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B1-C1 PSAT 10

PSAT 10 Practice Tests

6 full practice tests for the digital PSAT 10, covering both sections: Reading and Writing and Math. Each test follows the real adaptive design: in each section, your Module 1 score decides whether you get a harder or an easier Module 2. Reading and Writing modules have 27 questions in 32 minutes; Math modules have 22 questions in 35 minutes, with a calculator allowed. Every question has an explanation, and you get a practice score estimate from 320 to 1520. The first 3 tests are free; the other 3 come with 7ESL Pro.

6practice tests
134minutes per test
2papers
3free tests

PSAT 10 Practice Test 1 with Answers

A free, interactive PSAT 10 practice test with answers, about 134 minutes.

TopicsMeteor showersPetra's water engineeringEmoji and written toneBiodegradable plastics from milkOtters and kelpFood trucks and city planningThe history of the lightbulb filamentJumping spider visionWoodcut revival in picture booksA summer lifeguard (original story)

This PSAT 10 Practice Test 1 has 4 papers — Reading and Writing: Module 1, Reading and Writing: Module 2, Math: Module 1 and Math: Module 2. Choose a paper below to start; your browser will load the interactive version automatically.

Reading and Writing: Module 1

Question 1

In many dry regions, households install systems that collect the rain falling on their roofs. Gutters and pipes _____ the water into large storage tanks, where it can be kept for weeks until it is needed for watering gardens or flushing toilets.

  1. Which choice completes the text with the most logical and precise word or phrase? (A) dilute (B) channel (C) conceal (D) scatter

Question 2

The following text is from an original short story written for this practice test. Keisha, seventeen, is working her first summer as a lifeguard at a crowded lake beach.

For her first week on the job, Keisha had climbed the tall white chair each morning expecting drama: a swimmer in trouble, a daring rescue. Instead, the work proved to be a matter of _____ attention: hour after hour of scanning the same stretch of water, counting heads, and noting who had drifted too close to the ropes.

  1. Which choice completes the text with the most logical and precise word or phrase? (A) fleeting (B) sustained (C) reluctant (D) occasional

Question 3

Several contemporary picture-book illustrators have returned to the woodcut, a printing method in which an image is carved into a block of wood, inked, and pressed onto paper. Because a carver can remove wood but never add it back, each cut is _____: a slip of the knife cannot be erased, so artists must plan every line before they begin.

  1. Which choice completes the text with the most logical and precise word or phrase? (A) irreversible (B) decorative (C) tentative (D) inexpensive

Question 4

For decades, many psychologists regarded the “hot hand,” the belief that a basketball player who has made several shots in a row is more likely to make the next one, as _____: early statistical studies found no sign that players’ success rates rose after a streak. More recent analyses, however, have identified a subtle flaw in those studies’ methods and suggest that a modest hot hand may be real after all.

  1. Which choice completes the text with the most logical and precise word or phrase? (A) warranted (B) contagious (C) illusory (D) deliberate

Question 5

Potter wasps get their name from the tiny nests that the females build: rounded, jug-shaped containers, often smaller than a marble, made of mud that a wasp moistens with water and shapes with her jaws. When a pot is finished, the female fills it with caterpillars that she has paralyzed with her sting, lays a single egg inside, and seals the opening. The larva that hatches feeds on the stored caterpillars and stays inside the sealed pot until it has grown into an adult wasp.

  1. Which choice best describes the main purpose of the text? (A) To explain how scientists discovered what potter wasps store inside their nests (B) To compare the nests of potter wasps with the nests built by other kinds of wasps (C) To argue that potter wasps are more skilled builders than any other insect (D) To describe a structure that female potter wasps build and indicate the role it plays in raising their young

Question 6

The following text is from an original poem written for this practice test.

Outside, the fields lie buried and unmoving,
the fence posts capped in white, the sky gone gray;
only the crows keep up their dull complaining,
and even they fall silent by midday.
But here, beneath the fogged and sweating glass,
the tomato vines are climbing toward the light,
and Grandfather, humming, lets the hours pass
among green leaves that never heard of night.

  1. Which choice best describes the overall structure of the text? (A) It describes a cold, lifeless scene outdoors and then contrasts it with the warmth and growth inside a greenhouse. (B) It describes plants growing inside a greenhouse and then explains how the speaker’s grandfather built it. (C) It presents the speaker’s dislike of winter and then describes a decision to leave the countryside. (D) It traces a gradual change in the weather from the start of winter to the arrival of spring.

Question 7

In film, many everyday sounds are not recorded during shooting but are added later by Foley artists, who perform sounds in a studio while watching the footage. Their substitutions can be surprising: the crunch of footsteps in snow might be made by squeezing a pouch of cornstarch, and a bird’s flapping wings by shaking a pair of leather gloves. Such tricks are not merely conveniences. Microphones on a busy set are positioned to capture dialogue, so they often pick up the real sounds of movement faintly or not at all; moreover, a genuine sound does not always sound on screen the way audiences expect it to. Foley thus allows filmmakers to give sounds the clarity and character that make a scene feel real.

  1. Which choice best describes the function of the underlined sentence in the text as a whole? (A) It summarizes the examples of substitutions described in the previous sentence. (B) It concedes that filmmakers rely on Foley mainly because it saves time and money. (C) It signals that the text will go on to explain why Foley serves a purpose beyond making filmmaking easier. (D) It introduces a criticism of the unusual materials that Foley artists use.

Question 8

Many cities restrict where food trucks may park, often barring them from operating within a set distance of a restaurant. Supporters of such rules, including urban policy analyst Gavin Rourke, frame the restrictions as a matter of fairness: restaurants pay rent and property taxes for their locations, and a truck that parks outside can capture their customers without bearing any of those costs.

Urban planner Leah Whitcombe mapped food truck locations and restaurant sales in several mid-sized cities over five years. She found that blocks where trucks regularly gathered saw rising restaurant sales, not falling ones, because the trucks drew pedestrians into areas they had previously passed through. Trucks and restaurants, Whitcombe argues, are less often competitors for a fixed pool of diners than partners in creating one.

  1. Based on the texts, how would Whitcombe (Text 2) most likely respond to the reasoning of supporters of the restrictions such as Rourke (Text 1)? (A) By agreeing that food trucks should be required to pay the same taxes that restaurants pay (B) By arguing that the reasoning wrongly assumes that trucks take customers from restaurants rather than bringing more customers to an area (C) By suggesting that the restrictions are fair only in cities where restaurants pay unusually high rents (D) By pointing out that most food trucks operate in areas where there are no restaurants nearby

Question 9

The following text is from an original short story written for this practice test. Nadia is having her first driving lesson with her older sister.

Nadia gripped the steering wheel so tightly that her knuckles went pale, and when the car lurched forward she gasped. Her older sister, Amira, only leaned back in the passenger seat. “You’re doing fine,” she said, as if they were chatting over breakfast. “Just let it roll.” They circled the empty parking lot once, then again. By the fourth lap, Nadia’s shoulders had dropped, her hands had loosened on the wheel, and she was laughing at one of Amira’s terrible jokes.

  1. Which choice best states the main idea of the text? (A) Nadia becomes frustrated when her sister refuses to give her detailed instructions. (B) Nadia grows more relaxed during her driving lesson, helped by her sister’s calm manner. (C) Amira worries that Nadia is not yet ready to drive outside the parking lot. (D) Nadia is embarrassed when the car lurches forward in front of other drivers.

