Topic 1 – Core: Algebra
Sequences and Series
Working with Sequences and Series
Arithmetic Progressions
Geometric Series
Logarithmic and Exponential Functions
Exponential Functions and Logarithms
The Exponential Function ex and Natural Log Functions
Permutations and Combinations
Sequences and Series
Proof by mathematical induction
Sum of Series
Various Types of Proofs
Complex Numbers
Complex Numbers
- Real and imaginary numbers
- Addition, subtraction and multiplying complex numbers and simplifying powers of i
- Division of a complex number by a complex number
- Argand diagrams
- Modulus and argument of a complex number
- Solving problems with complex numbers
- Square roots of a complex number
- Solving quadratic equations with complex roots
- Solving cubic equations
- Solving quartic equations
- Exam Questions - Complex numbers
- Exam Questions - Finding roots
- Modulus-argument form of a complex number
- Exponential Form (Euler's relation)
- Multiplication and division rules for mod and argument of two complex numbers
- Exam Questions - Further complex numbers
- Complex numbers specimen questions (mixed exam boards)