PRACTICE TEST 2
SAT PRACTICE TEST 2 ANSWER KEY
Section 1: Reading
Total Reading Points (section 1)
Section 2: Writing and Language
Total Writing and Language Points (section 2)
Section 3: Math (No Calculator)
17. 2/3 or.666 or. 667
18. 1.2 or 6/5
19. 2.5 or 5/2
20. 7/3 or 2.33
Total Math Points (Section 3)
Section 4: Math (Calculator)
32. 3/2 or 1.5
35. 4/45 or. 088 or. 089
36. 75/4 or 18.75
Total Math Points (Section 4)
SCORE CONVERSION TABLE
Scoring Your Test
1. Use the answer key to mark your responses on each section.
2. Total the number of correct responses for each section:
3. Add the raw scores for sections 3 and 4. This is your Math Raw Score:_____________
4. Use the Table 1 to calculate your Scaled Test and Section Scores (10–40).
5. Add the Reading Test Scaled Score and the Writing and Language Test Scaled Score and multiply this sum by 10 to get your Reading and Writing Test Section Score (20–80).
Table 1: Scaled Section and Test Scores (10–40)
SAT PRACTICE TEST 2 DETAILED ANSWER KEY
Section 1: Reading
In the first paragraph, the author tells us that he has little prudence and no skill in inventing of means and methods … in adroit steering … nor in gentle repairing. He also has no skill to make money spend well. These are self-effacing descriptions. They are certainly not pontifical (speaking as a high priest), aspirational (expressing high hopes and goals), or sardonic (grimly cynical).
The statement that whoever sees my garden discovers that I must have some other garden is the last statement in the author’s list of his personal inadequacies. Therefore, this statement must be taken to be self-effacing as the other statements are, and specifically to mean that he lacks gardening skill.
Word in Context
Recall that the first paragraph begins with the question What right have I to write on prudence … ? The second provides a response to this question about his right: in saying I have the same title to write on prudence as I have to write on poetry or holiness, then, he is clearly saying that he has the standing or authority to write on prudence.
In following his declaration that he has the right to write on prudence (lines 11–12), Emerson states that [w]e write from aspiration as well as from experience. In other words, we gain the standing to write on prudence not only from expertise in prudent behavior, but also from a focusedyearning.
As the explanation to the previous question indicates, the best support for this answer is in lines 13–14.
The sixth paragraph (lines 39–57) discusses three classes of people according to their proficiency of knowledge of the world (lines 39–40). The first class values health and wealth [as] a final good (lines 42–43). The second class values the beauty of the symbol (line 46–47). The third classlives above the beauty of the symbol to the beauty of the thing signified (lines 46–47). This last group has spiritual perception (line 49). Therefore, its members are superior for their ability to discern sublime qualities.
This phrase appears in a discussion of the individual who traverses the whole scale (line 50–51), that is, who has the skills of all three classes: practicality, taste, and spiritual perception. In saying that such a person does not offer to build houses and barns (lines 54) on the sacred volcanic isle of nature (lines 53–54), Emerson is saying that nature is merely a symbol that points to the splendor of God (55), and therefore not what a truly wise person chooses to fix his or her gaze upon. In other words, the building of houses and barns is an unwise allegiance to worldly things.
Word in Context
In saying that the world is filled with the proverbs and acts of a base prudence (lines 58–59), Emerson means that most of our actions and words are devoted to practical things, like the question will it bake bread (lines 64)? As Emerson made clear in his previous paragraph, these considerations are those of the lowest and least noble class, so theirs is an ignoble prudence.
As a whole, this paragraph discusses the problem that the world is filled with the proverbs and acts of a base prudence (lines 58–59), in other words, that our words and actions are too focused on a devotion to matter (lines 59–60) and its effect on our senses, as if we possessed no other faculties than the palate, the nose, the eye and ear (lines 60–61). Emerson describes this problem with a simile: this is a disease like a thickening of the skin until the vital organs are destroyed (lines 64–66). To Emerson, then, the disease is the problem of sensuousness (devotion to the senses rather than the intellect).
In line 20, Emerson defines prudence as the virtue of the senses, but he regards the world of the senses [as] a world of shows (lines 22–23), that is false when detached (line 35) from the thing signified (line 47) by the natural, sensory, intellectual world, that is, from the splendor of God (lines 55). Furthermore, he says that prudence is a devotion to matter, as if we possessed no other faculties than the palate, the nose, the touch, the eye and ear (lines 59–61). Therefore, as a whole, the passage characterizes prudence as a pursuit of practical skills and sensory experience.
The opening paragraph describes this breathless pause at the threshold of a long passage (lines 8–9) in which the narrator and his crew seemed to be measuring our fitness for a long and arduous enterprise (lines 9–10). This describes the reflective anticipation of a journey. Notice that this description provides no evidence of anxiety or excitement. In fact, the scene is described in peaceful terms, with the ship very still in an immense stillness (line 2).
The narrator states that some glare in the air (lines 14–15) prevented him from seeing sooner something that did away with the solemnity of perfect solitude (lines 18–19). That is, he saw something that led him to believe they were not alone. In the next paragraph, this something is revealed to be the mastheads of a ship anchored inside the islands (lines 35–36).
This sentence describes the scene as the narrator surveys the tide of darkness and a swarm of stars (lines 20–21) while resting his hand on the rail of the ship as if it were the shoulder of a trusted friend (line 24). In the next sentence, he describes this as a moment of quiet communion (line 26) with the ship, now interrupted by the sight of a strange ship beyond and the disturbing sounds (lines 27–28) being made by the crew. In other words, this sentence describes a moment of wistful (expressing vague longing) contemplation. Choice (A) is incorrect because, although thedisturbing sounds and the omen of a distant ship may seem to be signs of impending danger, the sentence in lines 20–24 makes no mention of these things. Choice (B) is incorrect, because this moment is described as a moment of quiet communion, not deep inner turmoil. Choice (D) is incorrect, because there is no mention of any tragic experience.
Since this story is being told from the perspective of the captain, we can infer his character from the nature of his narration. In the opening paragraph, the captain states that we seemed to be measuring our fitness for a long arduous enterprise, the point of our existences to be carried out (lines 9–12), demonstrating that he is more reflective than reactive as a leader. Much later he says, what I felt most was my being a stranger to the ship; and if all the truth must be told, I was somewhat of a stranger to myself … I wondered how far I should turn out faithful to that ideal conception of one’s own personality every man sets up for himself secretly (lines 56–65). These descriptions of reflection and self-doubt reveal the captain as being self-conscious and diffident.
As the explanation to question 14 shows, the best evidence for this answer can be found in lines 63–65.
Word in Context
In saying I mention this because it has some bearing on what is to follow (lines 54–55), the narrator means that the fact that he was the only stranger on board (line 54) is relevant to what he is about to say.
Word in Context
This sentence describes how the chief mate, described as earnest (line 70) and painstaking (71), is trying strenuously to figure out why there is another ship anchored nearby. In saying that he was trying to evolve a theory, the narrator means he is pondering (thinking) strenuously.
The truth that the narrator mentions in line 57 is the fact that I am a stranger to myself. He later goes on to explain what he means by this: I wondered how far I should turn out faithful to that ideal conception of one’s own personality every man sets up for himself secretly (lines 63–65). In other words, this truth is the fact that he lacks self-confidence.
Word in Context
In saying that the why and the wherefore of that scorpion … had exercised him infinitely (lines 75–81), the narrator means that the chief mate was using his dominant trait … [of] earnest consideration (lines 69–71) to figure out how a scorpion had made its way into his cabin. That is, the questions about the scorpion had disquieted (unsettled) him infinitely.
The collaboration on the part of [the chief mate’s] round eyes and frightful whiskers (lines 67–68) describes his facial contortions as he deliberates about the anchored ship. In other words, it is an act of strained contemplation.
In the final line, the narrator says that the ship within the islands was much more easily accounted for. In other words, the scorpion was less easily accounted for, or less explicable.
