Foundation January 2021 Paper 2R Q20
20 Solve \(\;x^2 - 21x + 20 = 0\)
Show your working clearly.
(3)
| Scheme | Marks |
|---|---|
eg \((x \pm 20)(x \pm 1)\) or \(\dfrac{-(-21) \pm \sqrt{(-21)^2 - 4 \times 1 \times 20}}{2 \times 1}\) or \(\left(x - \dfrac{21}{2}\right)^2 - \left(\dfrac{21}{2}\right)^2 + 20 = 0\) | M1 |
\((x - 20)(x - 1)\) or eg \(\dfrac{21 \pm \sqrt{441 - 80}}{2}\) or \(\dfrac{21 \pm \sqrt{361}}{2}\) or \(\dfrac{21 \pm 19}{2}\) or \(x = \pm\sqrt{\dfrac{361}{4}} + \dfrac{21}{2}\) oe | M1 |
| Working required Answer: 1, 20 | A1 |
| (3) | |
| (3 marks) |
Notes
M1: If factorising, allow brackets which expanded give 2 out of 3 terms correct – if using formula or completing the square allow one sign error and some simplification – allow as far as eg \(\dfrac{21 \pm \sqrt{441 - 80}}{2}\) or eg \(\left(x - \dfrac{21}{2}\right)^2 - \dfrac{361}{4} = 0\) oe
M1: dep on M1
for correct factorisation,
or a correct expression for \(x\) if completing the square.
or a correct substitution into quadratic formula with some processing.
A1: for both correct values, dep on 1st M1 with no incorrect working.