Grade 11 Maths Practice Questions

Get a head start on Matric with Grade 11 Maths practice covering algebra, functions and trig — with step-by-step solutions.

Grade 11 sets the foundation for Matric. These practice questions strengthen the core topics — quadratics, functions, trig identities and analytical geometry — that you'll see again in Grade 12. Most Grade 12 questions assume Grade 11 skills: factorising, completing the square, the sine and cosine rules, gradients and number patterns. If Grade 12 work feels difficult, the gap is often a Grade 11 skill. Work through these questions and revise any topic where you needed the steps.

Practice questions with solutions

Solve: x² − 4 = 0

  1. x² = 4
  2. x = ±2

Answer: x = ±2

Simplify: 2(x + 3) − 4

  1. 2x + 6 − 4

Answer: 2x + 2

Solve: x² + 5x + 6 = 0

  1. Factorise: (x + 2)(x + 3) = 0

Answer: x = −2 or x = −3

Find the gradient of the line through (2; 3) and (6; 11)

  1. m = (11 − 3) / (6 − 2) = 8/4

Answer: m = 2

Simplify: tanx · cosx

  1. tanx = sinx/cosx
  2. (sinx/cosx) · cosx

Answer: sinx

Find the turning point of y = x² − 6x + 5

  1. x = −b/2a = 6/2 = 3
  2. y = 9 − 18 + 5 = −4

Answer: (3; −4)

Find the general term of 2; 5; 10; 17; …

  1. First differences: 3; 5; 7. Second difference: 2, so 2a = 2 and a = 1
  2. 3a + b = 3 gives b = 0
  3. a + b + c = 2 gives c = 1

Answer: Tₙ = n² + 1

Solve: x² − 2x − 8 ≤ 0

  1. Factorise: (x − 4)(x + 2) ≤ 0
  2. Critical values −2 and 4; the parabola opens upwards

Answer: −2 ≤ x ≤ 4

In △ABC, A = 40°, B = 60° and a = 10. Find b.

  1. Sine rule: b / sin B = a / sin A
  2. b = 10 sin 60° / sin 40°

Answer: b ≈ 13.47

Find the midpoint of (−2; 4) and (6; 0).

  1. M = ((−2 + 6)/2; (4 + 0)/2)

Answer: (2; 2)

Tips

  • Master Grade 11 algebra before Grade 12.
  • Don't skip number patterns.
  • Revise the sine, cosine and area rules: Grade 12 extends them to 3D problems.

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