Higher June 2023 Paper 6 Q10
10
(a) Show that 95 is not a prime number. [1]
(b)
(i) 2000 and 8750 are written below as the product of their prime factors.\[2000 = 2^4 \times 5^3\]\[8750 = 2 \times 5^4 \times 7\]Find the highest common factor (HCF) of 2000 and 8750. [2]
(ii) Write \(2 \times 10^{12}\) as a product of its prime factors. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Divisible by 5 or divisible by 19 or 95 ÷ 5 = 19 or 95 ÷ 19 = 5 or 5 × 19 | 1 | Accept factor tree showing 95, 5 and 19 Accept 5 and 19 are factors of 95 Do not accept 5 and 19 are multiples of 95 | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (b)(i) | |||
| 250 | 2 | B1 for 2 [×] \(5^3\) | Venn diagram on its own scores 0 unless 2 and \(5^3\) selected |
| (b)(ii) | |||
| \(2^{13} \times 5^{12}\) | 2 | M1 for \(10^k = 2^k \times 5^k\) where \(k\) is a positive integer implied by final answer of the form \(2^{k+1} \times 5^k\) or SC1 for \(2^{12} \times 5^{12}\) | e.g. 10 = 2 × 5 |