Sets practice questions

Secondary 4 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise sets free

What this topic covers

Worked examples

Example 1

Given that E={x:E = \{x : <i>x</i> is a positive integer that is a multiple of 33 and a factor of 36}36\}, find n(E)n(E).
Show the worked solution
  • First list all positive factors of $36$: $\{1, 2, 3, 4, 6, 9, 12, 18, 36\}$.
  • Now keep only those that are multiples of $3$:
  • $E = \{3, 6, 9, 12, 18, 36\}$
  • Count the elements: there are $6$ elements.
  • $n(E) = 6$

Answer: 66

Example 2

The universal set is ξ={x:x is a positive integer,x≤38}\xi = \{x : x \text{ is a positive integer}, x \leq 38\} and A={x:x is a perfect square,x∈ξ}A = \{x : x \text{ is a perfect square}, x \in \xi\}. Find n(A′)n(A').
Show the worked solution
  • $n(\xi) = 38$
  • The perfect squares in $\xi$ are: $1,\ 4,\ 9,\ 16,\ 25,\ 36$
  • $n(A) = 6$
  • $n(A') = n(\xi) - n(A)$
  • $n(A') = 38 - 6$
  • $n(A') = 32$

Answer: 3232

Example 3

ξ={1,2,…,24}\xi = \{1, 2, \ldots, 24\}, AA is the set of factors of 2424, and BB is the set of prime numbers in ξ\xi. Find n(A∩B)n(A \cap B).
Show the worked solution
  • $A = \{1, 2, 3, 4, 6, 8, 12, 24\} \quad \scriptsize\textit{factors of 24}$
  • $B = \{2, 3, 5, 7, 11, 13, 17, 19, 23\} \quad \scriptsize\textit{primes up to 24}$
  • $A \cap B$ consists of numbers that are both factors of $24$ and prime, i.e. the prime factors of $24$.
  • $A \cap B = \{2, 3\}$
  • $n(A \cap B) = 2$

Answer: 22

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

Other Secondary 4 topics