Algebra Quiz

Algebra uses symbols to describe relationships and solve problems. The quiz covers expressions, linear and quadratic equations, factorisation, exponents and simple word problems.

What this quiz covers

Study tip: Show every step on paper and substitute your answer back into the equation to check it.

Questions, answers and explanations

1. What is the value of x if x + 5 = 12?

  1. 5
  2. 6
  3. 7
  4. 8

Answer: 7

Subtract 5 from both sides: x = 12 - 5 = 7.

2. Simplify: 3x + 2x

  1. 5x
  2. 6x
  3. x²
  4. 3x²

Answer: 5x

Like terms are added together: 3x + 2x = 5x.

3. Solve: 2x = 18

  1. 6
  2. 7
  3. 8
  4. 9

Answer: 9

Divide both sides by 2: x = 9.

4. What is the value of 4²?

  1. 8
  2. 12
  3. 16
  4. 20

Answer: 16

4² means 4 × 4 = 16.

5. Simplify: x × x

  1. 2x
  2. x²
  3. x
  4. x³

Answer: x²

A variable multiplied by itself is written as x².

6. Solve: x - 9 = 15

  1. 6
  2. 24
  3. 15
  4. 18

Answer: 24

Add 9 to both sides: x = 15 + 9 = 24.

7. Simplify: 5(x + 2)

  1. 5x + 2
  2. 5x + 10
  3. 10x
  4. 7x

Answer: 5x + 10

Multiply 5 by both x and 2: 5x + 10.

8. What is the value of x if 3x = 27?

  1. 6
  2. 7
  3. 8
  4. 9

Answer: 9

Divide both sides by 3: x = 9.

9. Simplify: (a² × a³)

  1. a⁵
  2. a⁶
  3. a⁹
  4. a²

Answer: a⁵

When multiplying powers with the same base, add the exponents: 2 + 3 = 5.

10. If y = 4 and x = 3, what is the value of x + y?

  1. 5
  2. 6
  3. 7
  4. 8

Answer: 7

Substitute the values: 3 + 4 = 7.

11. Solve: 5x + 10 = 35

  1. 3
  2. 4
  3. 5
  4. 6

Answer: 5

Subtract 10 from both sides, then divide by 5: x = 5.

12. Simplify: (2x)(3x)

  1. 5x
  2. 6x
  3. 6x²
  4. 5x²

Answer: 6x²

Multiply coefficients and variables: 2×3 = 6 and x×x = x².

13. What is the value of 7²?

  1. 14
  2. 21
  3. 49
  4. 56

Answer: 49

7² = 7 × 7 = 49.

14. Solve: x/4 = 6

  1. 10
  2. 20
  3. 24
  4. 28

Answer: 24

Multiply both sides by 4: x = 24.

15. Which expression is a binomial?

  1. x
  2. x + 2
  3. x² + x + 1
  4. 5

Answer: x + 2

A binomial has exactly two terms.

16. Factorize: x² − 9

  1. (x − 3)(x + 3)
  2. (x − 9)(x + 1)
  3. (x − 3)²
  4. Cannot be factorized

Answer: (x − 3)(x + 3)

x² − 9 is a difference of squares: a² − b² = (a − b)(a + b).

17. What is the value of x if 2x + 4 = 18?

  1. 5
  2. 6
  3. 7
  4. 8

Answer: 7

Subtract 4 from both sides and divide by 2: x = 7.

18. Simplify: (x³ × x²)

  1. x⁵
  2. x⁶
  3. x⁹
  4. x

Answer: x⁵

When multiplying powers with the same base, add the exponents: 3 + 2 = 5.

19. Solve: 4x = 32

  1. 6
  2. 7
  3. 8
  4. 9

Answer: 8

Divide both sides by 4: x = 8.

20. Which of the following is a quadratic expression?

  1. 2x + 5
  2. x² + 3x + 2
  3. 7
  4. x³ + 1

Answer: x² + 3x + 2

A quadratic expression has the highest power of x equal to 2.

Take the timed quiz