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⬜ Surds and indices
⬜ Algebraic expressions
⬜ Equations and inequalities
⬜ The discriminant
⬜ Sketching graphs
⬜ Transformations of functions
⬜ Coordinate geometry
⬜ The equation of a circle and use theorems
⬜ The factor theorem and dividing polynomials
1 ⬜ Year methods of proof & disproof
⬜ Binomial expansion with positive integer powers
⬜ Trigonometry with triangles
1 ⬜ Year trigonometric equations & identities
1 ⬜ Year vectors
⬜ Differentiation from first principles
1 ⬜ Year differentiation of functions
⬜ Finding tangents and normals
⬜ Stationary points
1 ⬜ Year integration of functions
⬜ Area under curves
⬜ Exponential functions and e^x
⬜ Logarithms
⬜ Natural logarithms
⬜ Logarithms and non-linear data
⬜ Proof by contradiction
⬜ Standard proofs
⬜ Partial Fractions
⬜ Algebraic division
⬜ The modulus function
⬜ Modulus transformations
⬜ Functions and mappings
⬜ Arithmetic sequences/series
⬜ Geometric sequences/series
⬜ Sigma notation
⬜ Recurrence relations
⬜ Binomial expansion with negative/fractional powers
⬜ Radians and applications
⬜ Small angle approximations
⬜ Reciprocal trigonometric functions
⬜ Pythagorean identities
⬜ Inverse trig functions
⬜ Addition formulae
⬜ Double angle formulae
2 ⬜ Year trig equations
⬜ Harmonic identities
⬜ Parametric equations
⬜ Derivatives of sin(x) & cos(x) from first principles
⬜ Derivatives of standard functions
⬜ The chain rule
⬜ The product rule
⬜ The quotient rule
⬜ Parametric differentiation
⬜ Implicit differentiation
⬜ Concave/convex functions and points of inflection
⬜ Rates of change
⬜ Locating roots
⬜ Iteration
⬜ The Newton-Raphson method
⬜ Integrating standard functions
⬜ Integrating f(ax+b)
⬜ Integration using trig identities
⬜ Integration by substitution
⬜ Integration by parts
⬜ Integration using partial fractions
⬜ Integration by inspection/recognition
⬜ Parametric integration
⬜ The trapezium rule
⬜ Solving differential equations
⬜ 3D coordinates and vectors
⬜ Geometric vector problems
⬜ Populations and sampling
⬜ Median, quartiles and percentiles
⬜ Box plots
⬜ Histograms
⬜ Variance and standard deviation
⬜ Interpolation
⬜ Coding
⬜ Outliers
⬜ Histograms
⬜ Correlation, regression and outliers
1 ⬜ Year probability
⬜ Discrete random variables
⬜ The binomial distribution
⬜ Hypothesis testing with discrete data
⬜ Non-linear regression
⬜ Measuring correlation
⬜ Hypothesis testing for correlation
2 ⬜ Year probability
⬜ The normal distribution
⬜ Approximating a binomial distribution
⬜ Hypothesis testing with the normal distribution
⬜ Modelling in mechanics
⬜ Displacement-time & velocity-time graphs
⬜ Constant acceleration (SUVAT) equations
⬜ Vertical motion under gravity
⬜ Forces and Newton's laws
⬜ Use of vectors
⬜ Connected particles
⬜ Pulleys
⬜ Variable acceleration in 1D
⬜ Moments
⬜ Resolving forces (inclined planes)
⬜ Friction
⬜ Projectiles
⬜ Statics
⬜ Rigid bodies/moments
⬜ Dynamics
⬜ Vectors in kinematics
⬜ Variable acceleration in 2D