Algebra Practice Questions for Matric Maths

Practice questions with solutions

Solve: 2x² − 7x + 3 = 0

1. Use quadratic formula
2. x = (7 ± √(49 − 24)) / 4
3. x = (7 ± 5)/4

Answer: x = 3 or x = 1/2

Simplify: (x³ · x⁵) / x²

1. Add exponents in numerator
2. Subtract exponent in denominator

Answer: x⁶

Solve: 3x − 4 ≥ 11

1. Add 4 to both sides
2. Divide by 3

Answer: x ≥ 5

Solve simultaneously: y = x + 1 and x² + y² = 13

1. Substitute y = x + 1: x² + (x + 1)² = 13
2. 2x² + 2x − 12 = 0, so x² + x − 6 = 0
3. (x + 3)(x − 2) = 0, so x = −3 or x = 2
4. Substitute back: y = −2 or y = 3

Answer: (2; 3) or (−3; −2)

Solve: x² − x − 12 < 0

1. Factorise: (x − 4)(x + 3) < 0
2. Critical values: x = −3 and x = 4
3. The parabola opens upwards, so it is negative between the roots

Answer: −3 < x < 4

Simplify: √50 + √18

1. √50 = √(25 × 2) = 5√2
2. √18 = √(9 × 2) = 3√2
3. Add like surds

Answer: 8√2

Solve: 2ˣ⁺¹ = 32

1. Write 32 as a power of 2: 32 = 2⁵
2. Equate the exponents: x + 1 = 5

Answer: x = 4

For which value of k does x² + 4x + k = 0 have equal roots?

1. Equal roots means Δ = 0
2. Δ = b² − 4ac = 16 − 4k
3. 16 − 4k = 0

Answer: k = 4

Solve: x(x + 3) = 10

1. Expand and rearrange: x² + 3x − 10 = 0
2. Factorise: (x + 5)(x − 2) = 0

Answer: x = −5 or x = 2

Solve: √(2x + 3) = x

1. Square both sides: 2x + 3 = x²
2. x² − 2x − 3 = 0, so (x − 3)(x + 1) = 0
3. Check: x = −1 gives √1 = 1 ≠ −1, so reject it

Answer: x = 3

Simplify: (2ˣ⁺² − 2ˣ) / (3 · 2ˣ)

1. Factorise the numerator: 2ˣ(2² − 1) = 3 · 2ˣ
2. Cancel the common factor 3 · 2ˣ

Answer: 1

Tips

• Know the quadratic formula well, even though it is on the information sheet.
• Always check for extraneous solutions when squaring.
• Write a, b and c down before substituting into the formula.
• Give inequality answers in the notation the question asks for.
• Factorise completely before you cancel anything in a fraction.