Pure Notes [A Level material is in green] (See also STEP page)

 

 

Further Maths Exam Technique (14 pages; 10/12/19) 

Pure Topics by Exam Board (22 pages; 7/8/19)

Reference (Pure) (7 pages; 4/1/21)

 

 

Algebra - Introduction (3 pages; 25/8/20)

Algebra Methods [see STEP page] 5 pages; 23/1/18)

 

Circle Theorems (11 pages; 7/8/17)

 

 

Complex Numbers [Important Ideas] (2 pages; 22/10/20)

Complex Numbers - Part 1 (12 pages; 11/12/15)

Complex Numbers - Part 2 (11 pages; 18/9/19)

Complex Numbers - Part 3 (11 pages; 18/9/19)

Complex Number Methods [see STEP page] (9 pages; 28/2/15)

 

 

Conics

Conics (4 pages; 17/8/19)

Parabolas (10 pages; 16/7/19)

Ellipses (7 pages; 18/8/19)

Hyperbolas (13 pages; 11/9/19)

 

 

Differential Equations (see also Mechanics: Oscillations)

Models (4 pages, 19/2/20)

1st order (3 pages, 23/2/19)

2nd order (linear, constant coeffs) (9 pages; 28/5/20)

Approximate methods (9 pages; 27/2/21)

Linear systems (7 pages; 9/3/21)

Differential Eq'ns [see STEP page] (5 pages; 18/11/18)

 

 

Differentiation

Differentiation [Important Ideas] (1 page; 22/10/20)

Turning Points & Points of Inflexion [Important Ideas] (2 pages; 4/1/21)

Differentiation - Misc (4 pages; 3/9/18)

Turning points (3 pages; 7/4/20)

Points of inflexion (3 pages; 24/10/18)

 

 

Functions 

Functions [Important Ideas] (2 pages; 22/10/20)

Modulus Function [Important Ideas] (2 pages; 22/10/20)

Convexity & concavity (3 pages; 29/8/18)

Sketching rational functions (5 pages; 11/12/19)

y squared = f(x) (2 pages; 29/8/18)

Modulus function (3 pages; 4/9/18)

Transformations [Important Ideas] (3 pages; 22/10/20)

Transformations [see STEP page] (6 pages; 12/12/19)

Functions - Misc (7 pages; 4/9/18)

 

 

 

Groups - Part 1 (10 pages; 22/10/16)

Groups - Part 2 (12 pages; 23/10/16)

 

 

 

Hyperbolic Functions (10 pages; 26/7/16)

 

 

Induction [Important Ideas] (4 pages; 22/10/20)

Induction (4 pages; 4/10/20)

 

 

Inequalities [Important Ideas] (2 pages; 22/10/20)

Inequalities (7 pages; 5/9/18)

 

 

Integers [Important Ideas] (1 page; 22/10/20)

 

 

Integration methods (11 pages; 14/4/21)

Integration Ideas [see STEP page] (4 pages; 14/4/21)

Integration theory (5 pages; 28/9/18)

Integration: Arc lengths & Surface areas (3 pages; 10/5/17)

Improper integrals (3 pages; 20/9/18)

Fundamental Thm of Calculus (1 page; 10/7/21)

 

Linear Interpolation (5 pages; 7/2/16)

 

 

Logarithms [Important Ideas] (2 pages; 22/10/20)

Logarithms (4 pages; 13/2/17)

Modelling Curves using Logs (4 pages; 7/8/17)

 

 

Matrices

Determinants & Inverses (14 pages; 3/6/19)

Transformations (9 pages; 1/10/19)

Invariant points and lines - introduction (4 pages; 16/4/20)

Invariant points & lines - conditions (12 pages; 16/4/20) 

Shears (8 pages; 12/8/18) 

Eigenvectors (10 pages; 4/9/18)

Eigenvectors & Invariance (6 pages; 16/4/20) 

 

 

Number Theory (17 pages; 7/10/18)

 

 

Numerical Methods

Calculator method (1 page; 5/10/20)

Errors (10 pages; 27/3/20)

Sol'n of Eq'ns: Bisection method (2 pages; 22/10/18)

Sol'n of Eq'ns: Method of False Position (4 pages; 22/10/18)

Sol'n of Eq'ns: Newton-Raphson (4 pages; 22/10/18)

Sol'n of Eq'ns: Secant method (2 pages; 12/6/20)

Sol'n of Eq'ns: Fixed Point (16 pages; 27/3/20)

Sol'n of Eq'ns: Comparison of methods (2 pages; 22/10/18)

Sol'n of Eq'ns: Convergence (3 pages; 12/6/20)

Numerical Integration (20 pages; 31/3/20)

Numerical Differentiation (8 pages; 31/3/20)

Approximating F'ns: Newton's Forward Difference (9 pages; 12/6/20)

Approximating F'ns: Lagrange's method (2 pages; 27/3/20)

Differential Eq'ns:Approximate methods (9 pages; 27/2/21)

 

Parametric equations (7 pages; 5/5/21)

 

Partial Fractions (10 pages; 8/8/19)

 

 

Polar Curves (21 pages; 2/11/20)

Polar Curves - Summary (11 pages; 2/11/20)

 

 

Polynomials 

Polynomials [Important Ideas] (2 pages; 4/1/21)

Roots of polynomials (6 pages; 15/2/17)

Quadratic Functions [Important Ideas] (2 pages; 22/10/20)

Quadratics - factorising (3 pages; 21/1/17)

Cubics [Important Ideas] (3 pages; 24/10/20)

Cubics [see STEP page] (4 pages; 11/12/19)

  

Proof [Important Ideas] (3 pages; 22/10/20)

 

 

Sequences & Series

Series [Important Ideas] (3 pages; 11/3/21)

Arithmetic Sequences & Series (2 pages; 23/1/17)

Method of Differences (3 pages; 6/10/20)

Recurrence relations (16 pages; 5/9/18)

Maclaurin Series (7 pages; 23/7/21)

Taylor Series (5 pages; 23/7/21)

 

 

Trigonometry

Basics (2 pages; 15/4/21)

Relations (3 pages; 15/4/21)

Sine & Cosine Rules (5 pages; 15/4/21)

Radians (4 pages; 15/4/21)

Sol'n of eq'ns (2 pages; 15/4/21)

Compound Angle Formulae (4 pages; 15/4/21)

Small Angle Approximations (2 pages; 15/4/21) 

Inverse Functions (5 pages; 15/4/21)

Factor Formulae (1 page; 15/4/21)

t=tan(x/2) substitution (4 pages; 24/3/20)

 

 

Vectors

Vectors [Important ideas] (18 pages; 21/1/21)

Vector Methods [see STEP page] (5 pages; 26/3/21)

Vectors - Introduction (6 pages; 4/8/18)

Scalar Product (4 pages; 19/9/20)

Vectors - Lines (6 pages; 18/9/20)

Vectors - Planes (7 pages; 10/2/20)

Configuration of 3 planes (11 pages; 1/8/21)

Vectors - Angles (5 pages; 4/8/18)

Vectors - Intersections (3 pages; 4/8/18)

Vectors - Shortest distances (14 pages; 4/8/18)

Vector Product (8 pages; 4/8/18)

Triple Products (4 pages; 4/8/18)

Vectors: Misc (1 page; 4/4/18)

 

 

 

Miscellaneous [Important Ideas] (1 page; 22/10/20)