Every one of the 120 questions, in order, with the reasoning written out in full. Work each question in your official College Board test book first, then open the solution underneath it to check your method β not just your letter.
Prepared for AccelerateMyEdu students and tutors. Please don't redistribute this link.
How to use this companion. This is a solutions guide designed to sit beside the official SAT Practice Test #4 PDF, which College Board publishes free at satsuite.collegeboard.org. Every graph, table and diagram a question depends on is redrawn on this page, so you can work the questions here; open the official PDF for the full reading passages.
Reading & Writing passages are summarised in our own words here rather than reprinted. Every answer choice is quoted so you can follow the elimination reasoning without flipping back and forth.
Passage: In 2020 the OSIRIS-REx spacecraft briefly touched the asteroid Bennu. Despite finding a surface mostly covered in boulders, the craft successfully ______ a sample of the surface, gathering pieces of it to bring back to Earth.
Which choice completes the text with the most logical and precise word or phrase?
attached
collected
followed
replaced
Show solution
Answer: B β collected
The sentence defines the blank for you: the spacecraft was "gathering pieces of it to bring back." Gathering a sample is collecting it.
A (attached) describes fastening something on, not taking it away. C (followed) makes no sense for a stationary surface. D (replaced) would mean putting something back in its place β the opposite of bringing pieces home.
Method: Look for a phrase after a comma or colon that restates the blank. Here "gathering pieces" is the restatement.
Q2Words in Context
Passage: Research by planetary scientist Katarina Miljkovic suggests the Moon's surface may not accurately ______ early impact events: while the Moon was still forming, its soft surface kept less of an impression from impacts, so evidence of them may have disappeared.
Which choice completes the text with the most logical and precise word or phrase?
reflect
receive
evaluate
mimic
Show solution
Answer: A β reflect
The explanation says early impacts left weak impressions and their evidence "may no longer be present." So the surface does not accurately show or record those impacts β it doesn't reflect them.
B: the surface certainly received the impacts; the problem is that it didn't preserve the record. C: a surface cannot evaluate anything. D: "mimic" means imitate β the surface isn't copying the impacts.
Q3Words in Context
Passage: Handedness (preferring the left or right hand) is usually easy to observe in humans. Because the trait is present but less ______ in many other animals, researchers use specially designed tasks to reveal an individual animal's hand or paw preference.
Which choice completes the text with the most logical and precise word or phrase?
recognizable
intriguing
significant
useful
Show solution
Answer: A β recognizable
The contrast is with "easy to observe in humans." In animals, the trait is present but harder to observe β which is why researchers need special tasks to reveal it. "Less recognizable" = harder to see.
B, C and D talk about how interesting, important or helpful the trait is. None explains why special tasks are needed to reveal it; only visibility does.
Method: The purpose clause ("tasks β¦ designed to reveal") tells you the problem being solved: the trait is hard to see.
Q4Words in Context
Passage: It is by no means ______ to recognize Hieronymus Bosch's influence on Ali Banisadr's paintings β indeed, Banisadr names Bosch as an inspiration. However, some scholars think the ancient Epic of Gilgamesh may have influenced his work even more.
Which choice completes the text with the most logical and precise word or phrase?
substantial
satisfying
unimportant
appropriate
Show solution
Answer: C β unimportant
"By no means ______" is a double negative in disguise. The following clause ("indeed, Banisadr himself cites Bosch") shows Bosch's influence does matter. So the sentence must say recognizing that influence is "by no means unimportant" β i.e., it is important. The "However" sentence then adds that Gilgamesh may matter even more.
A, B and D would all become negative ("by no means substantial / satisfying / appropriate"), which clashes with "indeed, Banisadr himself cites Bosch" β that clause supports Bosch's relevance.
Watch negations. "By no means X" = "definitely not X." Decide what the whole phrase must mean, then pick the word that produces it.
Q5Text Structure & Purpose
Passage: From Susan Glaspell's 1912 story "Out There." An old framing-shop owner grumbles that a picture he recently bought cheaply doesn't belong among his city views, pet pictures and landscapes. Yet the second paragraph says he is secretly proud of it, and he carries a hidden dignity as he looks for a place to display it.
Which choice best states the main purpose of the text?
To reveal the shop owner's conflicted feelings about the new picture
To convey the shop owner's resentment of the person he got the new picture from
To describe the items that the shop owner most highly prizes
To explain differences between the new picture and other pictures in the shop
Show solution
Answer: A
The first paragraph shows him complaining ("Don't belong in here"); the second begins "And yet" and reveals he is secretly proud. Complaint + pride = conflicted feelings. That is the whole point of the passage.
B: the seller is mentioned but the owner never resents him. C: the shop's other items are listed only to show the new picture doesn't fit β not as things he prizes. D: the text says the picture doesn't fit but never explains how it differs.
Method: "And yet" at a paragraph break is a big signal that the passage is about a tension.
Which choice best describes the overall structure of the text?
The speaker assesses a natural phenomenon, then questions the accuracy of her assessment.
The speaker describes a distinctive sight in nature, then ponders what meaning to attribute to that sight.
The speaker presents an outdoor scene, then considers a human behavior occurring within that scene.
The speaker examines her surroundings, then speculates about their influence on her emotional state.
Show solution
Answer: B
Two halves: (1) a description of a striking sight β the cypress against the gold sky; (2) questions asking why it is black and why it points up, i.e. what the sight means. Choice B matches both halves.
A: she never doubts her description is accurate. C: there is no human behaviour β the "finger" is a tree. D: she asks about the tree's meaning, not about her own feelings.
Q7Text Structure & Purpose
Passage: Walt Whitman's 1860 poem "Calamus 24." The speaker says he hears he is accused of wanting to destroy institutions, replies that he is neither for nor against them, and then declares that he will establish β in every city, field and ship of the nation β "the institution of the dear love of comrades."
Which choice best describes the overall structure of the text?
The speaker questions an increasingly prevalent attitude, then summarizes his worldview.
The speaker regrets his isolation from others, then predicts a profound change in society.
The speaker concedes his personal shortcomings, then boasts of his many achievements.
The speaker addresses a criticism leveled against him, then announces a grand ambition of his.
Show solution
Answer: D
Part 1: "it is charged against me" β a criticism β which he answers. Part 2: "Only I will establish β¦ in every city of These States" β a sweeping, grand ambition. D matches.
A: the charge is aimed at him; it isn't described as a spreading attitude. B: no regret or isolation. C: he never admits any shortcomings; he denies the charge.
Q8Text Structure & Purpose
Passage: Mimosa trees evolved in East Asia alongside a seed-eating beetle, Bruchidius terrenus, and were brought to North America in 1785, far from the beetle. The third sentence says evolutionary links between predators and prey can last across centuries and continents. Around 2001 the beetle arrived near trees Shu-Mei Chang's team was monitoring, and within a year 93% of the trees had been attacked.
Which choice best describes the function of the third sentence in the overall structure of the text?
It states the hypothesis that Chang and colleagues had set out to investigate using mimosa trees and B. terrenus.
It presents a generalization that is exemplified by the discussion of the mimosa trees and B. terrenus.
It offers an alternative explanation for the findings of Chang and colleagues.
It provides context that clarifies why the species mentioned spread to new locations.
Show solution
Answer: B
The third sentence is a broad claim (predatorβprey links persist across time and space). The rest of the text is a specific case: after two centuries apart, the beetle immediately found and attacked the mimosas. So the sentence is a generalization, and the mimosa story is the example of it.
A: nothing says Chang's team set out to test this β they happened to be monitoring the trees. C: there's no competing explanation. D: the sentence doesn't explain why the species moved; humans introduced them.
Q9Cross-Text Connections
Passage:Text 1: The traditional view: human societies developed in stages β egalitarian hunter-gatherer bands, then (after farming, ~12,000 years ago) clans, chiefdoms and finally states. Text 2: Graeber and Wengrow argue humans have always been socially flexible, switching between hierarchical and collective systems; some hunter-gatherers 50,000 years ago changed structure with the seasons, including groups with high-status members.
Based on the texts, how would Graeber and Wengrow (Text 2) most likely respond to the "conventional wisdom" presented in Text 1?
By conceding the importance of hierarchical systems but asserting the greater significance of decentralized collective societies
By disputing the idea that developments in social structures have followed a linear progression through distinct stages
By acknowledging that hierarchical roles likely weren't a part of social systems before the rise of agriculture
By challenging the assumption that groupings of hunter-gatherers were among the earliest forms of social structure
Show solution
Answer: B
Text 1's key idea is a one-way sequence of stages. Text 2 says people moved back and forth between types of organisation, even seasonally β which directly rejects a linear, stage-by-stage progression.
A: Text 2 doesn't rank one system as more significant. C: the opposite β Text 2 says pre-farming groups included esteemed (high-status) individuals. D: Text 2 doesn't deny hunter-gatherers were early; its own evidence is from early hunter-gatherers.
Method: For "how would Text 2 respond" questions, identify Text 1's core claim in five words ("society evolved in linear stages"), then ask which part Text 2 attacks.
Q10Central Ideas
Passage: From Frances Hodgson Burnett's The Secret Garden (1911). Mary, a determined girl, is absorbed in working the hidden garden β digging and weeding steadily, growing more pleased each hour rather than tired, as if it were fascinating play.
Which choice best states the main idea of the text?
Mary hides in the garden to avoid doing her chores.
Mary is getting bored with pulling up so many weeds in the garden.
Mary is clearing out the garden to create a space to play.
Mary feels very satisfied when she's taking care of the garden.
Show solution
Answer: D
"More pleased with her work every hour instead of tiring of it" β she finds the work satisfying. D says exactly this.
A: no chores are mentioned. B contradicts the text ("instead of tiring of it"). C misreads the simile: the work seemed like play; she isn't building a play area.
Q11Command of Evidence (Textual)
Passage: Ezra Pound's 1909 poem "Hymn III." A flower blooms if dew and rain draw it out; likewise the speaker's mind flourishes if fed the "sweet dew" of the spirit β and without it, the mind withers like a flower on dry ground.
Based on the text, in what way is the human mind like a flower?
It becomes increasingly vigorous with the passage of time.
It draws strength from changes in the weather.
It requires proper nourishment in order to thrive.
It perseveres despite challenging circumstances.
Show solution
Answer: C β It requires proper nourishment in order to thrive.
Both halves of the comparison are conditional: the flower grows if it gets dew and rain; the mind flourishes if it be fed, and languishes when it lacks this. The shared point is dependence on nourishment.
A: nothing about growing stronger over time. B: dew and rain are the flower's food, not "changes in the weather" as a source of strength β and the mind has no weather. D: the opposite β without nourishment both wither.
Q12Central Ideas
Passage: From Jack London's The Call of the Wild (1903). Only Thornton matters to Buck; other people are nothing to him. He is cold to travellers who pet him, ignores Thornton's partners until he learns they are close to Thornton, and then merely tolerates them.
Which choice best states the main idea of the text?
Buck has become less social since he began living with Thornton.
Buck mistrusts humans and does his best to avoid them.
Buck has been especially well liked by most of Thornton's friends.
Buck holds Thornton in higher regard than any other person.
Show solution
Answer: D β Buck holds Thornton in higher regard than any other person.
"Thornton alone held [Buck]. The rest of mankind was as nothing." Everything after illustrates that one idea: Thornton ranks above everyone.
A: we aren't told how social Buck was before, so no change can be claimed. B is too strong β he tolerates Hans and Pete and accepts favours; he doesn't avoid people. C: the passage is about Buck's feelings toward people, not theirs toward him.
Q13Command of Evidence (Quantitative)
Passage: A bar graph shows the six US states with the most organic farms in 2016: California (β2,700), Wisconsin (β1,280), New York (β1,060), Pennsylvania (β800), Iowa (β730) and Washington (β680). The text says California had between 2,600 and 2,800 organic farms and ______.
Which choice most effectively uses data from the graph to complete the text?
Washington had between 600 and 800 organic farms.
New York had fewer than 800 organic farms.
Wisconsin and Iowa each had between 1,200 and 1,400 organic farms.
Pennsylvania had more than 1,200 organic farms.
