Advanced Practice Test 1

Correct choice: standing

“Consequence” is paired with “rank” as something people can possess and that Lady Russell values because of her “prejudices on the side of ancestry.” In this context it means social importance, or standing.

A: This is the common modern sense (a result), but a person cannot possess an outcome in the way the text says people possess rank and consequence.

B: Seriousness is a sense related to importance (a matter “of consequence”), but it describes the gravity of an issue, not a person’s social position.

C: The text calls Lady Russell “rational and consistent,” but “consequence” names something she values in others, not reasoning.

Watch for: Words paired in a phrase (“rank and consequence”) often share a meaning; let the partner word guide you.

Correct choice: coloring

The text contrasts the dark heath with the pale sky: darkness has arrived on the land while day remains in the sky, so a worker looking down would think it later than a worker looking up. The heath adds “half an hour to evening” by its “mere complexion,” that is, simply by its dark coloring.

B: Because the heath is personified (it can “sadden noon”), temperament is tempting, and it is an older sense of complexion. But the effect described is visual: the heath looks darker than the sky and so makes the evening seem to arrive earlier.

C: The text mentions “the distant rims of the world and of the firmament,” but that boundary is not what makes the land seem darker than the hour; the effect comes from the heath’s dark color.

D: The text says nothing about how the heath is regarded by others; its effect comes from its appearance.

Watch for: When a familiar word appears in older prose, test the modern sense and the older senses against what the sentence says the thing actually does.

Correct choice: apocryphal

The reasons given all concern where the story came from: it surfaced years after Washington’s death, rests on an unnamed source, and has no earlier record, yet it is widely retold. A story of doubtful authenticity that nonetheless circulates widely is apocryphal.

A: Specious describes something, usually an argument, that seems plausible but is actually false or misleading; the text’s evidence concerns the story’s uncertain origin, not a deceptive plausibility.

B: Anachronistic means placed in the wrong period, but nothing suggests the story is set in the wrong time; the problem is that it first appeared long after the events it describes.

C: Tendentious means written to promote a particular point of view; the text says nothing about Weems’s purpose, only about the lack of any reliable source for the story.

Watch for: Match the word to the reason the text gives: evidence about a story’s source points to doubtful authenticity, not to bias or misleading reasoning.

Correct choice: To explain how a voyage bore on a scholarly dispute about Polynesian settlement without settling it

The text sets out a dispute (accidental drift versus deliberate settlement), notes why one kind of evidence for deliberate settlement was contested, and then presents the 1976 voyage. Its final sentence states both what the voyage could not show and what it did accomplish: it undercut the premise that such navigation was impossible. The purpose is to explain the voyage’s bearing on the dispute without claiming that it resolved it.

B: The text reports that skeptics questioned the oral traditions and does not defend them.

C: This overstates the voyage’s significance: the text says it “could not show that ancient navigators had made the same trip.”

D: Piailug’s lack of instruments is a detail supporting the text’s point about the dispute; his methods are not described.

Watch for: In a main-purpose question, a choice that repeats the text’s strongest-sounding claim often overstates it; check the final, qualifying sentence.

Correct choice: It sets the poet’s ambitious work against the slighter verse that the world chose to praise.

The first six lines describe the poet’s elevated subjects: life, love, and “the world's absorbing beat,” voiced “from some high peak.” The underlined lines turn with “But ah”: the world praised instead “a jingle in a broken tongue,” a dismissive phrase for slighter verse. The lines therefore set the poet’s serious work against what the public chose to admire.

A: The lines describe the world’s response, not a change in the poet; nothing says he abandoned his serious themes.

B: This reverses the contrast: “But ah” signals that the praise went to something other than the poet’s serious work.

C: “A jingle in a broken tongue” is disparaging, not celebratory, and the poem does not discuss multiple languages.

Watch for: A turn word such as “But ah” usually marks the poem’s central contrast; decide what is being set against what.

Correct choice: It humorously denies the reader any verdict from the folk method just described, in keeping with the narrator’s opening claim.

The narrator begins by saying that “it is no use trying to sum people up,” then reports a folk method for doing so: cats go to good men. The underlined portion deflates that method at once. Jacob’s landlady loathed cats, so no cat’s verdict on Jacob is available. The comic dead end supports the opening claim that character cannot easily be summed up.

B: The landlady’s dislike is of cats, not a judgment of Jacob; the text reports no opinion of hers about his character.

C: The text never says that cats avoided Jacob. Their absence results from the landlady’s dislike of cats, not from anything about Jacob.

D: The narrator reports the test with gentle irony (“Kind old ladies assure us”) after declaring that “it is no use trying to sum people up,” so the text does not endorse the test as sound.

Watch for: Words like “but then” can introduce an ironic undercut. Read the detail against the narrator’s stated view, not just against the sentence before it.

Correct choice: By suggesting that the crusts may be younger than their dates indicate, so that the dates may not show the paintings to be old enough to rule out modern humans

If uranium lost from a crust is mistaken for uranium that has decayed, the method will overestimate how much time has passed, making a crust seem older than it is. Text 2’s author would therefore say the minimum ages might be too old, so the dates may not place the paintings before modern humans arrived.

A: Text 2 does not question the order of paint and crust, which Text 1 explains (a crust can form only over paint already there); it questions the dates themselves.

B: Text 2 says only that the method can overestimate ages; it does not give any new age for the crusts or show that Neanderthals could not have made the paintings.

D: Text 2 questions whether the dates are reliable, so its author would not accept them as reliable minimum ages; it says nothing about when modern humans arrived.

Watch for: Text 2 never says “too old”; work out what mistaking lost uranium for decayed uranium would do to the calculated age.

Correct choice: Unfamiliar signals repeatedly leave the narrator out of step with the others, until she is afraid to act.

Each signal catches the narrator out. She sits when the others stand, begins to rise just as the second bell seats everyone, and has to crawl back into her chair. When the others finally begin eating, she cries “for by this time I was afraid to venture anything more.” The text is about unexplained signals leaving her repeatedly out of step until she is afraid to act.

A: No punishment is described; the narrator’s fear comes from repeatedly misreading the signals.

C: She looks around “shyly,” but the text is about misreading the bells, not about being unable to ask for help.

D: She does watch the others, but the passage ends with her too afraid to act, not with her mastering the routine.

Watch for: For a main idea, follow the sequence to its end; the final sentence often states where the pattern leads.