Question 10

Meteor showers occur when Earth passes through streams of debris left behind by comets. Each time a comet nears the Sun, heat frees dust and small rocky particles that then spread out along the comet’s orbit. Because Earth crosses a given stream at about the same point in its own orbit every year, a shower recurs on roughly the same dates annually; the Perseids, for example, return each August. The number of meteors varies from year to year, however, because debris is not spread evenly along a stream: when Earth passes through a denser, more recently shed trail, observers may see far more meteors than usual.

  1. Which choice best states the main idea of the text? (A) The Perseids produce more meteors than any other shower because their debris stream is especially dense. (B) Comets release more debris each time they approach the Sun, so meteor showers are gradually becoming stronger. (C) Astronomers can predict both the dates of a meteor shower and the exact number of meteors that observers will see. (D) Meteor showers return at predictable times each year, but their intensity varies with how densely debris is packed where Earth crosses a stream.

Question 11

Jumping spiders have eight eyes, but they rely most on two pairs. Their large, forward-facing principal eyes produce sharp images but view only a narrow area at a time, while a pair of smaller secondary eyes on the sides of the head cover a much wider field with less detail. Biologist Nora Pettigrew hypothesizes that the secondary eyes serve mainly as motion detectors: they alert a spider to movement nearby, after which the spider turns its body so that its principal eyes can examine the object.

  1. Which finding, if true, would most directly support Pettigrew’s hypothesis? (A) When the secondary eyes of jumping spiders were temporarily covered, the spiders rarely turned toward objects moving at their sides, though they turned readily when only the principal eyes were covered. (B) The principal eyes of jumping spiders contain many more light-sensitive cells than their secondary eyes do. (C) Jumping spiders turned toward motionless objects placed at their sides as often as they turned toward moving objects. (D) Jumping spiders hunt mainly during daylight hours, when their prey is most active.

Question 12

“The Final Round” is an original short story written for this practice test. In the story, the narrator, a teacher named Mr. Hale, describes how Priyanka, one of his students, reacts when she learns that she has reached the final round of a regional spelling bee. Mr. Hale suggests that Priyanka’s calm appearance conceals considerable nervousness.

  1. Which quotation from “The Final Round” most effectively illustrates the claim? (A) “Priyanka had studied the word lists for months, sometimes whispering spellings to herself on the bus to school.” (B) “Priyanka went pale when she heard, and her voice shook as she asked whether her parents had found seats in the audience.” (C) “Priyanka nodded at the announcement as if she had been told the time, but when she reached for her water bottle, it took her three tries to unscrew the cap.” (D) “Priyanka smiled at the judges and told them she was ready, and for once she found that she truly believed it.”

Question 13

Written messages lack the tone of voice and facial expressions that help listeners interpret spoken words, and some researchers believe that emoji partly fill that gap. Linguist Tessa Monroe showed participants the same short workplace message, a request to send a file, in three versions and asked whether it seemed friendly. The version with a smiling emoji was judged friendly far more often than the version with no emoji: _____

  1. Which choice most effectively uses data from the graph to complete the statement? (A) 63% of participants judged the thumbs-up version friendly, compared with 42% for the version with no emoji. (B) 42% of participants judged the version with no emoji friendly. (C) 81% of participants judged the smiling-emoji version friendly, compared with 63% for the thumbs-up version. (D) 81% of participants judged the smiling-emoji version friendly, compared with 42% for the version with no emoji.

Question 14

Casein, the main protein in milk, can be formed into thin, flexible films that might replace some plastic packaging, and unlike most plastics, casein films break down in soil. Materials engineer Owen Tate made casein films containing different amounts of glycerol, a softening additive, and measured how long each took to break down in soil and how much pulling force it could withstand before tearing (its tensile strength). Tate concluded that adding glycerol involves a trade-off between how quickly a film breaks down and how durable it is in use: _____

  1. Which choice most effectively uses data from the table to complete the statement? (A) films with 30% glycerol broke down in 24 days, compared with 60 days for films with no glycerol, but their tensile strength was only 5 MPa, compared with 18 MPa. (B) films with 30% glycerol broke down in 24 days, less than half the time taken by films with no glycerol. (C) films with no glycerol had a tensile strength of 18 MPa, the highest of any film tested. (D) films with 10% glycerol broke down in 45 days, while films with 20% glycerol had a tensile strength of 9 MPa.

Question 15

Petra, the ancient Nabataean city carved into cliffs in what is now southern Jordan, receives little rain, and most of it falls in a few intense winter storms. To protect the narrow gorge that served as the city’s main entrance from flash floods, the Nabataeans built a dam and a diversion tunnel, and they carved channels and cisterns to capture runoff. Archaeologists have also uncovered, near the city center, the remains of a large ornamental pool with an island pavilion, surrounded by gardens. Since such a display required a lavish use of water in a desert, where every cistern mattered, these findings suggest that _____

  1. Which choice most logically completes the text? (A) Petra’s water systems may have served not only to meet residents’ basic needs but also to display the city’s wealth and ingenuity. (B) the Nabataeans built the pool and gardens mainly to store water for use during droughts. (C) flash floods were less of a threat to Petra than the dam and tunnel would seem to indicate. (D) Petra’s residents grew most of their food in gardens near the city center.

Question 16

Early incandescent light bulbs used filaments made of carbonized materials such as bamboo fiber, which glowed when an electric current passed through them but were fragile and wasted much of their power as _____ the 1910s, manufacturers had largely switched to tungsten, a metal with an extremely high melting point.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) heat, by (B) heat by (C) heat; by (D) heat by,

Question 17

Sea otters help protect kelp forests in an indirect _____ by eating sea urchins, which graze on kelp, otters keep urchin populations small enough for the forests to thrive.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) way: (B) way, (C) way (D) way, which

Question 18

The Voynich manuscript—an illustrated book from the early fifteenth century written in a script that no one has ever _____ named after Wilfrid Voynich, the book dealer who acquired it in 1912.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) deciphered—is (B) deciphered, is (C) deciphered; is (D) deciphered is

Question 19

Most colors in nature come from pigments, chemicals that absorb some wavelengths of light and reflect others. The brilliant blue of a morpho butterfly’s wings, which comes not from pigment but from microscopic ridges on the wing scales that reflect blue _____ does not fade over time the way many pigment-based colors do, a property that has interested researchers developing dye-free fabrics and paints.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) light—does (B) light, does (C) light; does (D) light does

Question 20

La Paz, Bolivia, lies in a steep canyon, while the neighboring city of El Alto spreads across a high plain several hundred meters above it. Since 2014, a public cable car network has linked the two cities. Every day, the network’s small cabins _____ passengers over rooftops and up the canyon walls, making in minutes a trip that can take far longer by road.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) carries (B) carry (C) has carried (D) is carrying

Question 21

Sundogs, the bright patches of light that sometimes appear on either side of the Sun, form when sunlight passes through flat, six-sided ice crystals in high clouds. Because the crystals tend to drift with _____ flat faces nearly horizontal, they bend the light at a consistent angle of about 22 degrees.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) its (B) it’s (C) they’re (D) their

Question 22

Hanji, a traditional Korean paper, is prized for its strength and durability; some hanji documents have survived for centuries. Using the inner bark of the paper mulberry tree rather than wood pulp, _____

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) the production of hanji by Korean papermakers yields sheets that resist tearing and yellowing. (B) hanji sheets that resist tearing and yellowing are produced by Korean papermakers. (C) Korean papermakers produce hanji sheets that resist tearing and yellowing. (D) there are hanji sheets, produced by Korean papermakers, that resist tearing and yellowing.

Question 23

A caddisfly larva, which lives on the bottom of streams, builds a protective case in stages. It first spins sticky silk from glands near its mouth. It then gathers tiny pebbles or bits of plants from the streambed and presses them onto the silk, adding pieces until a tube surrounds its soft body. _____ the larva drags the finished case along as it searches for food, pulling back inside whenever danger approaches.