Show solution
Answer: A β Washington had between 600 and 800 organic farms.
Check each claim against the bars. Washington's bar sits just under 700 β between 600 and 800. β
B: New York is above 1,000. C: Wisconsin is about 1,280, but Iowa is only about 730. D: Pennsylvania is about 800, not above 1,200.
Method: Data-completion questions are pure fact-checking: every wrong choice misreads at least one bar. Test each choice against the graph, not against what "sounds right."
Q14Command of Evidence (Textual)
Passage: Two subspecies of fork-tailed flycatcher share a region of Colombia; one migrates, one doesn't. Migratory males' feathers make a higher-pitched sound in flight. The researchers hypothesize that females prefer their own subspecies' sound and that, over time, this preference will push the two subspecies further apart genetically and anatomically.
Which finding, if true, would most directly support GΓ³mez-BahamΓ³n and her team's hypothesis?
The feathers located on the wings of the migratory fork-tailed flycatchers have a narrower shape than those of the nonmigratory birds, which allows them to fly long distances.
Over several generations, the sound made by the feathers of migratory male fork-tailed flycatchers grows progressively higher pitched relative to that made by the feathers of nonmigratory males.
Fork-tailed flycatchers communicate different messages to each other depending on whether their feathers create high-pitched or low-pitched sounds.
The breeding habits of the migratory and nonmigratory fork-tailed flycatchers remained generally the same over several generations.
Show solution
Answer: B
The hypothesis predicts increasing divergence over time driven by the sound preference. If, generation after generation, the migratory males' sound gets ever higher relative to the nonmigratory males', the two subspecies are diverging in exactly the trait females select on. That is direct support.
A links feather shape to flight distance, not to female choice or divergence. C is about communication in general, not mate preference or divergence. D suggests the subspecies are not changing, which weakens the hypothesis.
Method: For "support the hypothesis" questions, restate the hypothesis as a prediction ("the two groups will grow more different") and find the choice that shows that prediction coming true.
Q15Command of Evidence (Quantitative)
Passage: A table gives ablation rates (how much vaporizes in the atmosphere) for iron, potassium and sodium in dust from four sources: SPC and AST (slower dust) and HTC and OCC (faster dust). Iron: 20%, 28%, 90%, 98%. The text claims material in slower SPC/AST dust ablates less than the same material in faster HTC/OCC dust, and begins an example: "whereas the average ablation rate for iron from AST dust is 28%, the average rate for ______."
Ablation Rates for Three Elements in Cosmic Dust, by Dust Source
Element
SPC
AST
HTC
OCC
iron
20%
28%
90%
98%
potassium
44%
74%
97%
100%
sodium
45%
75%
99%
100%
Which choice most effectively uses data from the table to complete the example?
iron from SPC dust is 20%.
sodium from OCC dust is 100%.
iron from HTC dust is 90%.
sodium from AST dust is 75%.
Show solution
Answer: C β iron from HTC dust is 90%.
The example must compare the same element (iron) from a slow source (AST, 28%) with a fast source (HTC or OCC). Only C does that: iron from HTC dust, 90% β much higher.
A: SPC is also a slow source, so this doesn't illustrate the slow-vs-fast contrast. B and D switch to sodium, so they don't compare "the same material." (D is also a slow source.)
Method: Check every condition in the claim: same material AND slow vs. fast. Most wrong choices satisfy one condition but not both.
Q16Command of Evidence (Textual)
Passage: Art collectives are groups of artists who agree to work together. Collaboration is usually involved, and a journalist claims this can be difficult for artists who are used to having sole control of their work.
Which quotation from the interviews best illustrates the journalist's claim?
"The first collective I joined included many amazingly talented artists, and we enjoyed each other's company, but because we had a hard time sharing credit and responsibility for our work, the collective didn't last."
"We work together, but that doesn't mean that individual projects are equally the work of all of us. Many of our projects are primarily the responsibility of whoever originally proposed the work to the group."
"Having worked as a member of a collective for several years, it's sometimes hard to recall what it was like to work alone without the collective's support. But that support encourages my individual expression rather than limits it."
"Sometimes an artist from outside the collective will choose to collaborate with us on a project, but all of those projects fit within the larger themes of the work the collective does on its own."
Show solution
Answer: A
The claim has one key word: collaboration is difficult. Only A describes a difficulty β the artists "had a hard time sharing credit and responsibility," and the collective collapsed because of it.
B describes how work is divided, with no sign of difficulty. C is positive β the collective supports individual expression. D is about outside collaborators and themes, not difficulty.
Q17Command of Evidence (Quantitative)
Passage: A student grew two mycorrhizal-host species (corn, marigold) and one non-host (broccoli) in soil with fungi and in soil treated to kill fungi. Average masses (with fungi / treated): corn 15.1 / 3.8 g, marigold 10.2 / 2.4 g, broccoli 7.5 / 7.0 g. Non-host species don't benefit from the fungi and may even be harmed. The student was surprised to discover that ______.
Effects of Mycorrhizal Fungi on 3 Plant Species
Plant species
Mycorrhizal host
Average mass of plants grown in soil containing mycorrhizal fungi (in grams)
Average mass of plants grown in soil treated to kill fungi (in grams)
Corn
yes
15.1
3.8
Marigold
yes
10.2
2.4
Broccoli
no
7.5
7
Which choice most effectively uses data from the table to complete the statement?
broccoli grown in soil containing mycorrhizal fungi had a slightly higher average mass than broccoli grown in soil that had been treated to kill fungi.
corn grown in soil containing mycorrhizal fungi had a higher average mass than broccoli grown in soil containing mycorrhizal fungi.
marigolds grown in soil containing mycorrhizal fungi had a much higher average mass than marigolds grown in soil that had been treated to kill fungi.
corn had the highest average mass of all three species grown in soil that had been treated to kill fungi, while marigolds had the lowest.
Show solution
Answer: A
What would be surprising? The hosts doing better with fungi is expected. But broccoli is a non-host that shouldn't benefit β yet it was slightly heavier with fungi (7.5 g vs 7.0 g). That's the unexpected result, and the data confirm it.
C is true but expected β marigolds are hosts. B is true but isn't a surprise and compares different species. D is true of the data too, but nothing about it contradicts the student's expectations.
Method: When the blank follows "surprised," "unexpectedly," or "contrary to predictions," the right answer must be both true in the data and against the stated expectation.
Q18Inferences
Passage: Pompeii artworks show a woman fishing with a cupid nearby. Some scholars say she is Venus, because Venus is linked to cupids. But archaeologist Carla Brain suggests cupids may also have been associated with fishing in general. The presence of a cupid, therefore, ______.
Which choice most logically completes the text?
is not conclusive evidence that the figure is Venus.
suggests that Venus was often depicted fishing.
eliminates the possibility that the figure is Venus.
would be difficult to account for if the figure is not Venus.
Show solution
Answer: A β is not conclusive evidence that the figure is Venus.
If cupids go with fishing scenes in general, a cupid near a fishing woman might be there because of the fishing, not because she is Venus. So the cupid no longer proves she is Venus β it is not conclusive.
B assumes she is Venus, which is the very thing in doubt. C overshoots β Brain's point weakens the evidence but doesn't rule Venus out. D is the old argument that Brain is undercutting.
Method: "Suggests β¦ may also" introduces doubt, not disproof. Pick the choice that is exactly as strong as the evidence.
Q19Standard English
Passage: Many celebrity nonfiction books are written by ghostwriters β professional authors paid to write other ______ but whose names never appear on the cover.
Which choice completes the text so that it conforms to the conventions of Standard English?
people's stories
peoples story's
peoples stories
people's story's
Show solution
Answer: A β people's stories
Two decisions:
1. The stories belong to other people β possessive: people's ("people" is already plural, so add 's).
2. The ghostwriters write many stories β plain plural, no apostrophe: stories.
Why not the others: "Peoples" (B, C) means ethnic groups/nations and lacks the possessive. "Story's" (B, D) is possessive β but nothing belongs to the stories.
Apostrophe test: can you rephrase with "of"? "The stories of other people" β β people's. "Something of the story"? No β stories.
Q20Standard English
Passage: Like other amphibians, the wood frog can't make its own heat, so during freezing periods it ______ by producing lots of glucose, which helps prevent ice forming in its cells.
Which choice completes the text so that it conforms to the conventions of Standard English?
had survived
survived
would survive
survives
Show solution
Answer: D β survives
The passage states a general scientific fact in the present tense ("is unable," "helps prevent"). The verb must match: survives.
A and B are past tenses β wrong for a habitual, present-day fact. C ("would") makes it hypothetical.
Method: Match the tense of the surrounding verbs. General truths about nature = simple present.
Q21Standard English
Passage: Wilma Rudolph, told as a child she might never walk again, didn't just walk β she ran, fast. ______ the 1960 Rome Olympics, she won the 100 m and 200 m and anchored the relay to become the first US woman to win three golds at one Games.
Which choice completes the text so that it conforms to the conventions of Standard English?
ran--fast--during
ran--fast during
ran--fast, during
ran--fast. During
Show solution
Answer: D β ran--fast. During
"Rudolph didn't just walk, she ranβfast" is a complete sentence. "During the 1960 Summer Olympics β¦ she won β¦" is another complete sentence with its own subject and verb. Two independent clauses need a strong break β a period works.
A, B and C all run the two sentences together (C is a comma splice; A and B have no valid break at all).
Method: Find the subjectβverb pairs: she ran β¦ she won. Two complete clauses = period, semicolon, or comma + FANBOYS.
Q22Standard English
Passage: In her 1970sβ80s landscapes, Etel Adnan used splotches of colour to represent the Mount Tamalpais region. Interestingly, the triangle representing the mountain itself ______ among the few defined figures in her paintings.
Which choice completes the text so that it conforms to the conventions of Standard English?
are
have been
were
is
Show solution
Answer: D β is
The subject is the triangle β singular. "Representing the mountain itself" is a modifier, and "among the few defined figures" comes after the verb. Singular subject β is. Present tense fits because it describes what the paintings contain.
A, B and C are plural β they agree with "figures," which is not the subject.
Method: Cross out the modifier ("representing the mountain itself") and read "the triangle ___ amongβ¦".
Q23Standard English
Passage: Marie Watt's blanket art varies in size. In 2004, she sewed strips of blankets into a 10-by-13-inch ______ in 2014, she stacked folded blankets and cast them in bronze to make two 18-foot pillars.
Which choice completes the text so that it conforms to the conventions of Standard English?
sampler later,
sampler;
sampler,
sampler, later,
Show solution
Answer: B β sampler;
"In 2004, Watt sewed β¦ sampler" is a complete clause. "In 2014, she arranged β¦" is another. Joining two independent clauses with no conjunction requires a semicolon.
C is a comma splice. D is also a comma splice (and adds "later" awkwardly). A has no punctuation after "sampler" and a stray "later," β still two clauses fused together.
Q24Standard English
Passage: Percy Julian's work helped people see. "Named in 1999 as one of the greatest achievements by a US chemist in the past hundred years, ______ led to the first mass-produced treatment for glaucoma."
Which choice completes the text so that it conforms to the conventions of Standard English?
Julian synthesized the alkaloid physostigmine in 1935; it
in 1935 Julian synthesized the alkaloid physostigmine, which
Julian's 1935 synthesis of the alkaloid physostigmine
the alkaloid physostigmine was synthesized by Julian in 1935 and
Show solution
Answer: C β Julian's 1935 synthesis of the alkaloid physostigmine
The opening phrase "Named β¦ as one of the greatest achievements" must be followed immediately by the thing that was named an achievement. That's the synthesis, not Julian himself and not the chemical. Choice C also gives "led" a proper subject: "Julian's 1935 synthesis β¦ led to β¦"
A and B put Julian right after the modifier β but Julian is a person, not an achievement (dangling modifier). D puts the alkaloid there β a chemical, not an achievement β and "and led" is then awkwardly attached.
Dangling modifiers: an opening descriptive phrase describes whatever noun comes straight after the comma. Ask "who or what was named an achievement?"
Q25Standard English
Passage: Two botanical gardens are among many devoted to growing diverse plant ______ fostering scientific research; and educating the public about plant conservation.
