Praxis Core Math practice test (5733): free drill, formulas and worked examples

Praxis Core Mathematics (5733) is 56 questions in 90 minutes, about 96 seconds each, with an on-screen four-function calculator. Questions are multiple choice, select one or more, and numeric entry. Most states ask for 150. The free drill below is 12 original questions at the real pace, with every answer worked out.

56
questions on the real test: 90 min
about 96 seconds each: 150
most common cut score: 12
questions in the free drill

Last checked 13 November 2026 · Counts and calculator from ETS's study companion and test page for Core Math (5733)

Free Math drill: 12 original Praxis Core-style Math questions at the real pace, then every answer worked out. No sign-up.

12
questions
19:17
time limit
Free
every answer explained

By the LifeScore Editorial Team · Updated 13 November 2026 · How we check facts · How this is scored

What is on the Praxis Core Math test?

Three ETS categories: number and quantity (the largest), data and probability, and algebra and geometry. It is everyday and pre-algebra math, not calculus or trigonometry.

The three Math categories (ETS study companion 5733)
Category	Share	Topics
Number and Quantity	About 36%	Fractions, decimals and percents, ordering numbers, ratios, rates and proportions, unit conversions, place value
Data Interpretation and Representation, Statistics and Probability	About 32%	Tables and graphs, mean, median, mode and range, two-way tables, simple and compound probability
Algebra and Geometry	About 32%	Linear equations and inequalities, patterns and functions, perimeter, area and volume, angles, the Pythagorean theorem

Two-thirds of the test is number sense and data, the math a teacher uses with grades and budgets. That is where to start if your score is well below the cut.

Which formulas do I need for Praxis Core Math?

The percent, average and probability relationships, plus the basic area, volume and right-triangle formulas. Know what each is for, so you choose the right one quickly.

The relationships that appear most in our practice questions
Topic	Formula or fact
Percent	Part = percent × whole; whole = part ÷ percent
Percent change	(new − original) ÷ original
Mean and median	Mean = total ÷ count; median = middle value after sorting
Probability	Favorable ÷ total; without replacement, the second draw has one fewer
Rectangle and box	Area = length × width; volume = length × width × height
Circle	Area = πr²; circumference = 2πr; r = diameter ÷ 2
Triangle	Angles add to 180°; right triangle: a² + b² = c²
Slope	Change in y ÷ change in x

On select-one-or-more questions every correct choice must be selected and no wrong one; on numeric entry you type the exact value. Our practice questions are all single-answer, so read those two formats on the real test carefully.

What do Praxis Core Math questions look like?

Short problems with five options, one of which comes from the most common slip. Five examples follow, from percents to the Pythagorean theorem; the first is worked in full.

Praxis Core-style question 1 · Percent of a whole
A class has 28 students, and 75% of them returned their field trip permission slips. How many students did NOT return a slip?
1. A7
2. B21
3. C25
4. D3
5. E14
Worked answer
A: 7. 75% of 28 is 0.75 × 28 = 21 students who returned slips, so 28 − 21 = 7 did not. Or directly: 25% of 28 = 7.
1. Returned: 0.75 × 28 = 21.
2. Not returned: 28 − 21 = 7.
3. Check: 25% of 28 is 7.
The trap: Answering 21, the number who did return a slip. Underline "NOT" before you calculate.
Praxis Core-style question 2 · Percent change
The price of a classroom calculator rose from $16 to $20. By what percent did the price increase?
1. A20%
2. B25%
3. C4%
4. D80%
5. E125%
Show the worked answer
B: 25%. The increase is $4. Percent change divides by the original price: 4 ÷ 16 = 0.25, or 25%.
1. Change: 20 − 16 = $4.
2. Divide by the original: 4 ÷ 16 = 0.25.
3. Write as a percent: 25%.
The trap: Dividing by the new price: 4 ÷ 20 = 20%.
Praxis Core-style question 3 · Median
Six students scored 12, 15, 9, 20, 15 and 11 points on a quiz. What is the median score?
1. A13.5
2. B15
3. C13.67
4. D14.5
5. E12
Show the worked answer
A: 13.5. Sort the scores: 9, 11, 12, 15, 15, 20. With six values the median is the mean of the third and fourth: (12 + 15) ÷ 2 = 13.5.
1. Sort: 9, 11, 12, 15, 15, 20.
2. Six values, so take the 3rd and 4th: 12 and 15.
3. Average them: 27 ÷ 2 = 13.5.
The trap: Averaging the two middle numbers of the unsorted list (9 and 20) gives 14.5; the mean of all six is about 13.67; the mode is 15.
Praxis Core-style question 4 · Linear equation
If 3(x − 4) = 2x + 5, what is the value of x?
1. A17
2. B7
3. C9
4. D−7
5. E1
Show the worked answer
A: 17. Distribute: 3x − 12 = 2x + 5. Subtract 2x from both sides: x − 12 = 5. Add 12: x = 17.
1. Distribute the 3: 3x − 12.
2. Subtract 2x: x − 12 = 5.
3. Add 12: x = 17. Check: 3 × 13 = 39 and 2 × 17 + 5 = 39.
The trap: Distributing only to the x (3x − 4) gives 3x − 4 = 2x + 5, so x = 9.
Praxis Core-style question 5 · Pythagorean theorem
A ramp rises 9 feet over a horizontal distance of 12 feet. How long is the ramp's sloped surface?
1. A15 feet
2. B21 feet
3. C10.5 feet
4. D225 feet
5. E108 feet
Show the worked answer
A: 15 feet. The rise and the run are the legs of a right triangle and the ramp is the hypotenuse: 9² + 12² = 81 + 144 = 225, and √225 = 15.
1. Square the legs: 81 and 144.
2. Add: 225.
3. Take the square root: 15 feet.
The trap: Adding the legs (21) or stopping at 225 before taking the square root.

