Higher June 2022 Paper 1R Q12
12 \(P = 3^3 \times 5^2 \times 7\)
\(Q = 3^2 \times 5 \times 7^2\)
(a) Write down the highest common factor (HCF) of \(P\) and \(Q\) (1)
\(P = 3^3 \times 5^2 \times 7\)
\(Q = 3^2 \times 5 \times 7^2\)
(b) Work out the value of \(P^3 \times Q\)
Give your answer in the form \(3^x \times 5^y \times 7^z\) where \(x\), \(y\) and \(z\) are positive integers. (2)
Give your answer in the form \(3^x \times 5^y \times 7^z\) where \(x\), \(y\) and \(z\) are positive integers. (2)
| Scheme | Marks |
|---|---|
| \(3^2 \times 5 \times 7\) | B1 |
| (1) |
Notes
B1: accept \(3 \times 3 \times 5 \times 7\) oe or 315
| Scheme | Marks |
|---|---|
| \(3^{11} \times 5^7 \times 7^5\) | B2 |
| (2) | |
| (3 marks) |
Notes
B2: fully correct answer
(allow \(x = 11\), \(y = 7\), \(z = 5\))
(B1 for an answer in the form \(3^p \times 5^q \times 7^r\) where one or two of \(p\), \(q\) or \(r\) are correct)