CONTENTS (@20/1/22) 

 

Pure - Notes

 

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)

Prerequisite Pure Topics (for Further Maths and STEP) (4 pages; 6/12/21)

 

 

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 (8 pages; 8/10/21)

 

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)

 

 

Mechanics Notes

 

Exam Board Topics - Mechanics (8 pages; 9/7/21)

Useful Results (2 pages; 5/5/20) 

 

Centre of Mass - Contents (2 pages; 7/8/17)

Centre of Mass - Part 1 (13 pages; 7/8/17)

Centre of Mass - Part 2 (12 pages; 7/8/17) 

 

Circular Motion [Important Ideas] (2 pages; 25/10/20)

Circular Motion - Constant Speed (9 pages; 25/10/20)

Circular Motion - Variable Speed (13 pages; 30/9/15) 

 

Work & Energy

Work & Energy (4 pages; 21/11/20)

Gravitational Potential Energy (3 pages;15/2/19)

Hooke's Law (9 pages; 10/3/21) 

 

Forces

Forces [Important Ideas] (18 pages; 14/1/21)

Equilibrium [Important Ideas] (11 pages; 12/11/20)

Frameworks (9 pages; 25/3/21)

Bending moment & shearing force (5 pages; 25/3/21)

Fictitious forces (5 pages; 25/10/20)

Systems of forces (5 pages; 14/11/18)

Toppling (2 pages; 13/11/20)  

 

Impulse & Momentum

Collisions - Important Ideas (4 pages; 22/4/21)

Impulse & Momentum (14 pages; 19/2/17)

Collisions - reversal of direction (6 pages; 24/6/20)

Oblique impacts (4 pages; 23/8/18)

Impulses & connected particles (13 pages; 28/8/18) 

 

Kinematics

Kinematics (7 pages; 7/8/17)

Projectiles (11 pages; 10/3/21)

Suvat equations (5 pages; 24/1/17) 

 

Oscillations

Differential equations: Oscillations (11 pages; 29/5/20) 

 

Rotating Bodies

Rotating Bodies (5 pages; 19/8/19)

Rotating Bodies - Examples (6 pages; 16/3/18)

Moments of Inertia (7 pages; 23/3/18)

Rolling wheel - Point on circumference (5 pages; 1/2/21)

Rolling wheel - Friction (6 pages; 15/2/21)

 

 

Probability & Statistics Notes

  

Probability & Statistics [Important Ideas] (10 pages; 28/6/21)

Exam Board topics - Prob. & Stats (11 pages; 30/6/21)

Useful Results (4 pages; 9/7/21)

  

Binomial distribution (7 pages; 16/2/17)

 

Chi-Squared Test

Contingency Tables & Goodness of Fit (8 pages; 12/5/17)

Contingency Tables & Goodness of Fit - Important Ideas (3 pages; 9/7/21)

 

Confidence Intervals - Types (3 pages; 16/4/16)

 

Correlation & Regression

Correlation (12 pages; 28/6/21)

Rank Correlation (5 pages; 23/8/19)

Regression (8 pages; 23/8/19)

 

Discrete Random Variables

Laws of Total Expectation & Variance (3 pages; 16/4/21)

 

Geometric distribution (3 pages; 12/11/18)

  

Hypothesis Tests - General (3 pages; 22/5/20)

Hypothesis Tests - Types (8 pages; 24/1/20)

 

Linear Coding (2 pages; 8/7/21)

  

Normal distribution (9 pages; 21/2/17)

 

Poisson distribution (7 pages; 10/2/21)

Approximations to Binomial & Poisson (4 pages; 30/1/17)

 

Probability & Counting

Probability & Counting Approaches [see STEP page] (12 pages; 14/7/21)

Selections (6 pages; 14/7/21)

 

Probability Generating Functions (5 pages; 16/4/21)

 

Sample variance (3 pages; 8/7/21)

 

Sampling (4 pages; 7/8/17)

 

Uniform distribution (Discrete) (2 pages; 20/3/20)

 

 

Discrete (aka Decision) Maths Notes 

 

Topics by exam board (9 pages; 30/7/19)

 

 

Algorithms

Bin Packing Algorithms (3 pages; 7/8/18)

Maximum Matching algorithm (4 pages; 6/9/13)

 

 

Allocation Problems

Hungarian Algorithm  (9 pages; 28/8/17)

 

 

Critical Path Analysis - Part 1 (12 pages; 22/1/20)

Critical Path Analysis - Part 2 (14 pages; 7/11/20)

 

 

Graphs & Networks

Graphs Glossary (3 pages; 15/1/14)

Directed Edges (incl. Incidence & Distance matrices) (5 pages; 19/11/19)

Planarity Algorithm (5 pages; 30/6/20)

 

 

Linear Programming & Simplex method

Linear Programming (9 pages; 21/11/19)

Formulating network problems as LP problems (7 pages; 21/1/20)

Simplex method - Part 1 (15 pages; 31/1/18)

Simplex method - Part 2 (16 pages; 31/1/18)

 

Minimum Connector Problem (6 pages; 21/11/20)

 

Network Flows - Introduction (5 pages; 16/1/21)