The second paragraph discusses the “outsourcing” [of] the creation of human life (lines 8–9), so the design and control mentioned in line 13 refer specifically to the design and control of the process of conception.
The author of Passage 1 states that the “outsourcing” [of] the creation of human life … mocks the profundity of life (lines 8–12) and he provides no indication in the passage that he otherwise approves of it. Clearly, then, he regards it with blunt disdain.
Both of these quotations represent viewpoints with which the authors of the respective passages disagree. In Passage 1, the quotation “Sorry, but I think I can do better” (line 15) is from those who turn [their] noses up at the most precious gift in the universe (lines 13–14) much to the chagrin of the author. In Passage 2, the quotation “But you are playing God” (line 78) is described as the cry of all whose power is threatened by the march of human progress, and with whom the author clearly disagrees.
Jeremy Rifkin is described in Passage 2 as a cloning foe (line 63) who is quoted as saying “It’s a horrendous crime to make a Xerox of someone. You’re putting a human into a genetic straitjacket.” Presumably, then, he would agree that our attitude toward the creation of life must be one of humility (line 7).
The illustration shows a schematic overview of some Therapeutic Cloning Strategies that involve removing a somatic cell from a patient and transferring its nucleus to stem cells that can then be cultured into genetically matched tissue that can then replace diseased cells and tissues in the patient. This is an example of one of the procedures to clone human cells for seemingly beneficial purposes (lines 38–40) described in Passage 1. Choice (A) is incorrect because the guided purpose refers to a principle of creationism, which is not indicated at all in the diagram. Choice (B) is incorrect because, although the process in the diagram might resemble an assembly line, it is not the assembly line that could be used to create a child that is no longer uniquely human (lines 23–24), but with carefully designed and tested features (line 25). Choice (C) is incorrect because the diagram does not describe the course of human evolution, which would need to show how humans evolved from more primitive species.
The process of introducing degraded germs (lines 52–53) describes the basic process of vaccination, which, like cutting flesh (line 52) (that is, surgery), must have seemed dangerous at first, but in fact can be a life-saving technology. This process is the injection of vaccines.
In this paragraph, the author of Passage 2 describes the position of cloning foes who believe that cloning is the end of evolution, or at least the beginning of its corporate management (lines 59–61). The author of Passage 1 is deeply concerned that the executive boards of these [cloning] companies will decide the course of human evolution, with more concern for quarterly profit reports than for the sake of humanity (lines 32–35). Clearly, then, the author of Passage 1 regards this management as a regrettable invasion of commercial interests into human reproduction.
Jeremy Rifkin’s belief that cloning is a horrendous crime (line 64) directly contradicts the thesis of Passage 2, which is that cloning and similar technologies can provide ample food for a starving world, cure devastating illnesses, and replace diseased organs (lines 98–100). Therefore, to the author of Passage 2, Rifkin’s opinion exemplifies an untenable (indefensible) position. Choice (B) may seem plausible, since Rifkin is warning of the potential dangers of cloning, but notice that this cannot be the reason that the author of Passage 2 quotes Rifkin, because the passage clearly disagrees with his sentiments.
The author of Passage 2 mentions the Twins Days Festival (line 68) in order to demonstrate the absurdity of Jeremy Rifkin’s statement that creating a genetic Xerox of a person is a horrendous crime (line 64). To the author of Passage 2, then, the Twins Days Festival represents the innocuousness (harmlessness) of genetic duplication, since twins are genetic duplicates, and nothing to be feared.
The author of Passage 2 does not object to the procedures to clone human cells for seemingly beneficial purposes (lines 38–40), and in fact believes they are necessary contributions to medical progress since they potentially provide technologies to provide ample food for a starving world, cure devastating illnesses, and replace diseased organs (lines 98–100).
As the explanation to question 31 indicates, the best evidence for this answer is found in lines 95–100.
The first paragraph establishes that this passage is focused on the specific processes involved in children’s acquisition of language (line 12). Therefore, the passage is primarily concerned with exploring academic questions about how we learn language. Choice (A) is incorrect because the passage does not begin to delineate the general principles of linguistics, which is a far greater subject than simply language acquisition. Choice (B) is incorrect, because although the passage does refer to children’s ability to acquire diverse languages like English … Bantu or Vietnamese(lines 63–64), it does not compare their structural qualities. Choice (D) is incorrect because, although the passage does discuss the ideas of the influential linguists Benjamin Whorf (in the second paragraph) and Noam Chomsky (in the last paragraph), these references only serve the larger purpose of exploring the questions of language acquisition, and do not serve as the overall focus of the passage.
In the first paragraph, the author indicates that [e]very time we speak we are revealing something about language, so the facts of language structure are easy to come by (lines 3–6). Therefore, the data mentioned in line 6 are the facts of language structure, which would likely include the syntax (rules governing word order) of different languages. Choice (A) is incorrect because information about literacy levels is not information about language structure. Choice (B) is incorrect because methods of teaching are not facts of language structure. Choice (D) is incorrect because, although the passage does mention the innate structure (line 59) of the brain a few paragraphs later, this is clearly not what line 6 is referring to.
The phrase the two (line 2) refers to two nouns in the previous clause: language and thoughts, in other words, thinking and expressing.
Word in Context
The author uses the phrase sticking communicable labels on thoughts (lines 15–16) to describe one particularly simplistic theory about the language acquisition. The author is using the metaphor of applying name tags or labels to describe one way of describing how words are used. Choice (B) is incorrect because upholding refers to a process of confirming an official claim or pronouncement. Choice (C) is incorrect because, although sticking (as with a needle) can mean piercing, this reference clearly does not imply any act of puncturing. Choice (D) is incorrect because this phrase describes an act of acquisition, that is, learning something new, rather than maintaining something old.
After describing Benjamin Whorf’s theory, the author then states that virtually all modern cognitive scientists believe it is false (lines 25–26). The author’s ensuing discussion makes it clear that he agrees with these cognitive scientists. That is, he is antagonistic toward Whorf’s hypothesis. Choice (A) is wrong because the author does not dismiss Whorf’s hypothesis, but rather regards it as an intriguing hypothesis which just happens to be incorrect. (To dismiss an idea is to believe it is not even worthy of consideration, not merely to reject it after consideration.) Choice (B) is clearly wrong because the author does not support Whorf’s hypothesis. Choice (C) is wrong because the author does not have any conflicting feelings about the hypothesis.
The author states that babies can think before they can talk (line 27) in order to refute Whorf’s hypothesis that we can’t think in terms of categories and relations (line 19) until our language gives us the words to do so. Whorf believes that language precedes thought. The author of this passage is saying the opposite: that skills associated with basic reasoning are not dependent on verbal communication.
The author’s view on human language acquisition can be found in lines 95–97: language acquisition depends on an innate, species-specific module that is distinct from general intelligence. This module must have an intricate innate structure (line 59) in order to acquire a language that is itself intricately complex (line 55). Choice (A) is incorrect because it represents the Whorf hypothesis, which the author explicitly rejects. Choice (B) is incorrect because the author does not state that the structures for learning language are simple. Choice (D) is incorrect because the author places more emphasis on the innate structure in the brain that enables language acquisition than he does on environmental input.
As the explanation to question 39 indicates, the best evidence for this answer is found in lines 95–97.
Lines 58–64 discuss the author’s belief that the innate structure in the brain dedicated to language acquisition cannot be either too simple or too complex. This kind of structure refers to the functional organization of the mind. Notice that the structure being discussed here is not the same as the structure mentioned in line 5, which refers to the structure of language itself.
The author states that, in 1959, Anglo-American natural science, social science, and philosophy had come to a virtual consensus about the answers to the questions listed above (lines 78–81), that is, the questions listed in lines 14–17: Is language simply grafted on top of cognition as a way of sticking communicable labels on thoughts? Or does learning a language somehow mean learning to think in that language? The consensus on these topics was that language must be learned; it cannot be a module; and thinking must be a form of verbal behavior (lines 85–87) Therefore, the disciplines accepted the hypothesis that cognition depends on verbal skills.
