Build comprehensive math confidence through diverse practice questions spanning arithmetic, pre-algebra, geometry, trigonometry, statistics, and calculus. Test your conceptual understanding and computational skills across all major math topics. Perfect for homework practice, standardized test prep (SAT, ACT, GRE), or assessing your readiness for the next math level.
12 sample questions. Expand to see answers and explanations.
1. Solve for x: 3x + 7 = 22
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Answer
x = 5
Explanation
Subtract 7 from both sides: 3x = 15. Then divide both sides by 3: x = 5. Check by substitution: 3(5) + 7 = 15 + 7 = 22 ✓
Type: multiple choice
2. What is the area of a circle with radius 6 cm?
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Answer
36π cm² (approximately 113.10 cm²)
Explanation
Use the formula A = πr². With r = 6: A = π(6)² = 36π ≈ 113.10 cm². Remember: area grows with the square of the radius (quadratic relationship).
Type: multiple choice
3. What is the median of the data set: 3, 7, 2, 9, 5?
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Answer
5
Explanation
First, sort the data: 2, 3, 5, 7, 9. The median is the middle value: 5. With even number of values, average the two middle numbers.
Type: multiple choice
4. If sin(θ) = 0.5, what is θ in degrees (0° to 90°)?
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Answer
30°
Explanation
sin(30°) = 0.5 = 1/2. This is a special angle you should memorize. Also: sin(45°) = √2/2, sin(60°) = √3/2, sin(90°) = 1.
Type: multiple choice
5. Simplify: (2x³)(3x²)
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Answer
6x⁵
Explanation
Multiply coefficients: 2 × 3 = 6. Add exponents: x³ · x² = x⁵. Result: 6x⁵. Exponent rule: when multiplying like bases, add the exponents.
Type: multiple choice
6. What is 15% of 80?
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Answer
12
Explanation
Convert 15% to decimal: 0.15. Multiply: 0.15 × 80 = 12. Alternatively: 15% = 15/100, so (15/100) × 80 = 1200/100 = 12.
Type: multiple choice
7. True or False: A triangle can have two obtuse angles.
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Answer
False
Explanation
False. An obtuse angle is greater than 90°. Two obtuse angles would sum to more than 180°, but the total of all three angles in a triangle must equal exactly 180°. Maximum one obtuse angle per triangle.
Type: true false
8. Find the derivative of f(x) = 4x³ + 2x
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Answer
f'(x) = 12x² + 2
Explanation
Use power rule: d/dx[xⁿ] = nxⁿ⁻¹. For 4x³: 4·3·x² = 12x². For 2x: 2·1·x⁰ = 2. Sum: f'(x) = 12x² + 2.
Type: multiple choice
9. What is the volume of a rectangular prism with length 4, width 3, height 5?
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Answer
60 cubic units
Explanation
Volume = length × width × height = 4 × 3 × 5 = 60 cubic units. 3D volumes always have cubic units.
Type: multiple choice
10. Evaluate: 2³ + 3²
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Answer
17
Explanation
2³ = 2 × 2 × 2 = 8. 3² = 3 × 3 = 9. Sum: 8 + 9 = 17. Remember order of operations: exponents before addition.
Type: multiple choice
11. What is the distance between points (1, 2) and (4, 6)?
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Answer
5
Explanation
Use distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²] = √[(4-1)² + (6-2)²] = √[9 + 16] = √25 = 5. This is Pythagorean theorem applied to coordinate plane.
Type: multiple choice
12. If P(A) = 0.3 and P(B) = 0.4 (independent events), what is P(A and B)?
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Answer
0.12
Explanation
For independent events, P(A and B) = P(A) × P(B) = 0.3 × 0.4 = 0.12. Independence means one event doesn't affect probability of the other.
Type: multiple choice
Workflow
Take a diagnostic practice test across all math topics to identify which areas (algebra, geometry, trig, calculus) you struggle with most
Review the explanations for missed questions carefully—understand WHY you made errors, not just what the right answer is
Work through similar problems from your textbook or online resources for topics you missed
Practice mixed problem sets—don't just drill one topic at a time, since real tests mix topics
Retake the full practice test after a week of study to verify you've mastered those problem types and track improvement
Tips
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Generate Now — FreePractice questions span arithmetic, pre-algebra, algebra, geometry, trigonometry, statistics, pre-calculus, and basic calculus. Covers middle school through early college math. Upload your course notes or textbook to generate questions matching your specific curriculum.
Yes. Every question includes a detailed explanation showing the complete solution process, relevant formulas, common pitfalls to avoid, and why the method works. Learn from mistakes, not just answers.
Start with a mixed diagnostic test. Your results show which topics you've mastered vs need review. Then generate targeted practice for weak areas. Work from foundational topics (algebra) toward advanced (calculus).
Yes. Practice questions build the problem-solving skills tested on standardized exams. For test-specific prep, also upload official practice tests to generate questions matching exact exam format and difficulty.