Correct choice: Recordings of the trill-and-grunt call produced guiding far more often than recordings of spoken words or of another bird’s call.

The conclusion is specific: birds respond to this call, not merely to any human noise. The finding that supports it must compare the call with other sounds. Choice D does this, using recordings of spoken words and of another species’ call as controls. The trill-and-grunt call produced far more guiding.

A: Comparing the call with silence cannot separate a response to this particular call from a response to any human noise.

B: Areas with Yao hunters differ in many ways besides the call, so this does not isolate the birds’ response to it.

C: This concerns whether the source of the call matters, not whether the birds distinguish this call from other sounds.

Watch for: When a conclusion says “this, rather than that,” the best evidence includes a comparison that rules out “that.”

Correct choice: Plants that had stopped folding after repeated drops folded their leaves fully when they were then shaken, a disturbance they had not experienced before.

The rival explanation is exhaustion: a plant that had used up the energy needed to fold could not fold in response to anything. If plants that ignored drops still folded fully when shaken, they clearly still had that energy; they had stopped responding specifically to the harmless drops, as the researchers concluded.

B: Folding again after a long rest is what exhaustion would predict, since an exhausted plant would recover its energy over time; this finding does not favor learning.

C: Plants with less energy giving up sooner fits the exhaustion explanation at least as well as the learning explanation, so it cannot show that the plants learned rather than tired.

D: How quickly plants fold after drops of different heights says nothing about why the plants eventually stopped responding to repeated drops.

Watch for: To support one explanation over a rival, look for a finding the rival cannot explain; a new disturbance that still triggers folding shows that the plants were still able to fold.

Correct choice: Iron makes up only about 6% of Earth’s crust but about 32% of Earth as a whole.

If iron became concentrated beneath the crust, iron should make up a much smaller share of the crust than of the whole planet. The graph shows exactly that: about 6% of the crust but about 32% of Earth as a whole.

A: This is true (about 32% versus about 30%), but comparing iron with oxygen within the whole planet does not show that iron is scarcer in the crust than below it.

C: This has the right shape but misstates the graph: magnesium’s share rises from about 2% to about 14%, a sevenfold ratio, larger than iron’s ratio of about 5.3.

D: This is true and has the right shape, but it concerns magnesium, while the claim is about iron.

Watch for: A choice can use the right element and the right comparison and still misstate the graph; check a superlative such as “a larger ratio than for any other element” against every category.

Correct choice: Southwark and Vauxhall households had about 315 cholera deaths per 10,000 houses, compared with about 38 per 10,000 houses for Lambeth households.

The claim compares rates, so deaths must be divided by houses: 1,263 ÷ 40,046 ≈ 315 per 10,000 houses for Southwark and Vauxhall and 98 ÷ 26,107 ≈ 38 per 10,000 for Lambeth. Since 315 is about 8.4 times 38, this choice supports the claim.

A: These counts are accurate, but the companies supplied different numbers of houses, so a ratio of deaths is not a ratio of rates; the claim is about rates.

C: These rates are accurate (1,422 ÷ 256,423 ≈ 55 per 10,000), but they compare Southwark and Vauxhall with the rest of London rather than with Lambeth.

D: This misstates Lambeth’s rate: about 55 per 10,000 is the rate for the rest of London; Lambeth’s is about 38 (98 ÷ 26,107).

Watch for: When a claim is about rates, compute deaths per house for each group before comparing; a ratio of raw counts can be far from the ratio of rates.

Correct choice: locate each cache by its position relative to objects near it, rather than by the arrangement of objects across the aviary as a whole.

The misses on the altered side matched the shift in the objects, so the birds were guided by objects, not by the seeds themselves. And because searches on the undisturbed side stayed accurate even though half of the aviary’s objects had moved, the birds must have used the objects near each cache rather than the layout as a whole.

B: If the birds relied on the arrangement of all the objects, moving half of them would have disturbed searches on both sides; instead, searches on the undisturbed side stayed accurate.

C: If the birds found seeds by scent, their probes on the altered side would still have landed on the caches; instead they missed by the distance the objects had moved.

D: If the birds measured from the entrance, which did not move, shifting the objects would not have displaced their probes on the altered side.

Watch for: Use both halves of the experiment: the altered side shows that objects guide the search, and the undisturbed side shows which objects.

Correct choice: It turns an ordinary animal’s reaction to a threat the youth himself created into a law that excuses his own flight.

The youth provokes the squirrel’s flight himself by throwing a pine cone, then treats that reaction as “the law” and “a sign” that fleeing danger is natural, which excuses his own flight from battle. The narrator’s phrasing is ironic: the youth feels “triumphant,” and Nature “re-enforced his argument,” implying that he wanted a conclusion and found one. The inference is that the conclusion is a self-serving generalization from a trivial event he caused.

A: The narrator frames the conclusion ironically, as a “triumphant” discovery that “re-enforced his argument,” not as genuine self-recognition about his own flight.

B: The youth uses “no philosopher of his race” to strengthen his point: even an ordinary squirrel knows to flee. He does not doubt nature’s guidance.

D: The excerpt ends with the youth still “feeling that Nature was of his mind”; he does not abandon the conclusion.

Watch for: In ironic narration, separate what a character concludes from how the narrator frames that conclusion.

Correct choice: such as punctuation,

“Such as” introduces the examples directly, so no punctuation belongs between “such as” and the first item. The items in the series are then separated by commas: “such as punctuation, numerals, and musical notation.”

A: A colon cannot follow “such as,” because “features such as” is not a complete independent clause.

B: A comma after “such as” wrongly separates it from the examples it introduces.

C: A dash after “such as” wrongly separates it from the examples it introduces.

Watch for: Do not put a colon or other punctuation directly after “such as,” “including,” or a verb that introduces a list.

Correct choice: species, moreover,

“Moreover” interrupts a single independent clause, “Several surviving species … are threatened by avian malaria.” An interrupting word within a clause is set off by a pair of commas.

A: A semicolon would separate “Several surviving species” from its verb, leaving a fragment before it.

B: Without a closing comma, “moreover” is not fully set off from the rest of the clause.

C: Without an opening comma, “moreover” is not fully set off from the subject.

Watch for: A conjunctive adverb takes a semicolon only when it begins a new independent clause; inside one clause, set it off with two commas.

Correct choice: surfaces;

“Heavy seasonal rains erode its outer surfaces” and “each year, residents join in a festival …” are both independent clauses. A semicolon correctly joins two independent clauses without a conjunction.

