Year 13 Maths.
f(g(x)), domain/range, inverse relationship
Tree diagrams, Venn diagrams, independence
Domain restrictions, graphs, one-to-one
Force diagrams, F=ma, vector resolution
dy/dx from implicit eqns, chain rule
Parameters n,p, PMF, CDF, calculator use
All decomposition types (linear/quadratic)
Double-angle, compound angle, proofs
Continuity correction, conditions
General solutions, interval solutions, quadrants
Elimination, dy/dx, second deriv
Horizontal/vertical components, range, time of flight
u-substitution, definite/indefinite, limits
Critical regions, p-values, null/alternative
ILATE/tabular method, trig & log cases
Separable variables, modelling (growth/decay)
Reverse conditional, priors/posteriors
Stationary points, concavity, points of inflection
General term, validity range, approximations
Tension systems, pulleys, acceleration
Disk/washer method, around x/y axis, parametric
Model assumptions, goodness-of-fit, limitations
Complex proofs, synoptic applications
Multi-angle, modelling contexts
Related rates, mechanics links
Complex problems, normal links
Mixed substitution + parts + applications
Limiting equilibrium, inclined planes, dynamics
Modelling + integration links
Complex curves, parametric cases
Complex probabilities + hypothesis
Multi-step identities + equations
Mixed differentiation + integration
Force balance, pivots, torques
Timed sections (Papers 1 & 2 style)
All strands – full 2 hr Paper 3 style
Student-specific weak areas (data-driven)
Multi-strand problems, time management, common pitfalls
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