  1. Which choice completes the text with the most logical transition? (A) For example, (B) However, (C) In contrast, (D) Finally,

Question 24

The Uffington White Horse, a stylized figure about 110 meters long on a hillside in southern England, is made of deep trenches filled with crushed white chalk. Dated to roughly 3,000 years ago, it has survived only with help: left alone, the figure would soon vanish beneath creeping grass and soil. _____ nearby communities have gathered periodically for centuries to weed it and pack in fresh chalk, a tradition that continues today.

  1. Which choice completes the text with the most logical transition? (A) Likewise, (B) Consequently, (C) For instance, (D) By contrast,

Question 25

While researching a topic, a student has taken the following notes:

  • Movable books contain paper parts that move when a reader pulls a tab or turns a page.
  • Lothar Meggendorfer (1847–1925) was a German illustrator.
  • In the late 1800s he created dozens of movable books for children.
  • His designs used tiny metal rivets to connect paper levers hidden between the layers of a page.
  • A single pull of a tab could make several parts of a figure move at once.
  1. The student wants to introduce Lothar Meggendorfer to an audience unfamiliar with him. Which choice most effectively uses relevant information from the notes to accomplish this goal? (A) Lothar Meggendorfer (1847–1925), a German illustrator, created dozens of movable books for children in the late 1800s. (B) Movable books contain paper parts that move when a reader pulls a tab or turns a page. (C) A single pull of a tab could make several parts of a figure move at once. (D) Tiny metal rivets connected paper levers hidden between the layers of a page.

Question 26

While researching a topic, a student has taken the following notes:

  • The Chinchorro people lived along the coast of what is now northern Chile and southern Peru.
  • They were fishers and gatherers.
  • They began deliberately mummifying their dead around 5000 BCE.
  • That is centuries before the earliest known evidence of deliberate mummification in Egypt.
  • Chinchorro sites were added to UNESCO’s World Heritage List in 2021.
  1. The student wants to emphasize how early the Chinchorro people practiced mummification. Which choice most effectively uses relevant information from the notes to accomplish this goal? (A) The Chinchorro people, who lived along the coast of what is now northern Chile and southern Peru, were fishers and gatherers. (B) Chinchorro sites were added to UNESCO’s World Heritage List in 2021. (C) Egyptians are known for mummifying their dead, a practice that the Chinchorro people also followed. (D) Around 5000 BCE, centuries before the earliest known evidence of deliberate mummification in Egypt, the Chinchorro people were already deliberately mummifying their dead.

Question 27

While researching a topic, a student has taken the following notes:

  • Norse settlers established colonies in Greenland around 985 CE.
  • The settlements were abandoned by the mid-1400s.
  • One hypothesis holds that a cooling climate shortened growing seasons, making it too hard to raise livestock.
  • Another hypothesis holds that falling demand in Europe for walrus ivory, the colonies’ main export, cut off their income and trade links.
  • Walrus ivory from Greenland was once prized in Europe for carved objects such as chess pieces.
  1. The student wants to contrast the two hypotheses about why the Norse settlements in Greenland were abandoned. Which choice most effectively uses relevant information from the notes to accomplish this goal? (A) Norse settlers established colonies in Greenland around 985 CE, and the settlements were abandoned by the mid-1400s. (B) Walrus ivory from Greenland, the colonies’ main export, was once prized in Europe for carved objects such as chess pieces. (C) While one hypothesis holds that a cooling climate made it too hard for the Greenland Norse to raise livestock, another holds that falling European demand for walrus ivory cut off their income and trade. (D) A cooling climate shortened growing seasons in Greenland, which may explain why the Norse abandoned their settlements there.

Reading and Writing: Module 2

Question 1

Tektites are small pieces of natural glass, often shaped like buttons, teardrops, or dumbbells, that are found scattered across certain regions of Earth. Scientists once debated whether tektites might have come from the Moon, but chemical analyses have shown that they closely match rocks on Earth, _____ the view that they formed when large meteorite impacts melted terrestrial rock and hurled it through the air.

  1. Which choice completes the text with the most logical and precise word or phrase? (A) anticipating (B) undermining (C) bolstering (D) disguising

Question 2

In classic studies of belief perseverance, participants received false feedback suggesting that they were unusually skilled at a task and were later told plainly that the feedback had been invented. Even so, their inflated opinions of their own ability proved _____: many participants continued to rate themselves as better than average at the task.

  1. Which choice completes the text with the most logical and precise word or phrase? (A) conspicuous (B) ephemeral (C) tenacious (D) deliberate

Question 3

Medieval illuminated manuscripts were adorned with gold leaf and brilliant pigments, some ground from costly minerals such as lapis lazuli. Yet the splendor of the finished pages _____ the grueling labor behind them: in the margins, scribes sometimes complained of numb fingers, poor light, and aching backs.

  1. Which choice completes the text with the most logical and precise word or phrase? (A) documents (B) exaggerates (C) celebrates (D) belies

Question 4

The following text is from an original short story written for this practice test. Tomas plays the saxophone on a busy city street corner.

Tomas had long since stopped expecting anyone to pause and listen. Commuters flowed past him like water around a stone, and his music reached them, if at all, only _____: a few bars caught between one crosswalk and the next, a phrase that might follow someone down the subway stairs and then be gone.

  1. Which choice completes the text with the most logical and precise word or phrase? (A) wholesale (B) reluctantly (C) conspicuously (D) piecemeal

Question 5

The toco toucan’s enormous orange bill makes up about a third of the bird’s total length. Naturalists long assumed that the bill served mainly to help the bird reach fruit on thin branches or to attract mates. Studies using heat-sensing cameras have since pointed to an additional role: the bill is laced with blood vessels, and a toucan can send more blood to it on hot days, releasing excess body heat into the air, and then reduce that blood flow when temperatures drop.

  1. Which choice best describes the main purpose of the text? (A) To argue that the toucan’s bill evolved mainly to help the bird attract mates (B) To present evidence for a function of the toucan’s bill beyond the functions that were long assumed (C) To describe how toucans use their bills to reach fruit growing on thin branches (D) To explain how heat-sensing cameras detect blood vessels in animals’ bodies

Question 6

In 1970 the artist Robert Smithson built Spiral Jetty, a coil of black basalt rock and earth about 460 meters long that extends into Utah’s Great Salt Lake. Because the lake’s level rises and falls, the jetty has been submerged and re-exposed several times since its creation, and when visible its rocks are often crusted with white salt crystals. Some viewers regret these changes as damage to the original work. But Smithson was deeply interested in entropy, the tendency of ordered systems to break down over time, and many critics argue that the jetty’s alteration by natural forces is not a threat to the artwork but part of its meaning.

  1. Which choice best describes the overall structure of the text? (A) It describes an artwork and the physical changes it has undergone and then presents a view that treats those changes as meaningful rather than harmful. (B) It describes an artwork, explains how conservators have worked to reverse changes to it, and then evaluates their success. (C) It criticizes an artist’s choice of location for an artwork and then describes how the artist responded to that criticism. (D) It compares two artworks made by the same artist and then explains why one is more admired than the other.

Question 7

The following text is from an original poem written for this practice test.

All August the farm kept its daylight promises:
the hay came in, the creek ran low and clear,
the tractor coughed awake at every dawn.
Tonight the moon comes up enormous, orange,
resting its chin a moment on the barn,
and for once my father sets down the pail,
and for once nobody tells me to hurry.

