Cambridge IGCSE Question Simulator

IGCSE Mathematics (0580)

Algebra & graphs Banker

137 questions · about 31% of the marks we indexed · examined in 9 of 9 sessions.

Questions by year

2026

  • 2026 May/June · Paper 12 · Q10 (a, b)4 marksLinear equations & forming equations
  • 2026 May/June · Paper 12 · Q18 (a, b)4 marksExpanding, factorising & simplifying
  • 2026 May/June · Paper 12 · Q202 marksInequalities (incl. graphical regions)
  • 2026 May/June · Paper 12 · Q21 (a, b, c)6 marksSequences
  • 2026 May/June · Paper 12 · Q282 marksSubstitution, formulae & rearranging
  • 2026 May/June · Paper 22 · Q6 (a, b)5 marksSubstitution, formulae & rearranging
  • 2026 May/June · Paper 22 · Q72 marksExpanding, factorising & simplifying
  • 2026 May/June · Paper 22 · Q9 (c)2 marksExpanding, factorising & simplifying
  • 2026 May/June · Paper 22 · Q12 (a, b)7 marksInequalities (incl. graphical regions)
  • 2026 May/June · Paper 22 · Q14 (a, b)4 marksSequences
  • 2026 May/June · Paper 22 · Q193 marksExpanding, factorising & simplifying
  • 2026 May/June · Paper 22 · Q21 (a, b)3 marksQuadratics (solve, formula, completing the square)
  • 2026 May/June · Paper 22 · Q23 (a)3 marksDifferentiation
  • 2026 May/June · Paper 22 · Q255 marksSimultaneous equations
  • 2026 May/June · Paper 32 · Q121 markExpanding, factorising & simplifying
  • 2026 May/June · Paper 32 · Q13 (b)1 markAlgebraic indices
  • 2026 May/June · Paper 32 · Q14 (a, b(i), b(ii))7 marksLinear equations & forming equations
  • 2026 May/June · Paper 32 · Q15 (a, b)3 marksSequences
  • 2026 May/June · Paper 32 · Q18 (a, b, c, d)10 marksGraphs of functions (tables, plotting, solving)
  • 2026 May/June · Paper 42 · Q8 (a, b, c)11 marksGraphs of functions (tables, plotting, solving)
  • 2026 May/June · Paper 42 · Q93 marksLinear equations & forming equations
  • 2026 May/June · Paper 42 · Q133 marksDirect & inverse proportion
  • 2026 May/June · Paper 42 · Q153 marksAlgebraic fractions
  • 2026 May/June · Paper 42 · Q17 (a, b, c, d)7 marksFunctions
  • 2026 May/June · Paper 42 · Q18 (b, c)7 marksQuadratics (solve, formula, completing the square)
  • 2026 May/June · Paper 42 · Q223 marksAlgebraic fractions

