How do I revise Algebra for Pearson GCSE?

Always show full working to gain method marks.

What exam tips are there for Algebra? (2)

Check solutions by substituting back into the original equation.

What exam tips are there for Algebra? (3)

For inequalities, remember to flip the sign when multiplying/dividing by a negative.

What mistakes should I avoid in Algebra?

Sign errors when moving terms across the equals sign.

What are common errors in Algebra exams? (2)

Forgetting to change inequality sign when multiplying/dividing by a negative.

Algebra

PEARSON

GCSE

This topic covers solving linear and quadratic equations, as well as linear inequalities. Learners will use algebraic methods including factorising, completing the square, and the quadratic formula, and represent solutions on a number line.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

Subtopics in this area

Algebra

Topic Overview

Algebra is the branch of mathematics that uses symbols and letters to represent numbers and quantities in equations and expressions. It is a fundamental topic in the Pearson GCSE Mathematics curriculum, forming the basis for solving problems in areas such as geometry, trigonometry, and statistics. Mastering algebra allows you to model real-world situations, from calculating interest rates to predicting trends, and is essential for further study in maths, science, and engineering.

In this topic, you will learn to manipulate algebraic expressions, solve linear and quadratic equations, work with inequalities, and understand functions and graphs. You'll also explore sequences, factorisation, and algebraic fractions. Algebra is not just about finding x; it's about developing logical thinking and problem-solving skills that are valuable across all subjects and careers. By the end of this unit, you should be able to simplify complex expressions, rearrange formulas, and solve a variety of equations confidently.

Algebra is a core component of the GCSE exams, appearing in both the non-calculator and calculator papers. It typically accounts for around 20-30% of the total marks, so a strong grasp of algebraic techniques is crucial for achieving a high grade. The skills you develop here will be directly applied in other topics, such as solving simultaneous equations in geometry or using quadratic graphs in statistics. Consistent practice and understanding the underlying principles, rather than rote memorisation, are key to success.

What You Need to Demonstrate

Key skills and knowledge for this topic

Solves linear equations accurately using algebraic manipulation.
Solves quadratic equations by factorising, completing the square, or using the quadratic formula.
Solves linear inequalities and represents the solution set on a number line.
Rearranges equations where necessary before solving.
Checks solutions by substitution.
Plots points correctly in all four quadrants.
Draws straight-line graphs from equations.
Identifies parallel and perpendicular lines from equations.

Marking Points

Key points examiners look for in your answers

Solves linear equations accurately using algebraic manipulation.
Solves quadratic equations by factorising, completing the square, or using the quadratic formula.
Solves linear inequalities and represents the solution set on a number line.
Rearranges equations where necessary before solving.
Checks solutions by substitution.
Plots points correctly in all four quadrants.
Draws straight-line graphs from equations.
Identifies parallel and perpendicular lines from equations.
Calculates gradient from two points and interprets as rate of change.
Correctly interprets and uses algebraic notation including indices and brackets.
Substitutes numerical values into formulae and expressions accurately.
Simplifies expressions by collecting like terms and expanding brackets.
Factorises quadratic expressions and differences of two squares.
Generate terms of a sequence from a given rule.
Recognise and name special sequences.
Find the nth term of a linear sequence.
Find the nth term of a quadratic sequence.

Examiner Tips

Expert advice for maximising your marks

💡Always show full working to gain method marks.
💡Check solutions by substituting back into the original equation.
💡For inequalities, remember to flip the sign when multiplying/dividing by a negative.
💡Label axes and plot points carefully.
💡Use the formula gradient = (y2 - y1)/(x2 - x1).
💡Remember: parallel lines have same gradient; perpendicular gradients multiply to -1.
💡Practice expanding and factorising regularly to build fluency.
💡Check your work by substituting values into original and simplified forms.
💡Memorise common algebraic identities.
💡Practice finding nth term for linear sequences using the formula.
💡For quadratics, use the method of second differences.
💡Memorise the first few terms of common sequences.

Common Mistakes

Pitfalls to avoid in your exam answers

Sign errors when moving terms across the equals sign.
Forgetting to change inequality sign when multiplying/dividing by a negative.
Incorrectly factorising quadratics, especially when the coefficient of x² is not 1.
Confusing the x and y coordinates when plotting.
Miscalculating gradient (e.g., incorrect sign or division).
Not recognising that parallel lines have equal gradients.
Misapplying index laws when simplifying.
Errors in expanding brackets, especially with negative signs.
Incorrect factorisation of quadratics.
Confusing term-to-term and position-to-term rules.
Incorrectly calculating differences for quadratic sequences.
Mistaking arithmetic for geometric sequences.

Frequently Asked Questions

Common questions students ask about this topic

Key Terminology

Essential terms to know

Linear equations

Quadratic equations

Inequalities

Coordinates

Straight line graphs

Gradient and intercept

Algebraic notation

Substitution

Simplification and factorisation

Term-to-term rules

Position-to-term rules

nth term

Likely Command Words

How questions on this topic are typically asked

Solve

Find

Show

Represent

Calculate

Plot

Identify

Interpret

Simplify

Factorise

Expand

Substitute

Manipulate

Generate

Recognise

Deduce

Ready to test yourself?

Practice questions tailored to this topic

Algebra

Subtopics in this area

Topic Overview

What You Need to Demonstrate

Marking Points

Examiner Tips

Common Mistakes

Frequently Asked Questions

Key Terminology

Likely Command Words

Ready to test yourself?

Related Topics in PEARSON GCSE Mathematics

Probability

Probability

Statistics

E2E stub topic

Algebra

Subtopics in this area

Topic Overview

What You Need to Demonstrate

Marking Points

Examiner Tips

Common Mistakes

Frequently Asked Questions

How do I solve linear equations with fractions?

What is the difference between an expression and an equation?

How do I factorise a quadratic when the coefficient of x² is not 1?

What is the quadratic formula and when should I use it?

How do I rearrange formulas to make a specific variable the subject?

What are simultaneous equations and how do I solve them?

Key Terminology

Likely Command Words

Ready to test yourself?

Related Topics in PEARSON GCSE Mathematics

Probability

Probability

Statistics

E2E stub topic