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Cambridge IGCSE Mathematics · 0580

IGCSE Mathematics (0580) Algebra and graphs past paper questions

Algebra runs through the whole 0580 paper. These questions drill manipulation, solving equations, sequences, and reading and sketching graphs — the techniques that reappear inside geometry, mensuration, and later questions.

782 free questions from 2016–2025, each with its marking scheme. Open the full topical bank to filter by subtopic, paper, and year.

Algebra and graphs in IGCSE Mathematics 0580 exams, 2020–2025

Across 2020–2025, Algebra and graphs accounted for 834 questions worth 4,911 marks in Cambridge IGCSE Mathematics (0580) papers.

By year
YearQuestionsMarks
2020123834
2021122840
2022130838
2023135811
2024130798
2025194790

Most-tested subtopics

  1. 2.5 Equations2103 marks
  2. 2.2 Algebraic manipulation1354 marks
  3. 2.10 Graphs of functions1151 marks

Appears in

  • Paper 1 · 176 qs
  • Paper 2 · 328 qs
  • Paper 3 · 131 qs
  • Paper 4 · 199 qs
All most-tested Mathematics topics

  1. 2025 May/Jun · Paper 2 · Q18 · 4 marks

    18 (a) 3 9 Rationalise the denominator. Give your answer in its simplest form. … [2] (b) ( )( ) c k 5 2 1 3 2 2 - + = + Find…
    Marking scheme
    Mark scheme: 18(a) 3 3 cao 2 M1 for 9 3 × 3 3 oe 18(b) [c =] –1 [k =] 14 2 B1 for each or for 3 correct terms from 5 15 2 2 3 2 2 + − − oeGet Steven’s plain-English explanation

  2. 2025 May/Jun · Paper 4 · Q19 · 6 marks

    19 ( ) f x x 1 = + ( ) g x x 5 2 = - ( ) h x 2x = (a) Find ( ) f 3 – . … [1] (b) The domain of ( ) g x is {–3, 0, 2}. Find…
    Marking scheme
    Mark scheme: 19(a) –2 1 19(b) 11, 5, 1 2 B1 for 2 correct listed on answer line 19(c) –5 1 19(d) 8 2 M1 for [x =] h(3) or [x =] 23Get Steven’s plain-English explanation

  3. 2021 May/Jun · Paper 1 · Q5 · 2 marks

    5 The formula for changing a temperature measured in Celsius (°C) to Fahrenheit (°F) is 5 9 32 F C = + . Use this formula to…
    Marking scheme
    Mark scheme: 5 149 2 M1 for 9 × 65 ÷ 5 [+32]Get Steven’s plain-English explanation

  4. 2021 May/Jun · Paper 1 · Q6 · 3 marks

    6 12 00 13 00 14 00 Time 15 00 16 00 0 1 2 3 4 Distance (km) 5 6 7 8 The travel graph shows a student’s journey. (a) Explain…
    Marking scheme
    Mark scheme: 6(a) Student is stationary oe 1 6(b) 13 00 13 20 gradient is steepest 2 B1 for both times correct or correct reasonGet Steven’s plain-English explanation

  5. 2021 Oct/Nov · Paper 1 · Q7 · 2 marks

    7 r t u 2 3 = + Work out the value of t when r = 18 and u = 4. t = … [2]
    Marking scheme
    Mark scheme: 7 3 2 M1 for 18 = 2t + (3 × 4) or betterGet Steven’s plain-English explanation

Showing 5 of 782 free Algebra and graphs questions.

See them all in the topical bank

More Mathematics topics

NumberCoordinate geometryGeometryMensurationTrigonometryTransformations and vectorsProbabilityStatistics