Mathematics (9709) Paper 1 — Pure Mathematics 1

Completing the square · Discriminant and number of real roots · Solving quadratic equations and inequalities · Simultaneous equations (one linear, one quadratic) …

Function terminology (domain, range, one-one, inverse, composition) · Range of a function and composition of two functions · Determining one-one functions and finding inverses · Graphical relationship between a function and its inverse …

Equation of a straight line · Using line forms (y = mx + c, point-slope, general form) · Equation of a circle · Algebraic methods for lines and circles …

Radians and conversion between radians and degrees · Arc length and sector area formulae

Graphs of sine, cosine and tangent functions · Exact trigonometric values for 30, 45, 60 degrees and related angles · Inverse trigonometric notation (sin^-1, cos^-1, tan^-1) · Trigonometric identities (tan = sin/cos, sin^2 + cos^2 = 1) …

Binomial expansion of (a + b)^n for positive integer n · Recognising arithmetic and geometric progressions · nth term and sum formulae for arithmetic and geometric progressions · Convergence condition and sum to infinity of a geometric progression

Gradient of a curve as a limit; first and second derivative notation · Derivative of x^n; chain rule for composite functions · Applications to gradients, tangents, normals, and rates of change · Stationary points: finding and determining their nature

Integration as reverse differentiation; integrating (ax + b)^n · Finding the constant of integration · Evaluating definite integrals (including simple improper integrals) · Area between curves and lines …