GCSE Maths: Algebra — Topic Revision Workbook

Inside GCSE Maths: Algebra — Topic Revision Workbook

simplify expressions and expand brackets, factorise and solve linear equations and inequalities, rearrange and substitute into formulae, find the nth term of linear and special sequences, read gradient and intercept from y = mx + c, solve simultaneous equations and solve quadratics by factorising and with the formula. About 30 minutes.

Learning objectives

• algebraic notation and simplifying, including collecting like terms, index notation and expanding single and double brackets;
• factorising with a common factor and quadratics of the form x² + bx + c, and solving linear equations and inequalities;
• substituting into and rearranging formulae, and finding the nth term of linear and special sequences;
• reading gradient and intercept from y = mx + c, solving simultaneous equations, and solving quadratics by factorising and with the quadratic formula.

Activities in this book

1. Task 1 — Notation, Simplifying & Brackets

   collect only like terms (the same letter to the same power). To multiply a letter by itself, add the indices and write the answer with a power. To expand a bracket, multiply every term inside by the term outside; for double brackets, multiply each term in the first bracket by each term in the second, then collect like terms.

2. Task 2 — Factorising, Equations & Inequalities

   to factorise, take out the highest common factor of every term. A quadratic x² + bx + c factorises into two brackets whose numbers multiply to give c and add to give b. To solve an equation, do the same operation to both sides until the letter is on its own. Solve an inequality just like an equation — keep the inequality sign the same way round.

3. Task 3 — Substitution, Rearranging & Sequences

   to substitute, replace each letter with its number and then work out the answer using BIDMAS. To rearrange a formula, undo the operations step by step until the wanted letter is the subject. For a linear sequence, the coefficient of n is the common difference; find the constant by checking the first term.

4. Task 4 — Graphs, Simultaneous & Quadratics

   in y = mx + c the number in front of x is the gradient m and the constant is the y-intercept c. Solve simultaneous equations by adding or subtracting to eliminate a letter. A quadratic that factorises to (x - p)(x - q) = 0 has solutions x = p and x = q.

5. Task 5 — Exam-Style Challenge

   real exam questions ask you to link several skills. Show every line of working — examiners give method marks even when a final answer slips. Always check your solution by substituting it back into the original equation.

Suggestions for teaching

• Like terms first. Insist on tidy notation and index laws before moving to brackets and factorising.
• Balance method. Model solving equations by doing the same to both sides, and treat inequalities the same way.
• Product and sum. For x² + bx + c, find two numbers that multiply to c and add to b before writing the brackets.
• Link graphs to rules. Connect the nth term of a sequence to the gradient of its straight-line graph and to y = mx + c.