Algebra and Functions

Algebra Fundamentals

Understand, simplify and manipulate algebraic expressions
Familiarise yourself with equations and inequalities: Solve linear and quadratic equations and inequalities, simultaneous equations and equations involving fractions.
Expand products of two binomials and simplify expressions involving the sums and differences of cubes.
Develop effective ways to factorise quadratic and cubic equations.
Apply the laws of indices for real numbers.

Functions

Understand the concept of a function and the notation associated with it.
Be able to sketch simple functions.
Recognise the graph of a function and its related transformations.
Use addition, subtraction, multiplication, division and composition of functions.
Understand the inverse function and be able to find it.
Explore the modulus function including graphing and solving equations and inequalities involving modulus.
Analyse real-world situations and model them using functions.

Algebraic Methods

Comprehend and use the standard algebraic techniques: factorisation, completing the square in a quadratic, simple algebraic long division, simplifying rational expressions.
Be adept at the solution of equations and inequalities: forming and solving linear, quadratic and simple cubic equations and simultaneous equations; solving inequalities; solving equations and inequalities involving modulus functions.
Understand the binomial expansion of expressions including those involving fractional powers.
Be able to solve a variety of equations that require knowledge and understanding of functions, notation and terminology.

Sequence And Series

Understand the concepts of sequences and series, including arithmetic and geometric progressions.
Analyse Sigma notation and use it to find the sum of a finite arithmetic series.
Understand the concept of a limit of a sequence and a series.
Apply the binomial expansion to sequences and series to calculate a general term.

Algebraic Logarithms

Know how to calculate with logarithms and apply logarithmic identities.
Grasp the properties of logarithms and their use in solving equations.
Leverage logarithms to solve growth and decay problems.

Remember, these bullet points are not exhaustive and are provided as a guide to start your revision. Please refer to your class materials, textbooks, and past exam papers for a more in-depth revision.