IGCSE Math RevisionWorked example 1: Collecting like terms
Simplify \(3a+5b-a+2b\).
Solution
- Collect the \(a\) terms: \(3a-a=2a\).
- Collect the \(b\) terms: \(5b+2b=7b\).
Answer: \(2a+7b\)
Tip: The sign belongs to the term after it.
Edexcel IGCSE Maths (4MA1) · Unit 2: Algebra Basics
IGCSE Maths Algebraic Expressions Questions and Answers
Algebraic Expressions questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 5 worked examples first, then cover each solution and redo it yourself.
- 5 worked examples
- Higher tier · calculator allowed
- Free, no sign-in
What this topic covers
- Basic Algebra 1: Simplifying algebraic expressions by collecting like terms.
- Basic Algebra 2: Working with variables in arithmetic contexts.
- Expressions and Formulae 1: Writing algebraic expressions from words.
- Expressions and Formulae 2: Substituting values into formulae.
- Expressions and Formulae 3: Rearranging simple formulae.
Algebraic Expressions worked examples
Worked example 2: Multiplying terms
Simplify \(5x^2y\times2xy^3\).
Solution
- Numbers: \(5\times2=10\).
- \(x^2\times x=x^3\) and \(y\times y^3=y^4\).
Answer: \(10x^3y^4\)
Tip: Multiply numbers; add powers of each letter.
Worked example 3: Writing an expression
Pens cost 35p each and rulers cost \(r\) pence each. Write an expression for the cost, in pence, of \(n\) pens and 3 rulers.
Solution
- Cost of pens: \(35n\).
- Cost of rulers: \(3r\).
- Total: \(35n+3r\).
Answer: \(35n+3r\)
Tip: Write the number before the letter.
Worked example 4: Expressions from a diagram
A square has side \((x+3)\) cm. Write expressions for its perimeter and its area.
Solution
- Perimeter: \(4(x+3)=4x+12\).
- Area: \((x+3)^2=x^2+6x+9\).
Answer: Perimeter \(4x+12\); area \(x^2+6x+9\)
Tip: \((x+3)^2\) is not \(x^2+9\).
Worked example 5: Expanding and simplifying
Expand and simplify \(4(x+2)-3(x-5)\).
Solution
- \(4x+8-3x+15\) (note \(-3\times-5=+15\)).
- Collect: \(x+23\).
Answer: \(x+23\)
Tip: Multiply every term in the bracket, including the sign.
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Revise algebraic expressions for the exam
- Unit 2 practice: Algebra Basics in the student hub (more questions with mark schemes)
- IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
- Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
- IGCSE Maths 4MA1 examiner report summary: where students lose marks
Questions students ask
Which Edexcel IGCSE Maths papers test algebraic expressions?
Either Higher tier paper, 1H or 2H, can test algebraic expressions: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more algebraic expressions questions?
In the IGCSE student hub: Unit 2 (Algebra Basics) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.