A worksheet on factorizing algebraic expressions (quadratics included), simplifying algebraic expressions, performing the four operations between algebraic fractions, solving equations and word problems using factorization. detailed solutions are included.

Looking for a comprehensive, ready-to-use revision resource to help your students master factorising and algebraic fractions? This printable maths worksheet features 28 carefully scaffolded problems, ranging from basic highest common factor (HCF) expressions to complex rational equations. Best of all, it includes complete, step-by-step worked solutions for every single problem to save you hours of marking time!

Master Factorising and Algebraic Fractions with Ease!
Provide your students with the ultimate practice resource for algebraic fractions, rational expressions, and factorisation. This comprehensive revision worksheet is perfect for GCSE Higher, IGCSE, Key Stage 4 (KS4), and secondary maths students preparing for upcoming exams, assessments, or end-of-term mocks.
Designed for high utility with zero teacher preparation required, this 12-page resource includes a clean, student-friendly question packet followed by fully worked-out solutions. It provides clear, logical transitions from basic algebraic methods to multi-step fraction operations.

What is Included in This Resource?
• Section 1: Factorise Expressions – 11 problems covering HCF, grouping, quadratic trinomials, perfect squares, difference of two squares, and sum/difference of cubes.
• Section 2: Simplify Algebraic Fractions – 5 problems focusing on reducing rational expressions by factorising the numerator and denominator.
• Section 3: Operations with Algebraic Fractions – 8 advanced problems requiring students to multiply, divide, add, and subtract fractions with unlike denominators.
• Section 4: Solve Equations – 8 equations involving the zero-product property, quadratics solvable by factorising, and advanced rational equations.
• Section 5: Real-World Word Problem – A quadratic word problem focusing on consecutive number properties (difference and product relationships).
• Complete Step-by-Step Answer Key – 6 full pages of detailed solutions showing every mathematical step, making it perfect for student self-assessment, independent study, or quick marking.

Why Teachers Love This Worksheet:
• Ready to Teach: Just print and go! It is an instant, complete lesson addition.
• Scaffolded Learning: Problems gradually increase in difficulty, building student confidence.
• Versatile Use: Ideal for in-class independent practice, homework assignments, GCSE exam revision, or emergency cover work.