Which choice completes the text so that it conforms to the conventions of Standard English?
species, both native and nonnative,
species, both native and nonnative;
species; both native and nonnative,
species both native and nonnative,
Show solution
Answer: B β species, both native and nonnative;
The sentence lists three activities: growing β¦, fostering β¦, educating β¦. The last two are separated by a semicolon, so this is a list that uses semicolons (necessary because the first item contains its own commas: "species, both native and nonnative"). The first item must end with a semicolon too, and the internal phrase stays set off by a comma.
A and D end the first item with a comma, making the list's separators inconsistent. C puts the semicolon in the middle of the first item, cutting "both native and nonnative" off from "species."
Method: If one item in a list is separated by a semicolon, all items must be.
Q26Standard English
Passage: Alton Okinaka sits on the board that adds sites to the Hawai'i Register of Historic Places. He doesn't make these decisions ______ all designations must be approved by nine other experts.
Which choice completes the text so that it conforms to the conventions of Standard English?
single-handedly, however;
single-handedly; however,
single-handedly, however,
single-handedly however
Show solution
Answer: A β single-handedly, however;
Two things to decide: where the clause break goes, and which clause "however" belongs to.
The break: "Okinaka doesn't make such decisions single-handedly" and "all historical designations must be approvedβ¦" are both complete clauses, so they need a semicolon between them.
Where "however" goes: the contrast is with the previous sentence. He sits on the board β however, he doesn't decide alone. So "however" belongs at the end of the first clause, set off by a comma, and the semicolon comes after it: "β¦single-handedly, however; all historical designationsβ¦" The second clause doesn't contrast with the first β it explains it (he doesn't decide alone because nine others must approve).
B puts "however" at the start of the second clause, which would mean the nine-expert approval contrasts with his not deciding alone β but it actually explains it. C is a comma splice. D has no punctuation at all.
Method: "However" can sit at the start or the end of a clause. Ask which two ideas actually contrast, and attach "however" to the clause that turns against what came before.
Q27Transitions
Passage: In 1968 Congressman John Conyers proposed a national holiday honouring Dr. Martin Luther King Jr. The bill failed to reach a vote, but Conyers and Shirley Chisholm resubmitted it every session for fifteen years. ______ in 1983, the bill passed.
Which choice completes the text with the most logical transition?
Instead,
Likewise,
Finally,
Additionally,
Show solution
Answer: C β Finally,
Fifteen years of repeated attempts, then success. "Finally" marks the end of a long wait.
A (Instead) implies a replacement β nothing is replaced. B (Likewise) implies similarity; passing is the opposite of failing. D (Additionally) adds a new point rather than concluding the story.
Q28Transitions
Passage: Geoscientists long considered Mauna Loa the largest shield volcano by volume (~74,000 kmΒ³). ______ a 2020 study by Michael Garcia found Hawaii's PΕ«hΔhonu volcano is much larger, about 148,000 kmΒ³.
Which choice completes the text with the most logical transition?
Secondly,
Consequently,
Moreover,
However,
Show solution
Answer: D β However,
A long-held belief, then new evidence that overturns it. That's a contrast β However.
A and C add a second supporting point; B implies the new finding was caused by the old belief. All miss the contrast.
Q29Transitions
Passage: Composer Samuel Coleridge-Taylor emphasized his mixed-race ancestry β for example, calling himself Anglo-African. ______ he incorporated traditional African music into his classical compositions.
Which choice completes the text with the most logical transition?
In addition,
Actually,
However,
Regardless,
Show solution
Answer: A β In addition,
The sentence gives a second example of him emphasizing his heritage. Adding another example of the same point β In addition.
B (Actually) implies a correction. C (However) implies a contrast. D (Regardless) implies the previous point doesn't matter. The two sentences agree, so none of these fit.
Q30Transitions
Passage: In 2019 two researchers cooked a stew from a 4,000-year-old Mesopotamian recipe called paΕ‘rΕ«tum ("unwinding"). It tasted mild and made them feel calm. ______ knowing that dishes were sometimes named for their effects, they theorized the name referred to its purpose: to help diners relax.
Which choice completes the text with the most logical transition?
Therefore,
Alternately,
Nevertheless,
Likewise,
Show solution
Answer: A β Therefore,
Their experience (the stew was calming) is the reason for their theory (the name means it was for relaxing). Cause β conclusion = Therefore.
B offers an alternative, C sets up a contrast and D a similarity; the theory follows directly from the tasting, so none fits.
Q31Rhetorical Synthesis
Passage: Notes: both baking soda and baking powder are chemical leavening agents that release COβ in batter. Baking soda is pure sodium bicarbonate and needs an acidic ingredient (like honey) plus liquid. Baking powder already contains an acid and needs only liquid.
The student wants to emphasize a difference between baking soda and baking powder. Which choice most effectively uses relevant information from the notes to accomplish this goal?
To make batters rise, bakers use chemical leavening agents such as baking soda and baking powder.
Baking soda and baking powder are chemical leavening agents that, when mixed with other ingredients, cause carbon dioxide to be released within a batter.
Baking soda is pure sodium bicarbonate, and honey is a type of acidic ingredient.
To produce carbon dioxide within a liquid batter, baking soda needs to be mixed with an acidic ingredient, whereas baking powder does not.
Show solution
Answer: D
Goal = a difference. D contrasts them directly with "whereas": soda needs an acid, powder doesn't.
A and B describe what they have in common. C describes only baking soda (and honey) β no comparison at all.
Method: Rhetorical synthesis questions are graded on the goal, not on accuracy β every choice is accurate. Underline the goal word ("difference") and look for contrast language.
Q32Rhetorical Synthesis
Passage: Notes: Soo Sunny Park is a Korean American artist whose main medium is light. In 2013 she made Unwoven Light: a chain-link fence fitted with iridescent plexiglass tiles; light passing through it formed colourful prisms.
The student wants to describe Unwoven Light to an audience unfamiliar with Soo Sunny Park. Which choice most effectively uses relevant information from the notes to accomplish this goal?
Park's 2013 installation Unwoven Light, which included a chain-link fence and iridescent tiles made from plexiglass, featured light as its primary medium of expression.
Korean American light artist Soo Sunny Park created Unwoven Light in 2013.
The chain-link fence in Soo Sunny Park's Unwoven Light was fitted with tiles made from iridescent plexiglass.
In Unwoven Light, a 2013 work by Korean American artist Soo Sunny Park, light formed colorful prisms as it passed through a fence Park had fitted with iridescent tiles.
Show solution
Answer: D
Two requirements: (1) describe the work, and (2) the audience doesn't know Park, so she must be introduced. D names her fully with nationality and describes what the work is and does.
A uses only "Park," which assumes the reader knows her. B introduces her but doesn't describe the work. C describes only one detail and doesn't introduce her.
Method: "Unfamiliar with X" means X must be explained or introduced in the sentence.
Q33Rhetorical Synthesis
Passage: Notes: Angkor Wat, in Cambodia, was built in the 1100s for Vishnu and has been a Buddhist temple since the 1500s. Archaeologist Noel Hidalgo Tan applied a new colour-contrast imaging technique (decorrelation stretch) to photos of its plaster walls and revealed hundreds of unknown images.
The student wants to present Tan's research to an audience unfamiliar with Angkor Wat. Which choice most effectively uses relevant information from the notes to accomplish this goal?
Tan photographed Angkor Wat's plaster walls and then applied decorrelation stretch analysis to the photographs.
Decorrelation stretch analysis is a novel digital imaging technique that Tan used to enhance the contrast between colors in a photograph.
Using a novel digital imaging technique, Tan revealed hundreds of images hidden on the walls of Angkor Wat, a Cambodian temple.
Built to honor a Hindu god before becoming a Buddhist temple, Cambodia's Angkor Wat concealed hundreds of images on its plaster walls.
Show solution
Answer: C
Needs: (1) Tan's research β what he did and found; (2) an explanation of what Angkor Wat is. C gives the method, the finding (hundreds of hidden images) and identifies Angkor Wat as "a Cambodian temple."
A never explains Angkor Wat and omits the finding. B is about the technique, not the research or the site. D explains Angkor Wat but leaves Tan out entirely.
Passage: The fashion resale market earned nearly $30 billion in 2019. Expecting continued growth, some analysts ______ that revenues will more than double by 2028.
Which choice completes the text with the most logical and precise word or phrase?
produced
denied
worried
predicted
Show solution
Answer: D β predicted
"Expecting continued growth" + a statement about the future ("will more than double by 2028") = a forecast. Analysts predicted it.
A: you can't "produce that" something will happen. B (denied) contradicts "expecting continued growth." C (worried) is negative, but doubling revenue is good news for the market.
Q2Words in Context
Passage: Delivering biomolecules into plant cells helps protect plants from disease, but the cell wall makes it hard. Markita del Carpio Landry's team showed it may be possible to ______ this problem by sending molecules through carbon nanotubes, which can cross cell walls.
Which choice completes the text with the most logical and precise word or phrase?
conceptualize
neglect
illustrate
overcome
Show solution
Answer: D β overcome
The nanotubes can cross cell walls β they get around the obstacle. Getting past a problem = overcoming it.
A (conceptualize) and C (illustrate) mean describing or picturing the problem, not solving it. B (neglect) means ignoring it.
Q3Words in Context
Passage: Particle physicists such as Ayana Holloway Arce and Aida El-Khadra spend much of their time ______ what is invisible to the naked eye: using advanced technology, they closely examine the behavior of subatomic particles.
Which choice completes the text with the most logical and precise word or phrase?
selecting
inspecting
creating
deciding
Show solution
Answer: B β inspecting
The colon explains the blank: "they closely examine" subatomic particles. Inspecting = closely examining.
A (selecting) and D (deciding) are about choosing. C (creating) claims they make the particles β the text says they study them.
Q4Words in Context
Passage: Kristian Carlson's team studied the shoulder bones of "Little Foot," a 3.6-million-year-old hominin. The bones were ______ those of modern apes that climb often, such as gorillas and chimpanzees, suggesting Little Foot was adapted to life in trees.
Which choice completes the text with the most logical and precise word or phrase?
surpassed by
comparable to
independent of
obtained from
Show solution
Answer: B β comparable to
The conclusion β Little Foot was a tree-climber β only follows if its bones were similar to climbing apes' bones. Comparable to = similar to.
A (surpassed by) and C (independent of) don't show resemblance, so the climbing conclusion wouldn't follow. D is nonsensical β the fossil bones weren't taken from modern apes.
Q5Words in Context
Passage: Rydra Wong, the hero of Samuel R. Delany's Babel-17, is a poet β an occupation that is not ______ in Delany's work: nearly a dozen of his characters are poets or writers.
Which choice completes the text with the most logical and precise word or phrase?
infallible
atypical
lucrative
tedious
Show solution
Answer: B β atypical
The colon gives evidence: many of his characters are poets or writers. So being a poet is common in his work β "not atypical" (not unusual).
Why not the others: The evidence is about how often poets appear. A (never wrong), C (well-paid) and D (boring) say nothing about frequency.
Method: "Not + negative word" = positive meaning. "Not atypical" = typical. Predict "not unusual" and look for its match.
Q6Words in Context
Passage: For a 2020 exhibition, photographer and neurobiologist Okunola Jeyifous ______ a series of new images based on 1970s alphabet posters (the "Black ABCs") featuring Black children from Chicago. He photographed the now-adult models and layered those photos over magnified images of their cells.
Which choice completes the text with the most logical and precise word or phrase?
validated
created
challenged
restored
Show solution
Answer: B β created
The images are described as new, and the second sentence explains how he made them. He created them.
A (validated) means confirmed as correct. C (challenged) means disputed. D (restored) means repaired old work β but these are new images, not the original posters.
Q7Words in Context
Passage: Besides being an accomplished psychologist, Francis Cecil Sumner was a ______ increasing the opportunity for Black students to study psychology, helping found Howard University's psychology department in 1930.
Which choice completes the text with the most logical and precise word or phrase?
proponent of
supplement to
beneficiary of
distraction for
Show solution
Answer: A β proponent of
He helped found a department to widen access β he actively supported the cause. A proponent is a supporter or advocate.
