PSAT practice

Sample PSAT Math questions

Medium-difficulty questions, one from each Math domain on the PSAT.

1. Algebra · Linear equations in one variable · medium

   2(x + 4) = x - 1 What value of x is the solution to the equation above?

   1. A. -5
   2. B. -9
   3. C. 7
   4. D. 9
   Show answer and explanation

   Answer: B. Distribute: 2x + 8 = x - 1. Collect x terms: x = -9, so x = -9.

2. Advanced Math · Equivalent expressions · medium

   Which expression is equivalent to 36x² - 9y²?

   1. A. (6x - 3y)(6x + 3y)
   2. B. (6x + 3y)²
   3. C. (36x - 9y)(x + y)
   4. D. (6x - 3y)²
   Show answer and explanation

   Answer: A. This is a difference of squares: (6x)² - (3y)² = (6x - 3y)(6x + 3y).

3. Problem-Solving and Data Analysis · Ratios, rates, and proportions · medium

   A bus travels at a constant speed of 44 miles per hour. How many miles does it travel in 4 hours and 45 minutes?

   1. A. 176
   2. B. 209
   3. C. 195.8
   4. D. 221
   Show answer and explanation

   Answer: B. 45 minutes is 3 over 4 of an hour, so the time is 4.75 hours and the distance is 44 × 4.75 = 209 miles.

4. Geometry and Trigonometry · Area and volume · medium

   A cube has a volume of 34 cubic units. Each edge of the cube is multiplied by 2 to make a new cube. What is the volume of the new cube, in cubic units?

   1. A. 272
   2. B. 136
   3. C. 68
   4. D. 42
   Show answer and explanation

   Answer: A. Volume scales by the cube of the length factor: 34 × 2³ = 34 × 8 = 272.

Sample PSAT Reading and Writing questions

1. Information and Ideas · Central ideas and details · medium

   The following text is from a poem. They do not hurry and they do not stay. Each spring the gray whales turn their heads away from the warm lagoons where they were born, and swim north along the coast for weeks. No map, no star they need to keep; the path is older than their sleep. They follow it as rivers follow stone, as if the way had always been their own. Which choice best states the main idea of the text?

   1. A. The whales lose their way each spring and must search for the coast.
   2. B. The speaker wishes the whales would remain in the warm lagoons.
   3. C. The whales follow an ancient migration route as though by instinct.
   4. D. Rivers and whales both move faster in spring than in other seasons.
   Show answer and explanation

   Answer: C. The whales need 'no map, no star,' the path is 'older than their sleep,' and they follow it 'as if the way had always been their own,' which describes an old route followed by instinct. Choice A is wrong because the poem says they need no map, so they are not lost. Choice B is wrong because the speaker describes the departure calmly and never wishes they would stay. Choice D is wrong because rivers appear only in a comparison about following a path, not about speed.

2. Craft and Structure · Cross-text connections · medium

   Text 1 Oyster reefs are often valued for the seafood they provide, and restoration projects are frequently judged by how many oysters can eventually be harvested from them. Text 2 Ecologist Ruth Okonkwo argues that this measure misses much of a reef's worth. A single adult oyster can filter dozens of gallons of water a day, and reefs shelter young fish and soften waves that would otherwise wear away shorelines. Based on the texts, how would Okonkwo (Text 2) most likely respond to the way projects are judged in Text 1?

   1. A. By claiming that oysters have little value as seafood
   2. B. By agreeing that harvest is the best way to measure a reef's value
   3. C. By suggesting that oyster reefs make shoreline erosion worse
   4. D. By arguing that judging projects by harvest alone overlooks other benefits of reefs
   Show answer and explanation

   Answer: D. Okonkwo says the harvest measure misses much of a reef's worth and lists filtering, shelter, and shoreline protection. Choice A is wrong because Okonkwo adds to the reasons reefs matter; she does not deny their value as food. Choice B is wrong because she says this measure misses much of a reef's worth. Choice C is wrong because Text 2 says reefs soften waves that would wear away shorelines.

3. Expression of Ideas · Rhetorical synthesis · medium

   While researching a topic, a student has taken the following notes: - Tupaia was a navigator and priest from the island of Raiatea, near Tahiti. - In 1769, he joined the British expedition led by James Cook. - Working with the crew, he produced a chart showing more than 70 islands spread across thousands of kilometers of ocean. - He also helped Cook's crew communicate with Māori people in New Zealand. The student wants to emphasize how far Tupaia's geographic knowledge extended. Which choice most effectively uses relevant information from the notes to accomplish this goal?

   1. A. In 1769, Tupaia, a navigator from Raiatea, joined James Cook's British expedition.
   2. B. Tupaia helped Cook's crew communicate with Māori people in New Zealand.
   3. C. Tupaia produced a chart of more than 70 islands spread across thousands of kilometers of ocean.
   4. D. Tupaia was both a navigator and a priest on the island of Raiatea.
   Show answer and explanation

   Answer: C. The extent of his knowledge is best shown by the chart, which covered more than 70 islands across thousands of kilometers. Choice A is wrong because it tells how Tupaia came to join Cook, not how much of the ocean he knew. Choice B is wrong because it shows his skill with people and language, not the range of his geographic knowledge. Choice D is wrong because it describes his roles without showing how far his knowledge reached.

4. Standard English Conventions · Boundaries · medium

   Working out the structure of DNA required evidence from several laboratories. The famous X-ray image of DNA known as Photo 51 was taken in 1952 by the graduate student Raymond Gosling, working under Rosalind ______ had studied chemistry at the University of Cambridge. The image provided key evidence that DNA has a helical shape. Which choice completes the text so that it conforms to the conventions of Standard English?

   1. A. Franklin who
   2. B. Franklin; who
   3. C. Franklin. Who
   4. D. Franklin, who
   Show answer and explanation

   Answer: D. "who had studied chemistry at the University of Cambridge" adds extra information about Franklin, whose name already identifies her. Extra information like this is set off with a comma before "who." Choice A is wrong because a clause that adds nonessential information about a named person needs a comma before "who." Choice B is wrong because a semicolon would leave "who had studied chemistry ..." as a fragment. Choice C is wrong because a period would turn "Who had studied chemistry ..." into a fragment.