2026 NORTHBROOKS P2 Q7

2026 NORTHBROOKS P2 Q7

Secondary 4
9 marks
  1. \(\xi=\{\text{even integers}\hspace{0.5em}x:5\leq x\leq20\}\)
    \(A=\{\text{multiples of}\hspace{0.5em}3\}\)
    \(B=\{\text{factors of}\hspace{0.5em}120\}\)
    1. List the elements in \(A\cap B\).[1]
    2. State a possible element, \(x\), such that \(x\in A\) and \(x\in B^{\prime}\).[1]
  2. Use set notation to describe the shaded region.[1]
  3. The sets \(\xi,S\) and \(T\) satisfy the conditions \(n(\xi)=41\), \(n(S)=25\) and \(n(T)=7\).
    Find
    1. the largest possible value of \(n(S\cup T)^{\prime}\),[1]
    2. the smallest possible value of \(n(S\cup T)^{\prime}\).[1]
  4. A company has 28 employees.
    One of the 28 employees is selected at random.
    The probability that it is a woman working full-time is \(\dfrac27\).
    Two of the 28 employees are selected at random.
    The probability that both are men working part-time is \(\dfrac2{27}\).
    Complete the table of information about the 28 employees of the company.
    You must show your calculations.[4]
    Part-time employeesFull-time employees
    Women6
    Men

Solution:

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Answer:(a)(i) \(\{6,12\}\) (ii) \(18\). (b) \(P^{\prime}\cup Q\). (c)(i) 16 (ii) 9. (d) Women: 6 part-time, 8 full-time; men: 8 part-time, 6 full-time.

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