On this page you can find past paper questions separated by topic and topic tests, for both Foundation and Higher tiers. All question sets are taken from past papers, except for the third set, which features topic tests. Set 5 includes the latest past paper questions from 2021 to 2023. **Set 4** is from 2017-2021 and is the only set with **video solutions**.

**It is recommended to start with Set 4 and Set 5, and if you need additional practice, you can work on sets 1-3 afterwards.**

For notes, worksheets and their solutions, visit the GCSE Algebra Revision page. Full past papers and model solutions can be found on the Paper 1, Paper 2 and Paper 3 pages.

##### Notation Vocabulary and Manipulation

- Algebraic Proofs (FH)
- Deriving Expressions (F)
- Deriving Expressions (FH)
- Expanding Equations (F)
- Expanding Expressions (FH)
- Factorising Equations (F)
- Factorising Expressions (FH)
- Forming Equations (F)
- Forming Equations (FH)
- Input-Output (F)
- Manipulation of Formulae (F)
- Manipulation of Formulae (FH)
- Simplifying Expressions (F)
- Simplifying Expressions (FH)
- Solving Using Indices (FH)
- Substitution (F)
- Substitution Into Equations (FH)

##### Sequences

##### Graphs

- Conversion Graphs (F)
- Conversion Graphs (FH)
- Coordinates in 3D (FH)
- Distance-Time Graphs (F)
- Distance-Time Graphs (FH)
- Exponential Growth and Decay (FH)
- Gradients of Straight Lines (FH)
- Graphs of Circles (FH)
- Graphs of Linear Equations (FH)
- Graphs of Quadratic Equations (FH)
- Graphs of Trigonometrical Functions (FH)
- Line Graphs (F)
- Line Graphs of Real Situations (FH)
- Transformation of Graphs (FH)
- Using y=mx+c (FH)

##### Solving Equations and Inequalities

##### Notation Vocabulary and Manipulation

- Algebraic Proofs (FH)
- Algebraic Proofs (H)
- Deriving Expressions (FH)
- Expanding Equations (H)
- Expanding Expressions (FH)
- Factorising Expressions (FH)
- Factorising Expressions (H)
- Forming Equations (FH)
- Forming Equations (H)
- Manipulation of Formulae (FH)
- Manipulation of Formulae (H)
- Simplifying Expressions (FH)
- Simplifying Expressions (H)
- Solving Algebraic Fraction Equations (H)
- Solving Algebraic Fractions (H)
- Solving Using Indices (FH)
- Solving Using Indices (H)
- Substitution (H)
- Substitution Into Equations (FH)

##### Sequences

##### Graphs

- Conversion Graphs (FH)
- Coordinates in 3D (FH)
- Distance-Time Graphs (FH)
- Exponential Growth and Decay (FH)
- Exponential Growth and Decay (H)
- Gradients of Straight Lines (FH)
- Gradients of Straight Lines (H)
- Graphs of Circles (FH)
- Graphs of Circles (H)
- Graphs of Linear Equations (FH)
- Graphs of Linear Equations (H)
- Graphs of Quadratic Equations (FH)
- Graphs of Quadratic Equations (H)
- Graphs of Trigonometrical Functions (FH)
- Graphs of Trigonometrical Functions (H)
- Line Graphs of Real Situations (FH)
- Line Graphs of Real Situations (H)
- Transformation of Graphs (FH)
- Transformation of Graphs (H)
- Using y=mx+c (FH)
- Using y=mx+c (H)

##### Solving Equations and Inequalities

##### Notation Vocabulary and Manipulation

- Deriving Expressions (F)
- Deriving Expressions (FH)
- Expanding Expressions (F)
- Expanding Expressions (FH)
- Factorising Expressions (FH)
- Manipulation of Formulae (F)
- Manipulation of Formulae (FH)
- Simplfying Equations (FH) 2
- Simplifying Equations (F)
- Simplifying Equations (FH) 1
- Substituting Into Equations (F)
- Substituting Into Equations (FH)

##### Sequences

##### Notation Vocabulary and Manipulation

- Algebraic Proofs (H)
- Deriving Expressions (FH)
- Deriving Expressions (H)
- Expanding Expressions (FH)
- Expanding Expressions (H)
- Factorising Expressions (FH)
- Factorising Expressions (H)
- Functions (H)
- Manipulation of Formulae (FH)
- Manipulation of Formulae (H)
- Simplfying Equations (FH) 2
- Simplfying Equations (H) 2
- Simplifying Equations (FH) 1
- Simplifying Equations (H) 1
- Substituting Into Equations (FH)
- Substituting Into Equations (H)

##### Sequences

##### Graphs

- Conversion Graphs (FH)
- Distance-Time and Travel Graphs (FH)
- Gradients of Straight Lines (H)
- Graphs of Cubic Equations (H)
- Graphs of Linear Equations (FH)
- Graphs of Linear Equations (H)
- Graphs of Quadratic Equations (FH)
- Graphs of Quadratic Equations (H)
- Graphs of Reciprocal Equations (H)
- Graphs of Trigonometrical Functions (H)
- Transformation of Functions (H)

##### Solving Equations and Inequalities

##### Foundation

##### Notation, Vocabulary and Manipulation

- Deriving Expressions (F)
- Expanding Equations (F)
- Factorising Equations (F)
- Forming Equations (F)
- Inputs and Outputs (F)
- Manipulation of Formulae (F)
- Simplifying Expressions (F)
- Substitution into Equations (F)