  1. Which choice best describes the function of the underlined line in the text as a whole? (A) It gives an example of one of the “daylight promises” mentioned in the first line. (B) It marks a shift from a summary of the season’s steady work to a single evening when that work briefly pauses. (C) It explains why the speaker’s father has worked so hard throughout the summer. (D) It introduces a threat to the harvest that the earlier lines described as successful.

Question 8

In an influential early study, researchers asked participants to hold either expansive, open postures, such as leaning back with their hands behind their heads, or closed, hunched postures for two minutes. Participants who held expansive postures reportedly showed changes in hormone levels and were more willing to take risks in a betting game. The researchers concluded that briefly adopting a “power pose” produces physiological changes that make people bolder.

A later team of researchers repeated the experiment with a much larger group of participants. They found no meaningful differences in hormone levels or in willingness to take risks between participants who held expansive postures and those who held closed ones. Participants who held expansive postures did, however, report feeling somewhat more powerful afterward.

  1. Based on the texts, how would the researchers described in Text 2 most likely respond to the conclusion of the researchers described in Text 1? (A) By arguing that holding an expansive posture has no effect of any kind on the people who hold it (B) By agreeing that power poses change hormone levels but questioning whether those changes affect behavior (C) By suggesting that the original study would have been confirmed if participants had held the postures for longer (D) By contending that the evidence supports at most an effect on how powerful people feel, not the physiological and behavioral changes the conclusion describes

Question 9

The following text is from an original short story written for this practice test. Jonah is spending the summer on a crew that maintains mountain hiking trails.

Jonah had signed up for the trail crew picturing himself building bridges over rushing streams. Instead, he spent most of July digging shallow trenches across the path and lining them with flat stones so that rain would drain off the trail instead of running down it. It was slow, muddy work, and no one seemed to notice it. Then, on his last afternoon, a hiker paused beside him, looked back down the mountain, and said it was the first time in years she had climbed this trail without sinking to her ankles. Jonah looked at the row of stones and, for the first time, felt that he had built something.

  1. Which choice best states the main idea of the text? (A) Jonah is proud that he was finally allowed to build a bridge over a stream by the end of the summer. (B) Jonah regrets joining the trail crew because the work turned out to be less exciting than he expected. (C) Jonah wishes that the hikers who use the trail would thank the crew more often for its work. (D) Jonah realizes that unglamorous work he had undervalued makes a real difference to others.

Question 10

The Haleakalā silversword, a spiky, silvery plant found almost nowhere but the upper slopes of a mountain on the Hawaiian island of Maui, may live for decades as a low rosette of leaves before sending up a single tall stalk of flowers, after which it dies. Dense silvery hairs reflect the intense sunlight and help the plant hold moisture in its cold, dry, windy habitat. In the early twentieth century, grazing goats and visitors who uprooted the plants reduced the population drastically, but protection allowed it to rebound. Since the 1990s, however, researchers have documented a sharp decline, which they link to increasingly hot and dry conditions on the mountain.

  1. Which choice best states the main idea of the text? (A) The silversword, well adapted to a harsh habitat and able to recover from earlier threats, is now declining as its environment grows hotter and drier. (B) Because the silversword flowers many times during its life, it has been able to recover quickly from each decline. (C) The silversword’s silvery hairs, once its chief protection, have become the main reason for its recent decline. (D) Grazing goats and careless visitors remain the greatest threat to the silversword’s survival today.

Question 11

Decorator crabs camouflage themselves by attaching bits of algae, sponge, and other materials to tiny hooked hairs on their shells. Marine biologist Helena Marsh hypothesizes that the crabs do not simply use whatever material is closest at hand but instead select decorations that match their current surroundings.

  1. Which finding, if true, would most directly support Marsh’s hypothesis? (A) When crabs decorated with red algae were moved to a tank lined mostly with green algae, they replaced their red decorations with green algae, even though red algae were also available in the tank. (B) Crabs decorated their shells more heavily when a predator’s scent was added to the water than when it was not. (C) Crabs in tanks containing only one type of material decorated themselves exclusively with that material. (D) Larger decorator crabs covered a smaller proportion of their shells with decorations than smaller crabs did.

Question 12

Laugh tracks, recordings of audience laughter added to television comedies, became common in the 1950s. Defenders have long argued that the sound helps viewers at home recognize which lines are meant to be jokes. Media researcher Colin Aldridge contends instead that laugh tracks work mainly as a social cue: because people tend to laugh more when they hear others laughing, the sound makes jokes seem funnier even when viewers already know full well that a line is a joke.

  1. Which finding, if true, would most directly support Aldridge’s claim? (A) Viewers who had been told in advance exactly which lines were jokes still rated those jokes as funnier when they were followed by recorded laughter than when they were not. (B) Viewers who watched a comedy with a laugh track correctly identified more of its jokes than viewers who watched it without one. (C) Laugh tracks were used in fewer television comedies produced after 2000 than in comedies produced in earlier decades. (D) Viewers rated jokes as funnier with a laugh track only when the jokes were subtle and difficult to recognize as jokes.

Question 13

Night markets, open-air markets that operate after dark and feature rows of food stalls, are a fixture of many cities in East and Southeast Asia, and cities elsewhere have begun hosting their own. Economist Rachel Dunmore surveyed visitors to a new monthly night market in a mid-sized city’s downtown, asking what they would have done that evening if the market had not been open. Her results suggest that most of the market’s visitors would not otherwise have been downtown at all: _____

  1. Which choice most effectively uses data from the table to complete the statement? (A) 46% of visitors said they would have stayed home if the market had not been open. (B) only 18% of visitors said they would have come downtown that evening even if the market had not been open. (C) 36% of visitors said they would have gone out somewhere other than downtown. (D) more visitors said they would have stayed home than said they would have gone out somewhere other than downtown.

Question 14

Noctilucent clouds, the highest clouds in Earth’s atmosphere, form about 80 kilometers up and glow a silvery blue in summer twilight. Historically, they were seen almost exclusively between about 50° and 70° latitude. Atmospheric scientist Martin Kessler argues that the clouds are now appearing increasingly often closer to the equator, and he points to records from two observatories as evidence: _____

  1. Which choice most effectively uses data from the graph to complete the statement? (A) in every year shown, the observatory at 60°N recorded more nights with noctilucent clouds than the observatory at 45°N did. (B) at the observatory at 60°N, the number of nights with noctilucent clouds rose from 20 in 1995 to 27 in 2020. (C) the observatory at 60°N recorded its greatest number of nights with noctilucent clouds in 2020. (D) at the observatory at 45°N, which lies outside the clouds’ historical range, the number of nights with noctilucent clouds rose from 2 in 1995 to 16 in 2020.

Question 15

Many oak trees produce enormous crops of acorns in some years and very few in others, and oaks across a wide area tend to have their big years at the same time, a pattern known as masting. One explanation, the predator satiation hypothesis, holds that during the lean years, populations of acorn-eating animals such as mice and jays stay relatively small, so when a mast year arrives, the animals cannot possibly eat all the acorns. If this hypothesis is correct, then _____

  1. Which choice most logically completes the text? (A) an oak that produces a big crop in a year when its neighbors do not should lose a smaller share of its acorns than its neighbors do. (B) populations of acorn-eating animals should be largest in the lean years just before a mast year. (C) oaks should produce roughly the same number of acorns every year to keep seed eaters from starving. (D) the proportion of acorns that escape being eaten should be greater in mast years than in lean years.

