Cambridge · Form 4 · Syllabus 4037
Additional Mathematics
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- Permutations, combinations and series ⁿPᵣ = n!/(n − r)! (order matters); ⁿCᵣ = n!/(r!(n − r)!) (order does not matter); arrangements with restrictions (together, apart, ends).
- Vectors in two dimensions Column vectors and i, j notation; magnitude |xi + yj| = √(x² + y²); unit vectors; position vectors; parallel vectors are multiples of each other.
- Differentiation and its applications d/dx(xⁿ) = nxⁿ⁻¹; d/dx(eᵃˣ) = aeᵃˣ; d/dx(ln x) = 1/x; d/dx(sin x) = cos x; d/dx(cos x) = −sin x; d/dx(tan x) = sec²x. Chain, product and quotient rules.
- Integration and kinematics Reverse of differentiation: ∫xⁿ dx = xⁿ⁺¹/(n + 1) + c (n ≠ −1); ∫eᵃˣ dx = eᵃˣ/a + c; ∫1/x dx = ln x + c; ∫sin ax dx = −cos ax/a + c; ∫cos ax dx = sin ax/a + c; ∫(ax + b)ⁿ dx = (ax + b)ⁿ⁺¹/[a(n + 1)] + c.