first sentence of the second paragraph, the author calls the Alvarez theory important. The bulk of the passage explains and supports this theory, so (D) is correct. The implication is that the author believes the Alvarezes were on the right track, so we want a positive answer. Choices A and C are negative, and B is neutral.

G

Difficulty: High

Category: Detail

Getting to the Answer: According to the information in the second paragraph, soil displacement was the immediate result of a meteorite’s impact; it “blotted out” the sun, which reduced temperatures and caused plants to die, which matches (G). All of the other answer choices are in the correct order.

D

Difficulty: Medium

Category: Function

Getting to the Answer: Look back at the second paragraph; details there clarify how the impact led to extinctions—the meteorite didn’t simply smash all species into extinction. Choice A is incorrect not only because it uses the extreme word demonstrate, meaning prove, but also because the Alvarezes’ intent was to link a meteorite strike with extinction, not just prove that one had occurred. The lack of a known crater site, B, is mentioned at the end of the fourth paragraph, but that’s not relevant to the discussion in the second paragraph. The conditions that result from meteorite collisions aren’t evidence that the Earth is vulnerable to such collisions, as in C.

H

Difficulty: Medium

Category: Function

Getting to the Answer: The large number of asteroids implied by teeming in the first paragraph explains why Alvarez supporters believe frequent collisions capable of producing enormous damage, must have occurred. This makes it very likely that a meteorite strike caused the massive environmental changes which resulted in dinosaur extinction. This matches (H). The fact that an impact would result in certain effects, F, or the idea that the dust cloud would do more harm than the impact itself, G, and the traditional view about gradual processes, J, are not related to the number of impacts that are likely.

C

Difficulty: Medium

Category: Detail

Getting to the Answer: The two sentences at the end of the fourth paragraph offer the answer; only I and III explain this position. Iridium relates to a different argument entirely.

H

Difficulty: Low

Category: Vocab-in-Context

Getting to the Answer: All three answer choices are possible meanings for the word profound, but only one makes sense in the passage. The author doesn’t mention the depth of the crater, or of anything else for that matter, making F out of scope. Something very hard to understand might be profound, but the passage is very clear, so G would be the wrong definition. Sincere, J, is another definition of profound, but it doesn’t make sense in the context of the passage. This leaves (H), which is correct. The entire passage is about dinosaur extinction, indicating its high level of importance.

Science Test

Passage I

D

Difficulty: Low

Category: Data—Detail & Interpretation

Getting to the Answer: Finding the answer to this question depends on locating the appropriate part of Table 1. There are 2 rows in the table that refer to Lagerstroemia ‘Natchez’ grown at a latitude of 28 degrees. (Ignore the row containing Lagerstroemia ‘Natchez’ grown at a latitude of 33 degrees.) Reading across the 2 rows, you can see that the plants have heights of 8.6 and 7.6 meters. Both of these values are greater than 7.5 meters tall, so (D) presents the most reasonable expectation for the height of an adult plant of the same variety.

G

Difficulty: Low

Category: Data—Detail & Interpretation

Getting to the Answer: Flowering growth is represented by the y-axis of Figure 1. The slope of the line indicates the rate of increase for flowering growth, so you should look for the segment that has the steepest positive slope. According to the figure, flowering growth increases only slightly in the Juvenile and Adult phases, and it decreases during the Death phase. The only phase containing a large increase in flowering growth, indicated by a steep upward slope, is the Intermediate phase, (G).

B

Difficulty: Low

Category: Data—Detail & Interpretation

Getting to the Answer: This question merely requires you to read the table accurately. The 4 varieties mentioned in the answer choices typically grow to heights of 2.4, 6.4, 4.6, and 4.9 meters, respectively. Choice (B) has the greatest adult height, making it correct.