B (supplement to) doesn't fit a person and a goal. C (beneficiary of) would mean he gained from the increased opportunity rather than creating it. D (distraction) is the opposite of his role.
Q8Words in Context
Passage: Whether a French monarch's reign (such as Hugh Capet's or Henry I's) was important or uneventful, its course was shaped by questions of legitimacy β so it can't be understood without knowing what factors allowed the monarch to ______ his right to the throne.
Which choice completes the text with the most logical and precise word or phrase?
reciprocate
annotate
buttress
disengage
Show solution
Answer: C β buttress
If legitimacy was questioned, the monarch needed factors that strengthened or supported his claim. Buttress means to reinforce or support.
A (reciprocate) means to return a favour. B (annotate) means to add notes to a text. D (disengage) means to withdraw β the opposite of defending a claim.
Method: Hard vocabulary questions often have one sophisticated word that fits (buttress) and three that are real words used in the wrong sense. Eliminate by meaning.
Q9Text Structure & Purpose
Passage: Some bird species lay their eggs in other species' nests instead of raising their own chicks. The underlined sentence says female cuckoos have been seen quickly laying eggs in other birds' nests while those birds are away looking for food. After hatching, the host parents usually raise the cuckoo chicks as their own.
Which choice best describes the function of the underlined sentence in the text as a whole?
It introduces a physical feature of female cuckoos that is described later in the text.
It describes the appearance of the cuckoo nests mentioned earlier in the text.
It offers a detail about how female cuckoos carry out the behavior discussed in the text.
It explains how other birds react to the female cuckoo behavior discussed in the text.
Show solution
Answer: C
Sentence 2 introduces the behaviour (laying eggs in others' nests). The underlined sentence adds how cuckoos do it β quickly, while the hosts are out feeding. That's a detail about carrying out the behaviour.
A: no physical feature is mentioned. B: cuckoos don't have their own nests here, and nothing is described visually. D: the host birds' reaction is in the next sentence, not the underlined one.
Q10Command of Evidence (Textual)
Passage: Cats can tell where an unseen person is from their voice, and are surprised when the same person calls from two places in quick succession. Saho Takagi's team measured surprise from the cats' ear and head movements while they heard their owners' voices from two widely spaced speakers.
According to the text, how did the researchers determine the level of surprise displayed by the cats in the study?
They watched how each cat moved its ears and head.
They examined how each cat reacted to the voice of a stranger.
They studied how each cat physically interacted with its owner.
They tracked how each cat moved around the room.
Show solution
Answer: A β They watched how each cat moved its ears and head.
Straight retrieval: "measuring cats' levels of surprise based on their ear and head movements."
B: the recordings were of the owners' voices, not strangers'. C: the owners were only heard, not present. D: nothing about moving around the room.
Method: "According to the text" = the answer is stated almost word for word. Find the sentence; don't infer.
Q11Command of Evidence (Textual)
Passage: A student hypothesizes that slightly acidic soil is better for growing choy sum than neutral soil. She plants 16 seeds in soil mixed with acidic coffee grounds and 16 in plain potting soil (the control), then grows both under the same conditions for three weeks.
Which finding, if true, would most directly weaken the student's hypothesis?
The choy sum planted in the soil without coffee grounds were significantly taller at the end of the experiment than the choy sum planted in the mixture of soil and coffee grounds.
The choy sum grown in the soil without coffee grounds weighed significantly less at the end of the experiment than the choy sum grown in the mixture of soil and coffee grounds.
The choy sum seeds planted in the soil without coffee grounds sprouted significantly later in the experiment than did the seeds planted in the mixture of soil and coffee grounds.
Significantly fewer of the choy sum seeds planted in the soil without coffee grounds sprouted plants than did the seeds planted in the mixture of soil and coffee grounds.
Show solution
Answer: A
To weaken the hypothesis, the neutral (plain soil) plants must do better. Only A shows that: the control plants grew significantly taller.
B, C and D all show the plain-soil plants doing worse (lighter, later, fewer sprouts) β those support the hypothesis.
Method: Flip the hypothesis: "acidic is better" is weakened by any result where "neutral is better." Then find the only choice where the control wins.
Q12Command of Evidence (Textual)
Passage: In Katherine Mansfield's 1920 story "The Young Girl," the narrator takes a 17-year-old and her brother for a meal. The claim: Mansfield often contrasts the girl's pleasant appearance with her unpleasant attitude.
Which quotation from "The Young Girl" most effectively illustrates the claim?
"I heard her murmur, 'I can't bear flowers on a table.' They had evidently been giving her intense pain, for she positively closed her eyes as I moved them away."
"While we waited she took out a little, gold powder-box with a mirror in the lid, shook the poor little puff as though she loathed it, and dabbed her lovely nose."
"I saw, after that, she couldn't stand this place a moment longer, and, indeed, she jumped up and turned away while I went through the vulgar act of paying for the tea."
"She didn't even take her gloves off. She lowered her eyes and drummed on the table. When a faint violin sounded she winced and bit her lip again. Silence."
Show solution
Answer: B
The quotation needs both halves. B has the unpleasant attitude (she shakes the puff "as though she loathed it") and the pleasant appearance ("her lovely nose") in one sentence.
A, C and D all show her bad attitude but say nothing about her appearance, so none shows a contrast.
Method: If a claim has two parts (X contrasted with Y), the correct quotation must contain both. Most wrong choices contain only one.
Q13Command of Evidence (Quantitative)
Passage: A bar graph shows three UK policy-uncertainty measures, 2005β2010 (approximate): 2005 tax β 98, trade β 160, general β 90; 2007 tax β 60, trade β 75, general β 77; 2009 tax β 76, trade β 70, general β 80; 2010 tax β 165, trade β 70, general β 118. The claim: a general measure may not fully reflect uncertainty about specific policy areas, as in the UK, where general uncertainty ______.
Which choice most effectively uses data from the graph to illustrate the claim?
aligned closely with uncertainty about tax and public spending policy in 2005 but differed from uncertainty about tax and public spending policy by a large amount in 2009.
was substantially lower than uncertainty about tax and public spending policy each year from 2005 to 2010.
reached its highest level between 2005 and 2010 in the same year that uncertainty about trade policy and tax and public spending policy reached their lowest levels.
was substantially lower than uncertainty about trade policy in 2005 and substantially higher than uncertainty about trade policy in 2010.
Show solution
Answer: D
We need data showing the general measure failing to track a specific area. In 2005, general (β90) was far below trade (β160); in 2010, general (β118) was far above trade (β70). The general measure moved in the opposite direction from trade uncertainty β it clearly didn't reflect it. D is both accurate and on-claim.
A: in 2009 general (β80) and tax (β76) were close, not far apart. B: in 2007 and 2009 general was higher than tax. C: general peaked in 2010, but tax uncertainty also peaked in 2010, not bottomed out.
Method: With multi-series bar graphs, check every year a choice mentions. One wrong year sinks the whole choice.
Q14Command of Evidence (Textual)
Passage: Linguist Deborah Tannen argues that presenting issues as a two-sided debate strips away complexity and can be less informative for an audience than presenting multiple perspectives in a noncompetitive format. Students tested this by showing participants a two-person debate, a three-person panel with various views, or a single commentator.
Which finding from the students' study, if true, would most strongly support Tannen's hypothesis?
On average, participants perceived commentators in the debate as more knowledgeable about the issue than commentators in the panel.
On average, participants perceived commentators in the panel as more knowledgeable about the issue than the single commentator.
On average, participants who watched the panel correctly answered more questions about the issue than those who watched the debate or the single commentator did.
On average, participants who watched the single commentator correctly answered more questions about the issue than those who watched the debate did.
Show solution
Answer: C
Tannen's hypothesis compares the debate with multiple noncompetitive perspectives (the panel) on how informative they are. The best support: panel viewers learned more β answered more questions correctly β than debate viewers. C says this (and beats the single commentator too).
A favours the debate, and is about perceived knowledge, not what viewers learned. B measures perceptions, not how informative the presentation was, and doesn't involve the debate. D favours the single commentator β one perspective isn't "multiple perspectives," so it doesn't test her claim.
Q15Command of Evidence (Textual)
Passage: In Shakespeare's King Lear, Lear tests his three daughters' devotion. The claim: he later expresses regret for his actions.
Which choice most effectively uses a quotation from King Lear to illustrate the claim?
says of himself, "I am a man / more sinned against than sinning."
says during a growing storm, "This tempest will not give me leave to ponder / On things would hurt me more."
says to himself while striking his head, "Beat at this gate that let thy folly in / And thy dear judgement out!"
says of himself, "I will do such thingsβ / What they are yet, I know not; but they shall be / The terrors of the earth!"
Show solution
Answer: C
Regret = blaming yourself for a mistake. In C, Lear strikes his own head β the "gate" that let his "folly" in and his good judgement out. He is calling his own actions foolish.
A is the opposite of regret: he says others wronged him more than he wronged them. B says the storm distracts him from painful thoughts β no admission of fault. D threatens revenge.
Q16Inferences
Passage: Many of Shakespeare's tragedies explore broad themes that still appeal today β Romeo and Juliet is still widely read and staged. But understanding his history plays can require knowing centuries of English history. Consequently, ______.
Which choice most logically completes the text?
many theatergoers and readers today are likely to find Shakespeare's history plays less engaging than the tragedies.
some of Shakespeare's tragedies are more relevant to today's audiences than twentieth-century plays.
Romeo and Juliet is the most thematically accessible of all Shakespeare's tragedies.
experts in English history tend to prefer Shakespeare's history plays to his other works.
Show solution
Answer: A
Tragedies: universal themes, easy to connect with. History plays: need specialist background. The logical consequence is that modern audiences are likely to find the history plays less engaging than the tragedies.
B: twentieth-century plays are never discussed. C: Romeo and Juliet is one example; nothing ranks it above all others. D: the text says nothing about experts' preferences.
Q17Inferences
Passage: Ancestral Puebloans abandoned their villages (with farms for crops and turkeys) suddenly in the late 1200s. DNA analysis shows that modern turkeys in New Mexico's Rio Grande Valley descend partly from turkeys raised at Mesa Verde, with the shared markers appearing only after 1280. Thus, researchers concluded that ______.
Which choice most logically completes the text?
conditions of the terrains in the Rio Grande Valley and Mesa Verde had greater similarities in the past than they do today.
some Ancestral Puebloans migrated to the Rio Grande Valley in the late 1200s and carried farming practices with them.
Indigenous peoples living in the Rio Grande Valley primarily planted crops and did not cultivate turkeys before 1280.
the Ancestral Puebloans of Mesa Verde likely adopted the farming practices of Indigenous peoples living in other regions.
Show solution
Answer: B
Mesa Verde turkeys' genes show up in the Rio Grande Valley right after 1280 β exactly when the Puebloans left their villages. The simplest explanation: people moved there and brought their turkeys (farming practices) with them.
A: terrain isn't discussed. C: the text says nothing about whether turkeys were already raised there before 1280 β only that Mesa Verde genes arrived then. D reverses the direction: practices moved from Mesa Verde, not to it.
Q18Inferences
Passage: To see whether holding office changes behavior, researchers must compare office-holders with people who don't hold office but are otherwise similar. Since researchers can't control who wins elections, they therefore ______.
Which choice most logically completes the text?
struggle to find valid data about the behavior of politicians who do not currently hold office.
can only conduct valid studies with people who have previously held office rather than people who presently hold office.
should select a control group of people who differ from office holders in several significant ways.
will find it difficult to identify a group of people who can function as an appropriate control group for their studies.
Show solution
Answer: D
The first sentence names the challenge: finding an appropriate control group. Winners and losers differ in ways researchers can't randomize, so a truly comparable group is hard to find. D completes that loop.
A: the problem isn't missing data, it's comparability. B is an unsupported rule. C contradicts the text β the control group must be similar, not different.
Q19Standard English
Passage: In Bengali Harlem and the Lost Histories of South Asian America, Vivek Bald uses articles, census records, ships' logs and memoirs to tell the ______ who made New York City their home in the early 1900s.
