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 57 written questions. Open one to see it on the real paper.

1. 0580/12 · May/June 2026 · Q25a[2]
   25 $\mathcal{E}=\{1,2,3,4,5,6,7,8,9\}$ $P=\{\text{prime numbers}\}$ $N=\{\text{odd numbers}\}$ [Diagram: A Venn diagram with a universal set rectangle labeled $\mathcal{E}$ containing two overlapping circles labeled $P$ and $N$] (a) Complete the Venn diagram.See it on the paper →
2. 0580/12 · May/June 2026 · Q25b[1]
   25 $\mathcal{E}=\{1,2,3,4,5,6,7,8,9\}$ $P=\{\text{prime numbers}\}$ $N=\{\text{odd numbers}\}$ [Diagram: A Venn diagram with a rectangle labeled $\mathcal{E}$ containing two overlapping circles labeled $P$ and $N$] (b) Write down $\text{n}(P\cup N)$.See it on the paper →
3. 0580/23 · May/June 2026 · Q25a[3]
   25 $x$ is an integer. $\mathcal{E}=\{x:1⩽x⩽12\}$ $A=\{x:x\text{ is a square number}\}$ $B=\{x:4⩽x⩽8\}$ $C=\{x:x\text{ is a factor of }12\}$ (a) Complete the Venn diagram. [Diagram: A Venn diagram with a universal set rectangle labeled $\mathcal{E}$ containing...See it on the paper →
4. 0580/23 · May/June 2026 · Q25b[1]
   25 $x$ is an integer. $\mathcal{E}=\{x:1\le x\le 12\}$ $A=\{x:x\text{ is a square number}\}$ $B=\{x:4\le x\le 8\}$ $C=\{x:x\text{ is a factor of }12\}$ (b) Find $n(A\cap B\cap C^{\prime })$.See it on the paper →
5. 0580/33 · May/June 2026 · Q22b(ii)[1]
   (b) $\mathcal{E}=\{\text{A, B, E, H, M, O, Q, R, S, U}\}$ $X=\{\text{R, H, O, M, B, U, S}\}$ $Y=\{\text{S, Q, U, A, R, E}\}$ (ii) List the elements of $X^{\prime }$.See it on the paper →
6. 0580/33 · May/June 2026 · Q22b(iii)[1]
   (b) $\mathcal{E}=\{\text{A, B, E, H, M, O, Q, R, S, U}\}$ $X=\{\text{R, H, O, M, B, U, S}\}$ $Y=\{\text{S, Q, U, A, R, E}\}$ (iii) Find $n(X\cap Y)$.See it on the paper →
7. 0580/12 · February/March 2026 · Q19b[1]
   19 $\mathcal{E}=\{1,2,3,4,5,6,7,8,9,10,11,12\}$ $A=\{\text{multiples of }3\}$ $B=\{\text{multiples of }4\}$ [Diagram: Venn diagram with universal set $\mathcal{E}$ containing two overlapping sets $A$ and $B$] (b) Write down $\text{n}(A\cap B)$.See it on the paper →
8. 0580/22 · February/March 2026 · Q13a[1]
   13 $\mathcal{E}=\{x:x\text{ is an integer where }40<x<50\}$ $P=\{x:x\text{ is a square number}\}$ $Q=\{x:x\text{ is an odd number}\}$ $R=\{x:x\text{ is a multiple of }3\}$ (a) Use set notation to complete the statement. $P\cap R=$See it on the paper →
9. 0580/22 · February/March 2026 · Q13b[1]
   $\mathcal{E}=\{x:x\text{ is an integer where }40<x<50\}$ $P=\{x:x\text{ is a square number}\}$ $Q=\{x:x\text{ is an odd number}\}$ $R=\{x:x\text{ is a multiple of }3\}$ (b) Find $n(P\cap Q\cap R{)}^{\prime }$.See it on the paper →
10. 0580/32 · February/March 2026 · Q13[3]
    13 A set of five **different whole** numbers has \begin{itemize} \item the smallest number $-3$ \item a range of $14$ \item a median of $8$ \item a mean of $6$. \end{itemize} Work out the four other numbers. Write your numbers in order, starting with the smallest.See it on the paper →
11. 0580/03 · Specimen 2025 · Q7[1]