F

Difficulty: Medium

Category: Data—Detail & Interpretation

Getting to the Answer: Take a look at Table 1 and examine the information given about each plant variety. Of the two varieties with data about growth in soil and organic compost, Lagerstroemia indica ‘Catawba’ reaches a typical height of 2.7 meters while Lagerstroemia fauriei ‘Kiowa’ grows to 8.3 meters tall, which means H can safely be eliminated. Lagerstroemia ‘Chickasaw’ only includes data for when it is grown in soil alone (with a typical height of 0.9 meters), but the passage offers no reason to suspect that adding organic compost would triple its growth, so G can be eliminated too. Lagerstroemia ‘Natchez’ also has no data about growth with organic compost, but it consistently reaches heights of more than double the desired value when grown at 28 degrees of latitude, allowing J to be eliminated as well. Lagerstroemia indica ‘Catawba’ is the only variety that comes close to a height of 3 meters, so (F) is correct.

D

Difficulty: Medium

Category: Thinking Like a Scientist—Evaluating Hypotheses

Getting to the Answer: To answer this question, simply compare the statement in each choice to the information in Figure 1—only 1 choice should agree closely with the data. Choice A cannot be correct since the rate of increase for flowering growth (the slope of the curve) changes in each phase. Choices B and C don’t match the data either—the curve tapers upward slightly during the Juvenile phase, indicating neither a sharp increase nor a decrease but rather a gradual increase in flowering growth. Choice (D) is correct: Figure 1 shows that flowering growth remains relatively low until the onset of the Intermediate phase.

J

Difficulty: Medium

Category: Experiments—Synthesizing Data

Getting to the Answer: The introductory paragraph states that Table 1 includes a plant’s typical adult height—for Lagerstroemia indica ‘Potomac,’ that height is 4.6 meters. The question asks about a “Lagerstroemia indica ‘Potomac’ shrub that is almost 5 meters tall,” which would almost certainly be an adult since it is close to the typical height from the table. To find the trend for its flowering growth, look at the adult phase in Figure 1. The flowering growth rate increases only slightly during the beginning of the adult phase and then plateaus, meaning that the general trend is for flowering growth to stay about the same during this phase. Choice (J) is thus correct.

Passage II

B

Difficulty: Low

Category: Data—Detail & Interpretation

Getting to the Answer: Radiation energy emitted can be found in Table 2. Simply look up the value for the Isotope B row and the Daughter column. The radiation emitted by the daughter nucleus for Isotope B is 2.1 MeV, as in (B).

H

Difficulty: Medium

Category: Data—Inference & Calculation

Getting to the Answer: Look at Table 1 to determine the decay reaction Isotope C underwent during each generation. The parent and daughter nuclei both underwent alpha decay, but the granddaughter nucleus did not decay further. According to the passage, alpha decay involves the emission of 2 neutrons and 2 protons. Since Isotope C underwent alpha decay twice, 2 × 2 = 4 neutrons were emitted. The correct answer is (H).

B

Difficulty: Medium

Category: Data—Inference & Calculation

Getting to the Answer: Compare the values for Isotope G to the values of Isotopes A−F in Table 2. Isotope G (6.2 MeV and 0.7 MeV) is most similar to Isotope E (6.0 MeV and 1.8 MeV), which underwent alpha and then beta decay. Alternatively, compare Table 1 to Table 2 to determine the range of radiation energy emitted for alpha and beta decay. Radiation energy emitted from alpha decay ranges from 5.0 to 6.8 MeV, and from beta decay, it ranges from 0.1 to 2.1 MeV. For Isotope G, 6.2 MeV (parent) falls between 5.0 and 6.8 MeV and 0.7 MeV (daughter) falls between 0.1 and 2.1 MeV. Hence, the particles emitted during decay of the parent and of the daughter are most likely alpha and beta, respectively. The correct answer is (B).

J

Difficulty: Medium

Category: Data—Detail & Interpretation

Getting to the Answer: The second paragraph of the passage states that when an isotope is stable, it no longer emits radiation. According to Table 1, the daughter and granddaughter of Isotope F did not emit alpha or beta particles. Thus, Isotope F was stable after 1 generation. The correct answer is (J). Isotopes C and E became stable after 2 generations, and Isotope A did not become stable and continued to decay after 3 generations.

