Algebra Basics

Begin by understanding the fundamental concept of algebra which revolves around expressions, equations and functions involving letters called variables.
Familiarise yourself with the various operations used in Algebra such as addition, subtraction, multiplication and division, and how these operations can be performed on both numerical values and algebraic expressions.
Clearly comprehend the difference between an equation and an expression. An equation represents a statement of equality containing one or more variables while an expression is a phrase consisting of variables and/or numbers using mathematical operations.
Learn and remember the order of operations using the acronym ‘BIDMAS’ which states the order of operations: Brackets, Indices, Division, Multiplication, Addition, and Subtraction.
Master the concept of factorisation, which involves breaking down complex expressions into their individual factors. The most common types of factorisation include the Difference of Squares, Quadratic Trinomials, and the use of the Common Factor method.
Develop a solid understanding of expanding brackets. You can expand brackets by multiplying each term in the bracket by the term outside the bracket.
Grasp the principles of simplifying algebraic expressions by removing parentheses and combining like terms.
Understand how to solve linear equations. Remember that the goal is to isolate the variable on one side and to have numerical values on the other side of the equation.
Learn how to form and solve equations from word problems by identifying the unknowns, translating the words into algebraic expressions, and solving for the variables.
Further study should be on quadratic equations, including their graphs and how to solve these equations by factorisation and the quadratic formula.
Deeply understand and recognise the different forms of a quadratic equation and how they relate to the graph of the equation. The three forms are: standard form, vertex form and factorised form.
Be familiar with handling and manipulating algebraic fractions, these involve both numerical and variable expressions in the numerator and/or denominator.
Lastly, get comfortable with algebraic proofs which includes proving statements by forming and manipulating equations until the required result is obtained.

Remember algebra is the foundation of much of mathematics, becoming proficient in it opens up more advanced topics and it is thus an important focus area for revision.