PSAT Question of the Day

Sharpen your PSAT prep — and get a head start on the SAT — with a fresh practice question, updated daily.

25 October 2026

Subject: MathGeometry and TrigonometryVolume of prisms, cylinders, and rectangular solids

Question

Sarah, a homeschooled student, is designing a small terrarium for her biology project. She has chosen a rectangular glass container for her design. The container has an interior length of 20 centimeters, a width of 15 centimeters, and a height of 10 centimeters. Sarah needs to determine the maximum volume of soil and water the terrarium can hold to ensure her plants have enough space and moisture.

What is the maximum volume, in cubic centimeters, of soil and water the terrarium can hold?

Select an Answer

300 cm³
45 cm³
350 cm³
3000 cm³

Rationale:

The volume of a rectangular prism, such as the terrarium described, is calculated by multiplying its length, width, and height. Given the interior dimensions: length = 20 cm, width = 15 cm, and height = 10 cm, the volume is calculated as follows:

Volume = Length × Width × Height

Volume = 20 cm × 15 cm × 10 cm

Volume = 300 cm² × 10 cm

Volume = 3000 cm³

This means the terrarium can hold a maximum of 3000 cubic centimeters of soil and water.

The option 300 cm³ is incorrect because it results from multiplying only the length and width (20 × 15 = 300), which calculates the area of the base but omits the height necessary for volume.

The option 45 cm³ is incorrect because it results from adding the three dimensions (20 + 15 + 10 = 45), which is not the formula for calculating volume and would represent an incorrect understanding of how volume is measured.

The option 350 cm³ is incorrect because it could result from an incorrect calculation combining addition and multiplication, such as (length + width) × height = (20 + 15) × 10 = 35 × 10 = 350. This does not represent the correct formula for the volume of a rectangular prism.

24 October 2026

Subject: Reading and WritingStandard English ConventionsSentence boundaries — identifying and correcting fragments vs. complete sentences

Question

A recent analysis of global energy consumption, summarized in the accompanying chart, shows a clear upward trend in renewable energy adoption over the past decade. Notably, solar power experienced the most significant growth. Increasing by an average of 15% annually. While fossil fuel use still dominates, its proportional share has slightly declined. This shift suggests a growing worldwide commitment to sustainable practices. Though challenges remain, the data offers a promising outlook for future energy landscapes.

Which choice best combines the underlined text with the preceding sentence?

Select an Answer

Notably, solar power experienced the most significant growth. And increasing by an average of 15% annually.
Notably, solar power experienced the most significant growth; it increased by an average of 15% annually.
Notably, solar power experienced the most significant growth, and increasing by an average of 15% annually.
Notably, solar power experienced the most significant growth, increasing by an average of 15% annually.

Rationale:

The original text contains a sentence fragment: "Increasing by an average of 15% annually." This phrase lacks a subject and a finite verb to form a complete independent clause. The correct option (options[0]) integrates this participial phrase into the preceding sentence, where it functions as a nonessential modifier describing the "growth" or the manner in which solar power experienced growth. This creates a grammatically correct and concise sentence.

Options[1] corrects the fragment by creating a new independent clause ("it increased...") and joining it with a semicolon. While grammatically permissible, it is less concise and stylistically less effective than integrating the participial phrase directly, which is generally preferred for smooth flow when describing an action related to the main clause. Options[2] uses "and" but incorrectly pairs it with a participial phrase; "and" typically joins grammatically parallel elements, which is not the case here, thus creating a grammatical error. Options[3] fails to correct the fragment; by starting a new sentence with "And increasing," it leaves the participial phrase as an incomplete thought, essentially maintaining the original grammatical error.

23 October 2026

Subject: MathProblem-Solving and Data AnalysisStatistics — calculating and interpreting mean, median, mode, and range

Question

A science class with five students recorded their individual scores on a recent project: 72, 78, 80, 85, and 90. From these scores, the teacher calculated the mean, median, and range for the class. A new student then joined the class and completed the same project, earning a score of 100. The teacher updated the class's statistics to include this new score.

Based on this information, which of the following statements can be inferred about the updated statistics compared to the original statistics?

Select an Answer

The mean, median, and range all increased.
The mean increased, but the median decreased.
Only the mean and range increased, while the median remained the same.
The mean increased, but the median and range remained unchanged.

Rationale:

First, let's establish the original statistics for the five students' scores (72, 78, 80, 85, 90):

Original Mean: The sum of the scores is 72 + 78 + 80 + 85 + 90 = 405. The mean is 405 / 5 = 81.
Original Median: With the scores already in ascending order, the middle value of five scores is the third score, which is 80.
Original Range: The highest score (90) minus the lowest score (72) is 90 - 72 = 18.