Which choice completes the text so that it conforms to the conventions of Standard English?
story's of the South Asian immigrants
story's of the South Asian immigrants'
stories of the South Asian immigrants
stories' of the South Asian immigrant's
Show solution
Answer: C β stories of the South Asian immigrants
"The stories of the immigrants" β the "of" already shows the relationship, so neither word needs an apostrophe. Stories is a plain plural; immigrants is a plain plural (many people, and "who made β¦ their home" is plural).
Why not the others: Every other choice adds an apostrophe where nothing is being possessed. "Immigrant's" in D is also singular, clashing with "their home."
Q20Standard English
Passage: In her series "Memory Test" and "Autobiography," Howardena Pindell explored themes ______ healing, self-discovery, and memory by cutting and resewing canvas and adding personal artifacts.
Which choice completes the text so that it conforms to the conventions of Standard English?
of
of,
of--
of:
Show solution
Answer: A β of
"Themes of healing, self-discovery, and memory" β the preposition of flows directly into its objects. No punctuation belongs between a preposition and its object.
B, C and D all interrupt the phrase. A colon in particular can only follow a complete clause β "explored themes of" is not one.
Never put punctuation directly after a preposition (of, in, for, toβ¦) or between a verb and its object.
Q21Standard English
Passage: Sona Charaipotra and Dhonielle Clayton founded CAKE Literary in 2011, a book packaging ______ specializes in creating and promoting stories from diverse perspectives for young readers.
Which choice completes the text so that it conforms to the conventions of Standard English?
company,
company that
company
company, that
Show solution
Answer: B β company that
"Specializes" needs a subject. "A book packaging company that specializesβ¦" β that introduces an essential clause describing the company, and essential clauses take no comma.
A and C leave "specializes" without a subject. D puts a comma before "that," which Standard English doesn't allow.
Q22Standard English
Passage: Black bears that eat human food before hibernation have higher levels of a rare carbon isotope, ______ due to the higher 13C levels in corn and cane sugar.
Which choice completes the text so that it conforms to the conventions of Standard English?
carbon-13, (13C)
carbon-13 (13C)
carbon-13, (13C),
carbon-13 (13C),
Show solution
Answer: D β carbon-13 (13C),
Two things to handle:
1. The abbreviation "(13C)" attaches directly to the name it abbreviates β no comma between them.
2. "Carbon-13 (13C)" is an appositive renaming "a rare carbon isotope." It opened with a comma after "isotope," so it must close with one before "due toβ¦"
A and C separate the name from its abbreviation. B fails to close the appositive.
Q23Standard English
Passage: In 2010, archaeologist Noel Hidalgo Tan was visiting Angkor Wat when he noticed red paint markings on the temple ______ the help of digital imaging, he found they were part of a mural with over 200 paintings.
Which choice completes the text so that it conforms to the conventions of Standard English?
walls, with
walls with
walls so with
walls. With
Show solution
Answer: D β walls. With
Clause 1: "Tan was visiting β¦ when he noticed markings β¦ on the temple walls." Clause 2: "With the help of digital imaging techniques, he discoveredβ¦" β its own subject (he) and verb (discovered). Two independent clauses β a period.
A is a comma splice. B fuses the sentences (and makes it sound like the walls had the imaging). C β "so" without a comma is still a run-on, and "so" is illogical: noticing paint didn't cause the imaging.
Method: When the second clause opens with a prepositional phrase, find its real subject and verb ("he discovered") before deciding it's a fragment.
Q24Standard English
Passage: Building on an earlier discovery of Charpentier's, 2020 chemistry Nobel winners Emmanuelle Charpentier and Jennifer Doudna re-created and then reprogrammed the "genetic scissors" of a DNA-cutting bacterium ______ a tool that is revolutionizing gene technology.
Which choice completes the text so that it conforms to the conventions of Standard English?
to forge
forging
forged
and forging
Show solution
Answer: A β to forge
They reprogrammed the scissors in order to make a new tool. The infinitive of purpose "to forge" expresses that.
B: "-ing" with no comma would seem to describe the bacteria. C: "forged" creates a third verb with no conjunction (re-created, reprogrammed forged). D: "and forging" doesn't parallel the past-tense verbs "re-created" and "reprogrammed."
Q25Standard English
Passage: In 2016 engineer Vanessa Galvez oversaw the installation of 164 bioswales β planted channels that absorb stormwater β in Queens, New York. "By reducing the runoff flowing into city sewers, ______"
Which choice completes the text so that it conforms to the conventions of Standard English?
the mitigation of both street flooding and the resulting pollution of nearby waterways has been achieved by bioswales.
the bioswales have mitigated both street flooding and the resulting pollution of nearby waterways.
the bioswales' mitigation of both street flooding and the resulting pollution of nearby waterways has been achieved.
both street flooding and the resulting pollution of nearby waterways have been mitigated by bioswales.
Show solution
Answer: B
The opening phrase "By reducing the runoffβ¦" needs to describe whatever comes right after the comma. What reduces runoff? The bioswales. Only B puts "the bioswales" first.
A puts "the mitigation" first; C "the bioswales' mitigation"; D "street flooding and pollution." None of those reduce runoff β dangling modifiers.
Method: Opening modifier β ask "who or what did this?" That noun must be the subject immediately after the comma.
Q26Standard English
Passage: A 2019 study by Rice University geoscientist Ming Tang offers a new explanation for the origin of Earth's ______ structures called arcs, towering ridges that form when a dense oceanic plate slides under a continental plate, melts, rises and bursts through the crust.
Which choice completes the text so that it conforms to the conventions of Standard English?
continents geological
continents: geological
continents; geological
continents. Geological
Show solution
Answer: B β continents: geological
"A study β¦ offers a new explanation for the origin of Earth's continents" is a complete clause. What follows ("geological structures called arcs, towering ridgesβ¦") is not a clause β it has no main verb. It explains/elaborates the explanation. A colon introduces exactly that kind of elaboration after a complete clause.
A reads as "continents geological structures," which is garbled. C and D need a complete clause after them, but "geological structures called arcs, towering ridgesβ¦" is a fragment.
Q27Transitions
Passage: During a 2021 launch, Rocket Lab's Electron rocket failed unexpectedly when its second stage shut down after ignition. ______ instead of downplaying it, the CEO publicly acknowledged the failure and apologized for losing the two satellites it carried.
Which choice completes the text with the most logical transition?
Afterward,
Additionally,
Indeed,
Similarly,
Show solution
Answer: A β Afterward,
Sequence of events: the failure happened, then the CEO responded. Afterward marks what came next in time.
B (Additionally) adds a parallel fact, but the apology is a response, not another failure. C (Indeed) intensifies a previous claim β the apology doesn't confirm or strengthen "the rocket failed." D (Similarly) implies the apology resembles the failure.
Q28Transitions
Passage: Soil contaminated with toxic metals can be dug up and taken to a landfill. ______ it can be detoxified by phytoremediation, where metal-tolerant plants absorb the pollutants into their shoots, which are cut and disposed of.
Which choice completes the text with the most logical transition?
Alternatively,
Specifically,
For example,
As a result,
Show solution
Answer: A β Alternatively,
Two different methods for the same problem: removal or phytoremediation. Alternatively introduces a second option.
B and C would make phytoremediation a detail or example of landfill disposal β it isn't. D implies landfill disposal causes phytoremediation.
Q29Rhetorical Synthesis
Passage: Notes: the Gregorian calendar has 365 days, which isn't divisible by 7, so dates shift weekday each year. The Hanke-Henry calendar has 364 days (divisible by 7), so dates fall on the same weekday every year, allowing more predictable scheduling.
The student wants to explain an advantage of the Hanke-Henry calendar. Which choice most effectively uses relevant information from the notes to accomplish this goal?
The Gregorian calendar has 365 days, which is one day longer than the Hanke-Henry permanent calendar.
Adopting the Hanke-Henry permanent calendar would help solve a problem with the Gregorian calendar.
Designed so calendar dates would occur on the same day of the week each year, the Hanke-Henry calendar supports more predictable scheduling than does the Gregorian calendar.
The Hanke-Henry permanent calendar was developed as an alternative to the Gregorian calendar, which is currently the most-used calendar in the world.
Show solution
Answer: C
C names the advantage (more predictable scheduling) and explains why (dates land on the same weekday every year).
A states a difference in length but no advantage. B hints at an advantage but is too vague to explain it. D is background only.
Q30Rhetorical Synthesis
Passage: Notes: the Haudenosaunee Confederacy is a ~1,000-year-old alliance of six Native nations in the northeastern US, bound by the Great Law of Peace. Historian Bruce Johansen and others believe its principles influenced the US Constitution (the "influence theory"), citing that Franklin and Jefferson studied the Confederacy.
The student wants to present the influence theory to an audience unfamiliar with the Haudenosaunee Confederacy. Which choice most effectively uses relevant information from the notes to accomplish this goal?
Historian Bruce Johansen believes that the Great Law of Peace was very influential.
The influence theory is supported by the fact that Benjamin Franklin and Thomas Jefferson both studied the Haudenosaunee Confederacy.
The influence theory holds that the principles of the Great Law of Peace, a centuries-old agreement binding six Native nations in the northeastern US, influenced the US Constitution.
Native people, including the members of the Haudenosaunee Confederacy, influenced the founding of the US in many different ways.
Show solution
Answer: C
Two needs: state the influence theory, and explain the Confederacy/Great Law for a new audience. C does both β it states the theory and glosses the Great Law as "a centuries-old agreement binding six Native nations in the northeastern US."
A is vague ("very influential" on what?) and explains nothing. B gives evidence but not the theory itself, and doesn't explain the Confederacy. D is a broad claim not in the notes.
Q31Rhetorical Synthesis
Passage: Notes: the Sun's surface is about 9,800Β°F (a G star). Of 357 stars within 10 parsecs, 327 are cooler K or M stars (under 8,900Β°F) and 11 are hotter A or F stars (over 10,300Β°F).
The student wants to emphasize how hot the Sun is relative to nearby stars. Which choice most effectively uses relevant information from the notes to accomplish this goal?
At around 9,800Β°F, which classifies it as a G star, the Sun is hotter than most but not all of the stars within 10 parsecs of it.
Astronomer Todd Henry determined that the Sun, at around 9,800Β°F, is a G star, and several other stars within a 10-parsec range are A or F stars.
Of the 357 stars within ten parsecs of the Sun, 327 are classified as K or M stars, with surface temperatures under 8,900Β°F.
While most of the stars within 10 parsecs of the Sun are classified as K, M, A, or F stars, the Sun is classified as a G star due to its surface temperature of 9,800Β°F.
Show solution
Answer: A
Goal = the Sun's temperature relative to nearby stars. A makes the comparison directly: hotter than most, but not all.
B gives the Sun's class and mentions hotter stars but never compares. C gives data on other stars but never mentions the Sun's temperature. D explains classification, not relative heat.
Q32Rhetorical Synthesis
Passage: Notes: the Atlantic Monthly started in 1857 and covered politics, art and literature. In 2019, historian Cathryn Halverson published Faraway Women and the "Atlantic Monthly", about women whose autobiographies appeared in the magazine in the early 1900s β including Juanita Harrison.
The student wants to introduce Cathryn Halverson's book to an audience already familiar with the Atlantic Monthly. Which choice most effectively uses relevant information from the notes to accomplish this goal?
Cathryn Halverson's Faraway Women and the "Atlantic Monthly" discusses female authors whose autobiographies appeared in the magazine in the early 1900s.
A magazine called the Atlantic Monthly, referred to in Cathryn Halverson's book title, was first published in 1857.
Faraway Women and the "Atlantic Monthly" features contributors to the Atlantic Monthly, first published in 1857 as a magazine focusing on politics, art, and literature.
An author discussed by Cathryn Halverson is Juanita Harrison, whose autobiography appeared in the Atlantic Monthly in the early 1900s.
Show solution
Answer: A
The audience already knows the magazine, so no background on it is needed. The job is to introduce the book: author, title, subject. A does exactly that.
B and C spend their words explaining the magazine β which this audience already knows. D gives one example author rather than introducing the book.