The passage as a whole describes the history and scientific underpinnings of the medical technique of vaccination. Choice (A) is incorrect, because the passage does not discuss the various means by which the human immune system works, but only the particular method in which vaccination “tricks” our immune system into fighting particularly virulent infections that it could not fight on its own. Choice (C) is incorrect because, although the passage does discuss some medical practices of cultures like the Chinese and the Turks (lines 7–8), as well as techniques develop by German, British, and French scientists, the passage as a whole is not concerned with cross-cultural comparisons of medical practices. Choice (D) is incorrect because the passage does not focus on the controversies surrounding vaccination, but rather the science behind and history of the technique.
The Chinese and the Turks (lines 7–8) are mentioned as civilizations that produced a medicine against smallpox by grinding up the scabs of people with mild cases of the disease (lines 8–10). This process closely resembles the same process currently used in vaccinations, that is, infecting patients with mild forms of the disease agent.
From lines 23–25: Could it have been a bacterium? In Germany, in 1882, Robert Koch had shown that just such a germ caused tuberculosis. In other words, tuberculosis is cause by a bacterium, not a virus.
In the first paragraph, the passage states that Pasteur produced a rabies vaccine without actually realizing that he was enhancing the body’s own immune system; he knew only that the vaccine worked (lines 18–21). Therefore, some effective remedies for infectious disease were used before their mechanisms were understood.
As the explanation to the previous question indicates, the evidence for this answer is in lines 18–21.
The third paragraph states that a virus must attach itself to a cell, impregnate the cell with the viral genes, and then, parasite that it is, turn that cell into a reproductive machine for the virus’s benefit (lines 38–42). That is, it invades another organism and exploits its reproductive process. The cowbird-phoebe relationship as described in (A) is the closest to this relationship.
The passage indicates that both viruses and bacteria can be parasitic (that is, harmful to their hosts without providing any compensatory benefit). Viruses can cause measles, chicken pox, polio, herpes, and whooping cough, and bacteria can cause tuberculosis (line 25) as well as much human misery (line 28). Choice (A) is incorrect because the passage does not discuss any potential benefit of bacteria. Choice (B) is incorrect because the passage does not discuss the harshness of the conditions under which bacteria can live. Choice (C) is incorrect because bacteria were not to play the starring role in the vaccine story (lines 28–29).
Word in Context
This sentence says that the body, for the most part, is able to recognize these viruses as foreign invaders by the signature proteins on their surface (lines 42–46), in other words, the viruses have unique proteins that enable the body’s immune system to identify and attack them. That is, these are distinctive proteins that enable the immune systems to distinguish them from other proteins.
Structure and Purpose
The final paragraph begins by saying that although advances against viruses continue (line 68) … herpes, another viral affliction, still flourishes, and the most ubiquitous of all the viral maladies—the common cold … may never be thwarted (lines 71–75). This contrasts sharply with the triumphant tone of the previous paragraph, which said that thanks to advances in modern vaccines, measles are nearly gone, and chicken pox, whooping cough, typhoid, and cholera are under control (lines 56–58). Therefore, the final paragraph qualifies (makes less absolute) the tone of the previous paragraph.
The two graphs in Figure 1 and Figure 2 show the incidence of measles infections in the United States as well as in England and Wales from 1950 to 2000. The measles vaccine was introduced five years later in England and Wales than it was in the United States, but in both cases the decline in incidence occurred almost immediately. Therefore, the two graphs are presented together in order to illustrate the effects of the measles vaccine administered to comparable populations but at different times.
Section 2: Writing and Language
The original phrasing is best. Choice (B) is incorrect because choice with getting is not idiomatic. Choice (C) is incorrect because choice of the way is not idiomatic. Choice (D) is incorrect choice of getting, although idiomatic conveys an illogical idea in this context.
Here we are asked to choose the best word to convey the appropriate idea in this sentence. The sentence indicates that we might be surprised to learn something about the world of journalism, and hence that most of us are not as informed about the world of journalism as we could be. In other words, we are not particularly savvy (knowledgeable) about the world of journalism. Apt = suitable to the circumstances; acute = sharp; comprehensive = complete.
In the original phrasing, the pronoun which is illogical, since it refers to the media: that is, saying the media is 90% does not make sense. Choice (C) is incorrect because the phrase all 90% of it is illogical: all of it means 100% of it. Choice (D) is incorrect because it is both unidiomatic and illogical.
Possessive Form/Pronoun Agreement
In the original phrasing, the pronoun their disagrees with its antecedent corporation, which is singular. Recall that the possessive form of the pronoun it is its (it’s = it is). The only choice that avoids both the agreement error and the diction error is (C).
This phrase should be parallel to the subject-verb pair in the previous sentence, Some argue. The only choice with a parallel verb form is (B).
The original phrasing is the only option that represents the data in Figure 1 accurately. Since the second circle graph represents all broadcast television media and its ownership, it indicates that 3.2% (0.6% + 1.3% + 0.9% + 0.4%) of American broadcast television outlets were controlled by minorities.
The idiomatic form of this phrase is antidote to.
Clear Expression/Pronoun Antecedents
In choices (A), (B), and (D), the pronoun it lacks any clear referent. The only choice that avoids this problem is (C).
Examples that contrast civilized debate would have to be examples of uncivilized debate. Gossip and fear-mongering certainly qualify as relatively uncivilized and unsophisticated forms of discourse.
Idiom, Pronoun-Antecedent Agreement
Here, we are looking for the most appropriate logical transition from the previous paragraph to the new one. The last sentence of the previous paragraph gave examples of in-depth, nonprofit, public-supported journalism that is less influenced by any corporate or political agenda. The new paragraph, however, begins with a discussion of sensationalism and how it sells, which provides a stark contrast to the previous paragraph. This requires a contrasting coordinator, such as nevertheless or still.
Diction/Clear Expression of Ideas
We want a word to represent the websites like ProPublica and NPR, as mentioned in the previous paragraph, that engage in relatively noncorporate and apolitical journalism. The phrase instances of journalism indicates specific articles or broadcasts, rather than the organizations themselves. The phrase patterns of journalism indicates trends in those articles or broadcasts, rather than the organizations themselves. The phrase receptacles of journalism indicates containers that receive journalism rather than organizations that produce it. Only (D) repositories of journalism provides a phrase that refers to the organizations themselves.
The original phrasing creates a sentence fragment rather than an independent clause. Choice (B) is incorrect because it commits the same error. Choices (C) and (D) both form independent and idiomatic clauses, but choice (C) is incorrect because the sentence is clearly making a claim about the current state of being of these rituals, rather than the current status-as-consequence of these rituals, so the present perfect (or “present consequential”) form is not appropriate. (For more on using the “perfect” or “consequential” aspect, see Chapter 4, Lesson 23.)
The original phrasing is best. Choice (B) is incorrect because the second clause does not explain the first. Choice (C) is incorrect because the second clause does not follow as a consequence of the first. Choice (D) is incorrect because there is no tonal or semantic contrast between the clauses.
Diction/Clear Expression of Ideas
The phrase collide against is not idiomatic: collide with is the correct idiom, although this phrase would imply more of a physical relationship than the sentence intends. Since the sentence indicates a conflict between an event and a belief so the verb should express a relationship betweenideas, rather than objects. Of the choices, only (B) contradict serves this purpose effectively.
In this sentence, the conjunction and establishes the relationship between the coordinate independent clauses, so any subordinating conjunction like since, so, or because is inappropriate.
Colons must always follow independent clauses, so choices (A) and (D) are incorrect. This phrase must provide a definition of the term “agency,” which is precisely what choice (B) that is, intentional action does. Choice (C) is incorrect because it categorizes rather than defines.
This sentence presents a list of present tense verbs: design … compose … and formulate. The original phrasing is incorrect because it reinserts the auxiliary can, which breaks the parallel structure of the list. Only choice (D) maintains this parallel form.
