Pure Maths Notes & Exercises 

 

A Level (ie non-FM) items are in green

Items relevant to STEP are in blue 

 

Notes

 

Algebra methods (5 pages; 23/1/18)

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

Circle Theorems (11 pages; 7/8/17)

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

Complex Numbers - Part 2 (19 pages; 11/12/15)

Complex Numbers - methods (9 pages; 28/2/15)

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

Conics (4 pages; 30/10/15)

   Parabolas (6 pages; 30/10/15)

   Ellipses (7 pages; 30/10/15)

   Hyperbolas (12 pages; 30/10/15)

Cubic Functions (3 pages; 25/2/18)

Curves: (Sketching) Rational Functions (5 pages; 25/2/18)

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

Differential Equations (see also Applied/Mechanics)

  1st order (3 pages, 23/2/19)

  2nd order (linear, constant coeffs) (7 pages; 18/11/18)

  Substitutions (5 pages; 18/11/18)

  Approximate methods (4 pages; 18/11/18)

  Linear systems (2 pages; 18/11/18)

Functions - Misc (7 pages; 4/9/18)

  y squared = f(x) (2 pages; 29/8/18)

Groups - Part 1 (10 pages; 22/10/16)

Groups - Part 2 (12 pages; 23/10/16)

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

Induction (4 pages; 22/8/16)

Inequalities (7 pages; 5/9/18)

Integration

  Integration methods (13 pages; 6/2/18)

  Integration theory (5 pages; 28/9/18)

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

  Improper integrals (3 pages; 20/9/18)

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

Logarithms (4 pages; 13/2/17)

Maclaurin Series (7 pages; 25/3/17)

Matrices

  Determinants & Inverses (13 pages; 4/9/18)

  Transformations (8 pages; 4/9/18)

  Eigenvectors (10 pages; 4/9/18)

  Invariant points and lines (6 pages; 25/10/18)

  Eigenvectors & Invariance (5 pages; 29/10/18) 

  Shears (8 pages; 12/8/18)

Method of Differences (2 pages; 28/1/19)

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

Modulus function (3 pages; 4/9/18)

Number Theory (17 pages; 7/10/18)

Numerical Methods

  Calculator method (1 page; 22/10/18)

  Errors (9 pages; 22/10/18)

  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; 22/10/18)

  Sol'n of Eq'ns: Fixed Point (15 pages; 22/10/18)

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

  Approximating F'ns: Newton's Forward Difference (8 pages; 22/10/18)

  Approximating F'ns: Lagrange's method (2 pages; 22/10/18)

  Numerical Integration: Midpoint & Trapezium (7 pages; 22/10/18)

  Numerical Integration: Simpson (7 pages; 22/10/18)

  Convergence: Introduction (3 pages; 22/10/18)

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

  Convergence: Numerical Integration (5 pages; 22/10/18)

  Numerical Differentiation (3 pages; 22/10/18)

Parametric equations (8 pages; 30/8/13)

Partial Fractions (8 pages; 2/3/17)

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

Polar Curves (21 pages; 17/11/18)

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

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

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

Taylor Series (5 pages; 27/3/18)

Transformations of Functions (6 pages; 9/9/13)

Transformations  (STEP)(6 pages; 25/2/18)

Trigonometry - Part 1 (12 pages; 4/9/16)

Trigonometry - Part 2 (15 pages; 4/9/16)

Turning points (1 page; 24/10/18)

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

Scalar Product (2 pages; 4/8/18)

Vector Product (8 pages; 4/8/18)

Triple Products (4 pages; 4/8/18)

Vectors - Lines (4 pages; 4/8/18)

Vectors - Planes (4 pages; 4/8/18)

Vectors - Angles (5 pages; 4/8/18)

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

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

Vectors - consistency of 3 eq'ns (8 pages; 4/7/16)

Vectors - Summary of methods (7 pages; 4/8/18)

Vectors (STEP)(4 pages; 14/3/15)

Vectors: Misc (1 page; 4/4/18)

Miscellaneous Notes (1 page; 11/8/16)

Useful results (6 pages; 22/1/17)

 

 

Exercises 

 

Arithmetic Seqs & Series (2 pages; 23/1/17); Solutions (6 pages; 23/1/17)

Complex Nos - Part 1 (3 pages; 13/2/16); Solutions (12 pages; 13/2/16)

Complex Nos - Part 2 (1 page; 13/2/16); Solutions (5 pages; 13/2/16)

Conics (2 pages; 16/1/17); Solutions (5 pages; 16/1/17)

Cubic Graphs (3 pages; 29/7/16); Solutions (10 pages; 29/7/16)

Curve Sketching (1 page; 7/10/18); Solutions (4 pages; 7/10/18)

Differentiation (2 pages; 19/10/18); Solutions (6 pages; 19/10/18)

Geometry (2 pages; 7/10/18); Solutions (5 pages; 7/10/18)

Hyperbolic Functions (2 pages; 13/5/17); Solutions (9 pages; 13/5/17)

Induction (3 pages; 22/8/16); Solutions (23 pages; 30/1/18)

Inequalities (1 page; 7/10/18); Solutions (4 pages; 7/10/18)

Integration - Part 1 (1 page; 7/11/17); Solutions (8 pages; 7/11/17)

Integration - Part 2 (3 pages; 11/11/17); Solutions (21 pages; 11/11/17)

Integration - Part 3 (2 pages; 6/2/18); Solutions (12 pages; 6/2/18)

Integration - Misc (1 page; 7/10/18); Solutions (1 page; 7/10/18)

Logarithms (1 page; 7/10/18); Solutions (5 pages; 7/10/18)

Maclaurin Series (2 pages; 8/3/17); Solutions (8 pages; 8/3/17)

Matrices

  General (2 pages; 30/10/18); Solutions (6 pages; 30/10/18)

  General - Advanced (1 page; 30/10/18); Solutions (5 pages; 30/10/18)

  Transformations (3 pages; 30/10/18); Solutions (12 pages; 30/10/18)  

  Eigenvectors (2 pages; 30/10/18); Solutions (12 pages; 30/10/18)  

  Shears (1 page; 30/10/18); Solutions (4 pages; 30/10/18)

(Roots of) Polynomial eq'ns (2 pages; 15/2/17); Solutions (6 pages; 15/2/17)

Polynomials (1 page; 7/10/18); Solutions (4 pages; 7/10/18)

Quadratics (1 page; 7/10/18); Solutions (3 pages; 7/10/18)

Transformations (1 page; 7/10/18); Solutions (5 pages; 7/10/18)

Trigonometry (3 pages; 7/10/18); Solutions (12 pages; 7/10/18)

Vectors (5 pages; 7/10/18); Solutions (18 pages; 7/10/18)

Miscellaneous (2 pages; 7/10/18); Solutions (7 pages; 7/10/18)