##### Sequences

##### Graphs

- Conversion Graphs (F)
- Coordinates (F)
- Cubic and Reciprocal Graphs (F)
- Equations of Straight Lines (F)
- Graphs of Linear Equations (F)
- Graphs of Quadratic Equations (F)
- Interpreting Gradients (F)

##### Solving Equations and Inequalities

##### Notation, Vocabulary and Manipulation

- Algebraic Fractions (H)
- Algebraic Proof (H)
- Deriving Expressions (H)
- Expanding Equations (H)
- Expanding Triple Brackets (H)
- Factorising Equations (H)
- Forming Equations (H)
- Functions (Composite or Inverse) (H)
- Manipulation of Formulae (H)
- Simplifying Expressions (H)
- Solving Using Indices (H)
- Substitution into Equations (H)

##### Sequences

##### Graphs

- Circle Equations and Tangents (H)
- Coordinates (H)
- Cubic and Reciprocal Graphs (H)
- Distance-Time Graphs (H)
- Equations of Straight Lines (H)
- Exponential and Trigonometric Graphs (H)
- Graphs of Linear Equations (H)
- Graphs of Quadratic Equations (H)
- Interpreting Gradients (H)
- Parallel or Perpendicular Lines (H)
- Simultaneous Equations on Graphs (H)
- Translations and Reflections of Functions (H)
- Velocity-Time Graphs (H)

##### Solving Equations and Inequalities

Notation, Vocabulary and Manipulation || Sequences || Graphs || Solving Equations and Inequalities

Notation, Vocabulary and Manipulation

##### Question Papers

##### Mark Schemes

##### Model Answers

Sequences

##### Question Papers

##### Mark Schemes

##### Model Answers

Graphs

##### Question Papers

##### Mark Schemes

##### Model Answers

Solving Equations and Inequalities

##### Question Papers

##### Mark Schemes

Notation, Vocabulary and Manipulation || Sequences || Graphs || Solving Equations and Inequalities

Notation, Vocabulary and Manipulation

##### Question Papers

- Algebraic Fractions (H) QP
- Algebraic Proof (H) QP
- Deriving Expressions (H) QP
- Expanding Equations (H) QP
- Expanding Triple Brackets (H) QP
- Factorising Equations (H) QP
- Functions (Composite or Inverse) (H) QP
- Manipulation of Formulae (H) QP
- Simplifying Expressions (H) QP
- Solving using Indices (H) QP
- Substitution into Equations (H) QP

##### Mark Schemes

- Algebraic Fractions (H) MS
- Algebraic Proof (H) MS
- Deriving Expressions (H) MS
- Expanding Equations (H) MS
- Expanding Triple Brackets (H) MS
- Factorising Equations (H) MS
- Functions (Composite or Inverse) (H) MS
- Manipulation of Formulae (H) MS
- Simplifying Expressions (H) MS
- Solving using Indices (H) MS
- Substitution into Equations (H) MS

##### Model Answers

- Algebraic Fractions (H) MA
- Algebraic Proof (H) MA
- Deriving Expressions (H) MA
- Expanding Equations (H) MA
- Expanding Triple Brackets (H) MA
- Factorising Equations (H) MA
- Functions (Composite or Inverse) (H) MA
- Manipulation of Formulae (H) MA
- Simplifying Expressions (H) MA
- Solving using Indices (H) MA
- Substitution into Equations (H) MA

Sequences

##### Question Papers

##### Mark Schemes

##### Model Answers

Graphs

##### Question Papers

- Circles Equations and Tangents (H) QP
- Coordinates (H) QP
- Cubic and Reciprocal Graphs (H) QP
- Distance-time Graphs (H) QP
- Equations of Straight Lines (H) QP
- Exponential and Trigonometric Graphs (H) QP
- Graphs of Circles (H) QP
- Graphs of Linear Equations (H) QP
- Graphs of Quadratic Equations (H) QP
- Interpreting Gradients (H) QP
- Simultaneous Equations on Graphs (H) QP
- Translations and Reflections of Functions (H) QP
- Velocity-time graphs (H) QP

##### Mark Schemes

- Circle Equations and Tangents (H) MS
- Coordinates (H) MS
- Cubic and Reciprocal Graphs (H) MS
- Distance-time Graphs (H) MS
- Equations of Straight Lines (H) MS
- Exponential and Trigonometric Graphs (H) MS
- Graphs of Circles (H) MS
- Graphs of Linear Equations (H) MS
- Graphs of Quadratic Equations (H) MS
- Interpreting Gradients (H) MS
- Simultaneous Equations on Graphs (H) MS
- Translations and Reflections of Functions (H) MS
- Velocity-time graphs (H) MS

##### Model Answers

- Circle Equations and Tangents (H) MA
- Coordinates (H) MA
- Cubic and Reciprocal Graphs (H) MA
- Distance-time Graphs (H) MA
- Equations of Straight Lines (H) MA
- Exponential and Trigonometric Graphs (H) MA
- Graphs of Circles (H) MA
- Graphs of Linear Equations (H) MA
- Graphs of Quadratic Equations (H) MA
- Interpreting Gradients (H) MA
- Simultaneous Equations on Graphs (H) MA
- Translations and Reflections of Functions (H) MA
- Velocity-time graphs (H) MA