UniGeniusA-level Further Maths · Edexcel 9FM0

The whole Further Maths course

Everyone sits Core Pure 1 and 2. Your school picks two option papers.

Four papers, 75 marks each

PaperContentTime
1Core Pure Mathematics 190 minutes
2Core Pure Mathematics 290 minutes
3Your first option90 minutes
4Your second option90 minutes

Every lesson, in teaching order

Your two options

Core Pure plus all eight options: 90 lessons.

Core Pure: proof and complex numbers

  1. 1Induction for sums and divisibility
  2. 2Complex numbers and quadratic roots
  3. 3Conjugate pairs and polynomial roots
  4. 4The Argand diagram: modulus and argument
  5. 5Loci and regions in the Argand diagram
  6. 6De Moivre's theorem: identities and sums
  7. 7Exponential form and nth roots
  8. 8Roots of unity and their geometry

Core Pure: matrices

  1. 9Matrix arithmetic, identity and zero
  2. 10Matrices as transformations in 2D and 3D
  3. 11Determinants, invariant points and invariant lines
  4. 12Inverse matrices and singular matrices
  5. 13Three equations, three planes
  6. 14Induction for matrix powers

Core Pure: roots, series and expansions

  1. 15Roots and coefficients, transformed roots
  2. 16Standard sums and the method of differences
  3. 17Maclaurin series and validity

Core Pure: further calculus

  1. 18Volumes of revolution
  2. 19Improper integrals and mean values
  3. 20Partial fractions, inverse trig and substitution

Core Pure: vectors in 3D

  1. 21Lines and planes in three dimensions
  2. 22Scalar products, perpendicularity and angles
  3. 23Intersections and shortest distances

Core Pure: polar and hyperbolic

  1. 24Polar coordinates and sketches
  2. 25Polar areas and tangents
  3. 26Hyperbolic functions and identities
  4. 27Hyperbolic calculus
  5. 28Inverse hyperbolic functions as logarithms
  6. 29Integration with hyperbolic substitutions

Core Pure: differential equations

  1. 30Integrating factors and initial conditions
  2. 31Building first-order models
  3. 32Second-order equations: complementary functions
  4. 33Particular integrals and resonance
  5. 34Simple harmonic, damped and forced motion
  6. 35Coupled first-order systems

Core Pure: workshop

  1. 36Core Pure workshop

Further Pure 1

  1. 37t-formulae, identities and equations
  2. 38Taylor series and limits
  3. 39Leibniz, L'Hopital and the t-substitution
  4. 40Series solutions of differential equations
  5. 41Conics: eccentricity, foci and directrices
  6. 42Conics: tangents, normals and loci
  7. 43Vector and triple products
  8. 44Numerical methods and inequalities

Further Pure 2

  1. 45Groups: axioms and Cayley tables
  2. 46Subgroups, Lagrange and isomorphism
  3. 47Reduction formulae, arc length and surface area
  4. 48Eigenvalues, diagonalisation and Cayley-Hamilton
  5. 49Complex transformations of the plane
  6. 50Euclid, Bezout and Fermat
  7. 51Congruences and counting
  8. 52Recurrence relations and induction

Further Statistics 1

  1. 53Discrete distributions and the Poisson model
  2. 54Geometric and negative binomial models
  3. 55Poisson and geometric hypothesis tests
  4. 56The central limit theorem
  5. 57Chi-squared tests
  6. 58Probability generating functions
  7. 59Type I and Type II errors, size and power

Further Statistics 2

  1. 60Regression, residuals and correlation
  2. 61Continuous distributions
  3. 62Correlation tests and combining normals
  4. 63Estimation and confidence intervals
  5. 64Tests on two means
  6. 65Variance tests and the F-distribution
  7. 66t-tests: one sample, paired and pooled

Further Mechanics 1

  1. 67Momentum and impulse
  2. 68Work, energy and power
  3. 69Hooke's law and elastic energy
  4. 70Direct collisions and restitution
  5. 71Oblique collisions

Further Mechanics 2

  1. 72Motion in a circle
  2. 73Centres of mass of plane figures
  3. 74Centres of mass by integration
  4. 75Toppling and sliding
  5. 76Variable forces and elastic SHM
  6. 77Variable acceleration

Decision Maths 1

  1. 78Algorithms, sorting and packing
  2. 79Graphs, Euler routes and planarity
  3. 80Prim, Kruskal, Dijkstra and Floyd
  4. 81Route inspection and the travelling salesperson
  5. 82Critical path analysis
  6. 83Resource histograms and scheduling
  7. 84Linear programming and the simplex method

Decision Maths 2

  1. 85Transportation problems
  2. 86Allocation and the Hungarian algorithm
  3. 87Flows in networks
  4. 88Dynamic programming
  5. 89Game theory
  6. 90Recurrence models and decision trees

Independent practice for Pearson Edexcel A-level Further Mathematics (9FM0), not endorsed by Pearson.

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