HSPT math: 64 questions in 45 minutes, no calculator
Mathematics is the fourth and longest HSPT section: 64 questions in 45 minutes, about 42 seconds each, with no calculator. On STS's sample form, 29 questions are numbers and numeration (including word problems), 12 geometry, 9 statistics and probability, 7 measurement and 7 algebra.
Updated October 23, 2026 · by AdmitTest
The topics and counts are from STS's HSPT manual (one sample form); the 45 minutes from diocese pages; "calculators are not permitted" from STS's parents' page. Every sample below is a practice question written by us.
| Area | On the sample form | Includes |
|---|---|---|
| Numbers and numeration | 29 | Operations; roots, exponents and place value; ratio and proportion; factors and multiples; word problems (15) |
| Geometry | 12 | Points, lines and angles; plane and solid figures; perimeter, area and volume; circles; congruence, symmetry, the Pythagorean theorem |
| Statistics and probability | 9 | Mean, median, mode and range; probability; data, graphs and tables |
| Measurement | 7 | Weight, length and volume; time and temperature; metric and money conversion |
| Algebra | 7 | Equations and inequalities; functions and coordinates |
Numbers, operations and word problems
The biggest block. Write the numbers down rather than holding them in your head, and estimate first: if the choices are far apart, rounding finds the answer in seconds. With fractions and percents, turn everything into one form before comparing or adding.
Sample · Numbers and operations · written by AdmitTest
Which mixed number is equal to 4.36?
- 4 1/8
- 4 6/25
- 4 9/25
- 4 11/25
Answer: C. 0.36 = 36/100, which simplifies to 9/25. So 4.36 = 4 9/25.
Measurement
Most measurement mistakes are unit mistakes. Write the units next to every number (12 inches = 1 foot, 100 centimeters = 1 meter, 60 minutes = 1 hour) and check that the answer is in the unit the question asks for.
Sample · Measurement · written by AdmitTest
Grace is 6 feet 7 inches tall. What is Grace's height in inches?
- 79
- 81
- 83
- 91
Answer: A. 6 feet = 6 × 12 = 72 inches, and 72 + 7 = 79 inches.
Geometry
Draw or mark the figure, and write the formula before putting numbers into it. The ones to know by heart: rectangle area = length × width, triangle area = ½ × base × height, circle area = πr² and circumference = 2πr, box volume = length × width × height, and a² + b² = c² for right triangles.
Sample · Geometry · written by AdmitTest
Two lines intersect, forming four angles. One of the angles measures 128°. What is the measure of an angle directly across from it?
- 128°
- 130°
- 138°
- 232°
Answer: A. Angles directly across from each other (vertical angles) are equal, so it also measures 128°.
Algebra
Undo the operations in reverse order, the same on both sides, and check the answer by putting it back into the equation. With an inequality, multiplying or dividing by a negative number flips the sign.
Sample · Algebra · written by AdmitTest
If 82 − 6y = 40, what is the value of y?
- −7
- 6
- 7
- 10
Answer: C. Subtract 82 from both sides: −6y = −42. Divide by −6: y = 7.
Statistics and probability
Mean = total ÷ how many; median = the middle value once they are in order; mode = the most frequent; range = largest minus smallest. Probability = favorable outcomes ÷ all outcomes. For a graph or table, read the question first, then only the part of the chart it asks about.
Sample · Statistics and probability · written by AdmitTest
On four days, a shop sold 22, 95, 53, and 46 sandwiches. What is the mean of these numbers?
- 54
- 56
- 72
- 73
Answer: A. Add the numbers: 22 + 95 + 53 + 46 = 216. Divide by 4: 216 ÷ 4 = 54.
Pacing: about 42 seconds a question
The most time per question on the HSPT, all by hand. Do the questions you can do at once, and do not let one long word problem eat three minutes: mark a best guess and return to it if time remains (there is no penalty for a wrong answer). Leave a minute at the end to fill in an answer for anything still blank.
Free full-length HSPT practice test. 298 questions in five timed sections, no sign-up. Your child's score by section and by skill when it ends.
Start the free testCommon questions
What math is on the HSPT?
Computation, problem solving and concepts in numbers and numeration, measurement, geometry, algebra and statistics, in STS's words. That covers fractions, decimals, percents, ratios, exponents and roots, word problems, units and conversions, angles, area, perimeter, volume, circles, the Pythagorean theorem, equations and inequalities, coordinates, mean, median, mode, range, probability and reading graphs and tables.
Can you use a calculator on the HSPT math section?
No. STS says calculators are not permitted for the Mathematics subtest. Scratch paper or the test booklet may be used.
Is algebra on the HSPT?
Some: 7 of 64 questions on STS's sample form, on equations, inequalities, functions and coordinates. Most of the section is numbers and word problems (29) and geometry (12).
What formulas should my child know for the HSPT?
Area and perimeter of rectangles, triangles and circles, the circumference of a circle, the volume of a rectangular box, the Pythagorean theorem, percent and ratio, and mean, median, mode and range. Practice them by hand, without a calculator.