Higher June 2023 Paper 3 Q15
15
(a) Factorise \(a^2 - b^2\) (1)
(b) Show that \(2^{40} - 1\) is the product of two consecutive odd numbers. (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| \((a - b)(a + b)\) | B1 | for \((a - b)(a + b)\) oe |
| Answer | Mark | Mark scheme |
|---|---|---|
| Relationship shown | M1 | for factorising the expression, eg \((2^{20} - 1)(2^{20} + 1)\) or for \((2^{40} =)\ (2^{20})^2\) |
| C1 | for explanation, eg \(2^{20}\) is even so \(2^{20} - 1\) and \(2^{20} + 1\) are odd (leading to conclusion) |
Additional guidance
Note that 1048575 and 1048577 earns 2 marks as an alternative approach