Question 16

The didgeridoo, a long wooden wind instrument developed by Aboriginal peoples of northern Australia, can produce a continuous drone that lasts for minutes. To play without pausing, performers use a technique called circular _____ they breathe in through the nose while pushing air stored in their cheeks out through the mouth.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) breathing that, (B) breathing (C) breathing: (D) breathing,

Question 17

In sgraffito, an artist applies a layer of colored plaster or clay, covers it with a layer of a contrasting color, and then scratches a design through the top _____ the color beneath. The technique takes its name from the Italian verb graffiare, which means “to scratch.”

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) layer; exposing (B) layer. Exposing (C) layer and exposing (D) layer, exposing

Question 18

In 1927 Lithuanian-born _____ published a study showing that people tend to recall interrupted tasks better than completed ones. Her research grew out of an observation attributed to her mentor, Kurt Lewin, who had noticed that a café waiter remembered the details of unpaid orders but forgot them once the bill was settled.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) psychologist Bluma Zeigarnik, (B) psychologist Bluma Zeigarnik (C) psychologist, Bluma Zeigarnik, (D) psychologist, Bluma Zeigarnik

Question 19

An igloo stays surprisingly warm inside because packed snow is full of tiny air pockets that slow the escape of _____ a small oil lamp and the body heat of the people inside can keep the air in an igloo far warmer than the air outside.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) heat. Even (B) heat even (C) heat: even, (D) heat, even

Question 20

When a fox or other predator approaches its nest, a killdeer, a type of plover, often flutters along the ground dragging one wing as if it were injured. This convincing performance _____ the predator away from the eggs, and once the nest is safe, the bird suddenly flies off.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) lures (B) are luring (C) have lured (D) lure

Question 21

In 1900, as Paris prepared to host a world’s fair, the architect Hector Guimard _____ the first of his entrances for the city’s new subway system, the Métro. Made of cast iron and glass, the entrances featured curving stems and lamps that resembled the stalks and buds of plants.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) designs (B) will design (C) designed (D) has designed

Question 22

Before each modern Olympic Games, a flame is lit in Greece and carried by relay to the host city. The ceremony at Olympia, in which performers dressed as ancient priestesses use a curved mirror to focus the Sun’s rays onto a torch, _____ several months before the Games begin.

  1. Which choice completes the text so that it conforms to the conventions of Standard English? (A) take place (B) takes place (C) have taken place (D) are taking place

Question 23

In 1910, French engineer Georges Claude displayed glass tubes filled with glowing neon gas at an exhibition in Paris, and within two decades neon signs lit up city streets around the world. Neon itself glows red-orange, so sign makers who wanted other colors had to use other gases or coat the insides of the tubes. _____ argon mixed with a small amount of mercury vapor produces a blue glow.

  1. Which choice completes the text with the most logical transition? (A) For example, (B) Similarly, (C) In other words, (D) Nevertheless,

Question 24

The bystander effect is the tendency of people to be less likely to help someone in need when others are present. Classic laboratory experiments, in which participants heard or saw a staged emergency, suggested that this effect is strong and widespread. _____ a more recent analysis of security-camera footage of real public conflicts in several countries found that in the great majority of incidents at least one bystander stepped in, and that the more bystanders were present, the more likely it was that someone would help.

  1. Which choice completes the text with the most logical transition? (A) Consequently, (B) However, (C) For instance, (D) Moreover,

Question 25

While researching a topic, a student has taken the following notes:

  • A yurt is a round, portable dwelling traditionally used by herders in Central Asia.
  • Many herders move their camps several times a year to find fresh pasture for their animals.
  • A yurt’s frame is made up of a collapsible wooden lattice wall, roof poles, and a central ring.
  • The frame is covered with layers of felt made from sheep’s wool.
  • A yurt can be taken down or put up in just a few hours.
  • In Mongolia, yurts are called gers.
  1. The student wants to explain why yurts suit a nomadic way of life. Which choice most effectively uses relevant information from the notes to accomplish this goal? (A) In Mongolia, where many herders still live in yurts, the dwellings are called gers. (B) Because a yurt can be taken down or put up in just a few hours, it suits herders who move their camps several times a year. (C) A yurt’s frame is made up of a collapsible wooden lattice wall, roof poles, and a central ring. (D) Yurts are covered with layers of felt made from sheep’s wool.

Question 26

While researching a topic, a student has taken the following notes:

  • Nabta Playa is a site in the Nubian Desert of southern Egypt.
  • About 7,000 years ago, cattle herders gathered there seasonally, when rains filled a lake basin.
  • They set upright stones in a circle about 4 meters across.
  • Pairs of stones in the circle appear to align with the direction of sunrise at the summer solstice.
  • At that time, the summer solstice roughly coincided with the arrival of the seasonal rains.
  1. The student wants to suggest a possible purpose of the stone circle at Nabta Playa. Which choice most effectively uses relevant information from the notes to accomplish this goal? (A) When the rains came, a lake basin at Nabta Playa filled with water, and cattle herders gathered there. (B) The stone circle at Nabta Playa, which is about 4 meters across, was built by people who herded cattle. (C) Pairs of stones at Nabta Playa appear to align with the summer solstice sunrise, which roughly coincided with the arrival of the rains, so the circle may have helped people mark that important time of year. (D) About 7,000 years ago, cattle herders gathered seasonally at Nabta Playa, a site in the Nubian Desert of southern Egypt.

Question 27

While researching a topic, a student has taken the following notes:

  • A sonnet is a fourteen-line poem that usually contains a shift in thought, called the volta.
  • The Petrarchan sonnet, named for the Italian poet Petrarch (1304–1374), divides its lines into an octave (eight lines) and a sestet (six lines).
  • In a Petrarchan sonnet, the volta typically occurs at line 9, the start of the sestet.
  • The Shakespearean sonnet, named for William Shakespeare (1564–1616), consists of three quatrains (four-line units) and a couplet (two lines).
  • In a Shakespearean sonnet, the volta often comes in the final couplet.
  1. The student wants to emphasize a difference in where the two sonnet forms typically place their shift in thought. Which choice most effectively uses relevant information from the notes to accomplish this goal? (A) In a Shakespearean sonnet, which consists of three quatrains and a couplet, the volta often comes in the final two lines. (B) Both the Petrarchan sonnet and the Shakespearean sonnet are fourteen-line poems that include a shift in thought called a volta. (C) The volta usually arrives at line 9 of a Petrarchan sonnet, at the start of the sestet, but often not until the final couplet of a Shakespearean sonnet. (D) Whereas a Petrarchan sonnet divides its fourteen lines into an octave and a sestet, a Shakespearean sonnet divides them into three quatrains and a couplet.

Math: Module 1

Question 1

  1. A 3D printer feeds plastic filament into its nozzle at a constant rate of 18 millimeters every 5 seconds. At this rate, how many meters of filament does the printer use in 10 minutes? (1 meter = 1,000 millimeters) (A) 2.16 (B) 10.8 (C) 21.6 (D) 0.36

Question 2

  1. 7 - 3x = 22 What value of x is the solution to the given equation? (A) -(29)/(3) (B) -5 (C) 5 (D) 15

Question 3

Line graph titled Planetarium Visitors. The vertical axis shows number of visitors from 0 to 600 in steps of 50. The points are: January 300, February 350, March 450, April 400, May 500, June 450.

  1. The line graph shows the number of visitors to a small planetarium in each of the first six months of a year. According to the graph, by how many visitors did the monthly number of visitors increase from February to May? (A) 100 (B) 200 (C) 150 (D) 500

Question 4

  1. At a ski resort, a snow-making machine adds snow to a slope that already has natural snow on it. The equation d = 0.8h + 14 gives the estimated depth d, in inches, of snow on the slope h hours after the machine is turned on. What is the best interpretation of 14 in this context? (A) The depth of the snow increases by 14 inches each hour. (B) The machine runs for a total of 14 hours. (C) The depth of the snow 1 hour after the machine is turned on is 14 inches. (D) The depth of the snow is 14 inches when the machine is turned on.

