Hard Math quiz

Hard Math Quiz: Challenge Problems

Challenge yourself with harder math questions that mix algebra, arithmetic, fractions, geometry, patterns, percentages, and reasoning. Use hints when needed, choose an answer, and review the explanation after each question.

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1 Question 1 of 10

Not answered

If 3x + 7 = 2x + 19, what is the value of x?

Hint: Move all x-terms to one side and constants to the other side.

Explanation: Subtract 2x from both sides: x + 7 = 19. Subtract 7 from both sides: x = 12.

2 Question 2 of 10

Not answered

What is the value of 5² + 3³ - 4²?

Hint: Evaluate the powers first, then add and subtract.

Explanation: 5² = 25, 3³ = 27, and 4² = 16. So 25 + 27 - 16 = 36.

3 Question 3 of 10

Not answered

A number is increased by 25% and becomes 100. What was the original number?

Hint: After a 25% increase, the new value is 125% of the original.

Explanation: Let the original number be x. Then 1.25x = 100. Divide by 1.25: x = 80.

4 Question 4 of 10

Not answered

If a right triangle has hypotenuse 13 and one leg 5, what is the other leg?

Hint: Use the Pythagorean theorem: a² + b² = c².

Explanation: Let the missing leg be b. Then 5² + b² = 13². So 25 + b² = 169, b² = 144, and b = 12.

5 Question 5 of 10

Not answered

Simplify: 2/3 + 3/4.

Hint: Use 12 as a common denominator.

Explanation: Convert both fractions: 2/3 = 8/12 and 3/4 = 9/12. Then 8/12 + 9/12 = 17/12.

6 Question 6 of 10

Not answered

The average of 6, 10, x, and 20 is 13. What is x?

Hint: If the average of 4 numbers is 13, their total is 4 × 13.

Explanation: The total must be 4 × 13 = 52. The known numbers add to 6 + 10 + 20 = 36. So x = 52 - 36 = 16.

7 Question 7 of 10

Not answered

What is the next number in the pattern: 2, 6, 12, 20, 30, ?

Hint: Look at the differences between consecutive terms.

Explanation: The differences are 4, 6, 8, 10. The next difference is 12, so the next number is 30 + 12 = 42.

8 Question 8 of 10

Not answered

If y = 2x² - 3 and x = 4, what is y?

Hint: Substitute x = 4 into the expression and square 4 first.

Explanation: Since x = 4, y = 2(4²) - 3 = 2 × 16 - 3 = 32 - 3 = 29.

9 Question 9 of 10

Not answered

A rectangle has area 96 and width 8. What is its length?

Hint: For a rectangle, area = length × width.

Explanation: Use area = length × width. So 96 = length × 8. Divide by 8: length = 12.

10 Question 10 of 10

Not answered

There are 5 blue, 3 red, and 2 green marbles in a bag. What is the probability of not picking a red marble?

Hint: Count all marbles that are not red, then divide by the total number of marbles.

Explanation: There are 10 marbles total. Not red means blue or green: 5 + 2 = 7 marbles. The probability is 7/10.

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About this math quiz

This carousel quiz template shows one question at a time. Students can move back and forward, request a hint, answer the question, and then review the explanation.

You can reuse this file for Algebra, Geometry, Arithmetic, Fractions, Statistics, and Hard Math pages by changing the PHP array with questions at the top of the file.