This sentence belongs before sentence 5, because it provides a parallel idea to the one presented in sentence 4. Sentence 4 states that Many of these [superstitions] are harmless if not quaint, so the next sentence should provide a transition to some of the less pleasant aspects of superstitious thinking.
Pronoun-Antecedent Agreement/Verb Mood
In the original phrasing, the pronoun it does not agree with its plural antecedent explanations; therefore, choices (A) and (B) are incorrect. Choice (D) is incorrect because the auxiliary would implies necessity, rather than ability, which is illogical in this context.
Clear Expression/Pronoun Antecedents
The original phrasing is incorrect because the two instances of the pronoun their have conflicting antecedents, and the second clause is needlessly in the passive voice. Choices (C) and (D) have similar pronoun referent problems. Only choice (B) is phrased without ambiguous pronouns.
The previous sentence, as well as the passage as a whole, indicates that superstitious rituals are used to satisfy a craving in our brains for control.
Only choice (A) maintains the skeptical and analytical tone toward superstitious rituals that is established in the rest of the passage.
The original phrasing is incorrect because the phrase debating a warming planet is illogical: only theories, claims, or ideas can be topics of debate. Choices (B) and (D) are incorrect because the clause if we should lacks a logical object.
The original phrasing is incorrect because it creates a comma splice. Two independent clauses may not be joined by only a comma. Choice (B) is incorrect because the conjunction while is illogical. Choice (C) is incorrect because it forms a noun phrase, which does not coordinate with any part of the main clause. Choice (D) creates a participial phrase that appropriately modifies the subject of the main clause.
In the original phrasing, the verb provide is used illogically and the phrase cost of the American taxpayer is unidiomatic. Choice (B) is incorrect because needless in costing is unidiomatic. Choice (D) is incorrect because the verb is disagrees in number with its subject attempts.
The original phrasing is best. The verb is serves most effectively in the role of defining science.
The underlined phrase is the third item in a parallel list: identifying … gathering … and finding. Choice (B) best maintains this parallel structure without introducing any other error. Choice (D) provides a parallel form, but the phrase way for explaining is unidiomatic.
The underlined phrase is part of a parallel list: that the earth … that the effects … that there are things … and that many of these things … Only choice (D) maintains this parallel structure.
The original phrasing best, since the passage is about eliminating politics and ideology from discussions about climate change. The other choices insert points of advocacy that conflict with the tone and purpose of the passage as a whole.
Clear Expression of Ideas/Verb Mood/Verb
The original phrasing includes an illogical core: the fact … isn’t the same as it being true. Choice (B) is incorrect because a statement of general fact should not be in the future tense. Choice (C) is incorrect because a statement of general fact should not be in the subjunctive mood. Choice (D) uses the idiom make it so logically and grammatically.
The original phrasing is the only option that completes the parallel construction caused not by germs … but by demons.
Verb Form/Clear Expression
The original phrasing is the most logical and concise.
The adverb furthermore indicates that this sentence is extending a line of reasoning. Since it clearly follows the parallel clauses of sentence 2, When we … become … we become … and therefore it most logically follows sentence 2 but precedes sentence 3.
Pronoun Agreement/Verb Aspect
The original phrasing is incorrect because the pronoun they disagrees in number with the antecedent Bohemia. Choice (B) is incorrect because it produces a comma splice. Choice (D) is illogical because the use of the present perfect participle having been improperly implies a consequence.
The original phrasing is illogical because a country cannot regard (consider in a particular way; concern) anything. This verb must show a relationship between a particular country and a particular geographical region. Only choice (D) comprises (makes up) expresses this relationship in a logical way.
The original phrasing is incorrect because it creates a dangling participle: the participle designating does not share its subject with the main clause. Choice (C) is incorrect because it creates a comma splice. Choice (D) is incorrect because it also creates a dangling participle. Choice (B) is best because it avoids both the comma splice and dangling participle.
Verb Tense/Verb Aspect
The phrase by 1843 indicates that the status of the term Bohemian had become established prior to that point in time. Therefore, the verb requires the past perfect or past consequential form: had come to mean. Although choice (D) is a verb in the past consequential form, it incorrectly implies that the term no longer had that particular meaning in 1843.
This sentence is trying to convey the fact that [La Vie de Bohème] proved [to be so] extraordinarily successful that the stories themselves were published. This requires the active voice, so choices (B) and (C) are incorrect. Choice (D) is incorrect because it is unidiomatic.
The original phrasing is incorrect because of the number shift between it and elements. Choices (B) and (C) are needlessly wordy. Choice (D) is clear and concise.
This sentence indicates the effect that increased commodity production had on the commercial middle class. It is illogical to say that the middle class propagated (was transmitted), propitiated (won the favor of someone), or preempted (took action to prevent something) as a result of this increased production. It is, however, logical to say that the middle class prospered (flourished) as a result of it.
Coordination of Clauses
The original phrasing best coordinates the two related, but independent, clauses. Choice (B) produces a run-on sentence with a comma splice. Choice (C) is illogical and unidiomatic. Choice (D) is illogical and misuses the semicolon.
Clarity of Expression/Parallelism
Choice (B) provides the most parallel comparison: the production of art was in fact less important than the capacity for art.
Coordination of Ideas
The use of the adverb thus indicates that this sentence represents a logical consequence of some particular state of affairs. That state of affairs is best indicated by sentence 5: Most of its ingredients had existed in Paris for at least two decades before he started writing. This explains why Murger can be described as a Bohemian of the second generation.
This question is essentially asking us to describe the function of Claretie’s quotation. Since it refers to a poisonous element in the French character, it is clearly indicating a dire assessment of France’s national temperament.
Section 3: Math (No Calculator)
Algebra (solving equations) EASY
2b – 1 = 5
2b = 6
Divide by 2:
b = 3
Substitute b = 3 into 2b2 – 1:
2b2 – 1 = 2(3)2 – 1 = 18 – 1 = 17
Special Topics (circles) EASY
Marking up the diagram with the given information, as shown, shows that three of the smaller radii make up one larger radius. Therefore, the radius of each small circle is 6/3 = 2.
Algebra (word problems/fractions) EASY
If 1/5 of her term paper is 15 pages, then the entire paper must be 15 × 5 = 75 pages long. This means she has 75 – 15 = 60 more pages to edit.
Advanced Mathematics (functions and sequences) EASY
Notice that the rule in choice (C) generates the entire sequence: 7 (times 2 minus 2 equals) 12 (times 2 minus 2 equals) 22 (times 2 minus 2 equals) 42 (times 2 minus 2 equals) 82.
Special Topics (three dimensional geometry) MEDIUM
Notice that the question asks us for the longest length of a diagonal on one of the faces of the box, and that there are three different rectangles as faces: a 3 × 4 rectangle, a 3 × 5 rectangle, and a 4 × 5 rectangle. Clearly the one with the two greatest dimensions will have the longest diagonal, which we can find using the Pythagorean Theorem.
42 + 52 = d2
16 + 25 = d2
41 = d2
Take the square root:
Algebra (linear equations) MEDIUM
We can test each point to find the one that does NOT satisfy the equation.
(A) –2(–9) – 3(6) = 18 – 18 = 0 ≠ 36
(B) –2(–24) – 3(4) = 48 – 12 = 36
(C) –2(6) – 3(–16) = –12 + 48 = 36
(D) –2(12) – 3(–20) = –24 + 60 = 36
Therefore, the correct answer is (A).
Advanced Mathematics (parabolas) MEDIUM
The initial population, I, is the population when the time is 0. Therefore, I = 250(1.32)0 = 250(1) = 250. The annual percent increase in the population, r, can be calculated by finding the population at t = 1 and then calculating the percent change from the initial population. If t = 1, P = 250(1.32)1. As we discussed in Chapter 8, Lesson 7, multiplying a quantity by 1.32 is equivalent to increasing a number by 32% (that is, 1.32 = 100% + 32%), so r = 32%.