Question 5

  1. A line in the xy-plane has a slope of 3 and passes through the point (2, 5). The line crosses the y-axis at the point (0, b). What is the value of b? (type your answer)

Question 6

  1. A store reduced the price of a bicycle helmet by 15%. The reduced price of the helmet is $51. What was the original price of the helmet, in dollars? (type your answer)

Question 7

  1. (3x^2 - 5x + 2) - (x^2 + 4x - 6) Which of the following is equivalent to the given expression? (A) 2x^2 - x - 4 (B) 2x^2 - 9x + 8 (C) 4x^2 - x - 4 (D) 2x^2 - 9x - 4

Question 8

  1. A museum gift shop sells postcards for $2 each and posters for $9 each. A school group bought a total of 26 postcards and posters and paid $122. How many posters did the group buy? (A) 16 (B) 13 (C) 10 (D) 70

Question 9

  1. A community theater models its weekly ticket revenue R, in dollars, by R(x) = -40x^2 + 1,600x, where x is the price of one ticket, in dollars. According to the model, what ticket price gives the greatest weekly revenue? (A) $20 (B) $40 (C) $800 (D) $16,000

Question 10

Right triangle PQR with the right angle at Q. Side PQ is vertical with length 20, side QR is horizontal and unlabeled, and hypotenuse PR has length 29.

  1. In right triangle PQR shown, PQ = 20 and PR = 29. What is the value of tan R? (A) (21)/(20) (B) (20)/(29) (C) (21)/(29) (D) (20)/(21)

Question 11

Plot typeDrip irrigationHand wateringTotal
Vegetable281240
Flower92130
Herb11920
Total484290
  1. The table shows the 90 plots in a community garden, classified by what is grown in the plot and how the plot is watered. If one of the plots that uses drip irrigation is selected at random, what is the probability that it is an herb plot? (A) (11)/(48) (B) (11)/(20) (C) (11)/(90) (D) (8)/(15)

Question 12

  1. (x)/(2) + (y)/(3) = 4 x - y = 3 The solution to the given system of equations is (x, y). What is the value of y? (type your answer)

Question 13

  1. g(x) = (x - 4)(x + k) In the given function, k is a constant. In the xy-plane, the vertex of the graph of y = g(x) has an x-coordinate of 1. What is the value of k? (type your answer)

Question 14

Triangle ABC with base BC horizontal and vertex A above. Side BC is extended to the right past C to point D. The angle at A is labeled (3x) degrees, the angle at B is labeled (x + 12) degrees, and the exterior angle ACD, between CD and CA, is labeled 128 degrees.

  1. In the figure, point D lies on the extension of side BC of triangle ABC. The measure of angle A is (3x)^°, the measure of angle B is (x + 12)^°, and the measure of angle ACD is 128^°. What is the value of x? (A) 10 (B) 41 (C) 29 (D) 87

Question 15

  1. A freight elevator can safely carry at most 1,200 kilograms. A worker who weighs 80 kilograms rides the elevator with b boxes that each weigh 35 kilograms. Which inequality represents all possible numbers of boxes b the worker can take on one safe trip? (A) 35 + 80b ≤ 1,200 (B) 80 + 35b ≥ 1,200 (C) 35b ≤ 1,200 + 80 (D) 80 + 35b ≤ 1,200

Question 16

  1. 2x^2 + x - 15 = 0 What are the solutions to the given equation? (A) -(5)/(2) and 3 (B) (5)/(2) and -3 (C) 5 and -3 (D) (3)/(2) and -5

Question 17

  1. A delivery company bought a van for $24,000. The value of the van decreases by 12% each year. Which function gives the value V, in dollars, of the van t years after it was bought? (A) V(t) = 24,000(0.12)^t (B) V(t) = 24,000(0.88)^t (C) V(t) = 24,000(1.12)^t (D) V(t) = 24,000 - 0.12t

Question 18

Coordinate plane from -6 to 6 on both axes with grid lines every 1 unit. Line k slopes downward from left to right and passes through the labeled points (-3, 4) and (3, 0); it crosses the y-axis at (0, 2).

  1. The graph of line k is shown. Line p (not shown) is perpendicular to line k and passes through the point (2, -1). Line p crosses the y-axis at the point (0, b). What is the value of b? (A) -4 (B) -(7)/(3) (C) (1)/(3) (D) 2

Question 19

  1. 3x^2 - 12x + c = 0 In the given equation, c is a constant. The equation has exactly one real solution. What is the value of c? (type your answer)

Question 20

  1. x^2 + y^2 - 6x + 10y = 2 The graph of the given equation in the xy-plane is a circle. What is the radius of the circle? (type your answer)

Question 21

  1. y = x^2 - 4x + 1 y = 2x - 7 The given system of equations has two solutions, (x_1, y_1) and (x_2, y_2). What is the value of y_1 + y_2? (A) 6 (B) 1 (C) -2 (D) -8

Question 22

  1. For the linear function g, g(x + 3) = g(x) + 12 for all values of x, and g(0) = -5. Which equation defines g? (A) g(x) = 12x - 5 (B) g(x) = 3x - 5 (C) g(x) = 4x + 7 (D) g(x) = 4x - 5

Math: Module 2

Question 1

  1. A trail-mix recipe uses peanuts and raisins in the ratio of 3 cups of peanuts to 2 cups of raisins. A camp cook makes a large batch of the trail mix using 13.5 cups of peanuts. How many cups of raisins should the cook use to keep the same ratio? (A) 4.5 (B) 20.25 (C) 9 (D) 6.75

Question 2

  1. 4(2x - 5) = 3x + 15 What is the solution to the given equation? (A) 7 (B) -1 (C) (35)/(11) (D) 4

Question 3

Coordinate plane with x from -4 to 6 and y from -2 to 10, grid lines every 1 unit. A downward-opening parabola crosses the x-axis at the labeled points (-2, 0) and (4, 0) and has its highest point at the labeled point (1, 9). It crosses the y-axis at (0, 8).

  1. The graph of y = f(x) is shown, where f is a quadratic function. Which of the following could define f? (A) f(x) = (x + 2)(x - 4) (B) f(x) = -(x - 2)(x + 4) (C) f(x) = -(x + 2)(x + 4) (D) f(x) = -(x + 2)(x - 4)

Question 4

  1. A school theater sells adult tickets for $12 each and student tickets for $8 each. The equation 12a + 8s = 480 represents the numbers of adult tickets, a, and student tickets, s, that give total sales of $480. If the number of adult tickets sold increases by 2, how must the number of student tickets sold change so that total sales are still $480? (A) It must increase by 3. (B) It must decrease by 3. (C) It must decrease by 2. (D) It must decrease by 24.

Question 5

Number of guestsTotal charge (dollars)
401,150
651,675
  1. A caterer charges a fixed fee plus a constant price per guest for an event. The table shows the total charge for two events. What is the caterer’s fixed fee, in dollars? (type your answer)

Question 6

  1. (2x + a)(3x - 5) = 6x^2 + bx - 35 In the given equation, a and b are constants, and the equation is true for all values of x. What is the value of b? (type your answer)

Question 7

  1. At a charity run, each of the 84 participants ran either a 5-kilometer course or a 10-kilometer course. Together, the participants ran a total of 610 kilometers. How many participants ran the 10-kilometer course? (A) 38 (B) 46 (C) 42 (D) 61

Question 8

Scatterplot titled Elevation and July Temperature. Horizontal axis: elevation in hundreds of meters, 0 to 26 in steps of 2. Vertical axis: average July temperature in degrees Celsius, 0 to 26 in steps of 2. The 11 points are (4, 22), (6, 20), (8, 18), (10, 18), (12, 16), (14, 14), (16, 14), (18, 12), (20, 14), (22, 10), and (24, 8). A line of best fit, y = 24 - 0.65x, slopes downward from (0, 24).

