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GCSE Higher · grades 4–9 · 30% of marks

GCSE Higher — Algebra

This is the algebra practice for GCSE Higher, the content area that carries 30% of the paper. Coverage is complete: all 25 algebra statements, each with practice that matches how the topic is actually examined. Among them: algebraic notation, substitution into formulae, expressions, equations, formulae, identities and inequalities, simplifying, expanding and factorising, rearranging formulae and identities, equivalence and algebraic proof. Higher only: translations and reflections of graphs, gradients and areas under graphs, equation of a circle and its tangent and iteration. A Foundation entry is never asked for these. 40% of the marks are AO1, for applying a standard technique correctly, and the remaining 60% are for reasoning and for solving problems — so an answer with no working rarely scores everything that was available. The bulk of it sits comfortably on the non-calculator paper; a calculator quietly hides the gap until the exam.

  • A1 — Algebraic notation
  • A2 — Substitution into formulae
  • A3 — Expressions, equations, formulae, identities and inequalities
  • A4 — Simplifying, expanding and factorising (part Higher)
  • A5 — Rearranging formulae
  • A6 — Identities, equivalence and algebraic proof (part Higher)
  • A7 — Functions, inverse and composite functions (part Higher)
  • A8 — Coordinates in all four quadrants
  • A9 — Straight-line graphs and y = mx + c (part Higher)
  • A10 — Gradients and intercepts of linear functions
  • …and 15 more algebra statements at this tier

Practise

GCSE Higher · AlgebraQuestion 1 of 20 · 0 correct
Practice mode· no pressure · hints available

Algebra

A14

Intermediate

A cyclist's distance-time graph shows the following: she travels 12 km in the first 30 minutes at a steady speed, then rests for 30 minutes, then travels a further 8 km in the next 15 minutes. Work out her average speed, in km/h, for the whole journey.

💡 Hints:
Printable worksheetNon-calculator sheetSample Paper 1Sample Paper 2

The 25 DfE statements in algebra at Higher

A1Algebraic notationnon-calculator
30 questions
A2Substitution into formulaeeither paper
30 questions
A3Expressions, equations, formulae, identities and inequalitiesnon-calculator
30 questions
A4Simplifying, expanding and factorisingpart Highernon-calculator
Higher-only parts: "algebraic fractions"; "or more"; "factorising quadratic expressions of the form ax² + bx + c"30 questions
A5Rearranging formulaenon-calculator
30 questions
A6Identities, equivalence and algebraic proofpart Highernon-calculator
Higher-only part: "and proofs"30 questions
A7Functions, inverse and composite functionspart Highernon-calculator
Higher-only part: "interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’"30 questions
A8Coordinates in all four quadrantsnon-calculator
30 questions
A9Straight-line graphs and y = mx + cpart Highernon-calculator
Higher-only part: "and perpendicular lines"30 questions
A10Gradients and intercepts of linear functionsnon-calculator
30 questions
A11Roots, intercepts and turning points of quadraticspart Highernon-calculator
Higher-only part: "and turning points by completing the square"30 questions
A12Recognising and sketching graphspart Highernon-calculator
Higher-only part: "exponential functions y = kˣ for positive values of k, and the trigonometric functions (with arguments in degrees) y = sin x, y = cos x and y = tan x for angles of any size"15 questions
A13Translations and reflections of graphsHigher onlynon-calculator
30 questions
A14Real-life graphs and kinematicspart Highereither paper
Higher-only part: "and exponential graphs"30 questions
A15Gradients and areas under graphsHigher onlyeither paper
30 questions
A16Equation of a circle and its tangentHigher onlynon-calculator
30 questions
A17Linear equationsnon-calculator
30 questions
A18Solving quadratic equationspart Highernon-calculator
Higher-only parts: "including those that require rearrangement"; "by completing the square and by using the quadratic formula"29 questions
A19Simultaneous equationspart Highernon-calculator
Higher-only part: "or linear/quadratic"30 questions
A20IterationHigher onlycalculator
30 questions
A21Forming and solving equations from situationseither paper
30 questions
A22Linear and quadratic inequalitiespart Highernon-calculator
Higher-only parts: "or two"; "and quadratic inequalities in one variable"; "using set notation and on a graph"30 questions
A23Generating sequencesnon-calculator
30 questions
A24Special sequences: square, cube, Fibonacci, quadratic, geometricpart Highernon-calculator
Higher-only parts: "or a surd"; "and other sequences"30 questions
A25The nth term of linear and quadratic sequencespart Highernon-calculator
Higher-only part: "and quadratic"30 questions

Related

Algebra at Foundation20% of Higher marksNumberHigher · 15% of marksRatio, proportion and rates of changeHigher · 20% of marksGeometry and measuresHigher · 20% of marks

Questions people ask

How much of the GCSE Higher paper is algebra?

30% of the total marks, and the three papers each carry an equal share of the qualification, so it is spread across all of them rather than concentrated in one.

How many topics are there in algebra at GCSE Higher?

25 DfE content statements, coded A1 to A25 within this area. Every question in the bank is tagged to one of them.

Which algebra topics are Higher only?

Translations and reflections of graphs (A13), Gradients and areas under graphs (A15), Equation of a circle and its tangent (A16) and Iteration (A20). A further 12 statements have a Higher-only part inside otherwise shared content.

Can I use a calculator for algebra questions?

Paper 1 is non-calculator; Papers 2 and 3 allow one. Of the 25 statements in this area, 20 are naturally non-calculator and 1 naturally calculator, with the rest workable either way — so practise both.

What kind of marks does algebra carry?

The GCSE Higher split is 40% AO1 (use and apply standard techniques), 30% AO2 (reason, interpret and communicate) and 30% AO3 (solve problems in and out of context). Questions in this area are set across all three.

Are these past paper questions?

No. Every question at /gcse-higher is original, written to the DfE content statements and checked before it is published. We do not host past papers or mark schemes.

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