A

Difficulty: Medium

Category: Data—Inference & Calculation

Getting to the Answer: Look at Table 1 to determine which particle was emitted from the parent nucleus for Isotope A. According to the table, the parent underwent alpha decay. Alpha decay as defined in the third paragraph of the passage results in the emission of an alpha particle, which consists of 2 protons and 2 neutrons. Atomic mass is the sum of protons and neutrons, as noted in the first paragraph. If 2 protons and 2 neutrons were emitted, the atomic mass of the daughter nucleus would be 4 less than that of the parent, as in (A).

J

Difficulty: Medium

Category: Data—Inference & Calculation

Getting to the Answer: Refer to Table 2 to determine the total radiation energy emitted over 3 generations for Isotopes A, E, and F. For Isotope A, the total energy of the 3 generations is 5.4 + 5.7 + 6.3 = 17.4 MeV. The total radiation energy emitted for Isotope E is 6.0 + 1.8 = 7.8 MeV. The total radiation energy for Isotope F is 1.4 MeV. Thus, the appropriate ranking for energy emitted from least to greatest is Isotope F, Isotope E, and Isotope A. The correct answer is (J). Watch out for trap answer F, which ranks the isotopes from greatest to least energy emitted.

C

Difficulty: High

Category: Data—Inference & Calculation

Getting to the Answer: During the first decay in the question stem, the atomic mass decreases by 4 (from 212 to 208) and the atomic number decreases by 2 (from 83 to 81), which indicates alpha decay. During the second decay, the atomic mass does not change but the atomic number increases by 1 (from 81 to 82), which indicates beta decay. Look at Table 1 to see which isotope underwent first alpha decay and then beta decay. Only Isotope E matches that series. Choice (C) is thus correct.

Passage III

H

Difficulty: Medium

Category: Experiments—Design & Methodology

Getting to the Answer: The independent variable is the quantity that is manipulated by researchers and that impacts the dependent variable (or variables) that the researchers measure. Table 2 and the description for Experiment 3 both indicate that the experiment studied how levels of UV-B light varied based on the time of day during which they were measured. The time of day is thus the independent variable, and (H) is correct. Choice F is incorrect because Experiment 3 only considered UV-B levels. Choice G is incorrect because UV-B level was the dependent variable in Experiment 3, the one that the researchers measured. Choice J is incorrect because Experiment 3 was limited to a single season, the summer.

B

Difficulty: Medium

Category: Experiments—Synthesizing Data

Getting to the Answer: To answer this question, begin by considering the trends that are revealed by the experimental results. The results of Experiment 1 indicate that UV-A levels are greater during the summer and at higher elevations, while the results of Experiment 2 show that UV-A levels are lower the more time has passed after the sun has been directly overhead. Choice (B) is correct because living in an area with shorter summers and longer winters would mean fewer days with higher UV-A levels and more days with lower UV-A levels. Choice A is incorrect because there is no suggestion in the passage of an inverse relationship between UV-A levels and UV-B levels—if anything, the results of Experiment 2 suggest a direct relationship since levels of both decrease 2 hours after the sun is directly overhead. Choice C is the opposite of (B) and would likely result in greater UV-A levels. Choice D is incorrect because windows that filter out UV-B light would not necessarily filter out UV-A light as well.

G

Difficulty: Low

Category: Data—Detail & Interpretation

Getting to the Answer: Essentially, this question is asking how UV-B levels change from when the sun is overhead, in the middle of the day, to when it is low on the horizon, near the end of the day. Experiments 2 and 3 both investigate the relationship between time of day and UV-B levels, though it is probably easier to see this relationship in Experiment 3. According to Table 2, UV-B levels decrease every hour after the sun is directly overhead, so you should predict that UV-B levels will be lower when the sun is low on the horizon. This corresponds to (G).