  1. The scatterplot shows the elevation x, in hundreds of meters, and the average July temperature y, in degrees Celsius (°C), at 11 weather stations. A line of best fit for the data is also shown. Its equation is y = 24 - 0.65x. For the weather station at an elevation of 2,000 meters, how many degrees Celsius greater is the actual average July temperature than the temperature predicted by the line of best fit? (A) 8.7 (B) 11 (C) 14 (D) 3

Question 9

  1. |3x - 7| = 11 What is the sum of the solutions to the given equation? (A) 6 (B) (22)/(3) (C) (14)/(3) (D) -(4)/(3)

Question 10

Right triangle ABC with the right angle at C. Side CA is horizontal, side CB is vertical, and hypotenuse AB is labeled 39.

  1. In triangle ABC shown, angle C is a right angle, AB = 39, and sin A = (12)/(13). What is the perimeter of triangle ABC? (A) 30 (B) 75 (C) 90 (D) 270

Question 11

  1. Of the 400 runners in a race, 55% were adults and the rest were under 18 years old. Of the adults, 30% finished in less than 25 minutes. Of the runners under 18, 60% finished in less than 25 minutes. If one of the runners who finished in less than 25 minutes is selected at random, what is the probability that the runner is under 18 years old? (A) (27)/(100) (B) (18)/(29) (C) (3)/(5) (D) (9)/(20)

Question 12

  1. x^2 + bx + 20 = 0 In the given equation, b is a positive constant. The equation has two real solutions, and one solution is exactly 1 greater than the other. What is the value of b? (type your answer)

Question 13

  1. In a circle, a central angle of 72^° intercepts an arc of length 6π inches. The area of the circle is kπ square inches. What is the value of k? (type your answer)

Question 14

  1. A delivery truck can carry at most 1,500 pounds and at most 70 boxes. Small boxes weigh 12 pounds each, and large boxes weigh 30 pounds each. For one trip, the truck is loaded with 20 large boxes. What is the greatest number of small boxes that can also be loaded for this trip? (A) 50 (B) 75 (C) 70 (D) 125

Question 15

  1. (1)/(x + 3) + (2)/(x - 1) Which of the following is equivalent to the given expression for x > 1? (A) (3)/(2x + 2) (B) (3x + 7)/(x^2 + 2x - 3) (C) (3x + 5)/(x^2 - 3) (D) (3x + 5)/(x^2 + 2x - 3)

Question 16

Triangle ABC with base BC horizontal and vertex A at the top. Point D is on side AB and point E is on side AC, and segment DE is parallel to BC. AD is labeled 6, DB is labeled 4, and DE is labeled 9.

  1. In triangle ABC shown, point D lies on AB, point E lies on AC, and DE is parallel to BC. Also, AD = 6, DB = 4, and DE = 9. What is the length of BC? (A) 6 (B) 15 (C) 13.5 (D) 13

Question 17

  1. The mass M, in grams, of a radioactive sample t days after it was measured is modeled by M(t) = 96(0.5)^(t)/(5). According to the model, by what percent does the mass of the sample decrease every 10 days? (A) 25% (B) 50% (C) 75% (D) 100%

Question 18

  1. A researcher selected 500 adults at random from the adult residents of a city and asked whether they use public transit at least once a week. Of those surveyed, 38% said yes. The estimate has an associated margin of error of 4 percentage points. Which of the following is the most appropriate conclusion? (A) Exactly 38% of the adults in the city use public transit at least once a week. (B) At most 34% of the adults in the city use public transit at least once a week. (C) Between 34% and 42% of all adults in the country use public transit at least once a week. (D) It is plausible that between 34% and 42% of the adults in the city use public transit at least once a week.

Question 19

  1. 4x + ky = 22 3x - 2y = 5 In the given system of equations, k is a constant. The solution to the system is (x, y), where x = 3. What is the value of k? (type your answer)

Question 20

  1. f(x) = x^2 - 10x + c In the given function, c is a constant. The minimum value of f is 7. What is the value of f(2)? (type your answer)

Question 21

  1. The graph of the linear function f in the xy-plane passes through the points (a, 5) and (a + 4, -7), where a is a constant. Which of the following could define f? (A) f(x) = -3x + 2 (B) f(x) = 3x - 7 (C) f(x) = -(1)/(3)x + 5 (D) f(x) = -12x + 5

Question 22

  1. 4(ax - 3) = 12x + 2b In the given equation, a and b are constants. The equation has infinitely many solutions. What is the value of a - b? (A) -3 (B) 9 (C) 15 (D) 18

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PSAT 10 Practice Test 2 with Answers

Mantis shrimp strikesMars dust stormsCarthage harbor designHandwriting and memorySolar sailsDung beetles and the Milky WayMicroschoolsThe history of the umbrellaPermafrost thawMosaic art in RavennaNoise-cancelling technologyAn old map found in an attic (original story)

Reading and Writing · Math · about 134 min

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PSAT 10 Practice Test 3 with Answers

Horseshoe crab blood in medicineNeutron starsTimbuktu manuscriptsBird dialects3D-printed homesSea otter tool useReading clubs in prisons (education access)The history of ice harvestingGiant sequoia fire adaptationHarlem Renaissance magazinesE-waste recyclingA violinist's first recital (original poem)

Reading and Writing · Math · about 134 min

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PSAT 10 Practice Test 4 with Answers Pro

Naked mole-rat longevityThe Kuiper BeltAngkor's reservoirsGesture and learning mathFloating solar farmsLionfish invasionMuseum audio guidesThe history of the typewriter keyboardSpider silk strengthShaker furniture designFlood-resistant riceA lost dog returns (original story)

Reading and Writing · Math · about 134 min

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PSAT 10 Practice Test 5 with Answers Pro

Bowerbird decorationMoon water iceThe Olmec colossal headsCode-switchingSmart windowsFlamingo color and dietBike-share systemsThe history of canned foodHibernation in bearsSilent film musicTree planting and coolingA grandmother's recipe box (original story)

Reading and Writing · Math · about 134 min

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PSAT 10 Practice Test 6 with Answers Pro

Electric eel huntingPluto's heart-shaped plainBird names in Indigenous languages (respectful)Cool roofsCoral spawning timingPublic radio pledge drivesThe history of the elevatorGlacier mice (moss balls)Microplastics in riversA solo sailing trip (original poem)

Reading and Writing · Math · about 134 min

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The 0 PSAT 10 sections

The PSAT 10 has two sections, and each one has two modules. In both sections, how you do in Module 1 decides whether you get a harder or an easier Module 2. Take a full test in one go, or practise one section at a time:

How PSAT 10 is scored

The PSAT 10 reports a Reading and Writing score and a Math score, each from 160 to 760, for a total of 320 to 1520. On 7ESL, each module is marked instantly, and every question shows the correct answer and an explanation (for multiple-choice questions, also why your choice was wrong). In each section, Module 1 decides which Module 2 you get: 16 or more correct out of 27 in Reading and Writing, or 13 or more out of 22 in Math, opens the harder Module 2. After both modules of a section, you get a practice section score estimate based on your total correct answers and the Module 2 you took; after both sections, you also see an estimated total. The estimates come from 7ESL conversion tables, not from College Board, and every question counts here (the real test includes a few unscored questions per module).

