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High School Math quiz

High School Math Quiz

Practice high school math questions about algebra, functions, geometry, exponents, systems of equations, quadratic expressions, probability, and statistics. 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

Solve for x: 3x + 8 = 2x + 19

Hint: Move the x-terms to one side and the constants to the other side.
Explanation: Subtract 2x from both sides: x + 8 = 19. Subtract 8 from both sides: x = 11.
2 Question 2 of 10
Not answered

Factor the expression: x² + 7x + 12

Hint: Find two numbers that multiply to 12 and add to 7.
Explanation: The numbers 3 and 4 multiply to 12 and add to 7. So x² + 7x + 12 = (x + 3)(x + 4).
3 Question 3 of 10
Not answered

If f(x) = 2x² - 3x, what is f(4)?

Hint: Substitute x = 4 into the function and calculate the power first.
Explanation: f(4) = 2(4²) - 3(4) = 2(16) - 12 = 32 - 12 = 20.
4 Question 4 of 10
Not answered

What is the slope of the line through points (1, 4) and (5, 12)?

Hint: Slope = change in y divided by change in x.
Explanation: The change in y is 12 - 4 = 8. The change in x is 5 - 1 = 4. The slope is 8/4 = 2.
5 Question 5 of 10
Not answered

Solve the system: x + y = 14 and x - y = 2. What is y?

Hint: Add the equations first to find x, then substitute back to find y.
Explanation: Add the equations: 2x = 16, so x = 8. Substitute into x + y = 14: 8 + y = 14, so y = 6.
6 Question 6 of 10
Not answered

A right triangle has legs 10 and 24. What is the hypotenuse?

Hint: Use the Pythagorean theorem: a² + b² = c².
Explanation: 10² + 24² = 100 + 576 = 676. The square root of 676 is 26, so the hypotenuse is 26.
7 Question 7 of 10
Not answered

Simplify: (2³)(2⁵) / 2²

Hint: When multiplying powers with the same base, add exponents. When dividing, subtract exponents.
Explanation: (2³)(2⁵) / 2² = 2^(3+5-2) = 2⁶.
8 Question 8 of 10
Not answered

What is the solution to x² = 49?

Hint: A positive square can come from a positive or a negative number.
Explanation: Both 7² and (-7)² equal 49. Therefore, x = ±7.
9 Question 9 of 10
Not answered

A bag contains 5 red, 4 blue, and 3 green marbles. What is the probability of choosing a blue marble?

Hint: Probability = favorable outcomes divided by total outcomes, then simplify.
Explanation: There are 4 blue marbles and 12 marbles total. The probability is 4/12 = 1/3.
10 Question 10 of 10
Not answered

The scores are 72, 85, 90, 90, and 98. What is the median score?

Hint: The data is already in order. Choose the middle value.
Explanation: There are 5 scores, so the median is the 3rd value. The 3rd value is 90.

Your result

You answered 0 out of 10 questions correctly.

High school problem board

High school math is less about one formula and more about choosing the right structure

These 10 questions cover linear equations, factoring, functions, slope, systems, right triangles, exponent laws, square equations, probability, and median. A strong high-school solver should be able to move between symbolic, graphical, geometric, and statistical representations without treating them as separate subjects.

Algebraequations, factoring, roots
Functionsevaluation, slope
Geometryright triangles
Dataprobability, median
Factoring board

Factoring reverses multiplication

For x² + 7x + 12, look for two numbers whose product is 12 and whose sum is 7. That pair is 3 and 4.

Forward direction

Multiply two binomials and collect terms.

(x + 3)(x + 4) = x² + 7x + 12

Reverse direction

Start from the quadratic and recover the binomial factors.

x² + 7x + 12 = (x + 3)(x + 4)
Square equation

x² = 49 has two real solutions because squaring removes the sign

Both 7 and −7 produce the same square. That is why solving x² = 49 requires the ± symbol.

x² = 49
x = ±√49
x = ±7
Function & slope lab

A function rule describes output; slope describes change

Evaluate f(4)

f(x) = 2x² − 3x
f(4) = 2(4²) − 3(4)
= 32 − 12
= 20

Find slope

(1,4) → (5,12)
Δy = 12 − 4 = 8
Δx = 5 − 1 = 4
m = 8/4 = 2
System of equations

A solution to a system must satisfy both equations at once

For x + y = 14 and x − y = 2, adding the equations eliminates y immediately.

x + y = 14
x − y = 2
2x = 16 → x = 8
8 + y = 14 → y = 6
Geometry

10–24–26 is a scaled Pythagorean triple

10² + 24² = 26²
100 + 576 = 676
√676 = 26
Hypotenuse = 26
Exponent laws

Multiplication adds exponents; division subtracts them

(2³)(2⁵) / 2² = 2⁶
3 + 5 = 8
8 − 2 = 6
Same base: keep 2, update exponent
Probability vs statistics

Probability predicts uncertainty; statistics summarizes observed data

Probability

4 blue marbles out of 12 total gives a probability of 4/12 = 1/3.

Median

For 72, 85, 90, 90, 98, the middle ordered value is 90.

7285909098
High-school extension

Use factoring to solve a quadratic, not just rewrite it

The quiz asks only to factor x² + 7x + 12. A natural next step is to solve x² + 7x + 12 = 0.

x² + 7x + 12 = 0
(x + 3)(x + 4) = 0
x + 3 = 0 or x + 4 = 0
Read your result by domain

A single score hides which high-school skill actually needs work

Review the missed questions by mathematical domain rather than only by the total number correct.

Algebralinear equations, factoring, square equations
Functionssubstitution, slope, coordinate change
Geometry & powersPythagorean theorem, exponent laws
Dataprobability, median, interpretation
Grade-level quizzes Continue to Hard Math