B: A comma alone between two independent clauses creates a comma splice.

C: With no punctuation, the two independent clauses run together.

D: “Which” would begin a relative clause, but “each year, residents join …” cannot function as one, so the sentence becomes ungrammatical.

Watch for: Check whether the words on both sides of the blank could stand alone as sentences.

Correct choice: violin that he completed

“That he completed in 1716” is a restrictive clause: it identifies which of Stradivari’s many violins is meant. A clause introduced by “that” is always essential and is never set off with commas, and no punctuation should separate the subject from its verb, “is.”

A: A single comma after “completed” would split the clause (“that he completed … in 1716”) and wrongly separate part of the subject from the rest.

C: Paired commas would treat the “that” clause as nonessential, but a clause introduced by “that” cannot be set off with commas.

D: A comma before “that” wrongly separates “the violin” from the clause that identifies it, and the phrase is left half enclosed.

Watch for: A clause beginning with “that” is always essential; do not set it off with commas.

Correct choice: was

The subject is the title Lyrical Ballads, which names a single book and therefore takes the singular verb was. Neither the plural form of the title nor the two poets named in the appositive makes the subject plural.

A: Were treats Lyrical Ballads as plural because the title ends in -s, but the title names one book.

B: Is is singular, but it is in the present tense, and the book was published in 1798.

C: Are is plural and in the present tense, but the subject is a single book and the event took place in 1798.

Watch for: The title of a single work is singular even when the words in the title are plural.

Correct choice: elements proved

The long noun clause “What Dmitri Mendeleev chose to leave blank in his 1869 table of the elements” is the subject of the verb “proved.” No punctuation should separate a subject from its verb, however long the subject is.

A: A single comma wrongly separates the subject clause from its verb; the length of the subject makes this error tempting.

C: A semicolon must separate independent clauses, but the subject clause cannot stand alone.

D: A single dash wrongly separates the subject from its verb, and no second dash closes an interruption.

Watch for: Find the main verb. If everything before it is the subject, add no punctuation between them.

Correct choice: it weighs

The sentence compares a Fresnel lens with a conventional lens of the same diameter, so the pronoun must refer to the singular “A Fresnel lens”: “it weighs.” The plural “Fresnel and his colleagues” comes between the pronoun and its antecedent, but people are not what is being compared with a lens.

A: “They” is plural and would refer to Fresnel and his colleagues, who are not what the sentence compares with a conventional lens.

B: “Those” is plural and has the same problem as “they.”

C: “These” is plural and likewise points back to the people named rather than to the lens.

Watch for: When a plural noun comes between a pronoun and its antecedent, find the noun that the sentence’s logic, here a comparison with a lens, requires.

Correct choice: Instead

Maxwell ruled out solid and liquid rings. The final sentence offers the alternative that replaces them: separate orbiting particles. Instead signals that one possibility takes the place of rejected ones.

A: “Nonetheless” signals that something holds despite what came before, but Maxwell’s particle model follows from his rejection of the other models rather than holding in spite of it.

C: The particle model is not an example of the rejected sheet models.

D: “Likewise” would present the particle model as parallel to the rejected models, not as their replacement.

Watch for: Contrast transitions differ: instead replaces a rejected option, while nonetheless keeps a claim despite an obstacle.

Correct choice: Admittedly

The second sentence concedes a limitation to the first sentence’s claim of success, and the third sentence (“however”) returns to minimize that limitation. Admittedly is the transition that introduces such a concession.

A: Undeciphered signs are not a result of scholars’ being able to read most inscriptions.

B: The second sentence does not give details of the success described in the first; it notes exceptions to it.

C: The second sentence does not restate the first; it qualifies it.

Watch for: A concession transition is often confirmed by a later “however” that turns back toward the main claim.

Correct choice: Still

The first sentence concedes a weakness of lichens as indicators. The next sentence returns to the author’s point despite that weakness: the pattern across many species still points to pollution. Still marks this return after a concession.

A: “Granted” introduces a concession, but the concession has already been made; the sentence after the blank is the author’s counterpoint.

B: “Indeed” would reinforce the first sentence’s point about imperfection, but the next sentence argues the other way.

D: The imperfection of lichens is not a reason the multispecies pattern points to pollution.

Watch for: Place a concession transition (granted, admittedly) at the concession itself, and a transition such as still at the point where the argument resumes.

Correct choice: Both dyes were made soluble in a vat before cloth was dipped, and in both the color developed in air.

The goal asks for a similarity in application. Choice B describes the shared vat process and the color’s shared development on exposure to air, both steps in applying the dyes to cloth.

A: This states a difference in source, not a similarity in application.

C: This states two genuine similarities, but both concern the dyes’ chemistry, not how they were applied to cloth.

D: This concerns only Tyrian purple’s production and status.

Watch for: When a goal specifies the kind of similarity (here, application), a similarity of another kind does not meet it.

Correct choice: Carbon dioxide in the EPICA Dome C core rose and fell with temperature for 800,000 years, though this correlation alone does not show which drove the other.

The main finding is that carbon dioxide and temperature rose and fell together. The limit on what that finding shows is that a correlation does not establish which change drove the other. Choice A states both; B pairs the finding with a limitation of a different kind, and C gives the right limit without the finding.

B: This states the finding, but its caveat concerns the dating of the air, not what the correlation between carbon dioxide and temperature cannot show.

C: This states the right limit, but only in general terms; it never presents what the EPICA Dome C core showed.

D: This states the finding but omits any limit on it.

Watch for: A limit on a finding must qualify that finding itself; a caveat about a different aspect of the evidence does not meet the goal.

Correct choice: Kintsugi, a Japanese method of repairing broken ceramics, leaves the lines of breakage visible, often highlighted with gold, rather than hiding them.

Choice C identifies kintsugi for an unfamiliar audience (“a Japanese method of repairing broken ceramics”) and emphasizes its treatment of damage: the lines of breakage are left visible, even highlighted with gold. It meets both parts of the goal.

A: This explains the materials, but it does not state the method’s key treatment of damage: that the breaks are left visible.

B: This gives a date and a material but neither explains what kintsugi is nor how it treats damage.

D: This emphasizes the treatment of damage, but it never tells an unfamiliar audience what kintsugi is.

Watch for: “An audience unfamiliar with it” requires the choice to identify the subject, not just mention its name.

