ZIMSEC · Form 5 · Lower 6 · Syllabus 6042
Pure Mathematics
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- 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)…