Higher November 2023 Paper 6 Q15

OCRHigherCurrent spec5 marksSolving Quadratics

(a) Sasha and Taylor are asked to find how many solutions the equation \(5(x + 2)^2 = 45\) has.

Here is Sasha’s answer.	Here is Taylor’s answer.
\(5(x + 2)^2 = 45\) \((x + 2)^2 = 9\) \(x + 2 = 3\) \(x = 1\) There is one solution.	\(5(x + 2)^2 = 45\) \((x + 2)^2 = 9\) \(x + 2 = 3\) or \(x + 2 = -3\) \(x = 1\) or \(x = -5\) There are two solutions.

Decide who is correct, Sasha or Taylor, and give the reason for your decision. [1]

(b) Solve this equation algebraically.
Give your answers correct to 2 decimal places.
You must show your working.

\(x^2 - 5x + 3 = 0\) [4]

Mark scheme (a)

Answer	Marks	Part marks and guidance
Taylor and square root of 9 is 3 and −3 oe	1		Accept: Taylor because Sasha only used the positive square root; Taylor because verification of −5. Do not accept: Two solutions expected for a quadratic; Sasha because …

Mark scheme (b)

Answer	Marks	Part marks and guidance
4.30 and [0].70 with correct algebraic working	4		“Correct working” requires evidence of at least M2
		M2 for correct substitution into the formula, eg. \(\dfrac{-(-5) \pm \sqrt{(-5)^2 - 4[\times 1] \times 3}}{2[\times 1]}\) oe allowing one error or for solving by completing the square eg. \(\left(x - \frac{5}{2}\right)^2 - \left(\frac{5}{2}\right)^2 + 3 = 0\) oe and \(x = \pm\sqrt{(-3) + \left(\frac{5}{2}\right)^2} + \frac{5}{2}\) oe or better or M1 for correct substitution into the formula, allowing two errors, or for completing the square eg. \(\left(x - \frac{5}{2}\right)^2 - \left(\frac{5}{2}\right)^2 + 3\) [= 0] oe or better	For oe allow better up to \(\frac{5 \pm \sqrt{25 - 12}}{2}\) but do not allow \(\frac{5 \pm \sqrt{13}}{2}\) Condone \(5^2\) for \((-5)^2\)
		and A1 for 4.30 or [0].70 nfww or for both solutions correct nfww but to more than 2 dp, to just 1 dp or in exact form If 0 scored, instead award SC1 for both answers correct or to more than 2 dp, to just 1 dp or in exact form with no working or insufficient working	eg. 4.30277… and 0.69722…. 4.3 and 0.7, \(\frac{5 \pm \sqrt{13}}{2}\)