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Edexcel A-level Maths (9MA0) and Further Maths (9FM0) revision

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Specification map

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, 9.4, 9.5

10 VECTORS

• Vectors in three dimensions9MA0 10.1, 10.2, 10.3, 10.4, 10.5
• Vectors in two dimensions9MA0 10.1, 10.2, 10.3, 10.4, 10.5

Statistics — Paper 3 Section A

1 STATISTICAL SAMPLING

• Sampling and the large data set9MA0 P3 1.1

2 DATA PRESENTATION AND INTERPRETATION

• Correlation and regression9MA0 P3 2.2, 5.1
• Measures of location and spread9MA0 P3 2.3
• Representing and interpreting data9MA0 P3 2.1, 2.4

3 PROBABILITY

• Conditional probability9MA0 P3 3.2, 3.3
• Probability and Venn diagrams9MA0 P3 3.1, 3.2

4 STATISTICAL DISTRIBUTIONS

• The binomial distribution9MA0 P3 4.1, 4.3
• The normal distribution9MA0 P3 4.2, 4.3

5 STATISTICAL HYPOTHESIS TESTING

• Correlation and regression9MA0 P3 2.2, 5.1
• Hypothesis testing with the binomial9MA0 P3 5.1, 5.2
• Hypothesis testing: correlation and the normal9MA0 P3 5.1, 5.3

Mechanics — Paper 3 Section B

6 QUANTITIES AND UNITS IN MECHANICS

• Modelling, quantities and units9MA0 P3 6.1

7 KINEMATICS

• Kinematics with constant acceleration9MA0 P3 7.1, 7.2, 7.3
• Kinematics with variable acceleration9MA0 P3 7.4
• Projectiles9MA0 P3 7.5

8 FORCES AND NEWTON'S LAWS

• Connected particles and pulleys9MA0 P3 8.4
• Forces and Newton's laws9MA0 P3 8.1, 8.2, 8.3, 8.5
• Friction and inclined planes9MA0 P3 8.2, 8.6
• Statics of a particle9MA0 P3 8.4, 8.5, 8.6

9 MOMENTS

• Moments9MA0 P3 9.1

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.

Every lesson below names the numbered statements it teaches, so the figures under each paper count against Pearson’s list rather than against ours: 188 of the 188 statements across the nine papers have a lesson. The rows themselves are the specification’s topics; the count under each paper is the finer measure.

Core Pure — Papers 1 and 2

54 of the 54 statements Pearson lists for this paper.

1 PROOF

• Induction: divisibility and matrices9FM0 CP1 1.1
• Proof by induction: sums and series9FM0 CP1 1.1

2 COMPLEX NUMBERS

• Complex arithmetic and the Argand diagram9FM0 CP1 2.1, 2.2, 2.3, 2.4
• De Moivre's theorem and trigonometric identities9FM0 CP2 2.6, 2.8, 2.9
• Modulus, argument and loci9FM0 CP1 2.2, 2.5, 2.6, 2.7
• Roots of polynomials9FM0 CP1 2.1, 2.3, 4.1, 4.2
• Roots of unity and complex roots9FM0 CP2 2.10, 2.11

3 MATRICES

• Determinants and inverses9FM0 CP1 3.5, 3.6
• Matrix algebra and transformations9FM0 CP1 3.1, 3.2, 3.3
• Systems of equations and invariance9FM0 CP1 3.4, 3.7, 3.8

4 FURTHER ALGEBRA AND FUNCTIONS

• Maclaurin series9FM0 CP2 4.5, 4.6
• Roots of polynomials9FM0 CP1 2.1, 2.3, 4.1, 4.2
• Summing series and the method of differences9FM0 CP1 4.3, 4.4

5 FURTHER CALCULUS

• Calculus with inverse trigonometric functions9FM0 CP2 5.4, 5.5, 5.6
• Mean values and improper integrals9FM0 CP2 5.2, 5.3
• Volumes of revolution9FM0 CP1 5.1

6 FURTHER VECTORS

• Intersections, angles and distances9FM0 CP1 6.3, 6.5
• Lines and planes in three dimensions9FM0 CP1 6.1, 6.2, 6.3, 6.4

7 POLAR COORDINATES

• Areas with polar coordinates9FM0 CP2 7.3
• Polar curves9FM0 CP2 7.1, 7.2

8 HYPERBOLIC FUNCTIONS

• Calculus with hyperbolic functions9FM0 CP2 8.2, 8.5
• Hyperbolic functions and identities9FM0 CP2 8.1, 8.3, 8.4

9 DIFFERENTIAL EQUATIONS

• First order equations and integrating factors9FM0 CP2 9.1, 9.2
• Modelling with differential equations9FM0 CP2 9.3, 9.7, 9.8, 9.9
• Second order equations9FM0 CP2 9.2, 9.4, 9.5, 9.6

Further Pure 1 — Paper 3A

20 of the 20 statements Pearson lists for this paper.

