Cambridge · Form 3 · Syllabus 4037
Additional Mathematics
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- Functions Domain, range, one-one and many-one mappings; composite functions fg(x) = f(g(x)); inverse functions f⁻¹ (only for one-one functions); the graphs of f and f⁻¹ are reflections in y = x.
- Quadratics, inequalities and polynomials Completing the square: ax² + bx + c = a(x + p)² + q gives the vertex (−p, q). Discriminant b² − 4ac decides the number of real roots; conditions for a line to meet, be a tangent to, or miss a curve.
- Surds, indices, logarithms and exponentials Simplify √50 = 5√2; rationalise denominators: 1/(√3 − 1) = (√3 + 1)/2.
- Coordinate geometry and circles Gradient, midpoint and distance formulae; equations y − y₁ = m(x − x₁); parallel (equal gradients) and perpendicular lines (m₁m₂ = −1); perpendicular bisectors; area of a triangle or polygon using coordinates (shoelace method).
- Circular measure and trigonometry π rad = 180°; arc length s = rθ; sector area A = ½r²θ.