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Pearson Edexcel

Every lesson in the library carries its Edexcel specification reference, and the sections below collect those references so you can work through a paper in the order the specification sets out. A lesson serving two topics appears under both.

Jump to: A-level Mathematics · Further Mathematics

A-level Mathematics (9MA0)

Papers 1 and 2 examine the Pure content; Paper 3 is Statistics and Mechanics.

Pure — Papers 1 and 2

1 PROOF

• Disproof and proof by contradiction9MA0 1.1
• The structure of proof: deduction and exhaustion9MA0 1.1

2 ALGEBRA AND FUNCTIONS

• Functions in modelling9MA0 2.11
• Functions, inverses and the modulus9MA0 2.7, 2.8, 2.9
• Graphs, proportion and transformations9MA0 2.7, 2.9
• Indices and surds9MA0 2.1, 2.2
• Partial fractions9MA0 2.10
• Polynomials and the factor theorem9MA0 2.6
• Quadratic functions9MA0 2.3
• Simultaneous equations and inequalities9MA0 2.4, 2.5

3 COORDINATE GEOMETRY IN THE (X, Y) PLANE

• Circles9MA0 3.2
• Parametric equations9MA0 3.3, 3.4
• Straight lines9MA0 3.1

4 SEQUENCES AND SERIES

• Arithmetic series9MA0 4.4, 4.6
• Geometric series9MA0 4.5, 4.6
• Sequences and sigma notation9MA0 4.2, 4.3
• The binomial expansion9MA0 4.1
• The general binomial expansion9MA0 4.1

5 TRIGONOMETRY

• Compound angles and the harmonic form9MA0 5.6, 5.8
• Radians, arcs and small angles9MA0 5.1, 5.2
• Reciprocal and inverse trigonometric functions9MA0 5.4, 5.5
• Triangles and the sine and cosine rules9MA0 5.1
• Trigonometric graphs and equations9MA0 5.3, 5.5, 5.7
• Trigonometric modelling9MA0 5.9

6 EXPONENTIALS AND LOGARITHMS

• Exponential functions and e9MA0 6.1, 6.2
• Log graphs and exponential models9MA0 6.6, 6.7
• Logarithms and their laws9MA0 6.3, 6.4, 6.5

7 DIFFERENTIATION

• Differentiating powers of x9MA0 7.2
• Differentiating trig, exponentials and logs9MA0 7.1, 7.2
• Implicit and parametric differentiation9MA0 7.5
• Rates of change and building differential equations9MA0 7.4, 7.6
• Tangents, turning points and curve behaviour9MA0 7.3, 7.1
• The derivative from first principles9MA0 7.1
• The product, quotient and chain rules9MA0 7.4

8 INTEGRATION

• Areas, parametric curves and the limit of a sum9MA0 8.3, 8.4
• Definite integrals and areas9MA0 8.3
• Integrating rational functions9MA0 8.6
• Integrating standard functions9MA0 8.2
• Integration as antidifferentiation9MA0 8.1, 8.2
• Integration by substitution and by parts9MA0 8.5
• Solving differential equations9MA0 8.7, 8.8

9 NUMERICAL METHODS

• Locating roots and iteration9MA0 9.1, 9.2
• Newton-Raphson and the trapezium rule9MA0 9.3-9.5

10 VECTORS

• Vectors in three dimensions9MA0 10.1-10.5
• Vectors in two dimensions9MA0 10.1-10.5

Statistics — Paper 3 Section A

1 STATISTICAL SAMPLING

• Sampling and the large data set9MA0 S1

2 DATA PRESENTATION AND INTERPRETATION

• Correlation and regression9MA0 S2
• Measures of location and spread9MA0 S2
• Representing and interpreting data9MA0 S2

3 PROBABILITY

• Conditional probability9MA0 S3
• Probability and Venn diagrams9MA0 S3

4 STATISTICAL DISTRIBUTIONS

• The binomial distribution9MA0 S4
• The normal distribution9MA0 S4

5 STATISTICAL HYPOTHESIS TESTING

• Hypothesis testing with the binomial9MA0 S5
• Hypothesis testing: correlation and the normal9MA0 S5

Mechanics — Paper 3 Section B

6 QUANTITIES AND UNITS IN MECHANICS

• Modelling, quantities and units9MA0 M6

7 KINEMATICS

• Kinematics with constant acceleration9MA0 M7
• Kinematics with variable acceleration9MA0 M7
• Projectiles9MA0 M7

8 FORCES AND NEWTON'S LAWS

• Connected particles and pulleys9MA0 M8
• Forces and Newton's laws9MA0 M8
• Friction and inclined planes9MA0 M8
• Statics of a particle9MA0 M8

9 MOMENTS

• Moments9MA0 M9

A-level Further Mathematics (9FM0)

Papers 1 and 2 are compulsory Core Pure; Papers 3 and 4 are chosen from the eight option papers, all of which are covered here.

