Algebra Revision Notes for IGCSE Maths
These comprehensive revision notes cover everything you need to know about algebra for the Cambridge IGCSE Mathematics 0580 examination. Written by Teacher Rig, each section includes key concepts, essential formulas, and practical exam tips to help you achieve your best grade.
Expanding and Factorising
Expanding means removing brackets by multiplying. Single bracket: multiply each term inside by the term outside. Double brackets: use FOIL (First, Outer, Inner, Last). Factorising is the reverse - putting an expression into brackets. Always look for a common factor first, then try the difference of two squares or trinomial factorisation.
Key Formulas
- a(b + c) = ab + ac
- (x + a)(x + b) = x squared + (a+b)x + ab
- a squared - b squared = (a+b)(a-b)
Exam Tips
- Always check your expansion by substituting a value like x = 1
- For factorising trinomials, find two numbers that multiply to give c and add to give b
- Difference of two squares is very common - look for it whenever you see a subtraction of perfect squares
Solving Linear Equations
The goal is to isolate x by performing the same operation to both sides. Work systematically: expand brackets first, collect x terms on one side, collect number terms on the other, then divide. With fractions, multiply through by the LCM of the denominators first.
Exam Tips
- Show every step of working - method marks are awarded even if the final answer is wrong
- With fractions, multiply EVERY term by the common denominator
- Always check your answer by substituting back into the original equation
Solving Quadratic Equations
There are three methods: (1) Factorising - when the expression can be written as two brackets. (2) Quadratic formula - works for any quadratic but may give irrational answers. (3) Completing the square - useful for finding the turning point. Always try factorising first as it is quickest.
Key Formulas
- x = (-b +/- sqrt(b squared - 4ac)) / (2a)
- ax squared + bx + c = a(x + b/(2a)) squared + c - b squared/(4a)
Exam Tips
- If the question says 'give answers to 2 decimal places', you MUST use the quadratic formula (it will not factorise)
- The discriminant b squared - 4ac tells you the number of solutions: positive = 2, zero = 1, negative = 0
- When using the formula, write it down before substituting values
Simultaneous Equations
Two equations with two unknowns can be solved by elimination or substitution. Elimination: make the coefficients of one variable the same, then add or subtract. Substitution: rearrange one equation to express one variable in terms of the other, then substitute. For one linear and one quadratic, you must use substitution.
Exam Tips
- For elimination, multiply one or both equations to match coefficients before adding/subtracting
- For linear-quadratic pairs, substitute the linear into the quadratic, not the other way around
- Always check your answer in BOTH original equations
Rearranging Formulas
Treat formula rearrangement exactly like solving an equation, but instead of getting a number, you get an expression. The subject is the variable you are solving for. Perform inverse operations in the reverse order to how they would be applied.
Exam Tips
- If the new subject appears more than once, factorise to collect all instances together
- Squaring or square-rooting may be needed - remember to consider both positive and negative roots where appropriate
- Write down each step clearly showing what you did to both sides
Revision Checklist
- I understand all key concepts in algebra
- I have memorised the essential algebra formulas
- I can apply these concepts to exam-style questions
- I have practised past paper questions on algebra
- I know the common mistakes to avoid in algebra questions
Frequently Asked Questions
What algebra topics are covered in IGCSE Maths?
The IGCSE 0580 syllabus covers algebra across both Core and Extended tiers. Key areas include expanding and factorising. Key areas include solving linear equations. Key areas include solving quadratic equations.
How important is algebra in the IGCSE exam?
Algebra is a significant part of the IGCSE Mathematics exam, typically appearing in Paper 2 (non-calculator) and Paper 4 (calculator). Questions range from straightforward calculations to multi-step problems that combine algebra with other topics.
What are the most common mistakes in algebra?
Common mistakes include not showing full working, forgetting to state units, misreading the question, and rushing through calculations. For algebra specifically, make sure you understand the underlying concepts rather than just memorising procedures.
Need Help Revising Algebra?
Book a free trial class with Teacher Rig for targeted revision support.