Higher June 2024 Paper 1R Q11
11 \(A = 2^5 \times 5 \times 7^2\)
\(B = 2^3 \times 5^3 \times 7^4\)
(a) Write down the highest common factor (HCF) of \(5A\) and \(2B\)
Give your answer as a product of prime factors. (2)
Give your answer as a product of prime factors. (2)
(b) Work out the value of \((AB)^2\)
Give your answer as a product of prime factors. (2)
Give your answer as a product of prime factors. (2)
| Scheme | Marks |
|---|---|
 Answer: \(2^4 \times 5^2 \times 7^2\) | B2 |
| (2) |
Notes
B2: for \(2^4 \times 5^2 \times 7^2\)
oe eg \(2 \times 2 \times 2 \times 2 \times 5 \times 5 \times 7 \times 7\)
(B1 for \(2^m \times 5^n \times 7^p\) with 2 of \(m = 4\), \(n = 2\), \(p = 2\)
or for 19 600 without sight of the correct factorisation
or a fully correct Venn diagram for \(5A\) and \(2B\)
or an answer of \(2^3 \times 5 \times 7^2\) oe)
| Scheme | Marks |
|---|---|
\((AB =)\, 2^8 \times 5^4 \times 7^6\) or \((A^2 =)\, 2^{10} \times 5^2 \times 7^4\) or \((B^2) = 2^6 \times 5^6 \times 7^8\) or \(\left((AB)^2 =\right) 3.5... \times 10^{20}\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(2^{16} \times 5^8 \times 7^{12}\) | A1 |
| (2) | |
| (4 marks) |
Notes
M1: for a correct product of prime factors for \(AB\) or \(A^2\) or \(B^2\) or for \((AB)^2\) evaluated
A1: for \(2^{16} \times 5^8 \times 7^{12}\) oe
if no other marks are awarded, award SCB1 for \(2^c \times 5^d \times 7^f\) with 2 of \(c = 16\), \(d = 8\), \(f = 12\))