1MA0 Higher November 2012 Paper 2 Q22
22
(a) Solve \(2x^2 + 9x - 7 = 0\)
Give your solutions correct to 3 significant figures. (3)
Give your solutions correct to 3 significant figures. (3)
(b) Solve \(\dfrac{2}{y^2} + \dfrac{9}{y} - 7 = 0\)
Give your solutions correct to 3 significant figures. (2)
Give your solutions correct to 3 significant figures. (2)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(x = \dfrac{-9 \pm \sqrt{9^2 - 4 \times 2 \times -7}}{2 \times 2} = \dfrac{-9 \pm \sqrt{137}}{4}\) | 0.676, − 5.18 | 3 | M1 \(\dfrac{-9 \pm \sqrt{9^2 - 4 \times 2 \times -7}}{2 \times 2}\) allow substitution of \(\pm 7\) for \(c\) M1 \(\dfrac{-9 \pm \sqrt{137}}{4}\) A1 answers in ranges 0.67 - 0.68 and − 5.17 to − 5.18 OR M1 \(\left(x + \frac{9}{4}\right)^2\) oe M1 for method leading to \(\pm\sqrt{\dfrac{137}{16}} - \dfrac{9}{4}\) A1 answers in ranges 0.67 - 0.68 and − 5.17 to − 5.18 |
| Working | Answer | Mark | Notes |
|---|---|---|---|
| Put \(y = \dfrac{1}{x}\) and use part (a) Or \(7y^2 - 9y - 2 = 0\) \(y = \dfrac{--9 \pm \sqrt{(-9)^2 - 4 \times 7 \times (-2)}}{2 \times 7}\) \(\dfrac{9 \pm \sqrt{137}}{14}\) | 1.48, − 0.193 | 2 | M1 \(y = \dfrac{1}{x}\) or \(x = \dfrac{1}{y}\) A1 (ft) answers in range 1.47 - 1.48 and − 0.19 to − 0.194 OR M1 fully correct method which leads to \(7y^2 - 9y - 2 = 0\) or \(-7y^2 + 9y + 2 = 0\) with correct method to solve (condone sign errors in substitution) A1 (ft) answers in range 1.47 - 1.48 and − 0.19 to − 0.194 |