2025

  • 2025 Oct/Nov · Paper 22 · Q72 marksInequalities (incl. graphical regions)
  • 2025 Oct/Nov · Paper 22 · Q82 marksLinear equations & forming equations
  • 2025 Oct/Nov · Paper 22 · Q10 (b)2 marksSubstitution, formulae & rearranging
  • 2025 Oct/Nov · Paper 22 · Q15 (a, b)3 marksExpanding, factorising & simplifying
  • 2025 Oct/Nov · Paper 22 · Q20 (a(i), a(ii), a(iii), b)11 marksFunctions
  • 2025 Oct/Nov · Paper 22 · Q223 marksQuadratics (solve, formula, completing the square)
  • 2025 Oct/Nov · Paper 22 · Q242 marksAlgebraic indices
  • 2025 Oct/Nov · Paper 42 · Q22 marksLinear equations & forming equations
  • 2025 Oct/Nov · Paper 42 · Q93 marksGraphs in practical situations
  • 2025 Oct/Nov · Paper 42 · Q10 (a, b)4 marksSequences
  • 2025 Oct/Nov · Paper 42 · Q11 (a, b, c)10 marksGraphs of functions (tables, plotting, solving)
  • 2025 Oct/Nov · Paper 42 · Q132 marksAlgebraic fractions
  • 2025 Oct/Nov · Paper 42 · Q173 marksExpanding, factorising & simplifying
  • 2025 Oct/Nov · Paper 42 · Q196 marksSimultaneous equations
  • 2025 Oct/Nov · Paper 42 · Q214 marksDirect & inverse proportion
  • 2025 May/June · Paper 12 · Q14 (a, b, c, d, e)11 marksGraphs of functions (tables, plotting, solving)
  • 2025 May/June · Paper 12 · Q19 (b)2 marksInequalities (incl. graphical regions)
  • 2025 May/June · Paper 12 · Q23 (a, b)4 marksExpanding, factorising & simplifying
  • 2025 May/June · Paper 12 · Q243 marksSimultaneous equations
  • 2025 May/June · Paper 22 · Q6 (a, b)5 marksLinear equations & forming equations
  • 2025 May/June · Paper 22 · Q7 (a, b)3 marksSequences
  • 2025 May/June · Paper 22 · Q15 (a, b, c)6 marksGraphs of functions (tables, plotting, solving)
  • 2025 May/June · Paper 22 · Q19 (a, b, c)7 marksAlgebraic fractions
  • 2025 May/June · Paper 22 · Q20 (a, b)4 marksDirect & inverse proportion
  • 2025 May/June · Paper 22 · Q21 (a, b(i), b(ii))9 marksDifferentiation · Graphs of functions (tables, plotting, solving)
  • 2025 May/June · Paper 22 · Q245 marksSimultaneous equations
  • 2025 May/June · Paper 32 · Q13 (a, b)5 marksSequences
  • 2025 May/June · Paper 32 · Q14 (a, b)4 marksSubstitution, formulae & rearranging
  • 2025 May/June · Paper 32 · Q20 (a, b)3 marksLinear equations & forming equations
  • 2025 May/June · Paper 32 · Q21 (a, b)3 marksAlgebraic indices
  • 2025 May/June · Paper 32 · Q22 (a, b)4 marksLinear equations & forming equations
  • 2025 May/June · Paper 42 · Q72 marksSubstitution, formulae & rearranging
  • 2025 May/June · Paper 42 · Q93 marksSimultaneous equations
  • 2025 May/June · Paper 42 · Q103 marksLinear equations & forming equations
  • 2025 May/June · Paper 42 · Q142 marksExpanding, factorising & simplifying
  • 2025 May/June · Paper 42 · Q19 (a, b, c, d)6 marksFunctions
  • 2025 May/June · Paper 42 · Q21 (a, b)4 marksAlgebraic indices
  • 2025 May/June · Paper 42 · Q233 marksAlgebraic fractions
  • 2025 May/June · Paper 42 · Q24 (a, b)8 marksAlgebraic fractions · Quadratics (solve, formula, completing the square)
  • 2025 May/June · Paper 42 · Q262 marksDifferentiation

2024

  • 2024 Oct/Nov · Paper 22 · Q12 marksSequences
  • 2024 Oct/Nov · Paper 22 · Q11 (a, b)5 marksExpanding, factorising & simplifying
  • 2024 Oct/Nov · Paper 22 · Q123 marksDirect & inverse proportion
  • 2024 Oct/Nov · Paper 22 · Q134 marksInequalities (incl. graphical regions)
  • 2024 Oct/Nov · Paper 22 · Q14 (a, b)4 marksGraphs in practical situations
  • 2024 Oct/Nov · Paper 22 · Q202 marksSequences
  • 2024 Oct/Nov · Paper 22 · Q213 marksExpanding, factorising & simplifying
  • 2024 Oct/Nov · Paper 42 · Q2 (a, b, c(i), c(ii), d)13 marksGraphs of functions (tables, plotting, solving)
  • 2024 Oct/Nov · Paper 42 · Q3 (a(i), a(ii), a(iii), b, c, d)17 marksAlgebraic fractions · Algebraic indices · Expanding, factorising & simplifying · Linear equations & forming equations · Quadratics (solve, formula, completing the square) · Simultaneous equations
  • 2024 Oct/Nov · Paper 42 · Q9 (a(i), a(ii), a(iii), b)8 marksFunctions
  • 2024 Oct/Nov · Paper 42 · Q10 (a, b, c)9 marksDifferentiation
  • 2024 May/June · Paper 22 · Q16 (a, b)4 marksGraphs in practical situations
  • 2024 May/June · Paper 22 · Q18 (a, b)3 marksGraphs of functions (tables, plotting, solving)
  • 2024 May/June · Paper 22 · Q19 (a, b)4 marksDirect & inverse proportion
  • 2024 May/June · Paper 22 · Q215 marksSimultaneous equations
  • 2024 May/June · Paper 22 · Q22 (a(i), a(ii))2 marksSketching curves
  • 2024 May/June · Paper 42 · Q5 (a, b, c, d(i), d(ii))14 marksAlgebraic fractions · Algebraic indices · Expanding, factorising & simplifying · Quadratics (solve, formula, completing the square) · Sequences
  • 2024 May/June · Paper 42 · Q7 (a, b, c, d(i), d(ii), d(iii))11 marksExpanding, factorising & simplifying · Functions · Linear equations & forming equations
  • 2024 May/June · Paper 42 · Q8 (a, b, c)11 marksInequalities (incl. graphical regions)
  • 2024 May/June · Paper 42 · Q11 (a, b(i), b(ii))7 marksDifferentiation

