Your journey to excellence inMathematics
By Revision Genie
Laws of indices
Surds and rationalising
Quadratic functions and graphs
Completing the square
Quadratic equations (incl. in functions)
Simultaneous equations (linear–quadratic)
Linear inequalities
Quadratic inequalities
Inequalities on graphs
Polynomial manipulation
Factor theorem
Algebraic division (linear)
Rational expressions
Function graphs (cubic/quartic)
Modulus graphs
Reciprocal graphs and asymptotes
Graphical equation solving
Proportion and graphs
Composite functions
Inverse functions and graphs
Graph transformations
Partial fractions
Modelling with functions
Straight line forms
Parallel and perpendicular lines
Straight line modelling
Circle equations
Completing the square (circles)
Circle properties (chords, tangents)
Parametric equations
Parametric–Cartesian conversion
Parametric modelling
Binomial expansion (positive integer)
Binomial expansion (rational)
Binomial approximations and validity
Recurrence relations
Increasing/decreasing/periodic sequences
Sigma notation
Arithmetic sequences
Arithmetic series (sum formula proof)
Geometric sequences
Geometric series (finite)
Geometric series to infinity
Sequence and series modelling
Radian measure
Arc length and sector area
Sine rule
Cosine rule
Triangle area formula
Small-angle approximations
Sin/Cos/Tan graphs
Symmetry and periodicity
Exact trig values
Sec/Cosec/Cot definitions
Arcsin/Arccos/Arctan
Trig identities (basic)
Double-angle formulae
Compound-angle formulae
Half-angle applications
R-form (a cosθ + b sinθ)
Trig equations (interval)
Trig proofs
Trig in context problems
Exponential functions (a^x, e^x)
Transformations of exponentials
Exponential differentiation idea (k e^{kx})
Logarithms as inverses
ln(x) graphs and inverse of e^x
Log laws
Solving exponential equations
Logarithmic graphs (linearising data)
Exponential growth and decay models
Model limitations and refinements
Derivative as gradient
Derivative as rate of change
Differentiation from first principles
Gradient function sketches
Second derivative and concavity
Stationary points (f′=0)
Second derivative test
Points of inflection
Power rule (rational powers)
Derivatives of e^{kx}, a^{kx}, trig
Derivative of ln(x)
Tangents and normals
Increasing/decreasing intervals
Product rule
Quotient rule
Chain rule
Connected rates of change
Differentiation of inverse functions
Implicit differentiation (first derivative)
Parametric differentiation (first derivative)
Forming differential equations
Fundamental Theorem of Calculus
Indefinite integrals and +C
Power integrals (n ≠ −1)
Integrals of e^{kx} and 1/x
Integrals of trig functions
Trig identity integrals
Definite integrals
Area under a curve
Area between curves
Area for parametric curves
Integration as limit of a sum
Substitution
Integration by parts
Integrals involving ln(x)
Partial fractions integration (linear factors)
Separable differential equations
Particular solutions
Solution families (sketching)
Interpreting DE solutions in context
Limitations of DE models
Root locating by sign change
Failure of sign-change methods
Fixed-point iteration
Cobweb diagrams
Staircase diagrams
Newton–Raphson method
Failure of iterative methods
Numerical integration (trapezium rule)
Over/under-estimates (trapezium)
Numerical methods in context
2D and 3D vectors
Unit vectors (i, j, k) and column vectors
Magnitude and direction
Unit vectors
Vector addition and scaling
Geometric interpretation (triangle/parallelogram)
Parallel vectors
Position vectors
Distance between points (2D/3D)
Vector problem solving (incl. forces contexts)
Population vs sample
Census vs sample (pros/cons)
Simple random sampling
Stratified sampling
Systematic sampling
Quota sampling
Opportunity sampling
Sampling critique and bias
Inference variability (different samples)
Histograms (area = frequency)
Frequency polygons
Box plots and outliers
Cumulative frequency diagrams
Scatter diagrams
Regression lines (interpretation only)
Explanatory vs response variables
Interpolation
Extrapolation risks
Correlation strength and direction
Correlation vs causation
Coding in data
Mean, median, mode
Range and IQR
Variance and standard deviation
Standard deviation from summary statistics
Percentiles (grouped data interpolation)
Outlier rules (IQR / SD rules)
Data cleaning (missing data, errors, outliers)
Critiquing presentation choices
Large Data Set familiarity
Mutually exclusive events
Independent events
Venn diagrams
Tree diagrams
Two-way tables
Conditional probability
Complement rule
Addition rule
Multiplication rule
Probability modelling assumptions
Discrete uniform distribution
Binomial distribution as a model
Binomial probabilities (calculator)
Normal distribution as a model
Normal probabilities (calculator)
Standardisation ideas
Normal curve inflection points (µ ± σ)
Binomial–Normal approximation
Continuity correction
Choosing appropriate distribution models
Model suitability and limitations
Null and alternative hypotheses
Significance level
Test statistic
One-tailed tests
Two-tailed tests
Critical value and critical region
Acceptance region
p-values
Binomial test for a proportion
Interpreting test outcomes in context
Type I error (informal)
Normal test for a mean (known/assumed variance)
Sampling distribution of the mean (given)
Correlation coefficient as test statistic
Interpreting r using p-values/critical values
Displacement vs distance
Velocity vs speed
Acceleration
Displacement–time graphs
Velocity–time graphs
Gradient and area interpretations
Constant-acceleration (suvat) formulae
Deriving suvat relationships
2D kinematics with vectors
Calculus in kinematics (v = dr/dt, a = dv/dt)
Vector differentiation/integration in time
Force types and free-body diagrams
Newton’s first law
Newton’s second law (scalar)
Newton’s second law (2D vectors)
Resolving forces (inclined planes)
Weight under gravity (g)
Newton’s third law
Equilibrium of a particle
Connected particles and pulleys
Coplanar force equilibrium
Resultant forces and force addition
Dynamics in a plane
Friction model (F ≤ μR)
Limiting friction and statics