 

Route Inspection Problem (5 pages; 12/9/17)

 

Shortest Paths

Dijkstra's Algorithm (5 pages; 19/11/20)

Floyd's Algorithm (21 pages; 17/6/20)

 

Travelling Salesman problem (10 pages; 29/6/20)

 

 

Question Bank - Pure (with worked sol'ns)

Types: Exam-style / Practice / Problem

[E=easier; M=moderate; H=harder]

[See Complex Numbers & Counting for examples]

 

Misc. Problems 1

Tests 1 

Algebra 1 2

Arithmetic Series 1 2 3 4

Complex Numbers 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Counting 1 2 3 4 5 6 7

Cubics Qns [3 pages] Sol'ns [10 pages]

Differential Eq'ns 1 

Differentiation 1 2 3 4 5 6

Ellipses 1 2 3

Geometry 1 2 3 4 5 6

Graphs

  Sketches 1 2 3 4 7 8 12

  Transformations 5 6 9 10 11

Groups 1 2 3 4

Hyperbolas 1 2 4 5

Hyperbolic Functions 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Induction [3 pages] Sol'ns [23 pages]

Inequalities 1 2 3 4 5 6 7 8 9 10 11

Integers 1 2 3 4 5

Integration - P1 (E)(1 page; 7/11/17); Sol'ns (8 pages; 7/11/17)

Integration - P2 (H)(3 pages; 6/4/21); Sol'ns (23 pages; 6/4/21)

Integration - P3 (Hyperbolic)(2 pages; 6/2/18); Sol'ns (12 pages; 17/4/20)

Integration 2 5 6

   Improper Integrals 1  

   Volume of Revolution / Surface Area 3 4 7  

Linear Interpolation 1

Logarithms 1 2 3 4 5 6 7 8 9    

Maclaurin Series 1 2 3 4 5 6  

Matrices

  General 16 21 25

  Determinants 18 23 24 26

  Eigenvectors 4 5 6 7 8 9 10 11 12 13 14 15 47 48

  Invariant Points & Lines 27 28 29 30 42 43 45 46 49 52

  Inverses 19 22

  Shears 31 32 33 34

  Simultaneous Eq'ns 3 35 36 37 38 39

  Transformations 1 2 17 40 41 44 50

Numerical Methods

  Convergence 2

  Integration 3 4 5 6 7

  Sol'n of Eq'ns 1

Parabolas 1 2 3 4 5

Parametric Eq'ns 1

Partial Fractions 1

Polar Curves 1 2 3 4

Polynomials 4 5

   Factorisations 1 2 3

   Relations between roots 6 7 8 9 10 11 12

Quadratics 1 2 3 4 5

Recurrence relations 1

Series 5 6 7

   Method of Differences 1 2 3 4

Surds 1 2

Trigonometry 1 3 11 16

   Equations 2 12 13 17 19 20

   Identities 4 5 6 8 14 15 22 23 24 25

   Sketches 7 18

   Triangles 9 10 21

Vectors 2 4 14 16 21 24 25 26 27

   Lines 5 6

   Planes 7 9 11 15 34

   Lines & Planes 1 8 10 17 20 23

   Shortest Distance 3 12 13 18 19 22 32 33

   Vector Product  31

 

 

Question Bank - Mechanics (with worked sol'ns)

 Types: Exam-style / Practice / Problem

[E=easier; M=moderate; H=harder]

 

Centre of Mass 1 2 3 4 5  

Circular Motion 1 2

Forces 1 2 3 4 5 6 7 8 9 10 11 

Friction 1 2 3 4

Hooke's Law 1 2 3 4

Impulse & Momentum 1 2 3 4 5 6 7 8 9 10 11 12 13

   Oblique impact with plane Exs

Kinematics 1 2

Oscillations 1 2 3 4

Rotating Bodies 1

Work & Energy 1 2 3 4

 

  

Question Bank - Probability & Statistics (with worked sol'ns)

Types: Exam-style / Practice / Problem

[E=easier; M=moderate; H=harder]

 

Chi-Squared

  Contingency Tables 2a 2b

  Goodness of Fit 1

Correlation 1 2

Discrete Random Variables 1 2 3 4

Geometric Distribution 1 2

Normal Distribution 1 2

Poisson Distribution 1 2 3 4

Probability 1 2 3 4 5 6 7

Probability Generating Function 1 2

Uniform Distribution (Discrete) 1

 

Question Bank - Discrete (with worked sol'ns)

Types: Exam-style / Practice / Problem

[E=easier; M=moderate; H=harder]

 

Algorithms 1 7

   Bin Packing 3 5 6

   Sorting 2 4    

Critical Path Analysis 1a 1b 2

Dijkstra's algorithm 1

Floyd's Algorithm  1 2

Game Theory  1 2 3

Graphs 2

   Kuratowski's Thm 1

Linear Programming 1 2a 2b

   Formulate as LP problem 3 4 5 6 7

   Simplex 2c 8 9a 9b

Minimum Connector 1 2

Planarity algorithm 1

Route Inspection 1 2

Travelling Salesman problem 1

 