2023

  • 2023 Oct/Nov · Paper 22 · Q32 marksSubstitution, formulae & rearranging
  • 2023 Oct/Nov · Paper 22 · Q102 marksExpanding, factorising & simplifying
  • 2023 Oct/Nov · Paper 22 · Q12 (a, b)3 marksGraphs in practical situations
  • 2023 Oct/Nov · Paper 22 · Q13 (b)2 marksAlgebraic indices
  • 2023 Oct/Nov · Paper 22 · Q143 marksSubstitution, formulae & rearranging
  • 2023 Oct/Nov · Paper 22 · Q162 marksExpanding, factorising & simplifying
  • 2023 Oct/Nov · Paper 22 · Q19 (a, b)4 marksSequences
  • 2023 Oct/Nov · Paper 22 · Q214 marksSimultaneous equations
  • 2023 Oct/Nov · Paper 22 · Q222 marksDirect & inverse proportion
  • 2023 Oct/Nov · Paper 22 · Q244 marksAlgebraic fractions
  • 2023 Oct/Nov · Paper 22 · Q252 marksDifferentiation
  • 2023 Oct/Nov · Paper 42 · Q5 (a, b(i), b(ii), b(iii))9 marksLinear equations & forming equations · Quadratics (solve, formula, completing the square)
  • 2023 Oct/Nov · Paper 42 · Q9 (a, b, c)8 marksDifferentiation
  • 2023 Oct/Nov · Paper 42 · Q11 (a, b, c, d, e, f)14 marksFunctions
  • 2023 May/June · Paper 12 · Q162 marksInequalities (incl. graphical regions)
  • 2023 May/June · Paper 12 · Q192 marksAlgebraic indices
  • 2023 May/June · Paper 22 · Q8 (a, b)4 marksInequalities (incl. graphical regions) · Linear equations & forming equations
  • 2023 May/June · Paper 22 · Q12 (a, b)3 marksQuadratics (solve, formula, completing the square)
  • 2023 May/June · Paper 22 · Q142 marksFunctions
  • 2023 May/June · Paper 22 · Q184 marksSubstitution, formulae & rearranging
  • 2023 May/June · Paper 22 · Q193 marksDirect & inverse proportion
  • 2023 May/June · Paper 22 · Q223 marksAlgebraic fractions
  • 2023 May/June · Paper 32 · Q3 (a(i), a(ii))4 marksGraphs in practical situations
  • 2023 May/June · Paper 32 · Q7 (b(i), b(ii), b(iii), b(iv))9 marksGraphs of functions (tables, plotting, solving)
  • 2023 May/June · Paper 32 · Q8 (a, b, c, d, e, f)15 marksExpanding, factorising & simplifying · Linear equations & forming equations · Simultaneous equations · Substitution, formulae & rearranging
  • 2023 May/June · Paper 32 · Q9 (a(i), a(ii), a(iii), b(i), b(ii))7 marksSequences
  • 2023 May/June · Paper 42 · Q3 (a(i), a(ii))6 marksQuadratics (solve, formula, completing the square)
  • 2023 May/June · Paper 42 · Q6 (a(i), a(ii), b(i), b(ii))8 marksSequences
  • 2023 May/June · Paper 42 · Q8 (a(i), a(ii), b)13 marksDifferentiation · Expanding, factorising & simplifying · Sketching curves
  • 2023 May/June · Paper 42 · Q9 (a(i), a(ii), b(i), b(ii), c)15 marksAlgebraic fractions · Algebraic indices · Expanding, factorising & simplifying · Simultaneous equations

