Free Praxis Core Math Practice Questions (With Worked Solutions)

The Praxis Core Math test (5733) doesn’t test advanced math — it tests whether you can apply high-school-level number sense, algebra, geometry and statistics accurately and under time. The best prep is practicing that exact style of question and locking in a reliable method for each. Below are 8 practice questions at Praxis Core level, each with a full worked solution that shows the method.

An on-screen four-function calculator is available on the real test, so a couple of these are quicker with it — but knowing the method still saves you time and catches careless errors. When you’re done, take the complete, full-length Praxis Core Math mock exam — free for instant scoring and a worked explanation on every question.

Try each one first, then read the solution. Understanding why an approach works is what makes it stick.

The questions

1. Percent increase

A teacher’s salary of $48,000 rises by 5%. What is the new salary?

Worked solution. 5% of 48,000 = 48,000 × 0.05 = $2,400. New salary = 48,000 + 2,400 = $50,400.

2. Proportion (unit rate)

If 3 markers cost $4.50, how much do 7 markers cost at the same rate?

Worked solution. Find the unit rate: 4.50 ÷ 3 = $1.50 each. Then 7 × 1.50 = $10.50.

3. Solve a linear equation

Solve for x: 3x − 7 = 20.

Worked solution. Add 7 to both sides: 3x = 27. Divide by 3: x = 9. (Check: 3 × 9 − 7 = 27 − 7 = 20 ✓.)

4. Statistics — median

Find the median of: 4, 8, 8, 10, 15.

Worked solution. The values are already in order; the median is the middle one. With five values, the middle is the 3rd: 8. (Don’t confuse it with the mean, which here would be 45 ÷ 5 = 9.)

5. Geometry — area

A rectangular classroom is 12 ft by 9 ft. What is its area?

Worked solution. Area of a rectangle = length × width = 12 × 9 = 108 square feet.

6. Probability

A bag holds 3 red and 5 blue marbles. If you draw one at random, what is the probability it’s red?

Worked solution. Probability = favorable ÷ total = 3 ÷ (3 + 5) = 3/8 (0.375, or 37.5%).

7. Average speed (rate)

A car travels 150 miles in 3 hours. What is its average speed?

Worked solution. Speed = distance ÷ time = 150 ÷ 3 = 50 miles per hour.

8. Adding fractions

Calculate: 2/5 + 1/10.

Worked solution. Use a common denominator of 10: 2/5 = 4/10. Then 4/10 + 1/10 = 5/10 = 1/2.

How to turn practice into a passing score

Score isn’t about speed — it’s about a small set of methods you can run without hesitating: unit rates, “percent means × 0.0-something”, isolate the variable, mean vs median, area formulas, probability as a fraction. For every question you miss, note the single step that tripped you and redo a similar one a day later.

Not sure what’s actually tested? Start with Praxis Core Math: what’s tested and the on-screen calculator, then get the full picture in Praxis Core, explained.

Ready for the real thing?

These 8 are a sample. Take the full-length Praxis Core Math mock exam — free, no card — real length and timing, instant scoring, and a worked solution for every question, so you know exactly which topics to prioritize before test day.

FAQ

Are these real Praxis Core questions? No — real Praxis questions are secure. These are original questions written at the same level and testing the same skills, so the methods transfer directly to the exam.

Is a calculator allowed on Praxis Core Math? Yes — an on-screen four-function calculator is provided. Questions 1, 6 and 7 above are quick with it, but the method matters more than the button-pushing.

What’s a passing score? See what score you need to pass the Praxis Core for how the passing standard works in your state.

How long is the real test? The free mock exam mirrors the real length and timing so you can practice pacing, not just the math.