0580.C1.2.01 — n(A) Number of elements in set A.: past paper questions

Real questions on 0580.c1.2.01 — n(a) number of elements in set a.

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

1. 0980/11 · October/November 2025 · Q24a[2]
   24 $\mathcal{E}=\{\text{students in a year group}\}$ $H=\{\text{students who study History}\}$ $G=\{\text{students who study Geography}\}$ 80 students are in the year group. 40 students study History. [Diagram: A Venn diagram with a universal set rectangle labeled $\mathcal{E}$. Two intersecting circles labeled...See it on the paper →
2. 0980/11 · October/November 2025 · Q24b[1]
   $\mathcal{E}=\{\text{students in a year group}\}$ $H=\{\text{students who study History}\}$ $G=\{\text{students who study Geography}\}$ 80 students are in the year group. 40 students study History. [Diagram: A Venn diagram inside a rectangle labelled $\mathcal{E}$. Two overlapping circles labelled $H$ and $G$. Th...See it on the paper →
3. 0980/21 · October/November 2025 · Q10b[1]
   $\mathcal{E}=\{n:n\text{ is an integer and }1⩽n⩽8\}$ $A=\{\text{factors of }12\}$ $B=\{\text{odd numbers}\}$ Find (b) $\text{n}(A^{\prime }\cup B)$.See it on the paper →
4. 0980/41 · October/November 2025 · Q12a[1]
   12 Some students are asked if they like football ($F$) or rugby ($R$). The Venn diagram shows the results. [Diagram: A Venn diagram with a universal set $\mathcal{E}$. Two overlapping circles labeled $F$ and $R$. The region only in $F$ contains 33. The intersection of $F$ and $R$ contains 7. The region only in $R$ cont...See it on the paper →
5. 0980/41 · October/November 2025 · Q12b[1]
   12 Some students are asked if they like football ($F$) or rugby ($R$). The Venn diagram shows the results. [Diagram: A Venn diagram with a universal set $\mathcal{E}$ containing two overlapping sets $F$ and $R$. The region only in $F$ contains 33. The intersection of $F$ and $R$ contains 7. The region only in $R$ conta...See it on the paper →
6. 0980/42 · May/June 2025 · Q1[1]
   1 A quadrilateral has these properties • the diagonals are the only lines of symmetry • it has rotational symmetry of order 2. Write down the mathematical name of this quadrilateral.See it on the paper →
7. 0980/42 · May/June 2025 · Q11[2]
   11 In a sale, the original price of a shirt is reduced by $15\%$. The sale price of the shirt is \23.63$ . Find the original price of the shirt.See it on the paper →
8. 0980/42 · May/June 2025 · Q22a(i)[1]
   [Diagram: A Venn diagram with a universal set $\mathcal{E}$ containing two intersecting sets $G$ and $H$. The region only in $G$ contains 8, the intersection contains 13, the region only in $H$ contains 7, and the region outside both sets contains 5.] $\mathcal{E}=\{\text{number of students in a class}\}$ $G = \{\tex...See it on the paper →
9. 0980/42 · May/June 2025 · Q22a(ii)[1]
   [Diagram: A Venn diagram with a universal set $\mathcal{E}$ containing two intersecting sets $G$ and $H$. The region only in $G$ contains 8, the intersection $G\cap H$ contains 13, the region only in $H$ contains 7, and the region outside both sets contains 5.] $\mathcal{E}=\{\text{number of students in a class}\}$...See it on the paper →
10. 0980/11 · October/November 2024 · Q19b[1]
    19 Jo asks some people if they own a car ($C$) and if they own a motorbike ($M$). 86 people own a car. 39 people own a motorbike. 7 people do not own a car and do not own a motorbike. [Diagram: Venn diagram with universal set $\mathcal{E}$, two overlapping circles $C$ and $M$. The region of $C$ only contains 74.] (b...See it on the paper →
11. 0980/11 · October/November 2024 · Q19c[1]
    19 Jo asks some people if they own a car ($C$) and if they own a motorbike ($M$). 86 people own a car. 39 people own a motorbike. 7 people do not own a car and do not own a motorbike. [Diagram: Venn diagram with universal set $\mathcal{E}$, two overlapping circles $C$ and $M$. The region of $C$ only contains 74.] (e)...See it on the paper →