Advanced Mathematics (rational expressions) MEDIUM
3 + 1
Multiply the numerator and denominator by the conjugate :
Algebra (linear relationships) MEDIUM
As we discussed in Chapter 7, Lesson 5, a line in the form ax + by = c has a slope of –a/b. Therefore, the line 3x + 6y = 0 has a slope of –3/6 = –1/2. Recall, also, from Chapter 7, Lesson 7, that perpendicular lines have slopes that are opposite reciprocals. Therefore, the line we are looking for must have a slope of 2. You might draw a quick sketch of the xy-plane and plot the points given in each choice to find the line that has a slope of 2, or you could use the slope formula from Chapter 7, Lesson 5: slope = (y2 – y1)/(x2 – x1).
(A) slope = (3 – 0)/(0 – (–6)) = 3/6 = 1/2
(B) slope = (–6 – 0)/(0 – 3) = –6/–3 = 2
(C) slope = (6 – 0)/(0 – 3) = 6/–3 = –2
(D) slope = (3 – 0)/(0 – 6) = 3/–6 = –1/2
The only choice that gives a slope of 2 is (B).
Advanced Mathematics (quadratics) HARD
Perhaps the simplest way to begin this problem is to draw a quick sketch of the function in the xy-plane, and then compare this graph to the transformations of the original function given in the choices. Notice that the original function f(x) = x – x2 is easily factored as f(x) = x (1 – x). The Zero Product Property (Chapter 9, Lesson 5) tells us that this function must have zeros at x = 0 and x = 1. Notice, also, that since the coefficient of the x2 term in the original function is negative (–1), the graph of this quadratic is an “open-down” parabola. Also, the axis of symmetry is halfway between the zeros, at x = ½. Plugging x = ½ back into the function gives us , and therefore, the vertex of the parabola is .
The question asks us to find the function that has no real zeros. This means that the graph of this function must not intersect the x-axis at all. Each answer choice indicates a different transformation of the function f. Recall from Chapter 9, Lesson 3, that choice (A) f(x) + ½ is the graph of fshifted up ½ unit, choice (B) f(x) – ½ is the graph of f shifted down ½ unit, choice (C) f(x/2) is the graph of f stretched by a factor of 2 in the horizontal direction, and choice (D) f(x – ½) is the graph of f shifted right ½ unit. As the sketch above shows, only (B) yields a graph that does not intersect the x-axis.
Advanced Mathematics (polynomials) MEDIUM-HARD
y = x2 + x
Multiply by 4:
15 = 4x2 + 4x
0 = 4x2 + 4x – 15
Factor using the Product-Sum Method (Chapter 9, Lesson 4):
0 = (2x + 5)(2x – 3)
Use Zero Product Property (Chapter 9, Lesson 5):
2x + 5 = 0; 2x – 3 = 0
Solve each equation for x:
x = –5/2; x = 3/2
Therefore, the two points of intersection are and , and the distance between these points is
Special Topics (complex numbers) MEDIUM-HARD
Recall from Chapter 10, Lesson 10, that in = 1 if and only if n is a multiple of 4. (If you need refreshing, just confirm that i4 = 1, i8 = 1, i12 = 1, etc.) Therefore, if i2k = 1, then 2k must be a multiple of 4, and therefore, k must be a multiple of 2. If k is a multiple of 2, then k/2 must be an integer. Choice (A) is incorrect, because k = 2 is a solution, but 2 is not a multiple of 4. Choice (B) is incorrect because k = –2 is a solution, and –2 is not a positive integer. Choice (C) is incorrect because k = 2 is a solution, but when 2(2) = 4 is divided by 4, the remainder is 0, not 1.
Algebra (absolute values) MEDIUM-HARD
In order to minimize the value of |22 – x2 – y2| + 22, we must minimize the absolute value. But the least possible value of any absolute value expression is 0, so we must ask: is it possible for the expression inside the absolute value operator to equal 0? A little trial and error should reveal that it can if, for instance, x = 2 and y = 0. Notice that this gives us |2 – 22 – 02| + 2 = |0| + 22 = 4. Since the absolute value cannot be less than 0, this must be the minimum possible value.
Advanced Mathematics (analyzing polynomial functions) HARD
The simplest polynomial with factors of 12, (x – 5), and (x + 4) is P(x) = 12(x – 5)(x + 4). The completely factored form (including the prime factorization of the coefficient) of this polynomial is P(x) = (2)2 (3)(x – 5)(x + 4).
Now, using the methods we discussed in Chapter 9, Lesson 4, we can look at the factored form of each choice:
(A) 2x2 + 8 = 2(x2 + 8) (x2 + 8 is not factorable over the
reals, but it does equal
(C) 6x2 – 6x – 120 = 6(x2 – x – 20) = (2)(3)(x – 5)(x + 4)
(D) x2 – 10x + 25 = (x – 5)(x – 5)
Notice that every polynomial in (A), (B), and (D) contains at least one factor that is NOT in the factored form of P(x). (In (D), the factor (x – 5) appears twice, but it appears only once in P(x).) Only choice (C) contains ONLY factors that appear in P(x), so it is the only choice that must be a factor of P(x).
Advanced Mathematics (functions) HARD
g(f(x)) = 2x + 1
Substitute f(x) = –x + 7:
g(–x + 7) = 2x + 1
To evaluate g(2), we must let –x + 7 = 2:
–x + 7 = 2
–x = –5
Multiply by –1:
x = 5
Substitute x = 5:
g(–5 + 7) = 2(5) + 1
g(2) = 11
Algebra (ratios/word problems) EASY
Let x equal the number of men in the workshop. If there are half as many men as women, there must be 2x women in the workshop, or a total of x + 2x = 3x men and women in the workshop. Since this total equals 24:
3x = 24
Divide by 3:
x = 8
As with all algebra problems, make sure you confirm that the value you’ve solved for is the value the question is asking for. Since x is in fact the number of men, it is the final answer.
17. 2/3 or .666 or .667
Advanced Mathematics (rational equations) EASY
Multiply by the common denominator, 2b:
6b – 2 = 3b
6b = 3b + 2
3b = 2
Divide by 3:
18. 1.2 or 6/5
Algebra (word problems) HARD
First, translate the given fact into an equation.
The square of a positive number is 0.24 greater than the number itself:
x2 = x + 0.24
Subtract x and 0.24:
x2 – x – 0.24 = 0
Multiply by 100 to eliminate the decimal:
100x2 – 100x – 24 = 0
Now we factor using Product-Sum Method. Remember that the product number is ac = (100)(–24) = –2,400, and the sum number is b = –100. The two numbers with a sum of –100 and a product of –2,400 are 20 and –120.
Expand middle term using –100 = 20 – 120:
100x2 + 20x – 120x – 24 = 0
Factor by grouping in pairs:
20x(5x + 1) – 24(5x + 1) = 0
Take out common factor:
(5x + 1)(20x – 24) = 0
Using the Zero Product Property, we see that x = –1/5 or x = 24/20 = 6/5. Since we are told that x is a positive number, x = 6/5 or 1.2.
19. 5/2 or 2.5
Advanced Mathematics (quadratics) MEDIUM-HARD
Using the Factor Theorem from Chapter 9, Lesson 7, we know that if a quadratic has zeroes at x = 1 and x = 5, it must have factors of (x – 1) and (x – 5). Since a quadratic can only have two linear factors, f must be of the form f(x) = k(x – 1)(x – 5).