STEP   

General Notes

STEP Exams - Tips (3 pages; 14/2/21)

STEP Exams - Preparation (3 pages; 4/6/20)

STEP Exams - Methods (8 pages; 4/6/20)

STEP Exams - Technique (7 pages; 4/6/20)

Index of q'ns: Pure (24 pages; 2/9/20)

Index of q'ns: Mechanics (9 pages; 2/9/20)

Index of q'ns: Probability & Statistics (7 pages; 2/9/20)

 

Topic Notes & Exercises

Miscellaneous (5 pages; 14/7/21)

Algebra Methods 5 pages; 23/1/18)

Complex Number Methods (9 pages; 28/2/15)

Cubics (4 pages; 11/12/19)

Curve Sketching (12 pages; 14/7/21)

Differential Equations (5 pages; 18/11/18)

Inequalities (2 pages; 14/7/21)

Integration Ideas (4 pages; 14/4/21)

Logarithms (2 pages; 14/7/21)

Probability & Counting Approaches (12 pages; 14/7/21)

Transformations (6 pages; 12/12/19)

Trigonometry (5 pages; 15/4/21)

Vector Methods (5 pages; 26/3/21)

STEP Exercises (5 pages; 2/12/20); Sol'ns (24 pages; 2/12/20)

 

Solutions for Past Papers

2005, Paper 1: 1  3  4  5  11  12  13  14

2005, Paper 2: 1  4  6  10  11

2005, Paper 3: 2  3  7 8 13

2006, Paper 1: 1  2  3  4  5  6  7  8  9  10  11  12  13  14

2006, Paper 2: 2  4  6  10 12  

2006, Paper 3: 3  4  10  11  12  13 

2007, Paper 1: 1  2  3  4  5  7  12 

2007, Paper 2: 1  2  3  4  5

2007, Paper 3: 1  2  3  7  12

2008, Paper 1: 1  2  6  9  13 

2008, Paper 2: 1  3  4  5  6  7  10 

2008, Paper 3: 1  2  5  8  13 

2009, Paper 1: 1  2  9  12  13

2009, Paper 2: 5  8  10  11  13

2009, Paper 3: 1  4  6  7  8  11 

2010, Paper 1: 1  2  3  5  9 

2010, Paper 2: 4  5  7  12  13

2010, Paper 3: 2  3  8  9 12

2011, Paper 1: 1  2  6  9  10

2011, Paper 2: 1  2  5  6  9  11  12

2011, Paper 3: 1  2  3  4  5  6  7  8  9  10  11  12  13

2012, Paper 1: 2  5  8  9  11  13

2012, Paper 2: 3  5  7  9  10  11  12  13

2012, Paper 3: 1  6  7  9  10  11  12  13

2013, Paper 1: 1 4 10 12 13

2013, Paper 2: 1 2 11 12 13

2013, Paper 3: 1 6 7 8 9

2014, Paper 1: 2 3 4 9 11

2014, Paper 2: 4 5 9 11 12

2014, Paper 3: 2 7 9 10 13

2015, Paper 1: 3 9 10 12 13

2015, Paper 2: 2 6 10 11 12

2015, Paper 3: 1 6 9 12 13

2016, Paper 1: 2 10 11 12 13

2016, Paper 2: 3 6 7 9 13

2016, Paper 3: 1 2 3 8 11

2017, Paper 1: 1 2 10 12 13

2017, Paper 2: 1 9 10 12 13

2017, Paper 3: 3 4 9 12 13

2018, Paper 1: 7 9 10 12 13

2018, Paper 2: 2 6 8 10 11 13

2018, Paper 3: 1 2 3 8 11

2019, Paper 1: 3 4 9 10 11

2019, Paper 2: 1 2 7 10 11

2019, Paper 3: 3 5 9 11 12

2020, Paper 2: 1 6 9 10 11 12

2020, Paper 3: 1

 

MAT

 

General Notes

Notes on MAT paper (3 pages; 6/8/20)

MAT Exam Technique (12 pages; 4/9/20)

MAT - Extra Material (2 pages; 28/9/21)

MAT - Index of Q'ns (14 pages; 4/11/20)

  

Topic Notes & Exercises

Important Ideas (17 pages; 15/2/20)

MAT Exercises (3 pages; 2/12/20); Sol'ns (12 pages; 2/12/20)

 

Solutions for Past Papers

Specimen 1: MC 3 4 5

Specimen 2: MC 2 4

2007: MC 4 5

2008: MC 2 3 5

2009: MC 2

2010: MC 3

2011: MC 2

2012: MC 5

2013: MC 2 3 4 5

2014: MC 2 3 4 5

2015: MC 2 3 4 5

2016: MC

2017: MC 2

2018: MC

2019: MC 2 3 5

2020: MC 2 4

 

TMUA 

 

General Notes 

TMUA Exam Technique (8 pages; 29/9/21)

TMUA - Extra Material (1 page; 28/9/21)

 

Topic Notes

Important Ideas (17 pages; 28/9/21)

 

Solutions for Past Papers

Specimen Paper 1

2020 [also used for Computer-based Demo] Paper 1

2020 [also used for Computer-based Demo] Paper 2