Grade 11 Maths Questions and Answers (CAPS)

Grade 11 maths questions and answers for CAPS tests and exams: completing the square, nature of roots, patterns, inequalities and the sine rule, worked.

· 6 min read · Snap&Learn

Most Matric questions build on Grade 11 skills. Use these questions to prepare for a test or your November exam: try each one on paper first, then compare your working line by line.

Question 1: Completing the square

Solve x² + 6x + 2 = 0 by completing the square. x² + 6x + 9 = −2 + 9, so (x + 3)² = 7. Answer: x = −3 ± √7.

Question 2: Nature of roots

Describe the roots of x² − 4x + 4 = 0. Δ = b² − 4ac = 16 − 16 = 0. Answer: the roots are real and equal.

Question 3: Quadratic pattern

Find the general term of 4; 9; 16; 25; …. These are the squares of 2, 3, 4 and 5. Answer: Tₙ = (n + 1)².

Question 4: Quadratic inequality

Solve x² − x − 12 < 0. Factorise: (x − 4)(x + 3) < 0. The parabola opens upwards, so it is below the x-axis between its roots. Answer: −3 < x < 4.

Question 5: Turning point

Find the turning point of y = 2(x − 1)² + 3. In the form y = a(x − p)² + q, the turning point is (p; q). Answer: (1; 3).

Question 6: Sine rule

In △ABC, A = 30°, B = 45° and a = 5. Find b. b / sin B = a / sin A, so b = 5 sin 45° / sin 30°. Answer: b ≈ 7.07.

Question 7: Surd equation

Solve √(x + 3) = 4. Square both sides: x + 3 = 16. Answer: x = 13. Always check a surd equation in the original: √16 = 4, so this answer is valid.

When you get stuck

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Frequently asked questions

What does the discriminant tell me?

If Δ is negative, the roots are not real. If Δ = 0, they are real and equal. If Δ is positive, they are real and unequal, and rational if Δ is a perfect square.

When do I use the sine rule or the cosine rule?

Use the sine rule when you know an angle and its opposite side. Use the cosine rule when you know two sides and the angle between them, or all three sides.

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