0580.C1.1.11 — Identify and use: rational and irrational numbers.: past paper questions

Real questions on 0580.c1.1.11 — identify and use: rational and irrational numbers.

The newest 20 of 25 written questions. Open one to see it on the real paper.

1. 0580/11 · May/June 2026 · Q1e[1]
   1 | $1.694$ | $\sqrt{18}$ | $6$ | $6.666$ | $7$ | $\sqrt{225}$ | $25$ | $27$ | $39$ | $56$ | $1000$ | From the list of numbers, write down (e) an irrational number.See it on the paper →
2. 0580/22 · May/June 2026 · Q18a[3]
   Marwa has these 10 numbered tiles. [Diagram: 10 tiles in a row with numbers 1, 2, 2, 3, 3, 4, 4, 4, 4, 4] (a) Marwa picks one of the tiles at random. She replaces the tile and then picks a second tile at random. Find the probability that the two tiles have the same even number.See it on the paper →
3. 0580/22 · May/June 2026 · Q18b[3]
   18 Marwa has these 10 numbered tiles. [Diagram: 10 tiles in a row containing the numbers 1, 2, 2, 3, 3, 4, 4, 4, 4, 4] (b) From the 10 numbered tiles, Marwa now picks three tiles at random without replacement. Find the probability that the sum of the numbers on the three tiles is 11.See it on the paper →
4. 0580/32 · May/June 2026 · Q10[2]
   10 Dave invests $8500 at a rate of 4.5% per year simple interest. Calculate the total interest earned at the end of 3 years.See it on the paper →
5. 0580/32 · May/June 2026 · Q25[1]

   1-mark “Draw” question — its maths and diagrams are best seen on the paper.

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6. 0580/12 · February/March 2026 · Q9c[1]
   (c) Write down an irrational number that is between 4 and 5.See it on the paper →
7. 0580/23 · October/November 2025 · Q24c[2]
   (c) Rationalise the denominator. $\frac{1}{\sqrt{7}+2}$See it on the paper →
8. 0580/13 · May/June 2025 · Q3d[1]
   (d) Work out $-18÷-4$.See it on the paper →
9. 0580/43 · October/November 2024 · Q1a[2]
   1 Dinari sells fruit and vegetables. (a) One day the mass of fruit and vegetables he sells is in the ratio fruit : vegetables = $9:8$. He sells $48$ kg of vegetables. Find the mass of the fruit he sells.See it on the paper →
10. 0580/11 · May/June 2023 · Q2[1]

    1-mark “Write” question — its maths and diagrams are best seen on the paper.

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11. 0580/13 · May/June 2023 · Q18[1]
    18 The probability that Tom is late for school is $0.12$. There are $200$ school days this year. Work out the expected number of times that Tom is late for school this year.See it on the paper →
12. 0580/23 · May/June 2023 · Q3[3]
    [Diagram: A cuboid with dimensions 8 cm, 3 cm, and 5 cm. Labelled "NOT TO SCALE".] Find the total surface area of the cuboid.See it on the paper →
13. 0580/23 · May/June 2023 · Q14[3]
    14 Write $0.58\dot{1}$ as a fraction. You must show all your working and give your answer in its simplest form.See it on the paper →
14. 0580/32 · February/March 2023 · Q4e[1]
    (e) Write down an irrational number with a value between 15 and 20.See it on the paper →
15. 0580/42 · February/March 2023 · Q7c[3]
    $\mathcal{E}=\{\text{students in a class}\}$ $P=\{\text{students who study Physics}\}$ $C=\{\text{students who study Chemistry}\}$ $n(\mathcal{E})=24n(P)=17n(C)=14n(P\cap C)=9$ (c) Two students are picked from the class at random. Find the probability that one student studies both s...See it on the paper →
16. 0580/42 · February/March 2023 · Q7d[2]
    $\mathcal{E}=\{\text{students in a class}\}$ $P=\{\text{students who study Physics}\}$ $C=\{\text{students who study Chemistry}\}$ $n(\mathcal{E})=24n(P)=17n(C)=14n(P\cap C)=9$ (d) Two of the students who study Physics are picked at random. Find the probability that they both study C...See it on the paper →
17. 0580/11 · May/June 2021 · Q19[1]
    19 Write down an irrational number, $n$, where $31<n<32$. $n=$See it on the paper →
18. 0580/13 · October/November 2020 · Q1a[1]

    1-mark “Write down” question — its maths and diagrams are best seen on the paper.

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19. 0580/31 · October/November 2020 · Q1a[1]

    1-mark “Work out” question — its maths and diagrams are best seen on the paper.

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20. 0580/22 · February/March 2020 · Q1d[1]

    1-mark question — its maths and diagrams are best seen on the paper.

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What examiners said

Comprehensive responses • Answers between 4 and 5, especially those with decimals indicated an attempt at a square root of a number between 16 and 25. A few gave correct answer using this method such as root 17. Limited responses, • Many responses were terminating decimals between 4 and 5, in particular 4.5, while some gave answers such as 4.5 .

— Examiner report, February/March 2026, 0580/12 Q9(c) (Cambridge)

The question was generally well answered with incorrect answers stemming from candidates understanding of negatives.

— Examiner report, May/June 2025, 0580/13 Q3(d) (Cambridge)

The majority gave the correct answer. Some worked out how many times Tom was not late as they had not read the question carefully.

— Examiner report, May/June 2023, 0580/13 Q18 (Cambridge)