Higher June 2022 Paper 2 Q29
29 The equation of a curve is \(\quad y = x^2 - 18x + 70\)
By completing the square, work out the coordinates of the turning point.
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((x - 9)^2 \ldots\) | M1 | allow \(\left(x - \dfrac{18}{2}\right)^2 \ldots\) may be implied by a grid for \((x - 9)^2\) |
| \((x - 9)^2 - 9^2 + 70\) or \((x - 9)^2 - 81 + 70\) or \((x - 9)^2 - 11\) | M1dep | oe completing the square eg \(\left(x - \dfrac{18}{2}\right)^2 - \left(\dfrac{18}{2}\right)^2 + 70\) |
| (9, \(-11\)) with correct completing the square seen | A1 | eg (9, \(-11\)) with \((x - 9)^2 - 9^2 + 70\) seen SC1 (9, \(-11\)) with correct completing the square not seen |
Additional guidance
| Allow \((x - 9)^2\) to be \((9 - x)^2\) throughout | ||||||||||
| Allow \((x - 9)^2\) to be \((x - 9)(x - 9)\) throughout | ||||||||||
| Condone expression = 0 throughout | ||||||||||
| \((x - 9)^2 = 11\) with \((x - 9)^2 - 11\) (= 0) also seen scores M1M1 Also scores A1 if answer correct | ||||||||||
| \((x - 9)^2 = 11\) without \((x - 9)^2 - 11\) (= 0) also seen Answer correct would still mean M1M0 (or SC1) | M1M0 | |||||||||
| Allow as a slip if completing the square seen but the squared is omitted in a subsequent line | ||||||||||
| eg \((x - 9)^2 - 81 + 70 = (x - 9) - 11\) | M1M1 | |||||||||
| Answer (9, \(-11\)) | A1 | |||||||||
| \((x - 9) - 11\) and answer (9, \(-11\)) | SC1 | |||||||||
| \((x - 9) - 11\) and answer not (9, \(-11\)) | M0M0A0 | |||||||||
| (9, \(-11\)) with no method or from a different method eg calculus | SC1 | |||||||||
| M1 |