12. 0980/21 · October/November 2024 · Q19b(ii)[1]
    $\mathcal{E}=\{1,2,3,4,5,6,7,8,9,10\}$ $P=\{\text{odd numbers}\}$ $Q=\{\text{multiples of }3\}$ $R=\{\text{square numbers}\}$ (ii) Find $n(P\cap (Q\cup R{)}^{\prime })$.See it on the paper →
13. 0980/12 · May/June 2023 · Q13a[1]
    $\mathcal{E}=\{x:1⩽x⩽20\}$ $E=\{\text{even numbers}\}$ $M=\{\text{multiples of 5}\}$ (a) Find $n(M)$.See it on the paper →
14. 0980/22 · May/June 2023 · Q6a[1]
    6 $\mathcal{E}=\{x:1⩽x⩽20\}$ $E=\{\text{even numbers}\}$ $M=\{\text{multiples of 5}\}$ (a) Find $n(M)$.See it on the paper →
15. 0980/22 · May/June 2023 · Q6c[1]
    6 $\mathcal{E}=\{x:1⩽x⩽20\}$ $E=\{\text{even numbers}\}$ $M=\{\text{multiples of 5}\}$ (c) $y\notin E$. Write down a possible value of $y$.See it on the paper →
16. 0980/11 · October/November 2022 · Q18a[1]
    [Diagram: A Venn diagram with a universal set $\mathcal{E}$ containing two intersecting sets $P$ and $Q$. The regions are labelled: $a,b,c$ in $P$ only; $d$ in $P\cap Q$; $e,f$ in $Q$ only; $g$ in $\mathcal{E}$ only.] The Venn diagram shows the elements of the sets $\mathcal{E}$, $P$ and $Q$. Complete the statement...See it on the paper →
17. 0980/11 · October/November 2022 · Q18b[1]
    [Diagram: A Venn diagram with a universal set $\mathcal{E}$ containing two overlapping circles $P$ and $Q$. The regions are labelled: $a,b,c$ in $P$ only; $d$ in $P\cap Q$; $e,f$ in $Q$ only; $g$ in $\mathcal{E}$ only.] The Venn diagram shows the elements of the sets $\mathcal{E}$, $P$ and $Q$. Complete the stateme...See it on the paper →
18. 0980/22 · May/June 2022 · Q16b[1]
    16 The Venn diagram shows the number of students in a class of 40 who study physics ($P$), mathematics ($M$) and geography ($G$). [Diagram: A Venn diagram with three intersecting circles labeled $P$, $M$, and $G$ inside a rectangle labeled $\mathcal{E}$. The regions are filled with numbers: $P$ only = 4, $M$ only = 11,...See it on the paper →
19. 0980/22 · May/June 2021 · Q12a(ii)[1]
    $\mathcal{E}=\{\text{integers greater than }2\}$ $A=\{\text{prime numbers}\}$ $B=\{\text{odd numbers}\}$ $C=\{\text{square numbers}\}$ (ii) Complete the set labels on the Venn diagram. [Diagram: A rectangle labelled $\mathcal{E}$ containing three overlapping circles labelled $A$, $B$ and $C$. Circle $A$ is on...See it on the paper →
20. 0980/32 · May/June 2021 · Q7b(ii)[1]
    (b) 135 girls are asked if they like soccer ($S$) and if they like hockey ($H$). n($S$) = 53, n($H$) = 68 and n($S\cup H$) = 110. (ii) Write down n($S\cap H$).See it on the paper →

What examiners said

This proved to be a difficult first question for many. Candidates struggled to use the properties of quadrilaterals to correctly identify the rhombus. The most common incorrect answers included kite and parallelogram, but most other quadrilaterals and occasionally even a triangle or a solid were also given.

— Examiner report, May/June 2025, 0980/42 Q1 (Cambridge)

This was a familiar question for most candidates. The most efficient method seen was for candidates to go straight to 23.63 ÷ 0.85 after recognising that 23.63 was 85% of the original price. An alternative approach was to recognize that 23.63 was 85% of the cost, then work out 1%, then 100%. Common errors included finding 115%, 15% or 85% of the sale price. In some other cases, the candidates divi...

— Examiner report, May/June 2025, 0980/42 Q11 (Cambridge)

Almost all candidates gave a correct answer to this question. A few incorrectly gave the number of students rather than the probability, or gave an insufficiently accurate decimal answer of 0.15.

— Examiner report, May/June 2025, 0980/42 Q22(a)(i) (Cambridge)