Questions marked the way the scheme marks them
Pure, first pass
- Algebra entry check: indices, surds and exact valuesFree
- Quadratics: square form, discriminants and rootsFree
- Linear and quadratic simultaneous equations
- Inequalities and solution sets
- Polynomial algebra and the factor theorem
- Sketching polynomial and reciprocal graphs
- Lines, gradients and perpendicularity
- Circles, tangents and intersections
- Shifts, stretches and reflections
- Deduction, exhaustion and counterexamples
- Vectors: components, position and subtraction
- Magnitude, direction and vector geometry
- Unit-circle trigonometry and periodic graphs
- Trig identities and interval equations
- Non-right triangles and the ambiguous case
- Radians, arc lengths and sector areas
- Exponential graphs and transformations
- Logarithms and exponential equations
- Exponential models and their parameters
- Derivatives from first principles
- Power, exponential and basic trig derivatives
- Tangents, normals and increasing/decreasing intervals
- Stationary points, optimisation and curvature
- Antiderivatives and the fundamental theorem
- Definite integrals, areas and limiting strips
- Integer binomial expansions and coefficients
Statistics, first pass
- Sampling and the population questionFree
- Meet the LDS: locations, units and cleaning
- Histograms, box plots and cumulative frequency
- Averages, spread and grouped percentiles
- Variance, standard deviation and coding
- Scatter plots, regression and contextual interpretation
- Sample spaces, exclusivity and independence
- Conditional probability: trees, tables and sets
- Probability assumptions and model criticism
- Discrete random variables and binomial assumptions
- Binomial point and cumulative probabilities
- Hypothesis tests for a binomial proportion
- Year-one model and calculator clinic
Mechanics, first pass
- Mechanics units and signed quantitiesFree
- Position, displacement, distance, speed and velocity
- Motion graphs and area/gradient reasoning
- Constant-acceleration equations and derivations
- Force diagrams, weight and Newton's first law
- Newton's second law in one dimension
- Equilibrium and Newton's third-law pairs
- Connected particles and smooth pulleys
- Variable-acceleration motion in one dimension
Pure, second pass
- Composite/inverse functions and domain/range
- Modulus graphs, equations and inequalities
- Rational expressions and partial fractions
- Recursive sequences, monotonicity, periodicity and sigma
- Arithmetic progressions and proof of their sum
- Geometric progressions and convergence
- Sequences and series as financial/physical models
- Rational binomial expansions and approximation
- Reciprocal and inverse trig functions
- Addition, double-angle and half-angle identities
- R-sine/cosine forms and extrema
- Advanced trig equations and proofs
- Small-angle approximations
- Periodic models and realistic domains
- Linearising power/exponential models with logs
- Product, quotient and chain rules
- Implicit differentiation and parametric curves
- Parametric models, tangents and parameter domains
- Connected rates and setting up differential equations
- Standard advanced integrals and trig rewrites
- Integration by substitution
- Integration by parts, including repeated use
- Rational integration and logarithmic forms
- Area between curves and parametric areas
- Separable differential equations and interpretation
- Bracketing roots and failure of sign-change arguments
- Fixed-point iteration and staircase/cobweb diagrams
- Newton-Raphson, failure cases and contextual roots
- Trapezium estimates and bounds
- Contradiction and first-principles proof clinic