Ben records the favourite sport of each of 20 students.
Football Cricket Hockey Rugby Football Tennis Rugby Football Football Rugby
Tennis Football Rugby Football Cricket Football Rugby Football Cricket Cricket
Complete the frequency table. You may use the tally column to help you.
Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):
Count the occurrences of each sport from the list provided:
Cricket appears \(4\) times.
Football appears \(8\) times.
Hockey appears \(1\) time.
Rugby appears \(5\) times.
Tennis appears \(2\) times.
Check the sum: \(4 + 8 + 1 + 5 + 2 = 20\), which matches the total number of students.
✅ Answer:
Cricket: \(4\)
Football: \(8\)
Hockey: \(1\)
Rugby: \(5\)
Tennis: \(2\)
Given the sets:
$$ \begin{aligned} & \mathscr{E}=\{\mathrm{a}, \mathrm{~b}, \mathrm{c}, \mathrm{~d}, \mathrm{e}, \mathrm{f}, \mathrm{~g}, \mathrm{~h}, \mathrm{i}, \mathrm{j}, \mathrm{k}\} \\ & F=\{\mathrm{f}, \mathrm{a}, \mathrm{c}, \mathrm{e}\} \\ & B=\{\mathrm{b}, \mathrm{a}, \mathrm{c}, \mathrm{k}\} \end{aligned} $$
(a) Complete the Venn diagram.
(b) Find $\mathrm{n}(F \cup B)$.
(a)
The Venn diagram is completed by placing:
(b) Ans: 6
$F \cup B = \{\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{e}, \mathrm{f}, \mathrm{k}\}$.
Count the elements: $\mathrm{n}(F \cup B) = 6$.
(a) Mei writes down five integers.
Write down the five integers.
(b) Huan writes down four numbers.
Find the fifth number.
(a) Ans: 8, 10, 15, 16, 17
Given the lowest number is 8 and range is 9, the highest number is 17. With median 15, the third number must be 15. The remaining two numbers must be between 8-15, distinct (no mode), and sum to 66-(8+15+17)=26. The only pair satisfying these conditions is 10 and 16.
(b) Ans: 32
Total of first four numbers = 4 × 17 = 68. Total of five numbers = 5 × 20 = 100. Therefore, the fifth number = 100 – 68 = 32.