Method: "Already familiar with X" means don't waste words explaining X.
Q33Rhetorical Synthesis
Passage: Notes: the magnificent frigatebird is a seabird that, unusually, doesn't dive for prey. It either snatches prey from the water's surface with its hooked bill, or steals food from weaker birds by force (kleptoparasitism).
The student wants to emphasize a similarity between the two ways a magnificent frigatebird acquires food. Which choice most effectively uses relevant information from the notes to accomplish this goal?
A magnificent frigatebird never dives into the water, instead using its hook-tipped bill to snatch prey from the surface.
Neither of a magnificent frigatebird's two ways of acquiring food requires the bird to dive into the water.
Of the magnificent frigatebird's two ways of acquiring food, only one is known as kleptoparasitism.
In addition to snatching prey from the water with its hook-tipped bill, a magnificent frigatebird takes food from other birds by force.
Show solution
Answer: B
A similarity must be something both methods share. B identifies it: neither method involves diving.
A describes only one method. C states a difference. D lists both methods but draws no similarity.
A group of students voted on five after-school activities. The bar graph shows the number of students who voted for each of the five activities. How many students chose activity 3?
25
39
48
50
Show solution
Answer: B β 39
Read the top of bar 3 against the vertical axis: it sits between the 35 and 40 gridlines, just under 40 β that's 39.
48 is activity 5 and 50 is the top of the axis. 25 doesn't match any bar.
Read the right bar. Put your finger on the "3" label, go straight up, then straight across.
Q2Percentages
What percentage of 300 is 75?
25%
50%
75%
225%
Show solution
Answer: A β 25%
\[\frac{75}{300} = 0.25 = 25\%\]
C just repeats the number 75. D is 300 β 75.
Method: "What percent of whole is part" β part Γ· whole Γ 100.
Q3Quadratics
What is a solution to the given equation?
\[\frac{x^2}{25} = 36\]
6
30
450
900
Show solution
Answer: B β 30
Multiply both sides by 25, then take square roots:
\[x^2 = 900 \quad\Longrightarrow\quad x = \pm 30\]
30 is among the choices.
A is \(\sqrt{36}\) β it forgets the 25. C halves 900 instead of square-rooting. D is \(x^2\), not \(x\).
Q4Linear Equations
3 more than 8 times a number \(x\) is equal to 83. Which equation represents this situation?
\((3)(8)x = 83\)
\(8x = 83 + 3\)
\(3x + 8 = 83\)
\(8x + 3 = 83\)
Show solution
Answer: D β \(8x + 3 = 83\)
"8 times a number" β \(8x\). "3 more than" that β \(8x + 3\). "Is equal to 83" β \(= 83\).
C swaps the 3 and the 8. B is equivalent to \(8x - 3 = 83\) (3 less). A multiplies instead of adds.
Q5Linear Functions
Hana deposited a fixed amount into her bank account each month. The function \(f(t) = 100 + 25t\) gives the amount, in dollars, in Hana's bank account after \(t\) monthly deposits. What is the best interpretation of 25 in this context?
With each monthly deposit, the amount in Hana's bank account increased by $25.
Before Hana made any monthly deposits, the amount in her bank account was $25.
After 1 monthly deposit, the amount in Hana's bank account was $25.
Hana made a total of 25 monthly deposits.
Show solution
Answer: A
In \(f(t) = 100 + 25t\), 25 is the coefficient of \(t\) β the slope. Each time \(t\) goes up by 1 (one more deposit), \(f\) goes up by 25 dollars.
B describes \(f(0) = 100\), the starting amount β which is $100, not $25. C: \(f(1) = 125\). D confuses the rate with the number of deposits.
Method: In any linear model \(y = b + mx\): \(b\) = starting value, \(m\) = change per one unit of \(x\).
Q6Ratios & Rates
A customer spent $27 to purchase oranges at $3 per pound. How many pounds of oranges did the customer purchase?
Student-produced response β enter your own answer.
Show solution
Answer: 9
\[\frac{\$27}{\$3 \text{ per pound}} = 9 \text{ pounds}\]
Units check: dollars Γ· (dollars per pound) = pounds.
Q7Linear Equations
Nasir bought 9 storage bins that were each the same price. He used a coupon for $63 off the entire purchase. The cost for the entire purchase after using the coupon was $27. What was the original price, in dollars, for 1 storage bin?
Student-produced response β enter your own answer.
The trap: dividing $27 by 9 = $3 gives the price after the coupon. Add the $63 back first: the original total was $90.
Check: 9 bins Γ $10 = $90; $90 β $63 = $27 β
Q8Linear Functions
\(x\)
\(f(x)\)
0
29
1
32
2
35
For the linear function \(f\), the table shows three values of \(x\) and their corresponding values of \(f(x)\). Which equation defines \(f(x)\)?
\(f(x) = 3x + 29\)
\(f(x) = 29x + 32\)
\(f(x) = 35x + 29\)
\(f(x) = 32x + 35\)
Show solution
Answer: A β \(f(x) = 3x + 29\)
Slope: each time \(x\) rises by 1, \(f(x)\) rises by 3 (29 β 32 β 35), so \(m = 3\).
Intercept: \(f(0) = 29\), so \(b = 29\).
\[f(x) = 3x + 29\]
Method: If the table includes \(x = 0\), the \(y\)-intercept is sitting right there.
Q9Similar Triangles
Note: Figures not drawn to scale.
Right triangles \(PQR\) and \(STU\) are similar, where \(P\) corresponds to \(S\). If the measure of angle \(Q\) is 18Β°, what is the measure of angle \(S\)?
18Β°
72Β°
82Β°
162Β°
Show solution
Answer: B β 72Β°
In triangle \(PQR\), angle \(R = 90^\circ\) and angle \(Q = 18^\circ\), so
\[\angle P = 180 - 90 - 18 = 72^\circ\]
Similar triangles have equal corresponding angles, and \(S\) corresponds to \(P\). So \(\angle S = 72^\circ\).
A (18Β°) would be angle \(T\), which corresponds to \(Q\). D (162Β°) is \(180 - 18\), ignoring the right angle.
Method: Always match vertices in the order given: \(PQR \leftrightarrow STU\) means \(P\to S\), \(Q\to T\), \(R\to U\).
Q10Scatterplots & Models
The scatterplot shows the relationship between two variables, \(x\) and \(y\). Which of the following equations is the most appropriate linear model for the data shown?
\(y = 0.9 + 9.4x\)
\(y = 0.9 - 9.4x\)
\(y = 9.4 + 0.9x\)
\(y = 9.4 - 0.9x\)
Show solution
Answer: D β \(y = 9.4 - 0.9x\)
Two features to match:
1. The data decrease β negative slope. That leaves B or D.
2. The \(y\)-intercept is about 9β10, and \(y\) drops by roughly 8 over about 9 units of \(x\) β slope β \(-0.9\). That's \(y = 9.4 - 0.9x\).
B has intercept 0.9 and slope β9.4 β it would plunge to about β84 by \(x = 9\). A and C slope upward.
Method: Check the sign of the slope first, then the intercept. That eliminates three choices in seconds.
Q11Linear Equations
\(2.5b + 5r = 80\) describes the relationship between the number of birds, \(b\), and the number of reptiles, \(r\), that can be cared for at a pet care business on a given day. If the business cares for 16 reptiles on a given day, how many birds can it care for on this day?
Why not the others: All four choices share the intercept β8, so the slope decides it. B and D rise. A falls twice as steeply β it would cross the \(x\)-axis at β4, not β8.
Q13Algebraic Expressions
If \(\dfrac{x}{8} = 5\), what is the value of \(\dfrac{8}{x}\)?
Student-produced response β enter your own answer.
Show solution
Answer: 1/5 (or .2)
\(\dfrac{8}{x}\) is the reciprocal of \(\dfrac{x}{8}\). The reciprocal of 5 is \(\dfrac{1}{5}\).
Method: Spot reciprocals β flipping both sides of an equation is legal, and it saves solving for \(x\).
Q14Systems of Equations
The solution to the given system of equations is \((x, y)\). What is the value of \(y\)?
\[24x + y = 48 \qquad 6x + y = 72\]
Student-produced response β enter your own answer.
Show solution
Answer: 80
Subtract the second equation from the first to eliminate \(y\):
\[18x = -24 \quad\Longrightarrow\quad x = -\tfrac{4}{3}\]
Substitute into \(6x + y = 72\):
\[6\left(-\tfrac{4}{3}\right) + y = 72 \quad\Longrightarrow\quad -8 + y = 72 \quad\Longrightarrow\quad y = 80\]
Check: \(24(-\tfrac43) + 80 = -32 + 80 = 48\) β
Method: Both equations have \(+y\), so subtracting kills \(y\) instantly. Choose elimination when a variable has matching coefficients.
Q15Linear Functions
Line \(t\) in the \(xy\)-plane has a slope of \(-\frac{1}{3}\) and passes through the point \((9, 10)\). Which equation defines line \(t\)?
\(y = 13x - \frac{1}{3}\)
\(y = 9x + 10\)
\(y = -\frac{x}{3} + 10\)
\(y = -\frac{x}{3} + 13\)
Show solution
Answer: D β \(y = -\frac{x}{3} + 13\)
Use \(y = mx + b\) with \(m = -\tfrac13\), then substitute the point:
\[10 = -\tfrac13(9) + b = -3 + b \quad\Longrightarrow\quad b = 13\]
So \(y = -\dfrac{x}{3} + 13\).
C uses 10 as the intercept β but \((9, 10)\) isn't on the \(y\)-axis. A swaps slope and intercept. B builds the line from the coordinates of the point.
Q16Exponential Functions
The function \(f(x) = 206(1.034)^x\) models the value, in dollars, of a certain bank account by the end of each year from 1957 through 1972, where \(x\) is the number of years after 1957. Which of the following is the best interpretation of "\(f(5)\) is approximately equal to 243" in this context?
The value of the bank account is estimated to be approximately 5 dollars greater in 1962 than in 1957.
The value of the bank account is estimated to be approximately 243 dollars in 1962.
The value, in dollars, of the bank account is estimated to be approximately 5 times greater in 1962 than in 1957.
The value of the bank account is estimated to increase by approximately 243 dollars every 5 years between 1957 and 1972.
Show solution
Answer: B
\(x = 5\) means 5 years after 1957 β 1962. \(f(5)\) is the account's value then: about $243.
A and C treat 5 as an amount of money or a multiplier; it's a number of years. D treats 243 as a change; it's the total value (and exponential growth doesn't add a fixed amount anyway).
Method: \(f(\text{input}) = \text{output}\): the input is the when, the output is the how much.
Q17Ratios & Proportions
For a certain rectangular region, the ratio of its length to its width is 35 to 10. If the width of the rectangular region increases by 7 units, how must the length change to maintain this ratio?
It must decrease by 24.5 units.
It must increase by 24.5 units.
It must decrease by 7 units.
It must increase by 7 units.
Show solution
Answer: B β It must increase by 24.5 units.
Length Γ· width = \(\dfrac{35}{10} = 3.5\), so length is always 3.5 Γ width. Any change in width must be matched by 3.5 Γ that change in length:
\[\Delta L = 3.5 \times 7 = 24.5\]
The width went up, so the length must also go up β by 24.5 units.
D adds the same amount to both, which changes the ratio (e.g. 35:10 β 42:17). A and C move in the wrong direction.
Q18Functions
Square P has a side length of \(x\) inches. Square Q has a perimeter that is 176 inches greater than the perimeter of square P. The function \(f\) gives the area of square Q, in square inches. Which of the following defines \(f\)?
\(f(x) = (x + 44)^2\)
\(f(x) = (x + 176)^2\)
\(f(x) = (176x + 44)^2\)
\(f(x) = (176x + 176)^2\)
Show solution
Answer: A β \(f(x) = (x + 44)^2\)
Perimeter of P = \(4x\). Perimeter of Q = \(4x + 176\). Side of Q = \(\dfrac{4x + 176}{4} = x + 44\). Area of Q = side squared:
\[f(x) = (x + 44)^2\]
B adds 176 to the side β but 176 is extra perimeter, spread over 4 sides.
