ZIMSEC · A Level · Syllabus 6042
Pure Mathematics
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Form 5 · Lower 6 7 topics
- Functions and graphs A function maps each element of the domain to exactly one element of the range.
- Quadratics, polynomials and partial fractions Quadratics Completing the square: ax² + bx + c = a(x + b/2a)² + c − b²/4a. The…
- Coordinate geometry and circles x = f(t), y = g(t). Eliminate t to get the Cartesian equation; dy/dx = (dy/dt) ÷ (dx/dt).
- Sequences, series and the binomial expansion uₙ = a + (n − 1)d; Sₙ = (n/2)[2a + (n − 1)d] = (n/2)(a + l).
- Indices, logarithms and exponentials eˣ (e ≈ 2.718) and its inverse ln x (natural logarithm): e^(ln x) = x and ln(eˣ) = x.
- Trigonometry π radians = 180°. Arc length s = rθ; sector area = ½r²θ (θ in radians).
- Differentiation Rules d/dx(xⁿ) = nxⁿ⁻¹; d/dx(eˣ) = eˣ; d/dx(ln x) = 1/x; d/dx(sin x) = cos x; d/dx(cos x)…
Form 6 · Upper 6 5 topicsExam year
- Integration ∫xⁿ dx = xⁿ⁺¹/(n + 1) + c (n ≠ −1); ∫1/x dx = ln|x| + c; ∫eᵃˣ dx = eᵃˣ/a + c; ∫sin ax dx = −cos ax / a + c; ∫cos ax dx = sin ax / a + c; ∫sec²x dx = tan x + c.
- Differential equations A differential equation links a function with its derivatives.
- Vectors Vectors in 3D: a = xi + yj + zk. Magnitude |a| = √(x² + y² + z²). A unit vector is a/|a|. Position vectors: AB = b − a.
- Complex numbers i² = −1. A complex number z = x + iy has real part x and imaginary part y. The conjugate z* = x − iy.
- Numerical methods If f(x) is continuous and f(a) and f(b) have opposite signs, a root lies between a and b.