4MA0 Higher June 2017 Paper 4R Q17
17 Solve \(\quad 11x^2 - 3x - 5 = 0\)
Show your working clearly.
Give your solutions correct to 2 decimal places.
(3)
| Scheme | Marks |
|---|---|
\(\dfrac{3 \pm \sqrt{9 + 220}}{22}\) or \(\dfrac{3 \pm \sqrt{9 + 220}}{2 \times 11}\) or \(\dfrac{3 \pm \sqrt{(-3)^2 - -220}}{2 \times 11}\) or \(\dfrac{3 \pm \sqrt{(-3)^2 - -220}}{22}\) NB: denominator must be 2×11 or 22 and there must be evidence for correct order of operations in the numerator Do not accept sign error or omission of brackets | M2 |
| 0.82 and −0.55 | A1 |
| (3) | |
| (3 marks) |
Notes
M2: Or for
\(\dfrac{- -3 \pm \sqrt{(-3)^2 - 4 \times 11 \times -5}}{2 \times 11}\) (allow partial correct evaluation)
and \(\dfrac{3 \pm \sqrt{229}}{22}\)
If not M2 then
M1 for
\(\dfrac{- -3 \pm \sqrt{(-3)^2 - 4(11)(-5)}}{2 \times 11}\)
Condone one sign error in substitution;
Condone omission of brackets
Allow partial correct evaluation
A1: for awrt 0.82 and awrt −0.55
Award M2 A1 for awrt 0.82, −0.55 with sufficient correct working that would gain at least M1
Alternative scheme
| Scheme | Marks |
|---|---|
| \(11\left[\left(x - \dfrac{3}{22}\right)^2 - \dfrac{229}{484}\right]\) oe | M1 |
| \(\dfrac{3}{22} \pm \sqrt{\dfrac{229}{484}}\) oe | M1 |
| 0.82 and −0.55 | A1 |
Notes
A1: for awrt 0.82 and awrt −0.55
Award M2 A1 for awrt 0.82, −0.55 with sufficient correct working that would gain at least M1