Method: Convert perimeter to side (Γ· 4) before squaring for area.
Q19Radicals & Rearranging
The given equation relates the distinct positive real numbers \(w\), \(x\), and \(y\). Which equation correctly expresses \(w\) in terms of \(x\) and \(y\)?
\[\frac{14x}{7y} = 2\sqrt{w + 19}\]
\(w = \sqrt{\dfrac{x}{y}} - 19\)
\(w = \sqrt{\dfrac{28x}{14y}} - 19\)
\(w = \left(\dfrac{x}{y}\right)^2 - 19\)
\(w = \left(\dfrac{28x}{14y}\right)^2 - 19\)
Show solution
Answer: C β \(w = \left(\dfrac{x}{y}\right)^2 - 19\)
Simplify the left side: \(\dfrac{14x}{7y} = \dfrac{2x}{y}\). Divide both sides by 2:
\[\frac{x}{y} = \sqrt{w + 19}\]
Square both sides, then subtract 19:
\[\left(\frac{x}{y}\right)^2 = w + 19 \quad\Longrightarrow\quad w = \left(\frac{x}{y}\right)^2 - 19\]
A and B take a square root instead of squaring. D forgets to divide by 2 β \(\dfrac{28x}{14y} = \dfrac{2x}{y}\), which is double the correct base.
Q20Circles
Point \(O\) is the center of a circle. The measure of arc \(RS\) on this circle is 100Β°. What is the measure, in degrees, of its associated angle \(ROS\)?
Student-produced response β enter your own answer.
Show solution
Answer: 100
Angle \(ROS\) has its vertex at the centre β it is a central angle. A central angle always equals the measure of the arc it cuts off: 100Β°.
The trap: 50Β° is the answer for an inscribed angle (vertex on the circle), which is half the arc. Here the vertex is the centre \(O\).
Rule: central angle = arc; inscribed angle = Β½ arc.
Q21Exponents & Radicals
The expression \(6\sqrt[5]{3^5x^{45}} \cdot \sqrt[8]{2^8x}\) is equivalent to \(ax^b\), where \(a\) and \(b\) are positive constants and \(x > 1\). What is the value of \(a + b\)?
Student-produced response β enter your own answer.
Show solution
Answer: 361/8 (or 45.12, 45.13)
Take each root separately using \(\sqrt[n]{u^m} = u^{m/n}\):
Grid as 361/8 (five characters) or a truncated/rounded decimal, 45.12 or 45.13.
Common slip: treating \(\sqrt[8]{x}\) as \(x^8\) or forgetting it entirely. Only the \(x\) inside the eighth root is un-powered, so its exponent is \(\tfrac18\).
Grid-in length: 45.125 is six characters β too long. Use the fraction or cut to 4 digits.
Q22Right Triangles & Radicals
A right triangle has sides of length \(2\sqrt{2}\), \(6\sqrt{2}\), and \(\sqrt{80}\) units. What is the area of the triangle, in square units?
\(8\sqrt{2} + \sqrt{80}\)
12
\(24\sqrt{80}\)
24
Show solution
Answer: B β 12
First identify the hypotenuse (the longest side): \(\sqrt{80} \approx 8.94\) vs \(6\sqrt2 \approx 8.49\). Check with Pythagoras:
D (24) forgets the Β½. A is part of the perimeter. C multiplies by the hypotenuse, which is not a height.
Q23Quadratics (Factoring)
The expression \(4x^2 + bx - 45\), where \(b\) is a constant, can be rewritten as \((hx + k)(x + j)\), where \(h\), \(k\), and \(j\) are integer constants. Which of the following must be an integer?
\(\dfrac{b}{h}\)
\(\dfrac{b}{k}\)
\(\dfrac{45}{h}\)
\(\dfrac{45}{k}\)
Show solution
Answer: D β \(\dfrac{45}{k}\)
Expand:
\[(hx + k)(x + j) = hx^2 + (hj + k)x + kj\]
Match coefficients with \(4x^2 + bx - 45\): \(h = 4\), \(b = hj + k\), and \(kj = -45\).
Since \(kj = -45\), we have \(\dfrac{45}{k} = -j\), and \(j\) is an integer. So \(\dfrac{45}{k}\) is always an integer.
C: \(\frac{45}{4}\) is not an integer. A and B depend on the factorization β e.g. \((4x + 5)(x - 9)\): \(b = -31\), and \(-\frac{31}{4}\) and \(-\frac{31}{5}\) are not integers. But \(\frac{45}{5} = 9\) β.
Method: "Must be" questions: one counterexample kills a choice. Build a quick factorization and test.
Q24Systems (Linear & Quadratic)
In the given system of equations, \(a\) is a constant. The graphs of the equations in the given system intersect at exactly one point, \((x, y)\), in the \(xy\)-plane. What is the value of \(x\)?
\[y = 2x^2 - 21x + 64 \qquad y = 3x + a\]
\(-8\)
\(-6\)
6
8
Show solution
Answer: C β 6
Set the equations equal:
\[2x^2 - 21x + 64 = 3x + a \quad\Longrightarrow\quad 2x^2 - 24x + (64 - a) = 0\]
Exactly one intersection means this quadratic has exactly one (double) root. A double root sits at the vertex, \(x = -\dfrac{b}{2a}\):
\[x = \frac{24}{2 \cdot 2} = 6\]
(For completeness, the discriminant \(576 - 8(64 - a) = 0\) gives \(a = -8\), and the line is tangent at \(x = 6\).)
D (8) is the value of \(-a\), and A (β8) is \(a\) β both answer a different question. B has the wrong sign.
Method: When a line is tangent to a parabola, you don't need \(a\) to find \(x\): the double root is \(-\frac{b}{2a}\) of the combined quadratic.
Q25Right Triangles
An isosceles right triangle has a hypotenuse of length 58 inches. What is the perimeter, in inches, of this triangle?
\(29\sqrt2\)
\(58\sqrt2\)
\(58 + 58\sqrt2\)
\(58 + 116\sqrt2\)
Show solution
Answer: C β \(58 + 58\sqrt2\)
In a 45Β°β45Β°β90Β° triangle, hypotenuse = leg Γ \(\sqrt2\), so each leg is
A is one leg. B is both legs without the hypotenuse. D treats 58 as a leg length (legs would be 58 and hypotenuse \(58\sqrt2\) β that perimeter is \(116 + 58\sqrt2\), which isn't offered either).
Q26Quadratics (Vertex Form)
In the \(xy\)-plane, a parabola has vertex \((9, -14)\) and intersects the \(x\)-axis at two points. If the equation of the parabola is written in the form \(y = ax^2 + bx + c\), where \(a\), \(b\), and \(c\) are constants, which of the following could be the value of \(a + b + c\)?
\(-23\)
\(-19\)
\(-14\)
\(-12\)
Show solution
Answer: D β \(-12\)
The key insight: \(a + b + c\) is just \(y\) when \(x = 1\).
The vertex \((9, -14)\) is below the \(x\)-axis, and the parabola crosses the axis twice, so it must open upward: \(a > 0\). Its minimum value is \(-14\), reached only at \(x = 9\).
At \(x = 1\) (not the vertex) the value must be strictly greater than \(-14\). Only \(-12\) qualifies.
A and B are below the minimum. C equals the minimum, which happens only at the vertex \(x = 9\), not at \(x = 1\).
Method: \(a + b + c = f(1)\) is a classic SAT shortcut. Likewise \(c = f(0)\) and \(a - b + c = f(-1)\).
Q27Exponential Functions
Function \(f\) is defined by \(f(x) = -a^x + b\), where \(a\) and \(b\) are constants. In the \(xy\)-plane, the graph of \(y = f(x) - 15\) has a \(y\)-intercept at \(\left(0, -\frac{99}{7}\right)\). The product of \(a\) and \(b\) is \(\frac{65}{7}\). What is the value of \(a\)?
Student-produced response β enter your own answer.
Show solution
Answer: 5
At \(x = 0\), \(a^0 = 1\), so \(f(0) = -1 + b\). The \(y\)-intercept of \(y = f(x) - 15\) is therefore
\[-1 + b - 15 = -\frac{99}{7} \quad\Longrightarrow\quad b = 16 - \frac{99}{7} = \frac{112 - 99}{7} = \frac{13}{7}\]
The line graph shows the estimated number of chipmunks in a state park on April 1 of each year from 1989 to 1999. Based on the line graph, in which year was the estimated number of chipmunks in the state park the greatest?
1989
1994
1995
1998
Show solution
Answer: B β 1994
Find the highest point on the line. It is the sharp spike at 1994, a little above 150 β higher than every other year.
A (1989) is one of the lowest points (about 40). C (1995) is the dip straight after the peak. D (1998) is another low point (about 50).
Q2Unit Conversion
A fish swam a distance of 5,104 yards. How far did the fish swim, in miles? (1 mile = 1,760 yards)
C subtracts (5,104 β 1,760) and D adds. A divides the wrong way round (1,760 Γ· 5,104 β 0.34).
Method: Miles are bigger than yards, so the number of miles must be smaller than 5,104 β divide.
Q3Polynomials
Which expression is equivalent to \(12x^3 - 5x^3\)?
\(7x^6\)
\(17x^3\)
\(7x^3\)
\(17x^6\)
Show solution
Answer: C β \(7x^3\)
These are like terms (same variable, same power), so subtract the coefficients and keep \(x^3\) unchanged: \(12 - 5 = 7\), giving \(7x^3\).
A and D add the exponents β that only happens when you multiply powers. B and D add the coefficients instead of subtracting.
Q4Systems of Equations
What is the solution \((x, y)\) to the given system of equations?
\[x + y = 18 \qquad 5y = x\]
\((15, 3)\)
\((16, 2)\)
\((17, 1)\)
\((18, 0)\)
Show solution
Answer: A β \((15, 3)\)
Substitute \(x = 5y\) into the first equation:
\[5y + y = 18 \;\Rightarrow\; 6y = 18 \;\Rightarrow\; y = 3, \quad x = 5(3) = 15\]
Fastest check: every choice satisfies \(x + y = 18\), so just test \(5y = x\): only \(5(3) = 15\) works.
Q5Inequalities
The point \((8, 2)\) in the \(xy\)-plane is a solution to which of the following systems of inequalities?
\(x > 0\) and \(y > 0\)
\(x > 0\) and \(y < 0\)
\(x < 0\) and \(y > 0\)
\(x < 0\) and \(y < 0\)
Show solution
Answer: A β \(x > 0\) and \(y > 0\)
Both coordinates are positive: \(8 > 0\) and \(2 > 0\). The point is in Quadrant I, which is exactly the region \(x > 0,\ y > 0\).
Q6Absolute Value
What is one possible solution to the given equation?
\[|x - 5| = 10\]
Student-produced response β enter your own answer.
Show solution
Answer: 15 (or β5)
The expression inside the bars is either 10 or β10:
\[x - 5 = 10 \;\Rightarrow\; x = 15 \qquad\text{or}\qquad x - 5 = -10 \;\Rightarrow\; x = -5\]
Either 15 or β5 is accepted.
Method: \(|x - 5| = 10\) means "\(x\) is 10 units away from 5" β so 5 + 10 or 5 β 10.
Q7Linear Functions
The function \(f(x) = 7x + 1\) gives the total number of people on a company retreat with \(x\) managers. What is the total number of people on a company retreat with 7 managers?
Student-produced response β enter your own answer.
Show solution
Answer: 50
\[f(7) = 7(7) + 1 = 50\]
Q8Functions (Tables)
For the function \(h(x) = x^2 - 3\), which table gives three values of \(x\) and their corresponding values of \(h(x)\)?
D gets the first two right but uses \(3 \cdot 2 - 3\) instead of \(3^2 - 3\) for the last. A computes \(x + 3\). C computes \(2x - 3\).
Method: Test the last column first β that's where \(x^2\) grows away from linear guesses.
Q9Exponential Functions
The function \(f\) is defined by \(f(x) = 270(0.1)^x\). What is the value of \(f(0)\)?
