Paper 3
Pure and Statistics
Pure content (sections A–J)
Completing the square and the vertex · Solving quadratic equations · The discriminant and the nature of roots · Linear and quadratic inequalities · Simultaneous equations and lines meeting curves · Gradient, length, midpoint and equations of lines · Parallel and perpendicular lines · The equation of a circle · Tangents, chords and intersections · Radians · Arc length and sector area · Segments, chords and composite shapes · Exact values and the unit circle · Graphs and transformations · Inverse trigonometric functions · Trigonometric identities · Solving trigonometric equations · Binomial expansion · Arithmetic progressions · Geometric progressions · Sum to infinity · Gradients and the power rule · The chain rule · Tangents and normals · Stationary points and increasing functions · Optimisation and rates of change · Indefinite integration · Integrating (ax + b)ⁿ · Definite integrals · Areas under and between curves · Modulus graphs and equations · Modulus inequalities · Polynomials: division, factor and remainder theorems · Partial fractions · Binomial expansion for any rational n · Laws of logarithms · The functions eˣ and ln x · Exponential equations and inequalities · Logarithmic equations · Exponential models and linear forms · Reciprocal functions and their identities · Derivatives of eˣ, ln x and trigonometric functions · The product and quotient rules · Implicit differentiation · Parametric differentiation · Stationary points and tangents · Integrating eˣ, 1/x and trigonometric functions · Integration using trigonometric identities · Exact definite integrals and logarithms · The trapezium rule · Integration by substitution · Integration by parts · Compound-angle formulae · Double-angle formulae · The R-form (harmonic form) · Locating roots: sketches and sign changes · Fixed-point iteration · Rearrangements, staircases and cobwebs · Newton–Raphson, bisection and interpolation · Forming differential equations · Separating the variables · Particular solutions with harder integrals · Modelling with differential equations · Position vectors, magnitude and unit vectors · Deduction, exhaustion and counterexample · Proof by contradiction66 subtopic lessonsStatistical sampling
Populations and sampling methods1 subtopic lessonsData presentation and interpretation
Stem-and-leaf diagrams and box plots · Histograms and cumulative frequency · Mean and standard deviation · Coded and combined data · Summary statistics and the PMCC · The least squares regression line6 subtopic lessonsProbability
Combined events and Venn diagrams · Tree diagrams and conditional probability · Independent and mutually exclusive events3 subtopic lessonsStatistical distributions
Probability distributions · The binomial distribution · Standardising and normal probabilities · Inverse normal and finding μ and σ · Normal approximation to the binomial5 subtopic lessonsStatistical hypothesis testing
Binomial and Poisson tests · Tests for a population mean · Type I and Type II errors3 subtopic lessons