Core Pure — Papers 1 and 2

CORE PURE 1

• Complex arithmetic and the Argand diagram9FM0 CP1
• Determinants and inverses9FM0 CP1
• Induction: divisibility and matrices9FM0 CP1
• Intersections, angles and distances9FM0 CP1
• Lines and planes in three dimensions9FM0 CP1
• Matrix algebra and transformations9FM0 CP1
• Modulus, argument and loci9FM0 CP1
• Proof by induction: sums and series9FM0 CP1
• Roots of polynomials9FM0 CP1
• Summing series and the method of differences9FM0 CP1
• Systems of equations and invariance9FM0 CP1
• Volumes of revolution9FM0 CP1

CORE PURE 2

• Areas with polar coordinates9FM0 CP2
• Calculus with hyperbolic functions9FM0 CP2
• Calculus with inverse trigonometric functions9FM0 CP2
• De Moivre's theorem and trigonometric identities9FM0 CP2
• First order equations and integrating factors9FM0 CP2
• Hyperbolic functions and identities9FM0 CP2
• Maclaurin series9FM0 CP2
• Mean values and improper integrals9FM0 CP2
• Modelling with differential equations9FM0 CP2
• Polar curves9FM0 CP2
• Roots of unity and complex roots9FM0 CP2
• Second order equations9FM0 CP2

Options — Papers 3 and 4

FURTHER PURE 1

• Conic sections9FM0 FP1
• Inequalities and inequations9FM0 FP1
• Leibnitz's theorem and the Weierstrass substitution9FM0 FP1
• Limits and L'Hospital's rule9FM0 FP1
• Numerical methods for differential equations9FM0 FP1
• Series solutions of differential equations9FM0 FP1
• Tangents, normals and loci of conics9FM0 FP1
• Taylor series9FM0 FP1
• The t-formulae9FM0 FP1
• The vector product and the scalar triple product9FM0 FP1

FURTHER PURE 2

• Arc length and surface area9FM0 FP2
• Combinatorics9FM0 FP2
• Diagonalisation and the Cayley-Hamilton theorem9FM0 FP2
• Eigenvalues and eigenvectors9FM0 FP2
• Further loci and regions in the Argand diagram9FM0 FP2
• Groups and their axioms9FM0 FP2
• Modular arithmetic and Fermat's little theorem9FM0 FP2
• Recurrence relations9FM0 FP2
• Reduction formulae9FM0 FP2
• Subgroups, Lagrange's theorem and isomorphism9FM0 FP2
• The Euclidean algorithm and Bezout's identity9FM0 FP2
• Transformations of the complex plane9FM0 FP2

FURTHER STATISTICS 1

• Contingency tables9FM0 FS1
• Discrete random variables and expectation9FM0 FS1
• Geometric and negative binomial distributions9FM0 FS1
• Goodness-of-fit tests9FM0 FS1
• Hypothesis tests for Poisson and geometric models9FM0 FS1
• Probability generating functions9FM0 FS1
• The Central Limit Theorem9FM0 FS1
• The Poisson distribution9FM0 FS1
• The quality of tests9FM0 FS1

FURTHER STATISTICS 2

• Combinations of normal random variables9FM0 FS2
• Comparing two normal means9FM0 FS2
• Confidence intervals and tests with the t-distribution9FM0 FS2
• Continuous random variables: density and distribution functions9FM0 FS2
• Correlation coefficients: product moment and Spearman9FM0 FS2
• Estimators, standard error and confidence intervals9FM0 FS2
• Least squares regression and residuals9FM0 FS2
• Mean, variance and skewness of continuous variables9FM0 FS2
• Testing a correlation coefficient9FM0 FS2
• Testing variances: chi-squared and the F-distribution9FM0 FS2
• The continuous uniform distribution9FM0 FS2

FURTHER MECHANICS 1

• Direct impact and Newton's law of restitution9FM0 FM1
• Elastic potential energy9FM0 FM1
• Hooke's law and elastic strings9FM0 FM1
• Impulse and momentum as vectors9FM0 FM1
• Momentum and impulse9FM0 FM1
• Oblique impact and impact with a smooth surface9FM0 FM1
• Successive impacts and impacts with a wall9FM0 FM1
• Work, energy and power9FM0 FM1

FURTHER MECHANICS 2

• Angular speed and horizontal circular motion9FM0 FM2
• Centre of mass of a discrete distribution9FM0 FM2
• Centres of mass by integration9FM0 FM2
• Centres of mass of plane figures and frameworks9FM0 FM2
• Equilibrium, suspension, toppling and sliding9FM0 FM2
• Further kinematics: acceleration as a function of x, t or v9FM0 FM2
• Motion in a vertical circle9FM0 FM2
• Newton's laws with a variable force9FM0 FM2
• Oscillations on strings and springs9FM0 FM2
• Simple harmonic motion9FM0 FM2

DECISION MATHEMATICS 1

• Algorithms, sorting and bin packing9FM0 D1
• Critical path analysis9FM0 D1
• Float, Gantt charts and scheduling9FM0 D1
• Graphs: order, Eulerian paths and planarity9FM0 D1
• Linear programming: formulation and graphical solution9FM0 D1
• Minimum spanning trees: Prim and Kruskal9FM0 D1
• Route inspection9FM0 D1
• Shortest paths: Dijkstra and Floyd9FM0 D1
• The Simplex algorithm9FM0 D1
• The travelling salesman problem9FM0 D1

DECISION MATHEMATICS 2

• Allocation and the Hungarian algorithm9FM0 D2
• Decision analysis9FM0 D2
• Dynamic programming9FM0 D2
• Flows in networks: cuts and capacity9FM0 D2
• Game theory: play safe and stable solutions9FM0 D2
• Maximum flow and the labelling procedure9FM0 D2
• Mixed strategies9FM0 D2
• The stepping-stone method9FM0 D2
• Transportation problems9FM0 D2

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