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GCSE Foundation · grades 1–5 · 20% of marks

GCSE Foundation — Algebra

Every algebra statement a GCSE Foundation student may be asked is here; together they are 20% of the assessment. There are 21 algebra statements to cover. Working through them one at a time beats mixed practice while a topic is still shaky — mixed practice tells you that something is wrong, not what. Expect algebraic notation, substitution into formulae, expressions, equations, formulae, identities and inequalities, simplifying, expanding and factorising, rearranging formulae and identities, equivalence and algebraic proof. None of this is Higher-only material: it is the shared content both tiers sit. Only 50% of the paper is straight technique (AO1); 50% asks you to reason, interpret or solve a problem in context, and those marks are won by setting the work out clearly. 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
  • A5 — Rearranging formulae
  • A6 — Identities, equivalence and algebraic proof
  • A7 — Functions, inverse and composite functions
  • A8 — Coordinates in all four quadrants
  • A9 — Straight-line graphs and y = mx + c
  • A10 — Gradients and intercepts of linear functions
  • …and 11 more algebra statements at this tier

Practise

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

Algebra

A14

Intermediate

A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

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

The 21 DfE statements in algebra at Foundation

Higher-only statements are not listed here; statements with a Higher-only part are marked and the part is quoted.

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" — Foundation students can skip these.30 questions
A5Rearranging formulaenon-calculator
30 questions
A6Identities, equivalence and algebraic proofpart Highernon-calculator
Higher-only part: "and proofs" — Foundation students can skip these.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’" — Foundation students can skip these.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" — Foundation students can skip these.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" — Foundation students can skip these.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" — Foundation students can skip these.15 questions
A14Real-life graphs and kinematicspart Highereither paper
Higher-only part: "and exponential graphs" — Foundation students can skip these.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" — Foundation students can skip these.29 questions
A19Simultaneous equationspart Highernon-calculator
Higher-only part: "or linear/quadratic" — Foundation students can skip these.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" — Foundation students can skip these.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" — Foundation students can skip these.30 questions
A25The nth term of linear and quadratic sequencespart Highernon-calculator
Higher-only part: "and quadratic" — Foundation students can skip these.30 questions

Related

Algebra at Higher30% of Higher marksNumberFoundation · 25% of marksRatio, proportion and rates of changeFoundation · 25% of marksGeometry and measuresFoundation · 15% of marks

Questions people ask

How much of the GCSE Foundation paper is algebra?

20% 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 Foundation?

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

Is any algebra content on this page Higher only?

No. Foundation pages only show statements a Foundation entry may be asked. The Higher-only algebra material is on the GCSE Higher page for this area.

Can I use a calculator for algebra questions?

Paper 1 is non-calculator; Papers 2 and 3 allow one. Of the 21 statements in this area, 18 are naturally non-calculator and 0 naturally calculator, with the rest workable either way — so practise both.

What kind of marks does algebra carry?

The GCSE Foundation split is 50% AO1 (use and apply standard techniques), 25% AO2 (reason, interpret and communicate) and 25% 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-foundation 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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