C

Difficulty: Medium

Category: Data—Inference & Calculation

Getting to the Answer: The question stem asks you to predict how UV-C light would behave if it acted like UV-A and UV-B light did in the experiments from the passage. Here, it’s a good idea to examine the answer choices to narrow down what data from the passage will be relevant. Choices A and B concern the change in UV levels from year to year, but this was not investigated in any of the experiments, so both choices can be eliminated. The remaining choices concern the relative UV levels when the sun is directly overhead, so consider the findings from Experiments 2 and 3, which investigated this directly. In Experiment 2, both UV-A and UV-B levels were higher when the sun was directly overhead, while in Experiment 3, the highest UV-B levels were recorded at that time as well. Thus, if UV-C light behaved in the same way, its levels would be higher when the sun is directly overhead, as stated in (C).

J

Difficulty: Low

Category: Data—Detail & Interpretation

Getting to the Answer: While working on previous questions, you should have found that both UV-A and UV-B are higher when the sun is overhead and lower at later times of day, as reflected in the results from Experiments 2 and 3. That means that both levels decrease as the number of hours after the sun is overhead increases. Choice (J) is the only choice that captures these relationships accurately.

D

Difficulty: Medium

Category: Data—Inference & Calculation

Getting to the Answer: This question may look complex, but the mention of UV-A levels, the summer, and measuring 30 minutes after the sun is overhead all point to the design of Experiment 1, particularly the information in the second half of Table 1. Since the elevation mentioned in the question stem is higher than all of those in the table, and because UV-A levels increase with greater elevation, predict that the levels of UV-A in this community will be higher than all of the values in the “Summer” portion of Table 1. Only (D) matches this prediction.

F

Difficulty: Low

Category: Data—Inference & Calculation

Getting to the Answer: Experiment 2 investigated the change in UV-B levels over time at an elevation of 2,000 meters during winter. According to the description of that experiment, the UV-B measurement when the sun is directly overhead is 48 mJ/cm², and after 2 hours, it is 42 mJ/cm². The only answer choice that has a value between 42 mJ/cm² and 48 mJ/cm² is (F). Choice J is a trap because it reflects the value of UV-B after 1 hour in the summer, as listed in Table 2.

Passage IV

C

Difficulty: Medium

Category: Data—Inference & Calculation

Getting to the Answer: The question is asking you to predict a result for circumstances that were not tested in the original experiment, so look for the trend in Experiment 1’s results. According to Table 1, every 2 cm added to r results in an additional 4 or 5 rpm for the precession rate, so the relationship between r and precession rate is direct and roughly linear. Thus, a gyroscope with an r of 9 cm should have a precession rate that is halfway between the precession rates for gyroscopes with r values of 8 cm and 10 cm, which are 19 rpm and 24 rpm, respectively. Halfway between those values is 21.5 rpm, which corresponds to (C).

G

Difficulty: Low

Category: Data—Detail & Interpretation

Getting to the Answer: The results of Experiment 1 are presented in Table 1, so look for the general trend there. As the r value increases, so does the precession rate. Since r is a measure of how far the center of gravity is from the surface, (G) accurately reflects the direct relationship between these 2 quantities. Choices H and J are incorrect because Experiment 1 did not vary the distance of the center of gravity from the axis of rotation.

C

Difficulty: Medium

Category: Experiments—Synthesizing Data

Getting to the Answer: To answer this question, you don’t have to figure out the exact shape of the graph—just enough to distinguish it from the incorrect answer choices. The results of Experiment 2 consistently show a decrease in precession rate as spin rate increases, with no sign in Table 2 of this trend reversing. This best fits with (C), which also shows the precession rate (y-axis) decreasing as the spin rate (x-axis) increases. Choice A shows an initial increase in precession rate before it decreases, which is not supported by the data in the table. Choice B shows the opposite trend—precession rate increasing as spin rate increases. Choice D shows an initial decrease in precession rate, but the subsequent increase is not supported by the data in Table 2.

F

Difficulty: Medium

Category: Thinking Like a Scientist—Evaluating Hypotheses

Getting to the Answer: To test a hypothesis about precession rate and the acceleration due to gravity, the scientist would have to measure the precession rate at multiple locations that varied with respect to this quantity. The question tells you that gravitational acceleration decreases as distance from the Earth increases. Thus, one way to test this hypothesis would be to measure gyroscopes at different distances from Earth, which matches (F). Choice G would not provide any new data because a satellite at the exact same distance would experience the same gravitational acceleration as was encountered in Experiment 3. Choice H is incorrect because nothing in the passage or question stem indicates that orbital direction has an impact on acceleration due to gravity. Choice J would more or less replicate Experiment 2, which revealed nothing about the effect of gravitational acceleration on precession.