Substitute x = 3 and y = –2 for the coordinates of vertex:
–2 = k(3 – 1)(3 – 5)
–2 = k(2)(–2)
–2 = –4k
Divide by –4:
Therefore the equation of the function is , and we can find its y-intercept by
substituting x = 0:
20. 7/3 or 2.33
Special Topics (trigonometry) HARD
The graph of the line y = mx – 4 has a slope of m and a y-intercept of –4. Since m > 0, this slope is positive. We are told that this line intersects the x-axis at an angle of θ, where cos θ = . This gives us enough information
to sketch a fairly detailed graph:
Notice that this information lets us construct a right triangle that includes θ, in which the adjacent side has length 3 and the hypotenuse has length (remember cos θ = adjacent/hypotenuse). This triangle is particularly handy because it depicts the rise and the run for a portion of the line, which will enable us to find the slope. We simply have to find the rise with the
9 + rise2 = 58
rise2 = 49
Take square root:
rise = 7
Therefore, the slope of the line is m = rise/run = 7/3.
Section 4: Math (Calculator)
Algebra (systems) EASY
Since the question asks for the value of b, it makes sense to substitute for a so that we get a single equation in terms of b.
2a + 4b = 20
Simplify and combine:
b + 4b = 5b = 20
Divide by 5:
b = 4
Data Analysis (central tendency) EASY
The table summarizes the following list of 20 numbers: 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 5, 6, 7, 8, 8, 8, 9, 10, 10, 10. If a set of numbers is listed in increasing order, the median is the middle number (if the set contains an odd number of elements) or the average of the two middle terms (if the set contains an even number of elements). The median of a set of 20 numbers, therefore, is the average of the 10th and 11th terms. Since the 10th number is 3 and the 11th number is 5, the median is (3 + 5)/2 = 4.
Problem Solving/Data Analysis (proportions) EASY
Set up a proportion:
456 = 48x
Divide by 48:
9.5 = x
Data Analysis (tables) EASY
The ratio of applicants to finalists is simply the quotient of those two values, which we can calculate for each year.
(A) 8/25 = 0.32,
(B) 8/26 ≈ 0.31,
(C) 9/23 ≈ 0.39,
(D) 10/26 ≈ 0.38.
Algebra (exponentials) EASY
Although solving for y and z isn’t hard, it is even simpler to just express (yz)6 in terms of y3 and z2, using the Laws of Exponentials from Chapter 9, Lesson 9.
Law of Exponentials #5:
Law of Exponentials #8:
Substitute y3 = 20 and z2 = 10:
Substitute 20 = (2)(10):
Combine terms with like bases with Law of Exponents #4:
4 × 105
Algebra (word problems) EASY
The sum of a, b, and c is three times the sum of a and b:
a + b + c = 3(a + b)
a + b + c = 3a + 3b
b + c = 2a + 3b
–2b + c = 2a
Divide by 2:
Advanced Mathematics (triangle trigonometry) EASY
First, let’s mark up the diagram with the given lengths, as above. Remember from SOH CAH TOA that the tangent of an angle is equal to the opposite side over the adjacent side, so tan x = AB/EB. AB = AC – BC = 14 – 12 = 2, and we can find EB with the Pythagorean Theorem:
EB2 + 122 = 132
EB2 + 144 = 169
EB2 = 25
Take the square root:
EB = 5
Or, even better, just notice that triangle EBC is a 5–12–13 triangle.
So, tan x = AB/EB = 2/5 = 0.4
Advanced Math (quadratics) EASY
We can factor this quadratic easily with the Product-Sum Method from Chapter 9, Lesson 4.
x2 – 6x + 8 = (x – 4)(x – 2)
Data Analysis (pie graph) MEDIUM
Since Maria’s sales accounted for 25% of the total, her sector must be 0.25(360°) = 90°, which is sector D. This means that Eli ($3,000), Georgia ($5,000), and Zoe ($10,000) account for sectors A, B, and C. Since Georgia’s total is between Eli’s and Zoe’s, her sector is the neither the largest nor the smallest of the remaining sectors. Therefore, it must be sector A, which is in the middle.
Data Analysis (pie graph) MEDIUM
Perhaps the simplest way to approach this is to notice that, since Maria’s sales account for 25% of the total, the other salespeople must account for 100% – 25% = 75% of the total. Since this total is $3,000 + $5,000 + $10,000 = $18,000, we can find the total with a proportion.
$1,800,000 = 75x
Divide by 75:
$24,000 = x
Data Analysis (pie graph) MEDIUM
Since Maria accounted for 25% of the total sales, she accounted for (0.25)($24,000) = $6,000 in sales. If she earned 15% commission for all sales, she earned (0.15)($6,000) = $900 in commissions. If Georgia earns 10% in commissions, she earned (0.10)($5,000) = $500. Therefore, Maria earned $900 – $500 = $400 more in commissions that Georgia did.
Algebra (absolute value) MEDIUM
The function f(x) = 2 – |x – 4| reaches its greatest value when the absolute value is minimized. Since absolute values cannot be negative, the least value |x – 4| can have is 0, which it has when x = 4:
f(4) = 2 – |4 – 4| = 2 – 0 = 2
Advanced Math (rational equations) MEDIUM
Multiply both sides by common denominator 5b:
15 – 2b = 5b
15 = 7b
Divide by 7:
Advanced Mathematics (functions) MEDIUM
(A) f(1) = 12 + 3 = 4; f(2) = 22 + 3 = 7
(B) f(1) = 12 + 9 = 10; f(2) = 22 + 9 = 13
(C) f(1) = 2(1)2 + 2 = 4; f(2) = 2(2)2 + 2 = 10
(D) f (1) = 3(1)2 + 1 = 4; f(2) = 3(2)2 + 1 = 13
The only function that satisfies the two given equations is (D).
Advanced Mathematics (exponentials) MEDIUM
(A) (6b) (6b) = 36b2
(B) 12b(b) = 12b2
(D) 6b2 + 6b2 = b2(6 + 6) = 12b2
Data Analysis (probability) MEDIUM
One way to represent this problem clearly is to construct a table that shows all of the possible products mn. A representation of all the equally likely possible outcomes of an event is called the sample space for that event. We can label the columns with the possible values of m and the rows with the possible values of n. As we write in the products, let’s shade in those that are multiples of 12.
This shows that 4 out of the possible 16 products are multiples of 12, and therefore, the probability is 4/16 or .
Algebra (inequalities) MEDIUM
x < 3
Multiply by 3:
3x < 9
3x + 4 < 13
Substitute y = 3x + 4:
y < 13
Advanced Mathematics (functions) MEDIUM-HARD
Since the function takes “all values of x,” one way to solve this problem is to choose a value of x to work with, like x = 1.
g(x + 1) = x2 + 2x + 4
Substitute x = 1:
g(2) = (1)2 + 2(1) + 4 = 1 + 2 + 4 = 7
Therefore, the function g(x) will give an output of 7 for an input of 2. We can now test our choices for an input of x = 2. (Notice g(x) and g(x + 1) have different inputs.)
(A) (2)2 + 4 = 8
(B) (2)2 + 3 = 7
(C) (2 – 1)2 + 4 = 5
(D) (2 – 1)2 + 3 = 4
Notice that only the expression in (B) gives the correct output.
Advanced Mathematics (sequences) MEDIUM-HARD
The “brute force” method is to write out sequence A until you reach 72, and see which element in sequence B “matches up” to it. But first we must determine the rule for each sequence. A little guessing and checking should confirm that sequence A follows the “add 5” rule, and sequence B follows the “add 10” rule.
A more elegant method, however, is to find the formulas for the nth term of A and the nth term of B. This would be a much more efficient method, also, if it takes a while for 72 to appear in set A. If you recall the general formula for the nth term of an arithmetic sequence (an = a1 + (n – 1)d), then it’s straightforward to see that the formula for A is an = 2 + (n – 1)5 = 5n – 3 and the formula for B is bn = 5 + (n – 1)10 = 10n – 5. Since we’re looking for where the number 72 appears in set A, we can solve 5n – 3 = 72 to find n = 15, then insert this value for n into the formula for B:b15 = 10(15) – 5 = 145.
