Common Matric Maths Questions Explained

Practice questions with solutions

Common: factorise a trinomial

1. For x² − x − 12, find two factors of −12 that add up to −1
2. −4 and 3 work: −4 × 3 = −12 and −4 + 3 = −1

Answer: (x − 4)(x + 3)

Common: prove a trig identity

1. Prove sin x · tan x + cos x = 1/cos x. Work on the left-hand side only
2. sin x · (sin x / cos x) + cos x = (sin²x + cos²x) / cos x
3. sin²x + cos²x = 1

Answer: LHS = 1/cos x = RHS

Common: the nature of the roots

1. For 3x² − 2x + 4 = 0: Δ = (−2)² − 4(3)(4) = 4 − 48 = −44
2. Δ < 0

Answer: The roots are non-real.

Common: the sum of an arithmetic series

1. Find S₂₀ of 2; 5; 8; …: a = 2 and d = 3
2. S₂₀ = 20/2 [2(2) + 19(3)] = 10 × 61

Answer: S₂₀ = 610

Common: compound interest

1. R8 000 invested at 7% p.a. compounded annually for 4 years
2. A = 8 000(1,07)⁴

Answer: A ≈ R10 486,37

Common: the distance between two points

1. A(1; 2) and B(4; 6)
2. AB = √[(4 − 1)² + (6 − 2)²] = √(9 + 16)

Answer: AB = 5

Common: find the turning point of a parabola

1. For y = 2x² − 8x + 3: x = −b/2a = 8/4 = 2
2. y = 2(4) − 16 + 3 = −5

Answer: (2; −5)

Common: the equation of a tangent

1. For f(x) = x² − 2x at x = 3: f(3) = 3
2. f′(x) = 2x − 2, so the gradient is f′(3) = 4
3. y − 3 = 4(x − 3)

Answer: y = 4x − 9

Common: probability of independent events

1. P(A) = 0.3 and P(B) = 0.5, and A and B are independent
2. P(A and B) = P(A) × P(B) = 0.3 × 0.5

Answer: 0.15

Common: the inverse of an exponential function

1. f(x) = 5ˣ
2. Swap x and y: x = 5ʸ, so y = log₅ x

Answer: f⁻¹(x) = log₅ x, x > 0

Tips

• Drill the common 5 question types weekly.
• Use a question bank to vary practice.