C

Difficulty: High

Category: Experiments—Synthesizing Data

Getting to the Answer: In order to answer this question, you’ll need to relate 3 quantities together: r, spin rate, and precession rate. So start working on this question by considering the information revealed in Tables 1 and 2. Table 1 relates r and precession rate for a fixed spin rate, while Table 2 relates spin rate and precession rate for a fixed r, which you’re told in the question stem is equal to 6 cm. Call the fixed spin rate used in Experiment 1 s. Based on Table 1, when the spin rate is s and r is 6 cm, the precession rate is 14 rpm. Now, to find the value of s, just look for a matching precession rate in Table 2. When r is 6 cm (as it is for all of the entries in Table 2, according to the question stem) and the precession rate is 14 rpm, the spin rate is 750 rpm. So, you can conclude that s, the spin rate from Experiment 1, is 750 rpm, which matches (C).

G

Difficulty: High

Category: Experiments—Design & Methodology

Getting to the Answer: This question is effectively asking you to identify a variable that the researcher needed to control (that is, to keep constant) to ensure useful results in Experiment 2. The question stem says to assume that the results of Experiment 1 were not taken into account during Experiment 2’s design, which suggests that the relevant variable is precisely the one that was manipulated during Experiment 1. According to the description of Experiment 1, the gyroscopes “differed only in the distance (r) from the gyroscope’s center of gravity to the surface.” As Table 1 reveals, different r values produced different precession rates. This helps to explain why the scientist “used a gyroscope of fixed size” in Experiment 2: if the scientist had used gyroscopes with varying r values while also altering their spin rates, some of the precession rates measured would have differed from those found in Table 2—and this would have made it impossible to isolate the effect of changing spin rate on precession rate. Because using gyroscopes of various sizes would have altered the results of Experiment 2, (G) is correct. Choices F, H, and J all concern quantities that are not investigated in any of the experiments discussed in the passage.

B

Difficulty: High

Category: Experiments—Design & Methodology

Getting to the Answer: Always keep in mind that a well-designed experiment should involve manipulating only the variable being tested while keeping other quantities constant. To investigate the effects of gyroscope mass, you need to find a way to vary mass without changing other properties of the gyroscope, such as its size and shape. A fixed size and shape means a fixed volume, and the only way to alter the mass of an object without altering its volume is to alter its density, meaning its ratio of mass to volume. This can be done by using different materials that differ in density—for example, a gyroscope made of a denser metal like lead would have a greater mass than a gyroscope (of the same size and shape) made of a less dense metal like aluminum. Choice (B) is thus correct. Choice A is not specific enough to be correct: although gyroscopes from different companies could potentially have different masses, they might also differ in size and shape. Choice C would involve altering the acceleration due to gravity—and thus the weight—of the gyroscopes, but weight is different from mass (weight is equal to mass times the acceleration due to gravity). Choice D would test the effect of r on precession rate (as was investigated in Experiment 1), not the effect of mass.

Passage V

H

Difficulty: Low

Category: Thinking Like a Scientist—Evaluating Hypotheses

Getting to the Answer: The two theories differ on the details, but both describe how water droplets in clouds come together in some way until they become too heavy and fall to the ground. If there were an insufficient number of water droplets in a cloud, they would not be able to coalesce enough to form large water droplets (as in the first theory) or to evaporate to replace the water vapor that deposits onto miniature ice crystals (as in the second theory). According to either theory, no precipitation would form without enough water droplets, so (H) is correct. Choices F and G are incorrect because F would lead to precipitation in the first theory and G would lead to precipitation in the second. Choice J would lead to precipitation according to either, because the first theory involves large water drops that are too heavy while the second theory involves heavy ice crystals.

