Higher June 2019 Paper 1 Q18
18 Here is an identity.
\[x^2 - y^2 \equiv (x + y)(x - y)\](a) Use the identity to work out the value of \(\quad 193^2 - 7^2\)
You must show your working. [2 marks]
(b) Factorise \(\quad 100a^2 - 81b^2\) [1 mark]
| Answer | Mark | Comments |
|---|---|---|
| (193 + 7)(193 – 7) or (200)(186) or 200 (\(\times\)) 186 | M1 | either order |
| \((200)(186) = 37\,200\) or \(200\ (\times)\ 186 = 37\,200\) | A1 |
Additional guidance
| 37 200 with correct method not seen | M0A0 |
| 37 200 from 37 249 – 49 only | M0A0 |
| 37 200 from (200)(186) or 200 (\(\times\)) 186 and 37 249 – 49 also given | M1A1 |
| Do not award M1 for a ‘misread’ eg (193 + 2)(193 – 2) | M0A0 |
| Answer | Mark | Comments |
|---|---|---|
| \((10a + 9b)(10a - 9b)\) or \((9b + 10a)(10a - 9b)\) | B1 | either order |
Additional guidance
| Condone missing final bracket, eg \((10a + 9b)(10a - 9b\) | B1 |
| Condone a multiplication sign eg \((10a + 9b) \times (10a - 9b)\) | B1 |