Mathematics (9709) Paper 2 — Pure Mathematics 2

Modulus function: graph of y = |ax + b| and solving modulus equations/inequalities · Polynomial division by linear or quadratic polynomial · Factor theorem and remainder theorem

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 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) · Using trigonometric identities (e.g. double-angle formulae) in integration · Trapezium rule for estimating definite integrals

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)