Courses

6th Form

Algebraic Manipulation 23
Quadratic Equations and Inequalities 36
Simultaneous Equations 38
Solving Equations 16
Polynomials and Equations 21
Algebraic Proof and Identities 21
Inequalities and Proof 44
Inequalities - AM-GM 19
Coordinate Geometry - Lines 32
Coordinate Geometry - Circles 54
Coordinate Geometry - Loci 19
Coordinate Geometry - Pairs of Lines 16
Euclidean Geometry - Triangles 70
Euclidean Geometry - Circle Theorems 75
Euclidean Geometry - Circles & Tangents 45
Euclidean Geometry - Polygons & Angles 22
Euclidean Geometry - Similarity and Congruence 8
Euclidean Geometry - Loci and Constructions 11
Euclidean Geometry - Proofs & Constructions 75
Euclidean Geometry - Inequalities & Extrema 24
Euclidean Geometry - Trigonometry 16
3D Geometry 92
3D Geometry and Trigonometry 30
Trigonometry - Sine and Cosine Rules 34
Trigonometric Identities 21
Trigonometric Equations 9
Curve Sketching and Functions 27
Sequences and Series 30
Combinatorics 22
Probability 8
Number Theory and Divisibility 50
Optimisation 42
Problem Solving and Logic 32
Circle Theorems 76
Triangle Geometry 58

LFM Pure

Year 12 course on pure mathematics

Add Section
Coordinate Geometry 13
Proof 46
Proof by Induction 39
Trigonometric Identities - Proving 50
Trigonometric Identities and Equations 60
Trigonometric Identities and Elimination 8
Trigonometric Identities - Inequalities and Optimisation 11
Trigonometric Identities and Calculus 5
Trigonometric Equations 17
Trigonometric Series & Summation 12
Inverse Trigonometric Functions 5
Small Angle Approximations 4
2×2 Matrices 22
Differentiation Techniques 45
Analysis of Functions and Curve Sketching 68
Stationary Points and Turning Points 19
Differentiation - Optimisation 51
Differentiation - Inequalities & Proofs 13
Differentiation - Limits 10
Higher Derivatives and Leibniz Theorem 13
Implicit Differentiation 35
Integration Techniques 88
Integration by Substitution 13
Integration by Parts 5
Integration using Partial Fractions 14
Integration - Inequalities & Bounds 11
Differential Equations 24
3×3 Matrices 95

LFM Pure and Mechanics

Year 12 course on Pure and Mechanics

Add Section
Exponentials and Logarithms 7
Sequences and Series 41
Differentiation from First Principles 8
Integration as Area 56
Integration as Area - Bounds 20
Volumes of Revolution 31
Improper Integrals 2
Numerical Integration 10
Vectors - Geometric Proofs 54
Vectors - 3D Geometry 14
Vectors - Lines and Planes 7
Vectors - Scalar Product 6
Vectors and Forces 13
Kinematics - Constant Acceleration 17
Kinematics - Variable Acceleration 34
Kinematics - Relative Velocity 34
Newton's Laws 14
Connected Particles and Pulleys 32
Friction and Inclined Planes 21
Momentum and Impulse 13
Moments 23
Work, Energy and Power 32
Parametric Equations 43
Parametric Equations - Arc Length and Area 2
Projectiles - Range & Trajectory 63
Projectiles - Geometric Constraints 49
Projectiles on Inclined Planes 26
Projectiles - Envelope 30

LFM Stats And Pure

Year 12 course on Pure and Statistics

Add Section
Quadratics & Inequalities 3
Curve Sketching 75
Polynomials 78
Binomial Theorem 54
Generalised Binomial Series 25
Functions 2
Partial Fractions 49
Complex Numbers 49
Combinatorics 85
Probability 65
Discrete Distributions 24
Continuous Random Variables 10
Solving Equations Numerically 30

UFM Additional Further Pure

Year 13 course on additional further pure

Add Section
Number Theory 34
Number Theory - Modular Arithmetic 5
Groups - Structure and Axioms 50
Groups - Subgroups and Lagrange 1
Groups - Symmetry and Permutations 1
Reduction Formulae - Trigonometric 40
Reduction Formulae - Algebraic & Exponential 50
Reduction Formulae - Wallis & Definite Integrals 32
Reduction Formulae - Integration Techniques 16
Reduction Formulae - Beta and Gamma Functions 4
Combinatorics and Identities 7
Reduction Formulae - Wallis and Special Integrals 8

UFM Mechanics

Year 13 course on Further Mechanics

Add Section
Moments - Rigid Body Equilibrium 19
Moments - Ladder Problems 25
Ladder & Rod on Rough Surface 23
Rod Against Wall or Surface 2
Rod on Smooth Supports & Pegs 16
Rod on Inclined Planes 9
Moments and Friction - Rigid Bodies 65
Moments - Frameworks 51
Moments - Hinged Bodies and Frameworks 36
Jointed Rods & Frameworks 21
Jointed Bodies & Frameworks 20
Rods & Beams 39
Cylinder & Rod Systems 18
Cylinders & Spheres 37
Cylinder on Inclined Plane 6
Moments - Suspended Bodies 11
Moments - Virtual Work 7
Couples & Force Systems 13
General Rigid Body Equilibrium 14
Distributed Friction & Turning Point 13
Toppling, Sliding & Block Problems 18
Strings & Springs 11
Inclined Planes 16
Work, Energy and Power 53
Work, Energy and Elastic Strings 44
Energy & Momentum Combined 37
Variable Force and Energy Methods 15
Basic 1D Restitution 18
Momentum and Impulse 21
Momentum and Collisions 18
Sequential/Multiple Collisions 30
Impulsive Tensions 31
Oblique Collisions 76
Centre of Mass 49
Centre of Mass by Integration 15
Centre of Mass and Equilibrium 58
Centre of Mass and Stability 51
Circular Motion 48
Circular Motion - Conical Pendulum 15
Circular Motion - Vertical 23
Circular Motion - Vertical with Friction 7
Particle on String 25
Particle on Sphere/Hemisphere 22
Bead on Wire 11
Circular Motion - Constrained Systems 27
Circular Motion - Constrained & Special Cases 25
Circular Motion - Rotating Frames 14
Dimensional Analysis 10
Variable Force 96
Variable Force - Resisted Motion 63
Variable Force and Constrained Motion 14
Simple Harmonic Motion 65
SHM - Elastic Strings 90
SHM - Elastic Springs 47
SHM - Simple Pendulum 14
SHM - Coupled Oscillations 25
SHM - Damped Oscillations 10