Correct choice: latent

The text contrasts life that is “absent” with life that is present but undetectable and able to resume. Latent means present but not active or visible, which matches “hidden life.”

B: Residual means remaining after most has gone. The animals do lose most of their water, but the text’s contrast is between hidden and absent life, not between a remnant and a whole.

C: Tenuous means weak or slight; the text stresses that life is hidden and can fully resume, not that it is weak.

D: Nascent means just beginning to exist, which does not describe animals that resume a life already under way.

Watch for: Use the passage’s own contrast (“rather than absent”) and its label (“hidden life”) to pick among words that all suggest something reduced.

Correct choice: grudging

The reviewers “conceded” the poems’ originality and praised them “only while faulting” their form. Praise given reluctantly and with reservations is grudging.

B: Perfunctory means done routinely and without care or interest. The reviewers’ praise came with reservations, but nothing suggests it was careless or routine.

C: Effusive means unrestrained and gushing, the opposite of praise given only with objections.

D: Disingenuous means insincere. The text suggests the praise was reluctant, not that the reviewers did not mean it.

Watch for: Several choices can describe imperfect praise; the text’s verbs (“conceded,” “only while”) point to reluctance specifically.

Correct choice: qualified

Baade kept Leavitt’s relationship but showed that it holds separately for two types of Cepheids, which forced a large correction to galactic distances. To qualify a claim is to limit or modify it without rejecting it, which matches both “did not discard” and the change Baade required.

A: To corroborate is to confirm without change, but Baade’s work required a major revision: distances had to be roughly doubled.

B: To supplant is to replace, which contradicts the statement that Baade’s work “did not discard” the relationship.

C: To extrapolate is to extend a relationship beyond the range where it was established; Baade instead divided it according to type of star.

Watch for: Qualify here means limit or modify, not make eligible. “Did not discard … rather” signals a word between full acceptance and replacement.

Correct choice: It marks a turn from an optical illustration to an account of how self-regard shapes a person’s view of events.

The text first describes a physical effect: scratches going in every direction appear to form circles around a candle. The underlined sentence announces that this description is a parable. The final sentence then applies it: events are the scratches, and a person’s egoism is the candle that makes them seem arranged around that person. The underlined sentence marks the turn from illustration to application.

B: The parable concerns the egoism of “any person now absent,” with Miss Vincy as the example; it does not claim that the reader’s egoism blocks understanding of her.

C: Calling the image a parable does the opposite: it announces that the image carries an argument about people.

D: This reverses the text’s point: the concentric arrangement is a “flattering illusion” produced by the candle, not an independent order.

Watch for: A short sentence between an image and its explanation often signals a change in how the reader should take what came before.

Correct choice: It implies that the friend has taken the dead man’s place with his sweetheart, casting the earlier report that she is “well contented” in a new light.

In the last stanza the friend admits that he now “cheer[s] a dead man’s sweetheart” and tells the dead man not to ask whose. The only dead man whose sweetheart is at issue is the speaker, so the friend has taken his place. That changes how the earlier answer (“Your girl is well contented”) reads: she is content because of the friend.

A: The stanza does continue the pattern of life going on, but “a dead man’s sweetheart” and “Never ask me whose” add a revelation that makes it more than another sign of recovery.

C: The friend does withhold the name, but he says “I lie easy,” which does not suggest shame; the point is the revelation itself, not the friend’s guilt.

D: “Never ask me whose” deflects one question, but nothing suggests resentment of the questions; the line conceals an uncomfortable truth rather than cutting the conversation short.

Watch for: A final stanza can recast earlier lines; reread the friend’s earlier answer about the sweetheart once you understand the last stanza.

Correct choice: It rules out a possibility that would make the differences between the two islands’ lizard populations far less remarkable than they appear.

The differences would be striking only if the Pod Mrčaru lizards descended from the 1971 transplants; if another population had arrived, the differences could simply reflect that population’s ancestry. By ruling that out, the sentence shows the differences arose within the transplanted lineage in about three decades.

B: The genetic analysis concerned the lizards’ ancestry, not whether their traits are inherited; the text does not address whether the differences are genetic or a response to diet.

C: The sentence concerns where the lizards came from; it says nothing about whether their diet caused the changes in head size and bite strength.

D: The sentence identifies the population’s ancestors but does not explain how the population managed to thrive on the island.

Watch for: A sentence about genetic analysis need not be about inheritance; check what question the analysis actually answers in the text.

Correct choice: They would question it, because it assumes a stationary hot spot, whereas their data indicate that the hot spot moved while the Emperor seamounts were forming.

If the hot spot had stayed in place, every seamount would have formed at the hot spot’s latitude, near Hawaii’s. Text 2 finds that the older Emperor seamounts formed progressively farther north, which implies that the hot spot drifted south over time. That undercuts the fixed-hot-spot assumption on which Text 1’s reading depends.

A: Text 2 shows that the hot spot moved, which weakens Text 1’s reading, but it does not show a change in the hot spot’s direction and does not rule out a change in the plate’s; this goes beyond what the data show.

B: The magnetism records where the lava cooled, not where the seamounts sit now. A plate carrying seamounts away from a fixed hot spot would still produce seamounts that all formed at the same latitude.

D: A single hot spot that moved would also produce seamounts that formed at different latitudes, so the data do not require a second hot spot.

Watch for: Distinguish where a seamount formed (what the magnetism records) from where it is now; only the first bears on whether the hot spot moved.

Correct choice: Kober’s study of word patterns, made without naming the language or its sounds, laid the groundwork for decipherment.

The text centers on Kober’s method: she set aside the questions of language and sound and analyzed changing word endings. That analysis revealed inflection and let signs be grouped, which the text calls the groundwork for Ventris’s decipherment.

A: This is accurate, but it centers on Ventris’s result, which the text presents as building on Kober’s work, the focus of the passage.

B: This is accurate, but it states only her finding and omits both her method and its role in the decipherment, which the text emphasizes.

C: The text does not attribute the delay to the location of the tablets.

Watch for: Words like “instead” and “groundwork” often mark the method and contribution a text is built around.

Correct choice: The narrator presents himself as a cautious, unambitious lawyer, though his relish for Astor’s name suggests a vanity he claims not to have.

The narrator describes himself as devoted to “the easiest way of life,” an “unambitious” and “safe” lawyer. Yet after insisting that he does “not speak it in vanity,” he admits that he loves to repeat Astor’s name, which “rings like unto bullion.” The text presents a cautious man whose own words reveal the vanity he disclaims.

