Courses

LFM Pure

Year 12 course on pure mathematics

Coordinate Geometry 28
Simultaneous equations 9
Proof 52
Proof by induction 17
Introduction to trig 13
Modulus function 6
Matrices 9
Linear transformations 8
Invariant lines and eigenvalues and vectors 1
Trigonometry 2 51
Small angle approximation 8
Differentiation 43
Integration 112
Implicit equations and differentiation 14
Differential equations 35
3x3 Matrices 12
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LFM Pure and Mechanics

Year 12 course on Pure and Mechanics

Exponentials and Logarithms 7
Arithmetic and Geometric sequences 14
Differentiation from first principles 16
Integration as Area 9
Vectors 31
Constant Acceleration 8
Non-constant acceleration 1
Newton's laws and connected particles 9
Pulley systems 6
Motion on a slope 5
Friction 10
Momentum and Collisions 2
Moments 14
Parametric equations 16
Projectiles 51
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LFM Stats And Pure

Year 12 course on Pure and Statistics

Quadratics & Inequalities 24
Curve Sketching 25
Polynomials 28
Binomial Theorem (positive integer n) 9
Functions (Transformations and Inverses) 3
Partial Fractions 3
Generalised Binomial Theorem 16
Complex Numbers (L8th) 35
Combinatorics 7
Measures of Location and Spread 0
Probability Definitions 11
Tree Diagrams 14
Principle of Inclusion/Exclusion 3
Independent Events 7
Conditional Probability 31
Discrete Probability Distributions 16
Uniform Distribution 6
Binomial Distribution 7
Geometric Distribution 15
Hypergeometric Distribution 7
Negative Binomial Distribution 5
Modelling and Hypothesis Testing 3
Hypothesis test of binomial distributions 0
Data representation 0
Continuous Probability Distributions and Random Variables 18
Continuous Uniform Random Variables 6
Geometric Probability 14
Normal Distribution 8
Approximating Binomial to Normal Distribution 7
Solving equations numerically 1
Newton-Raphson method 1
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UFM Additional Further Pure

Year 13 course on additional further pure

Sequences and Series 12
Number Theory 5
Vector Product and Surfaces 4
Groups 14
Reduction Formulae 14
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UFM Mechanics

Year 13 course on Further Mechanics

Moments 21
Work, energy and Power 1 5
Momentum and Collisions 1 34
Centre of Mass 1 8
Circular Motion 1 10
Momentum and Collisions 2 17
Work, energy and Power 2 28
Centre of Mass 2 10
Circular Motion 2 28
Dimensional Analysis 0
Variable Force 23
Simple Harmonic Motion 15
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UFM Pure

Sequences and series, recurrence and convergence 33
Roots of polynomials 15
Polar coordinates 18
Conic sections 9
Taylor series 17
Hyperbolic functions 18
Integration using inverse trig and hyperbolic functions 11
Vectors 29
First order differential equations (integrating factor) 12
Complex numbers 2 32
Second order differential equations 29
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UFM Statistics

Year 13 course of Further Statistics

Discrete Random Variables 2
Poisson Distribution 26
Approximating the Poisson to the Normal distribution 1
Approximating the Binomial to the Poisson distribution 2
Probability Generating Functions 8
Cumulative distribution functions 14
Exponential Distribution 7
Bivariate data 16
Linear regression 0
Moment generating functions 4
Linear combinations of normal random variables 0
Central limit theorem 10
Hypothesis test of a normal distribution 1
Hypothesis test of Pearson’s product-moment correlation coefficient 0
Hypothesis test of Spearman’s rank correlation coefficien 0
Hypothesis test of a Poisson distribution 0
The Gamma Distribution 0
Chi-squared distribution 0
Yates’ continuity correction 0
Non-parametric tests 0
Wilcoxon tests 0
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zNo longer examinable

Problems which are no longer examinable from mechanics

Moments of inertia 22
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