| Proof | Red | Amber | Green |
| Proof by contradiction | |||
| Proof by exhaustion | |||
| Disproof by counter-example | |||
| Further Algebra and Functions | Red | Amber | Green |
| Partial fractions — distinct linear, repeated linear, improper | |||
| Modulus function — |f(x)|, solving equations and inequalities | |||
| Mappings — one-to-one, many-to-one, restricting domain | |||
| Composite and inverse functions (advanced) | |||
| Sequences and Series | Red | Amber | Green |
| Arithmetic sequences — nᵗʰ term and sum formulae | |||
| Geometric sequences — nᵗʰ term and sum formulae | |||
| Sum to infinity of a geometric series — |r| < 1 | |||
| Sigma notation — evaluating and manipulating | |||
| Recurrence relations | |||
| Binomial Expansion (General) | Red | Amber | Green |
| Expanding (1 + x)ⁿ for rational and negative n | |||
| Validity of expansion — |x| < 1 | |||
| Expanding (a + bx)ⁿ — factoring correctly | |||
| Using binomial with partial fractions | |||
| Radians | Red | Amber | Green |
| Converting between degrees and radians | |||
| Arc length — s = rθ | |||
| Area of sector — A = ½r²θ | |||
| Small angle approximations — sin θ ≈ θ, cos θ ≈ 1 − θ²/2 | |||
| Further Trigonometry | Red | Amber | Green |
| Reciprocal trig functions — sec, cosec, cot | |||
| Inverse trig functions — arcsin, arccos, arctan | |||
| Pythagorean identities — 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ | |||
| Addition formulae — sin(A ± B), cos(A ± B), tan(A ± B) | |||
| Double angle formulae — sin 2A, cos 2A, tan 2A | |||
| R-form — a sin θ + b cos θ = R sin(θ + φ) | |||
| Solving harder trig equations using identities | |||
| Proving trig identities | |||
| Parametric Equations | Red | Amber | Green |
| Converting between parametric and Cartesian form | |||
| Sketching parametric curves | |||
| Differentiating parametric equations — dy/dx = (dy/dt) / (dx/dt) | |||
| Further Differentiation | Red | Amber | Green |
| Chain rule — d/dx[f(g(x))] | |||
| Product rule — d/dx[uv] = u'v + uv' | |||
| Quotient rule — d/dx[u/v] = (u'v − uv') / v² | |||
| Differentiating trig functions — sin x, cos x, tan x, and reciprocals | |||
| Differentiating eˣ and ln x | |||
| Implicit differentiation | |||
| Connected rates of change — chain rule in context | |||
| Further Integration | Red | Amber | Green |
| Integrating standard functions — eˣ, 1/x, sin x, cos x | |||
| Integration by substitution | |||
| Integration by parts — ∫u dv = uv − ∫v du | |||
| Integration using partial fractions | |||
| Trapezium rule — numerical integration | |||
| Areas — under curves, between curves, parametric | |||
| Differential Equations | Red | Amber | Green |
| First-order separable differential equations | |||
| Finding general and particular solutions | |||
| Modelling with differential equations (growth/decay, rates) | |||
| Vectors in 3D | Red | Amber | Green |
| 3D vectors — i, j, k components and column form | |||
| Scalar (dot) product — a · b = |a||b|cos θ | |||
| Using dot product to find angles between vectors | |||
| Vector equation of a line — r = a + λb | |||
| Intersection and skew lines |
| Regression and Correlation | Red | Amber | Green |
| Pearson's product moment correlation coefficient (PMCC) | |||
| Regression lines — y on x, interpreting gradient and intercept | |||
| Hypothesis test for zero correlation | |||
| Causation vs correlation — interpreting in context | |||
| Conditional Probability | Red | Amber | Green |
| Conditional probability from two-way tables | |||
| Venn diagrams for conditional probability | |||
| Probability formulae — mutually exclusive, independent | |||
| Normal Distribution | Red | Amber | Green |
| Properties of the normal distribution — bell curve, symmetry | |||
| Standard normal distribution — Z scores, standardising | |||
| Finding probabilities using calculator / tables | |||
| Finding unknown mean or standard deviation | |||
| Normal approximation to the binomial distribution | |||
| Hypothesis Testing (Normal) | Red | Amber | Green |
| Hypothesis test for the mean of a normal distribution | |||
| One-tailed and two-tailed tests using normal | |||
| Interpreting p-values and critical regions in context |
| Moments | Red | Amber | Green |
| Moment of a force — moment = F × d (perpendicular distance) | |||
| Equilibrium — sum of moments = 0, sum of forces = 0 | |||
| Centre of mass — uniform rods and laminas | |||
| Forces at Angles | Red | Amber | Green |
| Resolving forces — horizontal and vertical components | |||
| Friction — F ≤ μN and limiting friction | |||
| Inclined planes — resolving parallel and perpendicular to slope | |||
| Equilibrium problems with multiple forces at angles | |||
| Projectiles | Red | Amber | Green |
| Projectile motion — horizontal and vertical components independent | |||
| Time of flight, range, maximum height | |||
| Projectiles launched at an angle — resolving initial velocity | |||
| Equation of the trajectory (Cartesian form) | |||
| Further Dynamics | Red | Amber | Green |
| Connected particles — Atwood machines, lifts | |||
| Variable acceleration in 2D — vectors for velocity and displacement | |||
| Using calculus with vector equations of motion |