PSAT Math Practice Test 2025 Question (Use Calculator)

1) A proton fired through medium B travels at half the velocity of a proton fired through medium A. If the proton in medium A travels 100,000 meters in 5 milliseconds, what is the velocity of the proton in medium B ?

2) Which of the following values is a solution of 6x − 5 > 2 + 15x ?

3) Which of the following values of r is a solution for the equation r + 22 = 3r − 26 +r² ?

4) To be eligible for Spartanville’s Super Service Award, a resident must complete at least 2,000 hours of community service through a designated program. There are two designated programs this year: volunteering at the Community Center for 7.5 hours per day and removing street litter for 4 hours per day. Which of the following inequalities represents the possible number of days spent volunteering at the Community Center c and days removing street litter l needed to be eligible for this year’s Spartanville Super Service Award?

5) The table above shows the lengths, in inches, of all the fish caught by a fisherman in one day. If the median length was 15, then what was the mean length?

6) A certain gold coin has a volume of 5 cubic centimeters. The density of gold is 19.3 grams per cubic centimeter. If 1 ounce is equal to 28.3 grams, what is the approximate mass of the coin in ounces? (Note: Density is mass divided by volume.)

7) Dr. Seeker, a noted paleontologist, polls colleagues around the world asking for the their theory on what caused the mass extinction of most dinosaur species and brought about the end of the Cretaceous Period. After polling 200,000 of his colleagues, 151,394 of them reply that they believe the mass extinction to be caused by the Chicxulub Asteroid impact. The remaining 48,606 reply with alternative theories. From this data, which is the best conclusion that Dr. Seeker could make?

8) A computer chip factory currently has 50 employees and has an output of 385 computer chips per day. A manager determined that for each additional employee hired, the output of the factory would increase by 42 computer chips. Which of the following functions, C(x), expresses the total output of the factory for x employees when x ≥ 50 ?

9) \frac{3 (t + 2)}{4} = \frac{100 - 5t + 44)}{8}

In the equation above, what is the value of t ?

10) In the xy-plane, the graph of y = (3x − 6)(x − 6) represents a parabola. If the x- and y-coordinates of the parabola’s vertex are to be expressed as constants or coefficients, which of the following forms of the equation is appropriate?

11) Taylor is preparing to write his next novel, which will be 700 pages long. While typing, Taylor types at a constant rate of 23 words per minute. If each page contains 800 words, which of the following functions p models the number of pages Taylor has left to type after typing for m minutes?

12)

Line b is shown above. Line c is parallel to line b and contains the point (3, −2). Which of the following could be the equation of line c ?

13) In State Q, the number of people in poverty halved each year from 2008 to 2012. There were 50,000 people in poverty in State Q in 2008, and m represents the number of months since January 2008, where 0 ≤ m ≤ 48. Which of the following functions f(m) could be used to estimate the number of people in poverty in State Q m months after January 2008 ?

14)

In the graph above, x represents the number of days Chris has worked his part-time job and y represents the total amount of money in his bank account. If the graph has a slope of 40, what is the value of b, assuming Chris deposits all his earnings and does not spend any of the money in his bank account?

15) If y = x² + x − 20 and z = x² + 10x + 25, what is  \frac{x^{2}} {z} , in terms of x ?

16) The Squared Up framing store charges $61 to frame a customer’s picture. The owner of the store calculated that the cost to frame each picture is $38 in materials plus $5 in the labor cost. The store must also pay $720 each month in general operating costs. Squared Up is profitable when the income from framing a customer’s picture exceeds the total cost of framing the picture plus the general operating cost. If p is the number of pictures framed in a month, which of the following gives all possible values of p for which Squared Up is profitable during that month?

17) Questions 17–18 refer to the following information.

A nonprofit group wanted to determine whether there is an association between a household’s income and the amount of money spent on groceries. After surveying 800 randomly selected households in Florida, the nonprofit found that as the household’s income increased, its spending on groceries decreased.

If the nonprofit wanted to determine whether an association exists between a household’s income and the average amount of money spent on groceries per person, which of the following changes to the survey would be most appropriate?

18) Questions 17–18 refer to the following information.

A nonprofit group wanted to determine whether there is an association between a household’s income and the amount of money spent on groceries. After surveying 800 randomly selected households in Florida, the nonprofit found that as the household’s income increased, its spending on groceries decreased.