1 FURTHER TRIGONOMETRY

• The t-formulae9FM0 FP1 1.1, 1.2, 1.3

2 FURTHER CALCULUS

• Leibnitz's theorem and the Weierstrass substitution9FM0 FP1 2.3, 2.5
• Limits and L'Hospital's rule9FM0 FP1 2.2, 2.4
• Taylor series9FM0 FP1 2.1

3 FURTHER DIFFERENTIAL EQUATIONS

• Series solutions of differential equations9FM0 FP1 3.1, 3.2

4 COORDINATE SYSTEMS

• Conic sections9FM0 FP1 4.1, 4.2
• Tangents, normals and loci of conics9FM0 FP1 4.3, 4.4

5 FURTHER VECTORS

• The vector product and the scalar triple product9FM0 FP1 5.1, 5.2, 5.3

6 FURTHER NUMERICAL METHODS

• Numerical methods for differential equations9FM0 FP1 6.1, 6.2

7 INEQUALITIES

• Inequalities and inequations9FM0 FP1 7.1

Further Pure 2 — Paper 4A

22 of the 22 statements Pearson lists for this paper.

1 GROUPS

• Groups and their axioms9FM0 FP2 1.1, 1.2, 1.3
• Subgroups, Lagrange's theorem and isomorphism9FM0 FP2 1.3, 1.4, 1.5

2 FURTHER CALCULUS

• Arc length and surface area9FM0 FP2 2.2
• Reduction formulae9FM0 FP2 2.1

3 FURTHER MATRIX ALGEBRA

• Diagonalisation and the Cayley-Hamilton theorem9FM0 FP2 3.2, 3.3
• Eigenvalues and eigenvectors9FM0 FP2 3.1

4 FURTHER COMPLEX NUMBERS

• Further loci and regions in the Argand diagram9FM0 FP2 4.1
• Transformations of the complex plane9FM0 FP2 4.2

5 NUMBER THEORY

• Combinatorics9FM0 FP2 5.7
• Modular arithmetic and Fermat's little theorem9FM0 FP2 5.3, 5.4, 5.5, 5.6
• The Euclidean algorithm and Bezout's identity9FM0 FP2 5.1, 5.2

6 FURTHER SEQUENCES AND SERIES

• Recurrence relations9FM0 FP2 6.1, 6.2, 6.3; 9FM0 D2 6.1, 6.2

Further Statistics 1 — Paper 3B

15 of the 15 statements Pearson lists for this paper.

1 DISCRETE PROBABILITY DISTRIBUTIONS

• Discrete random variables and expectation9FM0 FS1 1.1

2 POISSON AND BINOMIAL DISTRIBUTIONS

• The Poisson distribution9FM0 FS1 2.1, 2.2, 2.3

3 GEOMETRIC AND NEGATIVE BINOMIAL DISTRIBUTIONS

• Geometric and negative binomial distributions9FM0 FS1 3.1, 3.2, 3.3

4 HYPOTHESIS TESTING

• Hypothesis tests for Poisson and geometric models9FM0 FS1 4.1, 4.2

5 CENTRAL LIMIT THEOREM

• The Central Limit Theorem9FM0 FS1 5.1

6 CHI SQUARED TESTS

• Contingency tables9FM0 FS1 6.1
• Goodness-of-fit tests9FM0 FS1 6.1

7 PROBABILITY GENERATING FUNCTIONS

• Probability generating functions9FM0 FS1 7.1, 7.2, 7.3

8 QUALITY OF TESTS

• The quality of tests9FM0 FS1 8.1

Further Statistics 2 — Paper 4B

20 of the 20 statements Pearson lists for this paper.

1 LINEAR REGRESSION

• Least squares regression and residuals9FM0 FS2 1.1, 1.2

2 CONTINUOUS PROBABILITY DISTRIBUTIONS

• Continuous random variables: density and distribution functions9FM0 FS2 2.1, 2.2
• Mean, variance and skewness of continuous variables9FM0 FS2 2.3
• The continuous uniform distribution9FM0 FS2 2.4

3 CORRELATION

• Correlation coefficients: product moment and Spearman9FM0 FS2 3.1, 3.2
• Testing a correlation coefficient9FM0 FS2 3.3

4 COMBINATIONS OF RANDOM VARIABLES

• Combinations of normal random variables9FM0 FS2 4.1

5 ESTIMATION, CONFIDENCE INTERVALS AND TESTS USING A NORMAL DISTRIBUTION

• Comparing two normal means9FM0 FS2 5.4, 5.5
• Estimators, standard error and confidence intervals9FM0 FS2 5.1, 5.2, 5.3

6 OTHER HYPOTHESIS TESTS AND CONFIDENCE INTERVALS

• Testing variances: chi-squared and the F-distribution9FM0 FS2 6.1, 6.2

7 CONFIDENCE INTERVALS AND TESTS USING THE T-DISTRIBUTION

• Confidence intervals and tests with the t-distribution9FM0 FS2 7.1, 7.2, 7.3

Further Mechanics 1 — Paper 3C

9 of the 9 statements Pearson lists for this paper.

