The course

• 1

  Start here

  Paper 1 (non-calculator): 1 hour, 35 marks. Paper 2 (calculator): 2 hours 30 minutes, 80 marks. 115 marks in all.

  Free: A tour of the Advanced Higher Maths course
• 2

  Section 1: Partial fractions, binomial expansions and graphs

  2 of the 18 questions on the Paper 1 style timed check and 2 on the Paper 2 style timed check

  Partial fractions and the binomial theoremAsymptotes, features of graphs and related graphs27 questions
• 3

  Section 2: Differentiation

  2 of the 18 questions on the Paper 1 style timed check and 2 on the Paper 2 style timed check

  Free: Differentiation rules, including inverse trigonometric functionsImplicit, logarithmic and parametric differentiation, and related rates28 questions
• 4

  Section 3: Integration

  2 of the 18 questions on the Paper 1 style timed check and 2 on the Paper 2 style timed check

  Standard integrals, partial fractions and substitutionIntegration by parts, areas and volumes28 questions
• 5

  Section 4: Differential equations

  2 of the 18 questions on the Paper 1 style timed check and 2 on the Paper 2 style timed check

  First-order differential equationsSecond-order differential equations22 questions
• 6

  Section 5: Sequences and series

  2 of the 18 questions on the Paper 1 style timed check and 2 on the Paper 2 style timed check

  Free: Arithmetic and geometric series and summation formulaeMaclaurin series24 questions
• 7

  Section 6: Proof and number theory

  2 of the 18 questions on the Paper 1 style timed check and 2 on the Paper 2 style timed check

  Counterexamples, direct and indirect proof, and inductionEuclid's algorithm, number bases and prime factorisation25 questions
• 8

  Section 7: Matrices and systems of equations

  2 of the 18 questions on the Paper 1 style timed check and 2 on the Paper 2 style timed check

  Gaussian eliminationMatrix algebra, inverses and transformations26 questions
• 9

  Section 8: Vectors, lines and planes

  2 of the 18 questions on the Paper 1 style timed check and 2 on the Paper 2 style timed check

  The vector product and lines in three dimensionsPlanes and their intersections24 questions
• 10

  Section 9: Complex numbers

  2 of the 18 questions on the Paper 1 style timed check and 2 on the Paper 2 style timed check

  Complex arithmetic, polynomial roots and lociPolar form and de Moivre's theorem26 questions