A: This captures the narrator’s self-portrait but leaves out what the passage builds to: his relish for Astor’s name undercuts his claim that he speaks without vanity, so a main idea that omits it is incomplete.

B: The narrator denies vanity (“I do not speak it in vanity”); he never admits to it or apologizes, so the vanity is revealed rather than confessed.

C: The narrator avoids “public applause” by preference, not with regret, so the text does not suggest that his caution cost him recognition he wanted.

Watch for: When a narrator denies a motive (“I do not speak it in vanity”), check whether the rest of the passage bears the denial out.

Correct choice: Ants whose legs were altered before they left the nest, so that they walked both to the feeder and back on altered legs, stopped at the nest.

The proposal says the errors come from a mismatch between outbound and homeward strides. Ants that walked both ways on altered legs have no such mismatch, so the proposal predicts that they will find the nest. That result would also rule out a rival explanation—that altered legs simply disrupt navigation—since those ants would still err.

A: Longer legs would be expected to produce faster walking under any account, and ants judging distance by time would also overshoot if they walked faster, so this does not favor the stride proposal.

C: If ants counted strides, a mismatch in stride length should produce larger errors over longer distances; errors of the same size at 10 and 20 meters would count against the proposal.

D: Where the ants searched after they stopped says nothing about why they stopped where they did.

Watch for: The strongest support often comes from a condition the proposal predicts will remove the effect: matched strides both ways should mean no error.

Correct choice: At 20°C, potassium nitrate’s solubility of about 32 grams is the lowest of the three, but at 40°C its 64 grams is the highest.

The claim requires potassium nitrate to be least soluble at a lower temperature and most soluble at a warmer one. At 20°C its solubility (32 grams) is below potassium chloride’s (34) and sodium chloride’s (36). At 40°C its solubility (64 grams) is above potassium chloride’s (40) and sodium chloride’s (36). Choice C shows the change in ranking.

A: This shows potassium nitrate is the most soluble at 60°C but never shows it being least soluble at a lower temperature, so it supports only half the claim.

B: This is true, but it compares amounts of change rather than rankings, so it does not show potassium nitrate moving from least to most soluble.

D: This has the key’s shape but misreads the graph: at 20°C potassium nitrate (32 grams) is still the least soluble, below potassium chloride (34) and sodium chloride (36).

Watch for: When bars are close in height, read the labeled values; a claim about ranking depends on every bar at that temperature.

Correct choice: In the placebo-controlled areas, children who received a placebo had 71 cases per 100,000, compared with 46 per 100,000 among children whose parents did not consent.

The claim compares children whose parents consented with other children, so the fair comparison is between two unvaccinated groups that differ only in consent. In the placebo-controlled areas, placebo children (consent, no vaccine) had 71 cases per 100,000, while children whose parents did not consent had 46.

A: This compares vaccinated and placebo children, both from consenting families; it shows the vaccine’s effect, not a difference between consenting and nonconsenting families.

B: This reverses the table: children who received a placebo had 71 cases per 100,000, and children whose parents did not consent had 46; as stated, the comparison would point the opposite way from the claim.

D: Comparing nonconsenting children with vaccinated children mixes the effect of consent with the effect of the vaccine, so it cannot show that consent itself marked higher risk.

Watch for: To isolate one factor, compare groups that differ only in that factor; here both groups must be unvaccinated.

Correct choice: been consistent with waves bending around the edge of the core and would not by themselves have required an inner core.

The rival explanation predicted exactly what the counterfactual describes: weak arrivals that fade farther into the zone. Lehmann’s case against it rested on the arrivals’ being too strong. If they had instead been weak and fading, they would have fit the rival explanation, and no inner core would have been needed to account for them.

B: Weak, fading arrivals would say nothing about wave speeds in an inner core; they would remove the need for an inner core at all.

C: This reverses the logic: weak, fading arrivals are what the bending-around-the-edge explanation predicts, so they would support it.

D: Nothing in the text links weak arrivals to a solid outer core; the shadow zone itself depends on the outer core’s being liquid.

Watch for: In a counterfactual, identify which explanation predicted the imagined observation; the observation then supports that explanation.

Correct choice: could occur even if long-legged toads at the front survived and reproduced no better than their short-legged neighbors.

The process described sorts toads by where they end up: the fastest arrive first, breed mostly with one another, and pass long legs to their offspring, who are again among the fastest. Nothing in it requires long legs to improve survival or reproduction, so leg length at the front could rise even without such an advantage.

A: This is the intuitive explanation, but the process the researchers describe works through who breeds with whom at the front and does not require any survival advantage.

B: The text says fast toads breed at the newly invaded ground, so their offspring begin life at the front, not behind it.

C: The text says offspring “tend to inherit long legs,” which concerns inherited traits, not legs that parents developed by traveling.

Watch for: A process that sorts individuals by location can change a trait at the front without that trait helping individuals survive; do not assume an advantage the text does not state.

Correct choice: the Lion Man figurine is estimated to be about 40,000 years old.

The introductory phrase “Reassembled from hundreds of ivory fragments …” must describe the noun that immediately follows it. Only the figurine was reassembled, so “the Lion Man figurine” must be the subject: “the Lion Man figurine is estimated to be about 40,000 years old.”

A: This makes the archaeologists the ones reassembled from ivory fragments.

C: Here the subject is the figurine’s age, and an age cannot be reassembled from fragments; the possessive leaves the figurine out of the subject position.

D: This makes the years the thing reassembled from ivory fragments.

Watch for: A possessive such as “the figurine’s age” does not make “figurine” the subject; the modifier attaches to the head noun (“age”).

Correct choice: might never have identified

Had he thrown the plate away is an inverted form of If he had thrown the plate away, a condition contrary to past fact. Its result clause needs might (or would) have plus the past participle: might never have identified.

A: Might never identify refers to the present or future, but the unreal result concerns the past, when Fleming made his discovery.

B: Had never identified is the form used in the condition, not in the result; the result clause of a past unreal conditional requires might have or would have.

D: Would never identify also refers to the present or future; a result contrary to past fact needs would have identified.

Watch for: A sentence beginning Had he … is a past unreal condition; its result clause takes would have, could have, or might have plus a past participle.

Correct choice: will have rung

The sentence looks ahead to a point in the future (2040) and describes ringing that will be complete by then. After a real condition in the present tense (If it keeps ringing), the future perfect, will have rung, expresses an action completed by a future time.