Problem Solving and Data Analysis (ratios) MEDIUM
If the ratio of subscribers to nonsubscribers is 2:5, then we can say there are 2n subscribers and 5n non-subscribers, where n is some integer. This means there were a total of 2n + 5n = 7n July visitors to the website. Since we know that there were 2,100 visitors in July, we can solve for n:
2,100 = 7n
Divide by 7:
300 = n
Therefore, there were 2(300) = 600 subscriber visits and 5(300) = 1,500 nonsubscriber visits, and so there were 1,500 – 600 = 900 more nonsubscribing visitors than subscribing visitors.
Algebra (graphing lines) MEDIUM-HARD
In quadrant I, both the x- and y-coordinates are positive. Since y = 4 in all four systems, we simply need to find the system for which the x-coordinate of the solution is not positive. We can find the corresponding x-coordinate for each system by just substituting y = 4 and solving for x.
Substitute y = 4 into first equation in (A):
3x + 5(4) = 15
3x + 20 = 15
3x = –5
Divide by 3:
x = –5/3
In this case, we don’t need to go any further, because the solution to the system in (A) is (–5/3, 4), which is in quadrant II, not quadrant I.
Advanced Mathematics (quadratics) MEDIUM-HARD
Read the question carefully, and note particularly what it is asking for and what information can help you find it. We are asked to find an equation to relate two variables, q, the number of power units, and t, the number of hours the battery has been charging. We are told that the initial charge is 20 power units, so q = 20 when t = 0. We are also told that the charge increases from 50 power units to 106 power units in 40 minutes. But since our time unit t is in hours, we should convert 40 minutes to 40/60 = 2/3 hours. Therefore, the charging station charges at a rate of (106 – 50)/(2/3) = (56)/(2/3) = 84 charging units per hour. This unit rate is the slope of the line, as we discussed in Chapter 8, Lesson 5. Therefore, the equation should represent a line with slope of 84 that contains the point t = 0 and q = 20, which is the equation in (D) q = 84t + 20.
Data Analysis (scatterplots) EASY
This question simply asks us to find the point on the line of best fit that corresponds to a length of 95 centimeters. As the dotted lines show below, this corresponds to a weight less than halfway between 8 and 9 kilograms, so (C) 8.3 is the best approximation among the choices.
Data Analysis (scatterplots) HARD
To find the equation of the line of best fit, we can take two points on the line and then use the point-slope formula (Chapter 7, Lesson 5) to find the equation of the line. To get the most accurate representation of the line, we should choose two points that are fairly far apart, but whose coordinates are easy to determine. The graph shows that this line appears to pass through the points (60, 3) and (100, 9), and so, by the slope formula (Chapter 7, Lesson 5) we can calculate that the slope is (9 – 3)/ (100 – 60) = 6/40 = 3/20. Using the first point in the
point-slope formula gives
Problem Solving (rates) MEDIUM
If Ronika plans to use 85% of her 2 GB data plan for texting, she will have only (15%)(2 GB) = (0.15)(2,000 MB) = 300 MB = 300,000 kB available for image files. Since the average image file is 750 kB, she will be able to send 300,000 kB/750 kB = 400 images per month.
Problem Solving (rates) HARD
This question asks us to write a mathematical statement that “indicates the restrictions” in this situation. So, what keeps us from making as many truffles as we want? Simple: we are only allowed to spend $200 per week on cocoa powder. Therefore, we can state the restriction on truffles as “the total cost of cocoa powder for our weekly production of truffles must be less than or equal to $200.”
Now we must figure out a way to express “the total cost of cocoa powder for our weekly production of truffles.” Clearly, this is the total cost for the dark chocolate truffles plus the total cost for the milk chocolate truffles:
Cost of cocoa powder for d dark chocolate truffles:
Cost of cocoa powder for m milk chocolate truffles:
The total cost for cocoa powder must not be greater than $200:
Multiply by 16:
Divide by c:
Advanced Mathematics (exponentials) HARD
Notice that this question asks us to find the value of 2n + 3, so we should try to solve the given equation for 2n + 3.
m = 2n + 2 + 2n
Factor 2n from the terms on the right side:
m = 2n (22 + 1)
m = 2n (5)
Divide by 5:
Multiply by 23 :
Special Topics (trigonometry) HARD
Although this question can be solved by graphing, it is simpler and more efficient to imagine the unit circle, as we discussed in Chapter 10, Lesson 9.
We are asked to consider those angles that have a sine of ½. As you recall from Chapter 10, Lesson 9, the angles whose sine is ½ correspond to those angles that intersect the unit circle at any point where y = ½, as shown in the diagram above. Notice that the line y = ½ intersects the unit circle in two points. We are asked to consider sin 3x, where x takes values from 0 to 2π. This means that 3x takes values from 0 to 6π. In other words, we are taking three complete trips around the unit circle (since each trip around is 2π radians). How many times will we visit those two points if we take three trips around the circle? Clearly (3)(2) = 6 times.
Advanced Mathematics (function transformations) HARD
The figure clearly shows that the function y = f(x) is similar in shape to the function y = g(x), but is shifted to the left by some positive distance. Recall from Chapter 9, Lesson 3, that when the graph of y = g(x) is shifted to the left by k units, the equation of the new function is y = g(x + k). The only equation that has this form is (B) f(x) = g(x + 2).
Data Analysis (data spread) HARD
One important rule in data gathering is, the more data we can gather on a population, the more reliable our statistics about that population will be. More specifically, the greater fraction of the population we can sample, the smaller our margin of error from the true value of the population statistic. Another important rule in data gathering is the more similar our sample is to the population of interest, the smaller our statistical error will be. Since the sample size is highest and the group is most like the population (of undergraduate computer science majors) in choice (A), that group should produce the smallest margin of error in the data.
Algebra (percents) EASY
The sum of 40 and 80 is 120, and 40% of 120 is (0.40) (120) = 48, so the number that is 40% greater than 120 is 120 + 48 = 168. Also remember that increasing a number by 40% is equivalent to multiplying it by 1.4.
32. 3/2 or 1.5
Advance Mathematics (quadratics) MEDIUM
Substitute h(3) = 6 (from table):
6 = 4.5 + k
1.5 = k
To check your answer, you can plug in the second row of the table to verify that
Algebra (linear equations) MEDIUM
In Chapter 7, Lesson 5 we discussed the fact that the slope of a linear equation in “standard form,” ax + by = c is equal to –a/b. Therefore, the linear equation hx + 4y = –3 has a slope of –h/4. If this slope equals –3, then
Multiply by –4:
h = 52
Algebra (word problems) EASY
Let’s let x be the larger number. 15 is the smaller number.
The sum of the numbers is four times their difference:
x + 15 = 4(x – 15)
x + 15 = 4x – 60
x + 75 = 4x
75 = 3x
Divide by 3:
25 = x
35. 4/45 or .088 or .089
Special Topics (trigonometry) MEDIUM-HARD
Divide by 5:
This gives us the value of cos x, but we are asked to evaluate , which of course is in terms of sin x.
This should remind you of the Pythagorean Identity we discussed in Chapter 10, Lesson 9: for all real numbers x, sin2 x + cos2 x = 1.
sin2 x + cos2 x = 1
Subtract cos2 x:
sin2 x = 1 – cos2 x
Expression to be evaluated:
Substitute sin2 x = 1 – cos2 x:
Substitute cos :
Simplify by multiplying :
36. 75/4 or 18.75
Special Topics (arcs and triangles) MEDIUM-HARD
Let’s start by drawing the three radii OA, OB, and OC. Since these radii are all congruent, and because AB = BC, the triangles AOB and COB are congruent (by the SSS Theorem). This implies that OB bisects angle ABC, so the base angles of both isosceles triangles must have measure 45°/2 = 22.5°. Therefore, angle AOB, which is the central angle for arc AB, must have measure 180° – 22.5° − 22.5° = 135°. Now we can use the fact that the circumference of the circle is 50 to find the length or arc AB.