B

Difficulty: Medium

Category: Thinking Like a Scientist—Evaluating Hypotheses

Getting to the Answer: The major point of difference between the 2 theories concerns what actually forms in the clouds to become precipitation. According to the Collision-and-Coalescence Theory, large water drops become precipitation, while the Ice Crystal Theory maintains that precipitation results from the formation of ice crystals. Water drops are liquid but ice crystals are solid, meaning precipitation forms as 2 different phases of matter under the 2 theories, as in (B). Choices A, C, and D are incorrect because they concern aspects of precipitation that are not addressed in either theory as described in the passage.

F

Difficulty: Medium

Category: Thinking Like a Scientist—Evaluating Hypotheses

Getting to the Answer: The first theory described in the passage maintains that rainfall occurs after large water drops are formed from the repeated collision and coalescence of smaller droplets. According to this theory, rainfall is more likely to occur if more droplets coalesce, and more droplets are likely to coalesce if more of them collide. Consequently, a greater rate of collision translates to a higher probability of rainfall, making (F) correct. Choice G is incorrect because a variable rate could mean fewer collisions and therefore less coalescence and fewer raindrops, reducing the likelihood of rain. Choice H is incorrect because cold temperatures are necessary for the Ice Crystal Theory but not for the Collision-and-Coalescence Theory. Choice J is incorrect because the description of the theory in the passage does not address the time between rainfalls.

B

Difficulty: Medium

Category: Thinking Like a Scientist—Evaluating Hypotheses

Getting to the Answer: The Collision-and-Coalescence Theory maintains that water drops fall to the ground once they become “too heavy to remain suspended in the cloud.” Similarly, the Ice Crystal Theory holds that “ice crystals quickly become too heavy to remain suspended in the air and fall to the ground.” Thus, both theories agree that precipitation is the result of entities that are too heavy to stay suspended, so if a weather balloon discovers that there are many of these large entities within a cloud, it is highly likely that precipitation will soon follow. Choice (B) is correct. Choice A is incorrect because only the second theory concerns impurities in the air, while C is incorrect because only the first theory discusses colliding water droplets. Choice D is incorrect because the downward motion of entire clouds is not addressed in either theory as described in the passage.

H

Difficulty: Medium

Category: Thinking Like a Scientist—Evaluating Hypotheses

Getting to the Answer: According to the Ice Crystal Theory as described in the passage, precipitation is the result of the formation of ice crystals that become so heavy they can no longer be suspended in the air. For this process to begin, water droplets in the cloud must “freeze around tiny impurities in the air to form miniature ice crystals.” Thus, air impurities play a crucial role in the production of precipitation. A city that produces more of these impurities could be expected to have higher rates of precipitation according to the Ice Crystal Theory, precisely as is suggested in (H). Choices F and G cannot be correct because the description of the Ice Crystal Theory mentions neither thunder-and-lightning storms nor atmospheric density. Choice J is incorrect because it suggests an opposite result: less air pollution would lead to fewer impurities in the air, which would mean fewer ice crystals forming and less precipitation.

C

Difficulty: High

Category: Thinking Like a Scientist—Evaluating Hypotheses

Getting to the Answer: The question asks you to find a statement that makes the Collision-and-Coalescence Theory more likely to be true than the Ice Crystal Theory. Assess each answer choice individually and eliminate any that fail to provide the appropriate support. The Ice Crystal Theory requires that water droplets “freeze around tiny impurities in the air to form miniature ice crystals.” In this theory, fewer impurities means fewer crystals, which means less rainfall and other precipitation—so eliminate A for supporting the Ice Crystal Theory. The Ice Crystal Theory also maintains that “water droplets evaporate to maintain a constant level of water vapor,” so B is more consistent with it than with the Collision-and-Coalescence Theory, meaning B can be eliminated too. According to the Ice Crystal Theory, ice crystals that eventually become precipitation form after “tiny droplets in clouds rise to a point in Earth’s atmosphere where the temperature is lower than the freezing point of water.” However, if precipitation could form in clouds at higher temperatures, then precipitation could occur without the formation of ice crystals, which directly contradicts the Ice Crystal Theory. Moreover, this would be consistent with the Collision-and-Coalescence Theory, which only requires the presence of liquid water droplets for precipitation. Choice (C) supports the Collision-and-Coalescence Theory while weakening the Ice Crystal Theory, so it must be correct. This is confirmed by evaluating D, which is incorrect because only the Ice Crystal Theory depends on water’s changing between phases of matter.