2022

  • 2022 Oct/Nov · Paper 22 · Q21 markExpanding, factorising & simplifying
  • 2022 Oct/Nov · Paper 22 · Q42 marksExpanding, factorising & simplifying
  • 2022 Oct/Nov · Paper 22 · Q6 (a, b)6 marksSequences
  • 2022 Oct/Nov · Paper 22 · Q11 (a, b)3 marksGraphs of functions (tables, plotting, solving)
  • 2022 Oct/Nov · Paper 22 · Q17 (a, b, c)6 marksFunctions
  • 2022 Oct/Nov · Paper 22 · Q20 (a, b)3 marksAlgebraic indices
  • 2022 Oct/Nov · Paper 22 · Q237 marksAlgebraic fractions
  • 2022 Oct/Nov · Paper 42 · Q1 (b(i), b(ii), b(iii))7 marksLinear equations & forming equations
  • 2022 Oct/Nov · Paper 42 · Q2 (a(i), a(ii), a(iii), b(ii))10 marksGraphs of functions (tables, plotting, solving)
  • 2022 Oct/Nov · Paper 42 · Q5 (a(i), a(ii))5 marksGraphs in practical situations
  • 2022 Oct/Nov · Paper 42 · Q6 (a, b, c, d, e, f(i), f(ii), g, h)21 marksAlgebraic fractions · Algebraic indices · Differentiation · Direct & inverse proportion · Expanding, factorising & simplifying · Linear equations & forming equations · Quadratics (solve, formula, completing the square)
  • 2022 May/June · Paper 22 · Q82 marksSequences
  • 2022 May/June · Paper 22 · Q12 (a)3 marksGraphs in practical situations
  • 2022 May/June · Paper 22 · Q152 marksExpanding, factorising & simplifying
  • 2022 May/June · Paper 22 · Q18 (a, b)4 marksDirect & inverse proportion
  • 2022 May/June · Paper 22 · Q19 (a, b)4 marksFunctions
  • 2022 May/June · Paper 22 · Q20 (a, b)5 marksExpanding, factorising & simplifying
  • 2022 May/June · Paper 22 · Q215 marksSequences
  • 2022 May/June · Paper 42 · Q8 (a, b, c, d, e)18 marksAlgebraic fractions · Expanding, factorising & simplifying · Linear equations & forming equations · Simultaneous equations · Substitution, formulae & rearranging
  • 2022 May/June · Paper 42 · Q10 (a, b(i), b(ii))7 marksInequalities (incl. graphical regions)
  • 2022 May/June · Paper 42 · Q12 (a, b, c)11 marksDifferentiation · Sketching curves

Find the full paper on the official Cambridge past-papers page or ask your school. “Paper 42” means Paper 4, variant 2.

Similar questions

Questions that test the same subtopic in different years. Practise them together to master one skill.

Graphs of functions (tables, plotting, solving) 11 questions · 7/9 sessions
Expanding, factorising & simplifying Banker25 questions · 9/9 sessions
Sequences Banker15 questions · 9/9 sessions
Functions Banker9 questions · 9/9 sessions
Differentiation Banker10 questions · 8/9 sessions
Linear equations & forming equations Banker17 questions · 9/9 sessions
Algebraic fractions Banker14 questions · 9/9 sessions
Simultaneous equations Banker11 questions · 8/9 sessions
Quadratics (solve, formula, completing the square) Banker10 questions · 8/9 sessions
Inequalities (incl. graphical regions) 9 questions · 7/9 sessions
Direct & inverse proportion Banker9 questions · 9/9 sessions
Substitution, formulae & rearranging 10 questions · 6/9 sessions
Algebraic indices Banker11 questions · 8/9 sessions
Graphs in practical situations 7 questions · 7/9 sessions
Sketching curves 3 questions · 3/9 sessions

Subtopics

SubtopicMarks indexedSessions
Graphs of functions (tables, plotting, solving) 897/9
Expanding, factorising & simplifying Banker689/9
Sequences Banker639/9
Functions Banker639/9
Differentiation Banker558/9
Linear equations & forming equations Banker549/9
Algebraic fractions Banker549/9
Simultaneous equations Banker538/9
Quadratics (solve, formula, completing the square) Banker418/9
Inequalities (incl. graphical regions) 407/9
Direct & inverse proportion Banker329/9
Substitution, formulae & rearranging 316/9
Algebraic indices Banker288/9
Graphs in practical situations 267/9
Sketching curves 83/9

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