Let x = and cross multiply:
360x = 6,750
Divide by 360:
x = 75/4 = 18.75
Problem Solving (extended thinking) HARD
Let n equal the number of months that Isabelle has been on Plan A. If she has been on Plan A for over a year, then n > 12. This means that she has been on Plan A for n − 12 months beyond the first year. Since Plan A costs $500 for the first year and $80 per month thereafter, the total cost for her n months of service is $500 + $80(n − 12). If she had been on Plan B, the cost would have been $68 per month, or a total of $68n. If Plan B would have saved her $104 over this period,
500 + 80(n − 12) − 104 = 68n
Distribute and simplify:
396 + 80n − 960 = 68n
80n − 564 = 68n
80n = 68n + 564
12n = 564
Divide by 12:
n = 47
Problem Solving (extended thinking) HARD
Since Plan C costs $92 per month and Plan B costs $68 per month, Plan C costs $92 − $68 = $24 more dollars per month than plan B. Since shifting plans would save her only 45 minutes of work, or 3/4 hour, each month, she would have to value one hour of free time over one hour of work time at $24/(¾ hour) = $32.
Section 5: Essay
Reading Score: 8 out of 8
Analysis Score: 8 out of 8
Writing Score: 8 out of 8
James Schlesinger’s essay, “Cold Facts on Global Warming,” is a counterargument to the “political alarmism” (to use Schlesinger’s words) over global warming. His tone is critical but sober, and he makes frequent use of carefully selected scientific and historical data, juxtaposed with hints at the dangers of political posturing, to make the case for caution in addressing the issue of climate change. He appeals frequently to the ethics of economic prudence and global stewardship, as well as the value of scientific judiciousness. Unfortunately, because Schlesinger’s essay was written over a decade ago, it lacks the evidence from the current golden age of climate science. More substantially, however, Schlesinger undermines his own purpose by making political criticisms while calling for nonpartisan objectivity, by mongering fearsome scenarios while arguing against “scare tactics,” and by ignoring the scientific evidence against his claims while advocating an “emphasis on science.”
Schlesinger begins his discussion with a call for “facts and logic” over “rhetoric.” This is classic polemical posturing: we all believe that our positions are “factual and logical” and that our opponents’ are merely “rhetoric.” In Schlesinger’s view, the “rhetoric” includes the claims that “emissions of carbon dioxide are the primary cause of any change in global temperature and inevitably will lead to serious environmental harm in the decades ahead.” By inserting the modifiers “any” and “inevitably,” he creates a straw man. Most who argue about the seriousness of climate change generally avoid such absolute assertions and instead present evidence from satellites, ice cores, atmospheric analysis, and comprehensive long-term climatic studies to build a case for action. Schlesinger does not address this evidence.
In his argument, Schlesinger appears to value small government and the protection of American industry over the stewardship of the planet. His concern about the Kyoto Protocol of 1997 is not that it eschews the “facts and logic” of climate science, but rather that it “could cost $300 billion annually.” He presents no scientific critique of the Kyoto Protocol of 1997 beyond the assertion that Democrat Al Gore was “willing to embrace” a “treaty that would harm the economy,” and the vague claim that “the treaty’s flaws have become more evident.” His method of argumentation here appears to contradict his call for “facts and logic” over “rhetoric.”
In contrast to the irresponsibility of Al Gore and the Clinton administration, Schlesinger offers the soberly scientific Bush administration, which “focused on filling in gaps in our state of knowledge, promoting the development of new technology, encouraging volunteer programs, and working with other nations on controlling the growth of greenhouse gas emissions.” Schlesinger does not offer a specific benefit our planet has gained from these efforts, which even Schlesinger himself admits involved “spending more than $4 billion annually.” Someone pleading for fiscal responsibility might try to account for such a huge expenditure.
Schlesinger believes that our inaction on climate change is a virtue: that scientific prudence requires “filling the gaps in our state of knowledge” above everything else, including industrial restraint. He states that “what we know for sure is quite limited,” yet is confident enough in his limited knowledge to assert that “the theory that increasing concentrations of greenhouse gases like carbon dioxide will lead to further warming is at least an oversimplification,” directly contradicting the simple middle school experiment showing that a soda bottle filled with carbon dioxide warms far more quickly than one filled only with air.
Schlesinger then selects data trends that seem to support his call for caution, rather than action: he asserts that “satellite measurements over 35 years show no significant warming in the lower atmosphere” and that there was “atmospheric cooling from 1940 to around 1975.” Schlesinger does not explain why climate scientists, who are certainly aware of these data, nevertheless believe in anthropogenic global warming.
Not to be accused of cherry-picking data, Schlesinger next offers “a longer view of climate history.” He asserts that temperatures “were 1 to 2 degrees warmer than they are today” during the Climatic Optimum of the early Middle Ages, and this warming did not have “anything to do with man-made greenhouse gases.” Evidently, we should think that because it was warmer a very long time ago, burning coal today must not be changing the climate.
In the last two paragraphs, Schlesinger essentially retracts his concern about “filling the gaps in our state of knowledge” after all, because he believes it is impossible to fill the most important gaps: “It is not possible to know now how much of the warming over the last 100 years or so was caused by human activities and how much was because of natural forces.” So if it is impossible to know, we might ask, why should we expend “more than $4 billion annually” to study it? He does not say. We get Schlesinger’s most sonorous call to action in the last paragraph, where he suggests “engagement of the business community on voluntary programs.” That is, get big government off the backs of corporations and let them do as they please.
Reading—8 (both readers gave it a score of 4)
This response demonstrates a very strong and thorough comprehension of Schlesinger’s essay through skillful use of summary, paraphrase, and direct quotations. The author summarizes Schlesinger’s central tone, thesis, and modes of persuasion (His tone is critical but sober, and he makes frequent use of carefully selected scientific and historical data, juxtaposed with hints at the dangers of political posturing, to make the case for caution in addressing the issue of climate change.) and shows a clear understanding of how Schlesinger’s supporting ideas string together and serve his overall thesis (Schlesinger begins his discussion with a call … He appears to value small government … Schlesinger offers the soberly scientific Bush administration … Schlesinger believes that our inaction on global warming is a virtue … Schlesinger next offers … In the last two paragraph, Schlesinger essentially retracts his concern). Importantly, this response also offers abundant supporting quotations to illustrate each paraphrase. Taken together, these elements demonstrate outstanding comprehension of Schlesinger’s essay.
Analysis—8 (both readers gave it a score of 4)
Although this response occasionally veers toward advocacy, it never turns away from careful analysis. Indeed, its thoughtful and thorough critique of Schlesinger’s essay demonstrates a sophisticated understanding of the analytical task. The author has identified Schlesinger’s primary modes of argument (He appeals frequently to the ethics of economic prudence and global stewardship, as well as the value of scientific judiciousness) and even uses those standards to analyze Schlesinger’s essay itself, and indicates points at which Schlesinger’s argument seems self-defeating (Schlesinger undermines his own purpose by making political criticisms while calling for nonpartisan objectivity, by mongering fearsome scenarios while arguing against “scare tactics,” and by ignoring the scientific evidence against his claims while advocating an “emphasis on science”). Overall, this analysis of Schlesinger’s essays demonstrates a thorough understanding not only of the rhetorical task that Schlesinger has set for himself, but also of the degree to which it upholds its own standards.
Writing—8 (both readers gave it a score of 4)
This response demonstrates an articulate and effective use of language and sentence structure to establish and develop a clear and insightful central claim that Schlesinger’s essay is a counterargument to the “political alarmism” … over global warming … but that it undermines [its] own purpose. The response maintains a consistent focus on this central claim, and supports it with a well-developed and cohesive analysis of Schlesinger’s essay. The author demonstrates effective choice of words and phrasing (undermines his own purpose … mongering fearsome scenarios … Schlesinger believes that our inaction on climate change is a virtue), strong grasp of relevant analytical and rhetorical terms, like economic prudence, nonpartisan objectivity, and polemical posturing. The response is well-developed, progressing from general claim to specific analysis to considered evaluation. Largely free from grammatical error, this response demonstrates strong command of language and proficiency in writing.