2021 TJC IP1 FM EOY Q3

2021 TJC IP1 FM EOY Q3

IP 1
6 marks
  1. The numbers \(A\), \(B\) and \(C\), written as a product of their prime factors, are given below, where \(p\), \(q\) and \(r\) are prime numbers.
    \(A=p^2\times q^7\times r^{11}\)
    \(B=p^4\times q^2\times r\)
    \(C=2\times7^3\times13^2\)
    Using the prime factors given above, find
    1. the cube root of \(A\times B\),[2]
    2. the smallest positive integer, \(k\), such that \(\frac{C}{k}\) is a perfect square.[1]
  2. The area of a square is \(2\,601\text{ cm}^2\). Using prime factorisation, find the perimeter of the square.[3]

Solution:

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Answer:(a)(i) \(p^2q^3r^4\) (ii) \(k=14\) (b) \(204\text{ cm}\)

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