These are written for this page and are not in any mock. More are on Praxis Core sample questions.

More Math practice

Four Math drills and four full mocks with new numbers every time, every answer worked out.

The Praxis Core Pass Pack gives you 4 full mocks on the real clock, 12 drills of 12 questions for the sections that cost you points, and a predictor that turns your mocks into the odds of reaching your target. One payment, no subscription, and your free score stays free.

Prep courses for these tests usually cost $19 to $129. The Praxis Core Pass Pack is US$39 (£29), once.

See the Praxis Core Pass Pack How our questions are built and checked

4
timed mocks: 12
topic drills: 1
score predictor

How should I use the Praxis Core calculator?

For arithmetic you have already set up. It is a basic on-screen four-function calculator, so it cannot fix a wrong setup and it is slower than mental math for easy steps.

Write the one-line setup on your scratch paper first: 0.75 × 28, or (20 − 16) ÷ 16.
Estimate before you calculate, so an answer ten times too big stands out.
Use the calculator for multi-digit multiplication and division, not for 10% of 240.
Check whether the question asks for the part or the rest: "how many did NOT."

What are the most common Praxis Core Math mistakes?

Dividing percent change by the new value, taking a median without sorting, using the diameter as the radius, forgetting to flip an inequality, and answering the part when the question asks for the rest.

Every wrong option in a well-built math question is the answer to one of these slips. That is good news: it means most lost points come from a handful of habits, not from math you never learned. Our explanations name the slip behind each wrong option so you can see which ones are yours.

If you are far below the cut, start with percents and data, which are two-thirds of the test. The Praxis Core Reading and Writing pages cover the other tests the same way.

How should I practise for Praxis Core Math?

Take the free drill, sort every miss by topic and slip, rebuild the weakest topic untimed, then return to the clock. Most candidates move fastest on percents and data.

Fifteen minutes a day on one topic beats two hours once a week. Do five untimed questions, check each against the explanation, then do a timed set. The free Praxis Core practice test runs Math with the other two tests, and the full plan is in how to pass Praxis Core.

Frequently asked questions

Can I use a calculator on Praxis Core Math?

Yes. ETS provides an on-screen four-function calculator. You cannot bring your own.

What score do I need on Praxis Core Math?

150 in most states we could source; Pennsylvania uses 142 and Mississippi 130. See Praxis Core passing scores.

Is there a formula sheet on Praxis Core Math?

Some formulas may be given with a question, but plan to know the basic percent, average, area, volume and right-triangle relationships.

How long is Praxis Core Math?

ETS lists 90 minutes for 56 questions. One university page gives 85 minutes; we use ETS's figure.

Reach your Math cut score the first time

Four Praxis Core-style mocks, four Math drills and every answer worked out, for one payment.