Next, a new student joins with a score of 100. The new set of scores, in ascending order, is 72, 78, 80, 85, 90, 100. Now let's infer the changes to the statistics:

New Mean: The new score (100) is higher than the original mean (81). Adding a value greater than the existing mean will always increase the overall mean. The new sum is 405 + 100 = 505, and there are now 6 scores. The new mean is 505 / 6 ≈ 84.17. Thus, the mean increased.
New Median: The original set had 5 scores, so the median was the 3rd score (80). The new set has 6 scores. The median for an even number of data points is the average of the two middle scores (the 3rd and 4th scores in this case). In the new ordered list (72, 78, 80, 85, 90, 100), the median is (80 + 85) / 2 = 82.5. Since 82.5 is greater than the original median of 80, the median increased.
New Range: The new score (100) is the highest score in the updated set, and it is higher than the previous highest score (90). The lowest score remains 72. The new range is 100 - 72 = 28. Since 28 is greater than the original range of 18, the range increased.

Therefore, based on the addition of a score higher than all previous scores and the existing statistics, it can be inferred that the mean, median, and range all increased.

Why other options are incorrect:

"Only the mean and range increased, while the median remained the same." This is incorrect because the median increased from 80 to 82.5. Adding a value above the original median when going from an odd to an even number of data points will generally shift the median upwards.
"The mean increased, but the median and range remained unchanged." This is incorrect because both the median and the range increased, as explained above. The new score was higher than the original maximum, directly increasing the range, and it was higher than the original median, shifting the median upwards.
"The mean increased, but the median decreased." This is incorrect. The median increased because the new score (100) was significantly higher than the original median (80). A median would decrease only if a new score significantly lower than the original median were added.

22 October 2026

Subject: MathGeometry and TrigonometryArea and perimeter of triangles, rectangles, and composite figures

Question

Maria, a first-generation college applicant, is volunteering to help design a new community garden. She has been tasked with calculating the area of a specific section to determine how much topsoil is needed. This section consists of a rectangular herb garden connected to a triangular flower bed. The rectangular section measures 8 feet in length and 5 feet in width. The triangular flower bed is attached along the 5-foot side of the rectangle, and its height from that side is 6 feet.

What is the total area, in square feet, of Maria's garden section?

Select an Answer

Rationale:

To find the total area of Maria's garden section, we need to calculate the area of the rectangular herb garden and the area of the triangular flower bed, then add them together.

First, calculate the area of the rectangular herb garden. The formula for the area of a rectangle is length × width. Given the length is 8 feet and the width is 5 feet, the area of the rectangle is 8 feet × 5 feet = 40 square feet.

Next, calculate the area of the triangular flower bed. The formula for the area of a triangle is (1/2) × base × height. The triangle is attached along the 5-foot side of the rectangle, so its base is 5 feet. The height is given as 6 feet. Therefore, the area of the triangle is (1/2) × 5 feet × 6 feet = (1/2) × 30 square feet = 15 square feet.

Finally, add the areas of the rectangle and the triangle to find the total area: Total Area = 40 square feet + 15 square feet = 55 square feet.

Distractor '40' is incorrect because it represents only the area of the rectangular section, omitting the area of the triangular flower bed.

Distractor '70' is incorrect because it results from calculating the area of the triangle as base × height (5 × 6 = 30) instead of applying the correct formula (1/2) × base × height, and then adding it to the rectangle's area (40 + 30 = 70).

Distractor '26' is incorrect because it represents the perimeter of the rectangular section (2 × (8 + 5) = 2 × 13 = 26), not the total area of the composite figure. This choice reflects a common confusion between calculating area and perimeter.

21 October 2026

Subject: MathAlgebraLinear equations in two variables — writing and graphing equations from real-world scenarios

Question

Alex, a high school junior, is tracking their savings for a summer program. They started the month with $320 in their savings account. Alex works part-time, earning $15 per hour. From their earnings, they consistently set aside $5 for every hour worked for their personal spending, depositing the remainder into savings. Let S represent the total amount in Alex's savings account, and h represent the total number of hours Alex has worked since the beginning of the month.

Based on the information provided, which of the following equations best models Alex's total savings, S, after working h hours?

Select an Answer

S = 10h + 320
S = 15h + 320
S = 20h + 320
S = 10h

Rationale:

The problem asks for an equation that models Alex's total savings, S, after working h hours. This is a linear relationship where the initial amount represents the y-intercept and the net hourly earning represents the slope.

Alex starts with $320 in savings. This is the initial value (the constant term or y-intercept).

Alex earns $15 per hour. However, they set aside $5 for personal spending for every hour worked. Therefore, the actual amount deposited into savings per hour is the difference between earnings and personal spending: $15 - $5 = $10 per hour. This is the rate of change (the coefficient of h).

Combining these, the equation that models Alex's total savings is S = 10h + 320.

Distractor 1 (S = 15h + 320) is incorrect because it uses the gross earning rate ($15 per hour) without accounting for the $5 per hour Alex sets aside for personal spending before depositing the remainder. This overestimates the rate at which savings increase.

Distractor 2 (S = 20h + 320) is incorrect because it mistakenly adds the gross earning rate ($15 per hour) and the personal spending rate ($5 per hour) to get $20 per hour. This would imply Alex is saving $20 per hour, which is not true.

Distractor 3 (S = 10h) is incorrect because it calculates the correct rate of change ($10 per hour) but neglects to include Alex's initial savings of $320, making it an incomplete model of their total savings.