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

    See it on the paper →
12. 0580/11 · 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 box labeled $\mathcal{E}$. Two intersecting circles labeled $H$ a...See it on the paper →
13. 0580/11 · 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 →
14. 0580/12 · October/November 2025 · Q20a[2]
    20 $\mathcal{E}=\{1,2,3,4,5,6,7,8,9,10\}$ $A=\{1,3,5,7,9\}$ $B=\{1,3,6,10\}$ [Diagram: A Venn diagram with a rectangle labeled $\mathcal{E}$ containing two intersecting circles labeled $A$ and $B$] (a) Use this information to complete the Venn diagram.See it on the paper →
15. 0580/12 · October/November 2025 · Q20c[1]
    20 $\mathcal{E}=\{1,2,3,4,5,6,7,8,9,10\}$ $A=\{1,3,5,7,9\}$ $B=\{1,3,6,10\}$ [Diagram: Venn diagram with universal set $\mathcal{E}$ containing two intersecting sets $A$ and $B$] (c) Find $n(B^{\prime })$.See it on the paper →
16. 0580/13 · October/November 2025 · Q23b(i)[2]
    (b) $\mathcal{E}=\{\text{people in a club}\}$ $T=\{\text{people who play tennis}\}$ $S=\{\text{people who go swimming}\}$ There are 60 people in the club. 36 people go swimming. [Diagram: A Venn diagram with a universal set rectangle labeled $\mathcal{E}$. Two intersecting circles labeled $T$ and $S$. The regio...See it on the paper →
17. 0580/13 · October/November 2025 · Q23b(ii)[1]
    (b) $\mathcal{E}=\{\text{people in a club}\}$ $T=\{\text{people who play tennis}\}$ $S=\{\text{people who go swimming}\}$ There are 60 people in the club. 36 people go swimming. [Diagram: Venn diagram with universal set $\mathcal{E}$ containing two intersecting circles $T$ and $S$. The region outside the circle...See it on the paper →
18. 0580/21 · 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 →
19. 0580/22 · October/November 2025 · Q12a[3]
    12 A fitness club has 100 members. 60 swim ($S$). 70 cycle ($C$). 25 do not swim or cycle. [Diagram: A Venn diagram with a universal set rectangle labelled $\mathcal{E}$, containing two overlapping circles labelled $S$ and $C$] (a) Complete the Venn diagram.See it on the paper →
20. 0580/22 · October/November 2025 · Q12b(iii)[1]
    12 A fitness club has 100 members. 60 swim ($S$). 70 cycle ($C$). 25 do not swim or cycle. [Diagram: A Venn diagram with universal set $\mathcal{E}$ containing two overlapping circles labelled $S$ and $C$] (b) One member of the fitness club is chosen at random. For this member, find (iii) $P(S\cup C^{\prime })$.See it on the paper →

What examiners said

Comprehensive responses • A small number of candidates were familiar with the notation 𝑛(𝐴 ∩ 𝐵). Limited responses • Most candidates gave the list of numbers in the intersection or made no response.

— Examiner report, February/March 2026, 0580/12 Q19(b) (Cambridge)

Comprehensive responses • A few candidates expressed the empty set using the correct set notation, namely Ø or { }. Limited responses • Many candidates gave the incorrect answer 0. • Some candidates used incorrect notation for the empty set, such as {Ø} or ( ) or used words, rather than set notation, such as ‘nil’, ‘null’ or ‘empty’. • Some candidates thought that there were some elements in this...

— Examiner report, February/March 2026, 0580/22 Q13(a) (Cambridge)

Comprehensive responses • A small number of candidates had the correct answer of 9. Limited responses • A small number correctly listed the 9 elements of the set, without stating the number of elements. • Some candidates appeared to be giving what they thought were the elements of the set rather than the number of elements in the set. • Quite a few candidates offered no response to this question.

— Examiner report, February/March 2026, 0580/22 Q13(b) (Cambridge)