B: Has rung describes ringing up to the present, but the two full centuries will be reached only in 2040.

C: Would have rung belongs with an unreal past condition (if it had kept ringing), not with the real, open condition if it keeps ringing.

D: Had rung places the ringing before a past time, but the sentence refers to a future date.

Watch for: Match the result clause to the condition: “If it keeps …, it will have …” for a real future; “If it had kept …, it would have …” for an unreal past.

Correct choice: surf; and

The sentence lists three items, and the second item (“sounds of wind, rain, and surf”) contains its own commas. In such a list, semicolons separate the main items, as the semicolon after “languages” already does. A semicolon must therefore also precede the final item: “surf; and music.”

A: A comma here would make the list ambiguous, suggesting that “music” is a fourth sound in the inner list of sounds rather than a third main item.

B: Without punctuation, “music” joins the inner list of sounds, and the pattern set by the first semicolon is broken.

C: A colon cannot separate items in a list.

Watch for: Once a list uses semicolons between items, keep using them up to the last item.

Correct choice: is

The sentence is inverted: the subject, “a theremin,” follows the verb. Because the subject is singular, the verb must be singular: “is.” The plural “instruments” belongs to the introductory prepositional phrase and is not the subject.

A: “Are” is plural and agrees with “instruments,” which is not the subject.

C: “Were” is plural and also shifts to the past tense, although the instruments are displayed now.

D: “Have been” is plural and does not agree with the singular subject “a theremin.”

Watch for: In a sentence that begins with a prepositional phrase, look after the verb for the subject.

Correct choice: allows

The subject is “the collection,” which is singular. The phrase “of diaries, letters, and photographs …” modifies it, and “as well as the memoirs …” does not create a compound subject. The sentence needs a finite singular verb: “allows.”

A: “Allow” is plural, agreeing with the nearby plurals (“photographs,” “members,” “memoirs”) or treating the “as well as” phrase as part of the subject.

B: “Have allowed” is also a plural verb, so it too agrees with the nearby plurals rather than with “the collection.”

D: “Allowing” is not a finite verb, so the sentence would have no main verb.

Watch for: Strip away prepositional phrases and relative clauses to find the true subject before choosing the verb.

Correct choice: is

When every introduces each part of a compound subject joined by and, the subject is treated as singular: every fragment and every flake … is recorded. The present tense also matches attempt.

A: Are treats the compound subject as plural, but every … and every … takes a singular verb.

B: Was is singular, but it shifts to the past tense, although the sentence describes current practice (conservators attempt).

C: Were is plural, and it also shifts to the past tense although the sentence describes current practice (conservators attempt).

Watch for: Every X and every Y (or each X and each Y) is singular even though two nouns are joined by and.

Correct choice: Nonetheless

The projection’s distortion is a drawback, yet the projection remained standard for navigation because of a different advantage. Nonetheless signals that it continued to be used despite the drawback.

B: “Meanwhile” signals something happening at the same time, but the sentence reports what continued despite the distortion, not a simultaneous development.

C: “Rather” corrects or replaces a preceding statement, usually a negative one, but the first sentence is not being corrected; the projection stayed in use despite its distortion.

D: The distortion is not a reason the projection remained standard; its usefulness for navigation is, and that reason is given after the blank.

Watch for: Contrast transitions differ: nonetheless keeps a claim despite an obstacle, while rather replaces a statement that has been set aside.

Correct choice: Likewise

The fringed trailing edges work in the same way as the comb-like leading edges: both reduce the noise of flight. Likewise introduces a parallel feature.

A: “Conversely” signals an opposite relationship, but the trailing edges reinforce the effect of the leading edges.

C: “Even so” signals a contrast with what came before, but the trailing edges work in the same direction as the leading edges.

D: The trailing edges are not an example of the leading edges’ fringe; they are a second, similar feature.

Watch for: Distinguish a second parallel feature (likewise) from an instance of a general claim (for example).

Correct choice: In fact

The second sentence strengthens the first: Coptic did not merely help, it was indispensable. In fact introduces a stronger version of a claim just made.

B: “Rather” corrects a preceding negative statement (“not X; rather, Y”), but the first sentence makes a positive claim that the second builds on.

C: The second sentence does not describe a separate, similar case.

D: “Nevertheless” signals a contrast, but being indispensable is consistent with having helped.

Watch for: In fact intensifies a claim; rather replaces a claim that has been denied.

Correct choice: Though most fireflies flash independently, a few species flash in unison, including one in the southeastern United States and some in Southeast Asia.

Choice C meets both conditions: it marks synchrony as uncommon (“most fireflies flash independently … a few species”) and places it on two continents (the southeastern United States and Southeast Asia).

A: This places synchrony on two continents but never indicates that it is uncommon among fireflies.

B: This makes clear that the behavior is uncommon, but it names only a Southeast Asian species.

D: This covers two continents and adds a proposed function, but it does not say that synchrony is rare.

Watch for: For a two-condition goal, the strongest lures each satisfy exactly one condition; check both.

Correct choice: The cap carbonates suggest that the freeze ended abruptly: volcanic carbon dioxide built up until the ice melted and conditions turned hot enough for warm-water rock to form.

The goal has two parts: how the freeze ended, and why warm-water rock sits directly on glacial rock. Hoffman’s interpretation answers both: volcanic carbon dioxide built up until the ice melted and conditions shifted abruptly to hot, so warm-water carbonate formed right on top of the glacial deposits.

A: This explains why warm conditions followed the glaciations, but not how the freeze ended or why the change was abrupt enough to leave carbonate directly on glacial rock.

B: This explains how the Snowball Earth hypothesis arose but does not mention the cap carbonates or how the freeze ended.

C: This concerns how complete the freeze was, not how it ended, and it does not mention the cap carbonates.

Watch for: A choice can mention the right evidence and a true consequence yet stop short of the specific point the goal asks for—here, how the freeze ended.

Correct choice: Since people probably entered the Americas through the far north, Monte Verde’s age of about 14,500 years, so far south in Chile, implies an arrival well before Clovis points were made.

The goal asks why the site’s location strengthened the challenge. If people entered through the far north, reaching southern South America by 14,500 years ago means they must have arrived even earlier, long before Clovis points. Only this choice draws that inference from the location.

A: This places the location and the date side by side but never draws the inference that an early southern site implies an even earlier arrival, and it does not mention Clovis.