UFM Pure

Sequences & Series – Convergence 53
Sequences & Series – Standard Sums 6
Series – Method of Differences 26
Symmetric Functions & Vieta's Formulae 71
Newton's Sums & Power Sums 42
Transformations & Substitutions 37
Inequalities via Roots 17
Roots of Polynomials 1
Polar Coordinates – Sketching & Properties 29
Polar Coordinates – Areas 49
Polar Coordinates – Curvature 14
Polar Coordinates – Arc Length 9
Parabola - Tangent & Normal 62
Parabola - Normal Properties 67
Parabola - Chord Properties 31
Parabola - Focus-Directrix Properties 54
Parabola - Locus Problems 14
Parabola – Locus & Chord Problems 2
Parabola - Envelope 15
Ellipse - Tangent & Normal 75
Ellipse - Locus & Parametric 18
Ellipse - General Properties 15
Ellipse – Normals 20
Ellipse – Properties 12
Ellipse - Chord Properties 39
Ellipse - Focus & Eccentricity 31
Ellipse - Conjugate Diameters 24
Ellipse - Locus Problems 14
Hyperbola 54
Rectangular Hyperbola 88
Conics – General Theory 96
Conics – Focus-Directrix 20
Conics – Tangent Properties 13
Conics – Normals 13
Conics – Chord Properties 11
Conics – Pole & Polar 49
Conics – Locus Problems 8
Conics – Envelopes 42
Conics – Curvature 48
Conics – Osculating Conics 6
Conics – Confocal Systems 15
Conics – Polar Form 20
Finding Expansions 36
Standard Series & Manipulation 81
Series via DEs & nth Derivatives 73
Limits & L'Hôpital 25
Inequalities & Bounds 27
Taylor & Maclaurin Series – Inequalities 6
Taylor & Maclaurin Series – Limits 4
Taylor & Maclaurin Series – Generating Functions 3
Taylor & Maclaurin Series – Expansions 1
Generating Functions 14
Hyperbolic Functions 22
Integration – Hyperbolic & Inverse Functions 17
Integration – Advanced Techniques 48
Partial Fractions 7
Mean Values 4
Vectors – Lines & Planes 13
Vectors – Cross & Triple Products 10
Complex Numbers – De Moivre's Theorem 2
Roots & Factorisation 55
Complex Numbers – Roots of Unity 55
Trig Identities via De Moivre 42
Complex Numbers – Trig Identities via De Moivre 12
Complex Numbers – Series Summation 32
Series Summation using Complex Exponentials 21
Complex Numbers – Geometry 17
First-Order Differential Equations 14
Second-Order Differential Equations 59
Second-Order DEs – Series Solutions 8
SHM & Damped Oscillations 1
Recurrence Relations 77

UFM Statistics

Year 13 course of Further Statistics

Add Section
Expectation Algebra 12
Poisson Distribution 6
Continuous Distributions 4
Probability Generating Functions 2
Sampling & Estimation 13
Hypothesis Testing 17
Chi-Squared Tests 7
Regression & Correlation 2
Non-parametric Tests 1

zNo longer examinable

Problems which are no longer examinable from mechanics

Add Section
Beams & Bending Moments 62
Catenary & Flexible Chains 57
Central Force & Orbital Mechanics 58
Classical Geometry – 3D & Spheres 52
Classical Geometry – Areal & Trilinear Coordinates 29
Classical Geometry – Coaxal Circles 65
Classical Geometry – Conics 221
Classical Geometry – Pole & Polar 73
Classical Geometry – Projective Methods 39
Classical Geometry – Triangles 76
Continued Fractions 43
Differential Geometry – Curvature & Evolutes 118
Electrical Circuits & Magnetism 63
Fluid Mechanics 52
Friction on Flexible Bodies 29
Graphical Statics 20
Inversive Geometry 113
Lagrangian Mechanics 29
Mathematical Essays 155
Miscellaneous Advanced Topics 153
Moments of Inertia 47
Moments of Inertia & Rotational Dynamics 224
Multivariate Calculus 169
Projective Geometry 227
Projective Geometry – Conics 151
Projective Geometry – Cross-Ratio 26
Projective Geometry – Involutions 31
Projective Geometry – Pole & Polar 61
Question needs checking before classifying 2
Rigid Body Kinematics 38
Rotating Frames & Advanced Dynamics 128
Stability of Equilibrium 32
Statics – Flexible Bodies & Cables 17
Statics – Frameworks 54
Statics – Rigid Bodies & Forces 100
Thermodynamics & Heat 19
Variable Mass & Rockets 55
Virtual Work & Statics 37