Maths
The maths library
The Pure spine is being written now: 21 of 43 topics are live, organised by the maths rather than by any exam board.
Proof
Algebra and functions
Coordinate geometry
Sequences and series
Trigonometry
Exponentials and logarithms
Differentiation
Integration
Vectors
Every topic
PROOF
ALGEBRA AND FUNCTIONS
- Indices and surds
- Quadratic functions
- Simultaneous equations and inequalities
- Polynomials and the factor theorem
- Graphs, proportion and transformations
- Functions, inverses and the modulusWRITING
- Partial fractionsWRITING
- Functions in modellingWRITING
COORDINATE GEOMETRY
- Straight lines
- Circles
- Parametric equationsWRITING
SEQUENCES AND SERIES
- The binomial expansion
- The general binomial expansionWRITING
- Sequences and sigma notationWRITING
- Arithmetic seriesWRITING
- Geometric seriesWRITING
TRIGONOMETRY
- Triangles and the sine and cosine rules
- Trigonometric graphs and equations
- Radians, arcs and small anglesWRITING
- Reciprocal and inverse trigonometric functionsWRITING
- Compound angles and the harmonic formWRITING
- Trigonometric modellingWRITING
EXPONENTIALS AND LOGARITHMS
DIFFERENTIATION
- The derivative from first principles
- Differentiating powers of x
- Tangents, turning points and curve behaviour
- Differentiating trig, exponentials and logsWRITING
- The product, quotient and chain rulesWRITING
- Implicit and parametric differentiationWRITING
- Rates of change and building differential equationsWRITING
INTEGRATION
- Integration as antidifferentiation
- Definite integrals and areas
- Integrating standard functionsWRITING
- Integration by substitution and by partsWRITING
- Integrating rational functionsWRITING
- Areas, parametric curves and the limit of a sumWRITING
- Solving differential equationsWRITING
VECTORS
- Vectors in two dimensions
- Vectors in three dimensionsWRITING