H

Difficulty: High

Category: Thinking Like a Scientist—Evaluating Hypotheses

Getting to the Answer: Because the question asks for the least likely outcome, use process of elimination to remove any answer choices that seem likely to happen in the Ice Crystal Theory. According to the passage, in the final stage of the theory, “ice crystals quickly become too heavy to remain suspended in the air and fall to the ground, often melting again in the warmer temperatures near the ground to form rain.” Choice F closely reflects this account, so eliminate it. Similarly, it makes sense that in slightly colder temperatures, the ice crystals might melt only partially; therefore, G can be eliminated too. Choice (H) seems unlikely to occur in the Ice Crystal Theory because water drops do not fall from the cloud (as they do in the Collision-and-Coalescence Theory); only ice crystals fall from the cloud, so don’t eliminate this choice just yet. Choice J is not mentioned directly in the passage, but the Ice Crystal Theory maintains that some water droplets become water vapor (moving from liquid to gas) even though the temperature is so cold; so it is plausible that small ice crystals sometimes turn back into water droplets (moving from solid to liquid). Thus, J should be eliminated and (H) should be recognized as the correct answer.

Passage VI

C

Difficulty: Medium

Category: Data—Detail & Interpretation

Getting to the Answer: The question asks you to identify the trend between e and r for any value of n. If you look at Table 1, you’ll see that n can be either 2, 3, or 4. Start by looking at the n = 2 data. As the values of e increase from 4 to 7, the values of r decrease steadily from 9.1 to 5.7. In other words, the 2 variables are inversely related. Next, look at the n = 3 data—the same inverse relationship holds, as it does for the n = 4 data. Choice (C), then, is the correct answer.

F

Difficulty: Medium

Category: Data—Detail & Interpretation

Getting to the Answer: This question requires you to extrapolate for a value that doesn’t appear in Table 1, so use the trends in the data to make a prediction. You saw in the previous question that for a given value of n, higher values of e yield lower values of r, and vice versa. For n = 2, the lowest value of e given is 4, with a corresponding r of 9.1 × 10^–11 m. If the trend continues as expected, you can predict that a lower e of 3 would have a higher value for r. Choice (F) is correct because it’s the only value of r greater than 9.1 × 10^–11 m.

C

Difficulty: High

Category: Data—Detail & Interpretation

Getting to the Answer: While having background knowledge in chemistry could potentially help here, there is enough information directly in the passage to answer this question. The opening paragraph of the passage describes electrons as “negatively charged particles,” so anything that removes electrons would decrease an atom’s negative charge. According to the second paragraph, the ionization energy is the “energy in electron volts (eV) required to remove one electron from the atom’s outer shell.” Thus, applying energy to an atom could allow for the removal of an electron, which would decrease the atom’s negative charge. Choice (C) is therefore correct. Choice A is incorrect because, for a given n, smaller r values are associated with larger e values, meaning greater numbers of negatively-charged electrons in the outer shell. Choice B is incorrect because the passage offers no information about the impact of forming chemical bonds on the negative charge in an atom. Choice D is incorrect because shells contain electrons and adding more shells would only add more negative charge.

J

Difficulty: Medium

Category: Data—Detail & Interpretation

Getting to the Answer: This question asks you to examine the trend between the number of electrons in an atom’s outer shell (e) and electronegativity (c) when the value of n is fixed. Look for the trend between e and c for each value of n separately. For n = 2, c increases as e increases. Eliminate H because it doesn’t contain n = 2. For n = 3, c again increases as e increases. Eliminate F because it doesn’t contain n = 3. For n = 4, once again, c increases as e increases. Because the trend holds for all the values of n in the table, the correct answer must be (J).