1 MOMENTUM AND IMPULSE

• Impulse and momentum as vectors9FM0 FM1 1.2
• Momentum and impulse9FM0 FM1 1.1

2 WORK, ENERGY AND POWER

• Work, energy and power9FM0 FM1 2.1

3 ELASTIC STRINGS AND SPRINGS AND ELASTIC ENERGY

• Elastic potential energy9FM0 FM1 3.2
• Hooke's law and elastic strings9FM0 FM1 3.1

4 ELASTIC COLLISIONS IN ONE DIMENSION

• Direct impact and Newton's law of restitution9FM0 FM1 4.1
• Successive impacts and impacts with a wall9FM0 FM1 4.2

5 ELASTIC COLLISIONS IN TWO DIMENSIONS

• Oblique impact and impact with a smooth surface9FM0 FM1 5.1, 5.2

Further Mechanics 2 — Paper 4C

10 of the 10 statements Pearson lists for this paper.

1 MOTION IN A CIRCLE

• Angular speed and horizontal circular motion9FM0 FM2 1.1
• Motion in a vertical circle9FM0 FM2 1.2

2 CENTRES OF MASS OF PLANE FIGURES

• Centre of mass of a discrete distribution9FM0 FM2 2.1
• Centres of mass of plane figures and frameworks9FM0 FM2 2.2
• Equilibrium, suspension, toppling and sliding9FM0 FM2 2.2, 3.2, 3.3

3 FURTHER CENTRES OF MASS

• Centres of mass by integration9FM0 FM2 3.1
• Equilibrium, suspension, toppling and sliding9FM0 FM2 2.2, 3.2, 3.3

4 FURTHER DYNAMICS

• Newton's laws with a variable force9FM0 FM2 4.1
• Oscillations on strings and springs9FM0 FM2 4.2
• Simple harmonic motion9FM0 FM2 4.2

5 FURTHER KINEMATICS

• Further kinematics: acceleration as a function of x, t or v9FM0 FM2 5.1

Decision Mathematics 1 — Paper 3D

18 of the 18 statements Pearson lists for this paper.

1 ALGORITHMS AND GRAPH THEORY

• Algorithms, sorting and bin packing9FM0 D1 1.1, 1.2
• Graphs: order, Eulerian paths and planarity9FM0 D1 1.3, 1.4

2 ALGORITHMS ON GRAPHS

• Minimum spanning trees: Prim and Kruskal9FM0 D1 2.1
• Shortest paths: Dijkstra and Floyd9FM0 D1 2.2

3 ALGORITHMS ON GRAPHS II

• Route inspection9FM0 D1 3.1
• The travelling salesman problem9FM0 D1 3.2

4 CRITICAL PATH ANALYSIS

• Critical path analysis9FM0 D1 4.1, 4.2, 4.3
• Float, Gantt charts and scheduling9FM0 D1 4.4, 4.5, 4.6

5 LINEAR PROGRAMMING

• Linear programming: formulation and graphical solution9FM0 D1 5.1, 5.2
• The Simplex algorithm9FM0 D1 5.3, 5.4

Decision Mathematics 2 — Paper 4D

20 of the 20 statements Pearson lists for this paper.

1 TRANSPORTATION PROBLEMS

• The stepping-stone method9FM0 D2 1.2, 1.3
• Transportation problems9FM0 D2 1.1

2 ALLOCATION (ASSIGNMENT) PROBLEMS

• Allocation and the Hungarian algorithm9FM0 D2 2.1, 2.2

3 FLOWS IN NETWORKS

• Flows in networks: cuts and capacity9FM0 D2 3.1, 3.4
• Maximum flow and the labelling procedure9FM0 D2 3.2, 3.3, 3.5

4 DYNAMIC PROGRAMMING

• Dynamic programming9FM0 D2 4.1

5 GAME THEORY

• Game theory: play safe and stable solutions9FM0 D2 5.1, 5.2, 5.3
• Mixed strategies9FM0 D2 5.4, 5.5

6 RECURRENCE RELATIONS

• Recurrence relations9FM0 FP2 6.1, 6.2, 6.3; 9FM0 D2 6.1, 6.2

7 DECISION ANALYSIS

• Decision analysis9FM0 D2 7.1, 7.2

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