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A Level Maths · Pure · Year 12 and 13

A Level Maths Algebra and Functions revision

Algebra and functions is the largest pure topic and the one every other topic leans on. Fluent index laws, surds, quadratics and polynomial division save time on every paper.

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  • Same content for AQA, Edexcel and OCR
  • Step-by-step mark schemes
  • 48-hour free trial, no card
What you need to know

Algebra and Functions in Year 12 and Year 13

AS content is usually taught in Year 12. The full A Level adds the Year 13 content.

Year 12 (AS content)

  • Indices and surds, including rationalising the denominator
  • Quadratic functions: the discriminant, completing the square, solving and sketching
  • Simultaneous equations (one linear, one quadratic) and linear and quadratic inequalities
  • Expanding, factorising and dividing polynomials; the factor theorem
  • Sketching curves, including cubics, quartics and reciprocal graphs, and graph transformations

Year 13 (full A Level only)

  • The modulus function and modulus equations and inequalities
  • Composite and inverse functions, domain and range
  • Simplifying algebraic fractions and partial fractions
  • Combining transformations, including y = |f(x)|

Worked examplemedium5 marks

Express the rational function $\frac{5x - 3}{(x+1)(x-3)}$ in partial fractions.

Mark scheme and worked answer

M1 for setting up the decomposition: $\frac{5x - 3}{(x+1)(x-3)} = \frac{A}{x+1} + \frac{B}{x-3}$.
M1 for clearing denominators: $5x - 3 = A(x - 3) + B(x + 1)$.
M1 for substituting $x = 3$ to find $B$: $15 - 3 = 4B \implies 12 = 4B$.
A1 for finding $B = 3$.
M1 for substituting $x = -1$ to find $A$: $-5 - 3 = -4A \implies -8 = -4A$.
A1 for finding $A = 2$ and stating the final expression: $\frac{2}{x+1} + \frac{3}{x-3}$.

Then practise: skills to practise · open algebra and functions practice questions.

Where it's examined

Algebra and Functions on the AQA, Edexcel and OCR papers

Every board examines the same A Level Maths content, set by the Department for Education. Only the paper it appears on and the section numbering differ.

BoardSpecification referenceExamined in
AQA 7357AQA section BPaper 1, and Section A of Papers 2 and 3
Edexcel 9MA0Edexcel topic Pure 2Paper 1 and Paper 2
OCR A H240OCR reference 1.02Paper 1, and the pure sections of Papers 2 and 3
Practice questions

A Level Maths algebra and functions exam-style questions

Three examples from the question bank. Every question comes with a step-by-step mark scheme (M, A and B marks) once you start practising.

Question 1easy2 marks

Calculate the discriminant of the quadratic $2x^2 - 3x + 4$.

Mark scheme: in the 48-hour free trial.

Question 2medium5 marks

Express the rational function $\frac{x+5}{(x-1)(x+2)}$ in partial fractions.

Mark scheme: in the 48-hour free trial.

Question 3hard4 marks

A cubic curve crosses the x-axis at $x = -2$, $x = 1$, and $x = 4$. It crosses the y-axis at the point $(0, 16)$. Find the equation of the curve in the form $y = ax^3 + bx^2 + cx + d$.

Mark scheme: in the 48-hour free trial.

Questions are original and written in the style of Edexcel 9MA0, and cover content that AQA and OCR examine too. They are not past-paper questions.

In the practice engine

Skills you can practise

These skills sit in the Pure I unit of the UK A Level practice engine. Pick any mix of them, set the difficulty, and check each answer against its mark scheme.

Laws of indicesSurds: simplifying & rationalisingSolving quadratics & the discriminantCompleting the squareQuadratic graphs & rootsSimultaneous equations (linear & quadratic)Linear & quadratic inequalitiesExpanding & factorising polynomialsAlgebraic division & the factor theoremPartial fractionsThe modulus function & modulus equationsComposite functionsInverse functionsGraph transformations (translations, stretches, reflections)Sketching cubics, quartics & reciprocals

Open Pure I practice

Past papers

Past paper questions on algebra and functions

Algebra and functions can come up on these papers (from each board's paper structure). We haven't mapped individual questions yet, so open a recent paper and look for it.

BoardRecent papers that can test it
Edexcel 9MA0Paper 1: June 2024, June 2023, June 2022
Paper 2: June 2024, June 2023, June 2022
AQA 7357Paper 1: June 2023, June 2022, November 2021
Paper 2: June 2023, June 2022, November 2021
Paper 3: June 2023, June 2022, November 2021
OCR H240Paper 1: June 2024, June 2023, June 2022
Paper 2: June 2024, June 2023, June 2022
Paper 3: June 2024, June 2023, June 2022

Papers are © the exam boards; each page links to the official question paper and mark scheme. All A Level Maths past papers →

Algebra and Functions: common questions

Is algebra and functions on the AQA, Edexcel and OCR A Level Maths exams?

Yes. Algebra and Functions is part of the A Level Maths content that every board examines: AQA section B, Edexcel Pure 2, OCR 1.02. It is assessed in AQA Paper 1, and Section A of Papers 2 and 3; Edexcel Paper 1 and Paper 2; OCR A Paper 1, and the pure sections of Papers 2 and 3.

Is algebra and functions Year 12 or Year 13 content?

Both. The AS content, usually taught in Year 12, is: Indices and surds, including rationalising the denominator; Quadratic functions: the discriminant, completing the square, solving and sketching; Simultaneous equations (one linear, one quadratic) and linear and quadratic inequalities; Expanding, factorising and dividing polynomials; the factor theorem; Sketching curves, including cubics, quartics and reciprocal graphs, and graph transformations. The full A Level adds: The modulus function and modulus equations and inequalities; Composite and inverse functions, domain and range; Simplifying algebraic fractions and partial fractions; Combining transformations, including y = |f(x)|.

Which algebra topics come up most?

Quadratics (discriminant and completing the square), the factor theorem and curve sketching appear on almost every paper. In Year 13, composite and inverse functions and partial fractions are the most common.

More A Level Maths pure topics

ProofCoordinate GeometrySequences and SeriesTrigonometryExponentials and LogarithmsDifferentiationIntegrationNumerical MethodsVectorsAll A Level Maths topics

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