0
1
27
270
Show solution
Answer: D β 270
Any nonzero number to the power 0 is 1: \(f(0) = 270(0.1)^0 = 270 \cdot 1 = 270\).
A treats the power as multiplying by 0. B is \((0.1)^0\) alone. C is \(f(1)\).
Method: For \(f(x) = a \cdot b^x\), \(f(0) = a\) β the initial value β always.
Q10Statistics (Margin of Error)
To estimate the proportion of a population that has a certain characteristic, a random sample was selected from the population. Based on the sample, it is estimated that the proportion of the population that has the characteristic is 0.49, with an associated margin of error of 0.04. Based on this estimate and margin of error, which of the following is the most appropriate conclusion about the proportion of the population that has the characteristic?
It is plausible that the proportion is between 0.45 and 0.53.
It is plausible that the proportion is less than 0.45.
The proportion is exactly 0.49.
It is plausible that the proportion is greater than 0.53.
Show solution
Answer: A
The plausible range is estimate Β± margin of error: \(0.49 - 0.04 = 0.45\) to \(0.49 + 0.04 = 0.53\).
B and D are outside the plausible interval. C ignores sampling error β a sample never pins down the exact population value.
Q11Linear Inequalities
A moving truck can tow a trailer if the combined weight of the trailer and the boxes it contains is no more than 4,600 pounds. What is the maximum number of boxes this truck can tow in a trailer with a weight of 500 pounds if each box weighs 120 pounds?
Method: Stuck factoring? The quadratic formula (or graphing both sides on a calculator) gets you there too.
Q13Probability
Red
Blue
Yellow
Total
Square
10
20
25
55
Pentagon
20
10
15
45
Total
30
30
40
100
The table summarizes the distribution of color and shape for 100 tiles of equal area. If one of these tiles is selected at random, what is the probability of selecting a red tile? (Express your answer as a decimal or fraction, not as a percent.)
Student-produced response β enter your own answer.
Method: Use the Total row: red = 10 squares + 20 pentagons = 30.
Q14Linear Functions
For the function \(f(x) = 2x + 3\), the graph of \(y = f(x)\) in the \(xy\)-plane is parallel to line \(j\). What is the slope of line \(j\)?
Student-produced response β enter your own answer.
Show solution
Answer: 2
Parallel lines have equal slopes. The slope of \(y = 2x + 3\) is 2, so line \(j\) has slope 2.
Method: Perpendicular would be the negative reciprocal (\(-\tfrac12\)) β read carefully which one is asked.
Q15Systems (Word Problem)
A proposal for a new library was included on an election ballot. A radio show stated that 3 times as many people voted in favor of the proposal as people who voted against it. A social media post reported that 15,000 more people voted in favor of the proposal than voted against it. Based on these data, how many people voted against the proposal?
7,500
15,000
22,500
45,000
Show solution
Answer: A β 7,500
Let \(a\) = votes against. Then votes in favour = \(3a\), and
\[3a - a = 15{,}000 \;\Rightarrow\; 2a = 15{,}000 \;\Rightarrow\; a = 7{,}500\]
Check: 22,500 in favour β 7,500 against = 15,000 β
C (22,500) is the number in favour. B treats the difference as the number against.
Q16Parallel Lines & Angles
Note: Figure not drawn to scale.
In the figure, lines \(m\) and \(n\) are parallel. If \(x = 6k + 13\) and \(y = 8k - 29\), what is the value of \(z\)?
Step 2 β move to line \(n\): angle \(z\) matches the acute angle at line \(m\) (corresponding angles are equal), and the acute and obtuse angles at an intersection are supplementary:
\[z = 180 - 139 = 41\]
D (139) is \(x\), the obtuse angle. B (21) is \(k\), not an angle. A comes from solving \(x + y = 180\) incorrectly.
Method: With parallel lines there are only two angle sizes: every acute angle is equal, every obtuse angle is equal, and acute + obtuse = 180Β°.
Q17Linear Equations (No Solution)
In the given equation, \(p\) is a constant. The equation has no solution. What is the value of \(p\)?
\[-3x + 21px = 84\]
0
\(\frac{1}{7}\)
\(\frac{4}{3}\)
4
Show solution
Answer: B β \(\frac{1}{7}\)
Factor out \(x\):
\[x(21p - 3) = 84\]
If \(21p - 3 \ne 0\), you can divide and get a solution. The only way to have no solution is for the coefficient to vanish, giving \(0 = 84\) (false):
\[21p - 3 = 0 \;\Rightarrow\; p = \tfrac{1}{7}\]
Method: A linear equation has no solution when the \(x\)-terms cancel but the constants don't.
Q18Quadratics (Vertex)
The function \(f\) is defined by \(f(x) = (x - 10)(x + 13)\). For what value of \(x\) does \(f(x)\) reach its minimum?
\(-130\)
\(-13\)
\(-\frac{23}{2}\)
\(-\frac{3}{2}\)
Show solution
Answer: D β \(-\frac{3}{2}\)
The zeros are \(x = 10\) and \(x = -13\). A parabola is symmetric, so its vertex lies halfway between them:
\[x = \frac{10 + (-13)}{2} = -\frac{3}{2}\]
It opens upward (leading coefficient +1), so the vertex is a minimum.
A is \(f(0)\), the \(y\)-intercept. B is a zero. C is \(\frac{-13 - 10}{2}\) β the wrong sign on 10.
Q19Quadratics (Interpreting)
The function \(f(x) = \frac{1}{9}(x - 7)^2 + 3\) gives a metal ball's height above the ground \(f(x)\), in inches, \(x\) seconds after it started moving on a track, where \(0 \le x \le 10\). Which of the following is the best interpretation of the vertex of the graph of \(y = f(x)\) in the \(xy\)-plane?
The metal ball's minimum height was 3 inches above the ground.
The metal ball's minimum height was 7 inches above the ground.
The metal ball's height was 3 inches above the ground when it started moving.
The metal ball's height was 7 inches above the ground when it started moving.
Show solution
Answer: A
In vertex form \(a(x - h)^2 + k\), the vertex is \((h, k) = (7, 3)\). Since \(a = \tfrac19 > 0\), the parabola opens up, so the vertex is the minimum: the lowest height is 3 inches, reached at 7 seconds.
B and D read 7 (a time) as a height. C: the start is \(x = 0\), where \(f(0) = \tfrac{49}{9} + 3 \approx 8.4\) inches, not 3.
Q20Trigonometry
In triangle \(JKL\), \(\cos(K) = \frac{24}{51}\) and angle \(J\) is a right angle. What is the value of \(\cos(L)\)?
Student-produced response β enter your own answer.
Show solution
Answer: 15/17 (or .8823, .8824)
With the right angle at \(J\), the hypotenuse is \(KL\). \(\cos K = \dfrac{\text{adjacent}}{\text{hypotenuse}} = \dfrac{JK}{KL} = \dfrac{24}{51}\), so take \(JK = 24,\ KL = 51\).
(since \(\sqrt{2704} = 52\)). The greatest positive integer below 52 is 51.
The trap: 52 makes the discriminant exactly 0, which gives one real solution β not zero solutions.
Q22Systems of Equations
If a new graph of three linear equations is created using the system of equations shown and the equation \(x + 4y = -16\), how many solutions \((x, y)\) will the resulting system of three equations have?
Zero
Exactly one
Exactly two
Infinitely many
Show solution
Answer: A β Zero
A solution to all three equations must lie on all three lines. The only point on both graphed lines is \((8, 2)\). Test it in the new equation:
\[8 + 4(2) = 16 \ne -16\]
So no point satisfies all three: zero solutions.
(In fact \(x + 4y = -16\) is \(y = -\tfrac14 x - 4\), parallel to the slanted line \(y = -\tfrac14 x + 4\) β they never meet.)
Method: A system's solutions must satisfy every equation. Find the existing solution, then test it in the new equation.
Q23Exponential Functions
The function \(f(x) = 5{,}470(0.64)^{x/12}\) gives the value, in dollars, of a certain piece of equipment after \(x\) months of use. If the value of the equipment decreases each year by \(p\%\) of its value the preceding year, what is the value of \(p\)?
4
5
36
64
Show solution
Answer: C β 36
One year = 12 months. Each time \(x\) grows by 12, the exponent \(\tfrac{x}{12}\) grows by 1, so the value is multiplied by 0.64 once per year.
Multiplying by 0.64 means keeping 64% β a decrease of \(100 - 64 = 36\%\).
D (64) is the percent remaining, not the percent lost. A and B try to convert to a monthly rate, which isn't asked.
Q24Statistics (Transformations)
The dot plot represents the 15 values in data set A. Data set B is created by adding 56 to each of the values in data set A. Which of the following correctly compares the medians and the ranges of data sets A and B?
The median of data set B is equal to the median of data set A, and the range of data set B is equal to the range of data set A.
The median of data set B is equal to the median of data set A, and the range of data set B is greater than the range of data set A.
The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.
The median of data set B is greater than the median of data set A, and the range of data set B is greater than the range of data set A.
Show solution
Answer: C
Adding the same number to every value shifts the data. Measures of centre (median, mean) shift by 56; measures of spread (range, SD) don't change, because every gap between values stays the same.
Here: median A = 23 (8th value), median B = 79. Range A = 26 β 22 = 4 = range B.
Rule: add a constant β centre moves, spread stays. Multiply by a constant β both change.
Q25Circles
The equation \(x^2 + (y - 1)^2 = 49\) represents circle A. Circle B is obtained by shifting circle A down 2 units in the \(xy\)-plane. Which of the following equations represents circle B?
\((x - 2)^2 + (y - 1)^2 = 49\)
\(x^2 + (y - 3)^2 = 49\)
\((x + 2)^2 + (y - 1)^2 = 49\)
\(x^2 + (y + 1)^2 = 49\)
Show solution
Answer: D β \(x^2 + (y + 1)^2 = 49\)
Circle A has centre \((0, 1)\), radius 7. Moving down 2 gives centre \((0, -1)\), same radius:
B moves the centre up to \((0, 3)\). A and C shift horizontally.
Method: Shift the centre first, then rewrite. It avoids sign confusion inside the brackets.
Q26Surface Area
Two identical rectangular prisms each have a height of 90 centimeters (cm). The base of each prism is a square, and the surface area of each prism is \(K\) cmΒ². If the prisms are glued together along a square base, the resulting prism has a surface area of \(\frac{92}{47}K\) cmΒ². What is the side length, in cm, of each square base?
4
8
9
16
Show solution
Answer: B β 8
Let the base side be \(s\). One prism: two square faces + four side faces:
Equivalently: the increase is \(210 - 30 = 180\), and \(\frac{180}{30} = 6 = 600\%\).
The trap: 700 β 210 is 700% of 30, but only 600% greater than 30.
Complete Answer Key
For fast self-scoring. Work each question first, then check here β and return to the full solution for anything you missed.
Scoring note. This is an adaptive-format test: your performance on Module 1 determines which Module 2 you receive on the real digital SAT. Raw-score-to-scaled-score conversion tables are published by College Board with the official test; count your raw correct answers per section here, then convert using their table.
Reading & Writing
Q
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
Mod 1
B
A
A
C
A
B
D
B
B
D
C
D
A
B
C
A
A
Mod 2
D
D
B
B
B
B
A
C
C
A
A
B
D
C
C
A
B
Q
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
Mod 1
A
A
D
D
D
B
C
B
A
C
D
A
A
D
D
C
Mod 2
D
C
A
B
D
D
A
B
B
A
A
C
C
A
A
B
Math
Q
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mod 1
B
A
B
D
A
9
10
A
B
D
A
C
1/5
80
Mod 2
B
B
C
A
A
15
50
B
D
A
A
B
3/10
2
Q
15
16
17
18
19
20
21
22
23
24
25
26
27
Mod 1
D
B
B
A
C
100
361/8
B
D
C
C
D
5
Mod 2
A
C
B
D
A
15/17
51
A
C
C
D
B
600
Where to go next. Track which question types you missed, not just how many. The tags on each card (Words in Context, Transitions, Quadratics, Similar Trianglesβ¦) let you group your errors and target practice where it actually pays. Two or more misses in one tag is a topic to drill.