Chapter 1: Pure 1: Algebraic Expressions

A-level MathematicsPure7 topicsHigher

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Releases 1 August 2026

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Algebraic Expressions Long-Answer Questions

Examiner-style long-answer practice with automatic marking, improvement advice and ProofCoach tracking.

4 questions24 marks36 min

standard / hard / synoptic

6 marksfindstandardEdexcel

P01-1: (

2x^{2}

- 5x - 3)/(

x^{2}

- 9). Find (2x + 1)/(x + 3) for indices, surds and algebraic fractions. Show the method clearly by using factorise the numerator and denominator before cancelling a common factor.

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6 marksshow thatstandardEdexcel

P01-2 verification: show that the printed answer is valid by applying factorise the numerator and denominator before cancelling a common factor. Include a check using (

2x^{2}

- 5x - 3)/(

x^{2}

- 9).

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6 marksprovehardEdexcel

P01-3 proof: starting with (

2x^{2}

- 5x - 3)/(

x^{2}

- 9), prove (2x + 1)/(x + 3) for indices, surds and algebraic fractions; give restrictions.

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6 markshencesynopticEdexcel

Using P01-4's earlier result (2x + 1)/(x + 3), hence solve the linked problem in indices, surds and algebraic fractions and state whether the answer is exact or rounded.

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Start of Pure

2. Pure 1: Quadratics

Key learning objectives

Understand the key principles behind Pure 1: Algebraic Expressions.
Apply these ideas to exam-style questions.
Recall the essential definitions and key terms.