What is the PSAT 10?

PSAT 10 is a College Board test that schools give to grade 10 students in the spring. It has exactly the same content, format and 320-1520 score scale as the PSAT/NMSQT: a Reading and Writing section and a Math section, taken digitally in the Bluebook app. The difference is timing and purpose: PSAT 10 scores are not used for the National Merit Scholarship Program, but they show SAT readiness and help students and teachers plan.

PSAT 10 or PSAT/NMSQT?

The two tests have the same content, the same timing and the same 320–1520 score scale, so they prepare you in the same way. The differences are when you take them and what the scores are used for. Schools give the PSAT 10 in the spring, mainly to grade 10 students. The PSAT/NMSQT is given in the fall, and only the PSAT/NMSQT can enter students in the National Merit Scholarship Program.

Both scores show whether you are on track for the SAT and can connect you to scholarship opportunities through College Board. The 7ESL PSAT 10 and PSAT/NMSQT practice tests are different sets of original questions in the same format, so you can use both for extra practice.

PSAT 10 format at a glance

SectionModulesQuestionsTime
Reading and WritingModule 1 + adaptive Module 254 (27 + 27)64 minutes
MathModule 1 + adaptive Module 244 (22 + 22)70 minutes

There is a 10-minute break between the sections. Reading and Writing questions each have a short passage and four choices; they cover Craft and Structure, Information and Ideas, Standard English Conventions and Expression of Ideas. Math covers Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. A calculator is allowed throughout the Math section.

The PSAT 10 Math section

The Math section has two modules of 22 questions, each with 35 minutes. About three quarters of the questions are multiple choice; in the rest you type your own answer, such as a whole number, a fraction like 7/2 or a decimal. A calculator is allowed on every question, and a reference sheet with common formulas is available.

  • Algebra (about 35% of the questions): linear equations, linear functions, systems of two linear equations and linear inequalities.
  • Advanced Math (about 32.5%): equivalent expressions and nonlinear equations and functions, such as quadratic and exponential functions.
  • Problem-Solving and Data Analysis (about 20%): ratios, rates, percentages, units, probability, scatterplots and what you can conclude from a sample or a study.
  • Geometry and Trigonometry (about 12.5%): area and volume, lines, angles and triangles, right triangles and their trigonometric ratios, and circles.

Every 7ESL Math question comes with a worked solution, and each wrong multiple-choice option is explained, usually with the mistake that leads to it.

Understanding your PSAT 10 score

Your Reading and Writing and Math scores are each reported on a 160–760 scale, in steps of 10, and added together for a total from 320 to 1520. A section score is not a simple percentage. Because Module 2 adapts to you, a student who reached the harder Module 2 can score higher than a student with the same number of correct answers on the easier one, so careless mistakes in Module 1 can limit your top score.

On 7ESL every question is marked instantly with an explanation, and after both modules of a section you get a practice section estimate from a 7ESL conversion table based on College Board's published paper practice tests, rescaled to the digital test. It is an estimate only: the real test uses a statistical scoring method and includes a few unscored questions in each module.

How to prepare with 7ESL

Every 7ESL test copies the adaptive structure of the real digital PSAT 10. Take a full test to practise your timing across both sections, or focus on one section:

  • Reading and Writing practice: a 27-question Module 1, then a harder or an easier 27-question Module 2, 32 minutes each.
  • Math practice: a 22-question Module 1, then a harder or an easier 22-question Module 2, 35 minutes each, with a calculator and a reference sheet.

Take Module 1 under time, check it, then take the Module 2 it opens. Read every explanation, including the ones for questions you got right, and note which skill each mistake belongs to. For Reading and Writing, underline the words that prove your answer; for grammar questions, learn the few punctuation rules the test uses again and again. For Math, write the units, check your answer by substituting it back, and practise typing fraction and decimal answers correctly. Pro members can ask the AI tutor to explain any wrong answer step by step.

Tips for English learners

The Reading and Writing section is really an English test: short academic texts on science, history, the arts and literature. Build vocabulary from the words-in-context questions, read the question before the passage, and do not bring in outside knowledge. In Math, many word problems are mostly about reading carefully: find what is given, what is asked, and the units, before you calculate.

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PSAT 10 — frequently asked questions

What is on the PSAT 10?

The digital PSAT 10 has two sections. Reading and Writing has 54 questions in 64 minutes, split into two modules of 27 questions and 32 minutes each; every question has a short passage (or a pair of passages) and tests one of four areas: Craft and Structure, Information and Ideas, Standard English Conventions, and Expression of Ideas. After a 10-minute break comes Math: 44 questions in 70 minutes, in two modules of 22 questions and 35 minutes each, covering Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry. It is taken on a laptop or tablet in College Board's Bluebook app.

Is PSAT 10 different from the PSAT/NMSQT?

The test content, timing and score scale are the same. PSAT 10 is taken in spring by grade 10 students, and its scores do not count for the National Merit Scholarship Program. You can use the 7ESL PSAT/NMSQT and PSAT 10 practice tests interchangeably; they are different sets of original questions.

How does the adaptive Module 2 work?

The PSAT 10 is adaptive by module, in both sections. Everyone starts with a Module 1 that mixes easy, medium and hard questions. Module 2 is then, on average, harder or easier than Module 1, depending on how well you did. On 7ESL, 16 or more correct answers out of 27 in Reading and Writing Module 1, or 13 or more out of 22 in Math Module 1, opens the harder Module 2; a lower score opens the easier one. These cut-offs are 7ESL practice settings, because College Board does not publish its routing rules.

How is the PSAT 10 scored?

Reading and Writing and Math are each scored from 160 to 760, and together they give a total from 320 to 1520. On 7ESL, when you finish both modules of a section, you get a practice section score estimate based on your total correct answers and the Module 2 you took (only the harder Module 2 gives access to the top scores). Finish both sections of a test to see an estimated total. These are 7ESL estimates from conversion tables based on College Board's published paper practice tests, not official scores.

How many PSAT 10 practice tests are there on 7ESL?

There are 6 full practice tests. Each has a Reading and Writing Module 1 with a harder and an easier Module 2 (81 questions), and a Math Module 1 with a harder and an easier Module 2 (66 questions), so every test contains 147 original questions; in one sitting you answer 98 of them. Every question has an explanation, and 7ESL Pro members can also ask an AI tutor to explain a mistake. The first 3 tests are free; the other 3 come with 7ESL Pro.

How do I answer the Math questions where I type my answer?

About a quarter of the Math questions have no answer choices: you type your answer. Positive answers can use up to 5 characters and negative answers up to 6 (including the minus sign). You can enter a fraction such as 7/2 or a decimal such as 3.5, but not a mixed number, a percent sign, a comma or a dollar sign. If a decimal is too long, round or cut it at the fourth character. 7ESL accepts every correct form allowed by these rules, for example 2/3, .6666, .6667 or 0.667.

Is there an AI tutor?

Yes, for 7ESL Pro members. After you check a module, the “Explain my mistake” button on a wrong answer gives a step-by-step AI explanation (a worked solution for Math, the evidence and the trap for Reading and Writing). Every question also has a written explanation for everyone.

Are these official PSAT 10 tests?

No. They are original 7ESL practice questions written to follow the public format of the digital PSAT 10. 7ESL is not affiliated with College Board. For official practice, use College Board's Bluebook app.

7ESL practice material written in the public format of the digital PSAT 10. 7ESL is not affiliated with, or endorsed by, College Board. PSAT/NMSQT is a registered trademark of College Board and National Merit Scholarship Corporation; SAT is a registered trademark and PSAT a trademark of College Board. Score estimates are unofficial and for practice only.