Which of the following conclusions is supported by the data?

19) 2x − 96 = 4y − x
3y + 10x = y + 90

Based on the system of equations above, what is the value of  \frac{x} {y} ?

20) Larissa uploaded 40,000 songs from her computer to her web storage. The mean file size of a song is 0.022 gigabytes, and the total time to upload all the files was 7.5 hours. If 1 gigabyte is equal to 1,024 megabytes, what is the upload rate for the files in megabytes per second, rounded to the nearest hundredth?

21) As part of her research into the social behaviors of felines, Dr. Ivask begins to observe the cheetah population near a noted watering hole in Namibia at the start of the year 2012. After years of observing the cheetahs, she constructs the equation c(y) = 17y + 112, in which y represents the number of years since the start of 2012 and c represents the cheetah population at the start of that given year. Dr. Ivask notes that after the start of 2015, an additional 20 cheetahs from a different region of Namibia join her cheetah population. Which of the following would be the number of cheetahs in the population that Dr. Ivask is observing after the additional 20 cheetahs joined?

22)

The New York City Department of Motor Vehicles compiled the data for the number of cars owned in each of the city’s five boroughs. There are 8 million residents in all five boroughs. The table above shows the number of residents, in thousands, from each of the five boroughs who own the specified number of cars. What percent of the New York City residents own more than the median number of cars per person and live in Manhattan?

23) If 8s = 4t + 17 and 6t − 5s = 4, what is the value of 6s + 4t ?

24) Circle C is defined by the equation x² + y² − 8x + ky = 172, and parabola P is defined by the equation y = x² − 8x + 22. For which value of k will circle C be centered at the vertex of parabola P?

25)

An entomologist analyzed the populations of two bee colonies, H₁ and H₂. She documented the rate of increase, which is the number of bees added to a colony in that year, for each colony over a 10-year period starting in the year 2000. The findings are modeled in the graph above. Which of the following conclusions can be drawn based on the entomologist’s findings?

26) In 2007, a biologist introduced a colony of phytoplankton into Great Blue Fish Lake, which had never contained phytoplankton before. The number of phytoplankton y in Great Blue Fish Lake can be estimated using the equation y =  6.23^{\frac{k}{22}} , where k represents the number of months since the population was introduced. Which of the following is a proper interpretation of the elements of the equation?

27)

The scatterplot above show the size of the Arctic Ice Cap as observed from 1920 to 2015. Which of the following is the closest approximation of the average annual decrease in the area of the Arctic Ice Cap as indicated by the line of best fit?

28) For questions 28–31, solve the problem and enter your answer in the box below.

(x − 2)² + (y + 8)² = 144

The equation of a circle in the xy-plane is shown above. What is the length of the diameter of the circle?

29) For how many values of x does p(x) = 0 ?

30) Questions 30–31 refer to the following information.

A new car dealership offers a choice of two different compensation packages to its salespeople. With Package A, a salesperson is paid an annual salary of $10,000 plus a commission as a percentage of the sale price of each car sold that year. With Package B, a salesperson is not paid any salary but earns a fixed fee for each car sold that year. A salesperson must choose one of the packages at the time of hire and has the option to switch packages only on January 1 of each year.

On January 1, 2003, Jason chose compensation Package A. Jason sold 110 cars with a mean sales price of $30,000 that year. If Jason had chosen compensation Package B, his total compensation for the year would have been $1,550 more. If the commission percentage of Package A was 1%, what was the fixed fee per car, in dollars, for compensation Package B in 2003 ?

31) Questions 30–31 refer to the following information.

A new car dealership offers a choice of two different compensation packages to its salespeople. With Package A, a salesperson is paid an annual salary of $10,000 plus a commission as a percentage of the sale price of each car sold that year. With Package B, a salesperson is not paid any salary but earns a fixed fee for each car sold that year. A salesperson must choose one of the packages at the time of hire and has the option to switch packages only on January 1 of each year.

In 2005, the commission percentage of Package A was 1.5%, and the fixed fee per car of Package B was $725. Jason sold 80 cars that year and determined that his total compensation would be the same under both Package A and Package B. What is the mean price, in thousands of dollars, of the cars that Jason sold in 2005 ?