B: This shows that Monte Verde is older than Clovis points, which challenges the Clovis view, but it says nothing about why the site’s location matters.

D: This reports the site’s acceptance by former skeptics and mentions its location, but it does not explain how the location bears on the Clovis view.

Watch for: Placing two relevant facts side by side is not the same as explaining how one strengthens the other; look for the choice that states the inference.

Squaring a binomial gives $(a - b)^2 = a^2 - 2ab + b^2$, so $(3x - 4)^2 = 9x^2 - 2(3x)(4) + 16 = 9x^2 - 24x + 16$. Squaring each term separately and dropping the middle term gives $9x^2 + 16$. Using $ab$ rather than $2ab$ for the middle term gives $-12x$. Doubling the coefficient instead of squaring it gives $6x^2$.

Answer: B.

The model predicts $200(0.8)^1=160$ at $x=1$ and $200(0.8)^3=200(0.512)=102.4$ at $x=3$. The decrease is $160-102.4=57.6$.

Check: The predictions at $x=1$, $2$, and $3$ are $160$, $128$, and $102.4$, so the decreases are $32$ and then $25.6$, which add to $57.6$.

A: $32$ is the decrease from $x=1$ to $x=2$ only.

C: $64$ assumes the model decreases by the same $32$ in each step, as a linear model would.

D: $97.6$ is the decrease from $x=0$ to $x=3$, starting at the initial value $200$.

Watch for: An exponential model decreases by $20\%$ of the current value each step, so the drops get smaller.

To factor $x^2 - 2x - 15$, look for two numbers that multiply to $-15$ and add to $-2$.

The numbers $-5$ and $3$ satisfy both conditions, since their product is $-15$ and their sum is $-2$.

So the equation is

This form displays the $x$-intercepts, $5$ and $-3$, as constants.

Answer: 5

The horizontal change is 3 and the vertical change is $(5a-2)-(2a+1)=3a-3$. Thus $(3a-3)/3=4$, giving a - 1 = 4 and a = 5.

Check: The two points become (5,11) and (8,23), whose slope is 12/3 = 4.

Watch for: Subtract the entire first y-coordinate, including its constant term.

Answer: C.

The line is $1{,}200$ centimeters long, so it has $\dfrac{1{,}200}{30}=40$ gaps between emitters and $41$ emitters. Twenty-five minutes is $\dfrac{25}{60}$ hour, so the total is

$41(1.8)\left(\dfrac{25}{60}\right)=30.75$

liters.

Check: Together the emitters release $41(1.8)=73.8$ liters per hour, and $\dfrac{25}{60}$ of $73.8$ is $30.75$.

A: This treats $25$ minutes as $0.25$ hour.

B: This counts $40$ emitters, the number of gaps, instead of $41$.

D: This multiplies the hourly rate by $25$ without converting minutes to hours.

Watch for: With an emitter at each end, the number of emitters is one more than the number of equal gaps.

Answer: B.

Triangle $ACD$ has a right angle at $C$. Since $\cos(\angle ADC)=\dfrac{7}{25}$, its sides are in the ratio $7:24:25$, with $DC$ adjacent to angle $ADC$, $AC$ opposite it, and $AD$ the hypotenuse. So

$\sin(\angle ADC)=\dfrac{AC}{AD}=\dfrac{24}{25}$

and $AD=48\cdot\dfrac{25}{24}=50$. Then $DC=\dfrac{7}{25}\cdot50=14$.

Since $BD=AD=50$, $BC=50+14=64$. In right triangle $ACB$, $\tan(\angle ABC)=\dfrac{AC}{BC}=\dfrac{48}{64}=\dfrac34$.

Check: $AD=\sqrt{14^2+48^2}=\sqrt{2{,}500}=50=BD$, and $\cos(\angle ADC)=\dfrac{14}{50}=\dfrac{7}{25}$.

A: $\dfrac{7}{24}$ is $\dfrac{DC}{AC}$, a ratio in triangle $ACD$, not in triangle $ACB$.

C: $\dfrac{24}{25}$ is $\dfrac{AC}{BD}$, which uses $BD=50$ as if it were all of $\overline{BC}$.

D: $\dfrac{24}{7}$ is $\tan(\angle ADC)$, the tangent of the angle at $D$ rather than at $B$.

Watch for: Find $AD$ from the side opposite angle $ADC$, then use $AD=BD$ to get all of $\overline{BC}$ before forming the tangent at $B$.

The polynomial $q(x)$ is the quotient when $p(x)$ is divided by $x - 2$, and $r$ is the remainder. Synthetic division with $2$ finds both. Bring down the leading coefficient $2$, then at each step multiply the running value by $2$ and add the next coefficient.

Second coefficient:

Third coefficient:

Last value, which is the remainder:

The first three values, $2$, $-1$ and $1$, are the coefficients of the quotient, one degree lower than $p(x)$:

Check by expanding:

Distributing the right side gives $ax + 11 = 10x - 15$, and collecting the variable terms gives $(a - 10)x = -26$. For any $a$ other than $10$ that has exactly one solution; only $a = 10$ makes the left side $0$ and leaves $0 = -26$, which no value of $x$ satisfies. Matching the coefficient visible inside the parentheses, without distributing the $5$, gives $2$. Taking the multiplier outside them to be the coefficient gives $5$. And $-15$ is the distributed constant, which decides whether the equation has no solution or infinitely many, not what $a$ must be.

Answer: 37

The total mass rises by $427-242=185$ grams when five samples are added. Each sample therefore has mass 185/5 = 37 grams.

Check: The carrier itself has mass $242-5(37)=57$ grams, consistent with the other row.

Watch for: Subtract the totals to remove the unchanged carrier mass.

Answer: C.

Let s and l be the counts. The equations are $4s+7l=98$ and $9s+18l=234$. Divide the second by 9 to get $s+2l=26$, or $s=26-2l$. Substitute into the time equation: $104-8l+7l=98$, so $l=6$ and $s=14$.

Check: Fourteen short and six long cycles use $56+42=98$ minutes and bind $126+108=234$ sheets.

A: This is the long-cycle count.

B: This does not satisfy both batch totals.

D: This is the total cycle count.

Watch for: The output per long cycle doubles, but the time per long cycle does not; keep separate equations.

Answer: C.

