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- Lessons
- 28
- Topics
- 27
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Core Pure: proof and complex numbers
9 lessons
- 2 lessonsFreeInduction for sums and divisibilityProof by mathematical induction
- Complex numbers and quadratic rootsImaginary and complex numbers
- Conjugate pairs and polynomial rootsComplex conjugation
- The Argand diagram: modulus and argumentArgand diagrams
- Loci and regions in the Argand diagramLoci in the Argand diagram
- De Moivre's theorem: identities and sumsDe Moivre’s theorem
- Exponential form and nth rootsExponential form of complex numbers
- Roots of unity and their geometrySolving geometric problems
Core Pure: matrices
6 lessons
- Matrix arithmetic, identity and zeroIntroduction to matrices
- Matrices as transformations in 2D and 3DLinear transformations in two dimensions
- Determinants, invariant points and invariant linesDeterminants
- Inverse matrices and singular matricesInverting a 2 × 2 matrix
- Three equations, three planesSolving systems of equations using matrices
- Induction for matrix powersProof by mathematical induction
Core Pure: roots, series and expansions
1 lesson
Further Statistics 1
7 lessons
- Discrete distributions and the Poisson modelExpected value of a discrete random variable
- Geometric and negative binomial modelsThe geometric distribution
- Poisson and geometric hypothesis testsTesting for the mean of a Poisson distribution
- The central limit theoremThe central limit theorem
- Chi-squared testsGoodness of fit
- Probability generating functionsProbability generating functions
- Type I and Type II errors, size and powerType I and Type II errors
Further Mechanics 1
5 lessons
Independent practice for Pearson Edexcel A-level Further Mathematics (9FM0), not endorsed by Pearson.