D

Difficulty: Medium

Category: Data—Detail & Interpretation

Getting to the Answer: According to the passage, the “energy in electron volts (eV) required to remove one electron from the atom’s outer shell” is the ionization energy, symbolized in Table 1 by I. As can be seen by examining the table, the n values listed in the answer choices correspond to the outer shell for each element, so answering this question merely requires finding the highest value of I in Table 1. The I values for Si, Cl, C, and F are 8.2, 13.0, 11.2, and 17.4, respectively. Of these, 17.4, the value for F, is greatest, so the correct answer is (D).

F

Difficulty: Medium

Category: Data—Detail & Interpretation

Getting to the Answer: According to the passage, Pauling units are the units of measurement for electronegativity, which is represented by the variable c in Table 1. N and Cl share a c value of 3.0, Si and Ge share a c value of 1.8, and C and S share a c value of 2.5. The elements As and Se have the same value for I, but c is 2.0 for As and 2.4 for Se. So (F) is correct.

Writing Test

Model Essay

Below is an example of what a high-scoring essay might look like. Notice the author states her position clearly in the introductory paragraph and supports that position with evidence in the following paragraphs. This essay also uses transitions, some advanced vocabulary, and an effective “hook” to draw in the reader.

“Be cool; stay in school,” is the type of saying that may sound silly to high school students. Even though that phrase isn’t really sophisticated, it does provide very wise advice. Attending school is incredibly important, and some people argue that unexcused absences should be reported to the police. Other people want focus on treating the underlying causes of truancy rather than doling out harsh punishments. Still others think that schools should provide alternative instruction options for students who have trouble getting to school on a regular basis. All three options have the same goal, which is to help students most at risk for missing school, and I think that schools should incorporate the best parts of all three approaches into their truancy-reduction policies.

The idea of having a police record because I skipped school is extremely scary and would certainly prevent me from missing school. If students know that their school will report them to the police after a specific number of unexcused absences, they will be more likely to find a way to get to school. Teenagers don’t always do the right thing because it’s a good idea but rather because not doing the right thing will get them in a lot of trouble. For example, many high school students turn in their assignments on time because they don’t want teachers to deduct points for late submissions. The fear of consequence can promote good behavior in both homework habits and school attendance.

While avoiding a harsh consequence is a good reason to get to school, it’s sometimes not compelling enough for students who are struggling with issues that make attending school very difficult. The best way to increase attendance for these students is to address the underlying problems. If students have transportation trouble, schools should help coordinate carpools and bus schedules. School counselors should be available to help students who have social issues or violence concerns. As for lack of interest, schools can offer before- and after-school activities such as intramural sports and social clubs to give students a reason to stay throughout the day.

Even with the best efforts, some students will invariably struggle with attendance. For those students, schools should offer as many opportunities for them to complete their coursework as possible. It is in society’s best interest to facilitate education, especially for at-risk youth. Now that technology allows students to learn from nearly anywhere, schools should offer students the option to study remotely. Students will benefit from a high school diploma, of course, and they will be able to say that their teachers did everything they could to give them the best chance at a good life.

Attending school isn’t just about learning facts. The school environment provides students with the opportunity to learn how to employ necessary social skills, collaborate with peers, and communicate effectively. The only way for students to develop these skills is to actually attend school. Every measure should be taken to reduce truancy, including the threat of a criminal record, the mitigation of underlying causes, and the option to pursue alternative instruction. That way, students don’t have to just take our “be cool; stay in school” word for it — they’ll show up because, really, with all those measures in place, how could they not?

You can evaluate your essay and the model essay based on the following criteria:

Is the author’s own perspective clearly stated?

Does the body of the essay assess and analyze each perspective?

Is the relevance of each paragraph clear?

Does the author start a new paragraph for each new idea?

Is each sentence in a paragraph relevant to the point made in that paragraph?

Are transitions clear?

Is the essay easy to read? Is it engaging?

Are sentences varied?

Is vocabulary used effectively?

Is college-level vocabulary used?