Let the playlist contain $j$ jazz songs and $n$ songs in all. Either addition makes $n+4$ songs:

$\dfrac{j+4}{n+4}=\dfrac12$, so $j+4=\dfrac{n+4}{2}$

$\dfrac{j}{n+4}=\dfrac13$, so $j=\dfrac{n+4}{3}$

Subtracting the second equation from the first gives $4=\dfrac{n+4}{2}-\dfrac{n+4}{3}=\dfrac{n+4}{6}$, so $n+4=24$ and $n=20$ (with $j=8$).

Check: With $8$ jazz and $12$ rock songs, adding $4$ jazz songs gives $\dfrac{12}{24}=\dfrac12$, and adding $4$ rock songs gives $\dfrac{8}{24}=\dfrac13$.

A: $8$ is the number of jazz songs, not the number of songs on the playlist.

B: $12$ is the number of rock songs.

D: $24$ is the number of songs after $4$ are added.

Watch for: Both scenarios add $4$ songs, so both probabilities have the same denominator, $n+4$; solve for $n$, not for $n+4$ or $j$.

Answer: D.

Divide both sides of $a<b$ by $b$. Because $b$ is negative, dividing reverses the inequality: $\frac{a}{b}>\frac{b}{b}=1$. So $\frac{a}{b}>1$ must be true.

The other statements are false for every such pair. For example, with $a=-4$ and $b=-2$: $a^2=16>4=b^2$, $\frac1a=-\frac14>-\frac12=\frac1b$, and $ab=8>0$.

Check: With $a=-4$ and $b=-2$, $\frac ab=2>1$; with $a=-3$ and $b=-1$, $\frac ab=3>1$.

A: $a$ is farther from $0$ than $b$, so $a^2>b^2$; the statement reverses the inequality.

B: For negative numbers, the one farther from $0$ has the reciprocal closer to $0$: with $a=-4$ and $b=-2$, $-\frac14>-\frac12$.

C: The product of two negative numbers is positive.

Watch for: Multiplying or dividing an inequality by a negative number reverses it, and squaring or taking reciprocals of negative numbers also reverses their order.

Answer: B.

Let $P$ be the price, in dollars.

Discount first, then coupon: $0.85P-4$.

Coupon first, then discount: $0.85(P-4)=0.85P-3.40$.

The difference is $(0.85P-3.40)-(0.85P-4)=0.60$, so applying the discount first costs $0.60 less, whatever the price.

Check: For a $100 item: discount first gives $85-4=81$ dollars; coupon first gives $0.85(96)=81.60$ dollars. The difference is $0.60.

A: $0.00 assumes that the order of a percent discount and a fixed coupon does not matter.

C: $3.40 is how much the coupon lowers the final price when it is applied before the discount, $0.85(4)$, not the difference between the two orders.

D: $4.00 is the value of the coupon.

Watch for: When the coupon comes first, the discount is taken on $4 less, so the discount saves $0.15(4)=0.60$ dollars less; the price itself cancels.

Answer: 2

Let the inset dimensions be L and W, so $L+W=29$. The area added is $(L+2w)(W+2w)-LW=2w(L+W)+4w^2$. Thus $58w+4w^2=132$, or $2w^2+29w-66=0$. Factoring gives $(w-2)(2w+33)=0$. The positive width is 2.

Check: The four side strips contribute 116 square centimeters and the four corner squares contribute 16, totaling 132.

Watch for: Use perimeter to replace the unknown sum of dimensions; the inset’s individual sides are unnecessary.

Answer: B. $\frac{2592}{49}$ Let the vertical side be h and the horizontal side be $2h$. The hypotenuse joins (18, 0) and (0, 12), so a point on it satisfies $\frac{x}{18} + \frac{y}{12} = 1$. Thus $\frac{2h}{18} + \frac{h}{12} = 1$, giving $\frac{7h}{36} = 1$ and $h = \frac{36}{7}$. The area is $2h^{2} = \frac{2592}{49}$.

Watch for: The rectangle reaches the hypotenuse at one corner; its sides are not the full triangle legs.

Answer: 36 The second condition gives slope $\frac{48}{8} = 6$. Therefore $f(t + 2) = f(t) + 12$. Compare this with 3 f(t) to get $f(t) = 6$. The output five input units later is $f(t + 5) = 6 + 5(6) = 36$.

Watch for: The value of t itself is unnecessary; linear output changes depend only on input differences.

Answer: 19 The difference $g(x) - f(x) = x^{2} - (a + 4)x + (b - 12)$ has roots 1 and 5 and leading coefficient 1. It must equal $(x - 1)(x - 5) = x^{2} - 6x + 5$. Therefore $a + 4 = 6$ and $b - 12 = 5$, giving $a = 2$, $b = 17$, and sum 19.

Watch for: An intersection makes the difference of the functions zero, not either individual function zero.

Answer: C.

Let the radius be $r$ centimeters and the central angle $\theta$ radians. The arc has length $r\theta$, and the perimeter includes two radii:

$2r+r\theta=20$

The area is $\frac12r^2\theta=\frac12r(r\theta)=24$. From the first equation, $r\theta=20-2r$, so

$\frac12r(20-2r)=24$

which gives $r^2-10r+24=0$, so $r=4$ or $r=6$.

If $r=4$, then $\theta=\frac{20-8}{4}=3$. If $r=6$, then $\theta=\frac{20-12}{6}=\frac43$. Only $\theta=3$ is greater than $2$, so $r=4$.

Check: With $r=4$ and $\theta=3$: the perimeter is $4+4+4(3)=20$, and the area is $\frac12(16)(3)=24$.

A: $2.4$ leaves the two radii out of the perimeter, using $r\theta=20$, which gives $\frac12r(20)=24$.

B: $3$ is the central angle, in radians, not the radius.

D: $6$ is the other solution of the quadratic equation, but its central angle is $\frac43$ radian, which is less than $2$.

Watch for: The perimeter of a sector includes the two radii as well as the arc, and both solutions of the quadratic must be checked against the angle condition.

Answer: A.

At x = 1, $q(1)=a(4)(-6)=-24a=-48$, so a = 2. The roots -3 and 7 have midpoint 2. At that vertex, $q(2)=2(5)(-5)=-50$.

Check: Completing the square gives $q(x)=2(x-2)^2-50$, confirming the minimum.

B: This is the given value at x = 1, away from the vertex.

C: This is the unscaled product at x = 1.

D: This is the recovered leading coefficient, not the minimum.

Watch for: The midpoint of the zeros locates the vertex input; evaluate the function there to get the minimum output.