Mathematics (9709) Paper 3 — Pure Mathematics 3

Modulus function: graph of y = |ax + b| and solving modulus equations/inequalities · Polynomial division by linear or quadratic polynomial · Factor theorem and remainder theorem · Partial fractions (distinct linear, repeated linear, linear with irreducible quadratic) …

Laws of logarithms and relationship with indices · Properties and graphs of e^x and ln x as inverse functions · Using logarithms to solve equations and inequalities with unknown indices · Transforming relationships to linear form using logarithms

Secant, cosecant and cotangent functions and their graphs · Pythagorean identities (sec^2 = 1 + tan^2, cosec^2 = 1 + cot^2) · Compound angle expansions for sin, cos and tan · Double angle formulae (sin 2A, cos 2A, tan 2A) …

Derivatives of e^x, ln x, sin x, cos x, tan x, tan^-1(x) and composites · Product rule and quotient rule · Parametric and implicit differentiation

Integration of e^(ax+b), 1/(ax+b), sin(ax+b), cos(ax+b), sec^2(ax+b), 1/(x^2+a^2) · Using trigonometric identities in integration · Integration by partial fractions · Integration of the form kf'(x)/f(x) …

Locating roots by sign change or graphical methods · Convergent sequences of approximations to a root · Iterative formulae of the form x_(n+1) = F(x_n)

Vector notation in 2D and 3D · Addition, subtraction of vectors and multiplication by a scalar · Magnitude of a vector; unit, displacement and position vectors · Equation of a straight line in vector form r = a + tb …

Formulating differential equations from rate-of-change statements · Solving first-order separable differential equations by integration · Using initial conditions to find particular solutions · Interpreting solutions in real-life modelling contexts

Terminology: real part, imaginary part, modulus, argument, conjugate · Arithmetic of complex numbers in Cartesian form (x + iy) · Complex roots of polynomial equations with real coefficients · Argand diagram representation …