4MA0 Higher January 2015 Paper 3 Q22
22
Diagram NOT accurately drawn
The diagram shows a triangle ABC.
\(AB = (2x + 1)\) cm, \(AC = (2x - 1)\) cm and \(BC = 2\sqrt{7}\) cm.
Angle \(BAC = 60^\circ\)
Work out the value of \(x\).
Show clear algebraic working.
(3)
| Scheme | Marks |
|---|---|
\((2\sqrt{7})^2 = (2x + 1)^2 + (2x - 1)^2 - 2(2x + 1)(2x - 1)\cos 60^\circ\) or \(\cos 60 = \dfrac{(2x + 1)^2 + (2x - 1)^2 - (2\sqrt{7})^2}{2(2x + 1)(2x - 1)}\) | M1 |
\(28 = 4x^2 + 4x + 1 + 4x^2 - 4x + 1 - 2(4x^2 - 1)\dfrac{1}{2}\) or (e.g.) \(28 = 4x^2 + 4x + 1 + 4x^2 - 4x + 1 - 4x^2 + 1\) or \(28 = 4x^2 + 3\) or \(25 = 4x^2\) | M1 |
| \(2\frac{1}{2}\) | A1 |
| (3 marks) |
Notes
M1: Accept 5.29(1502622...) in place of \(2\sqrt{7}\) rounded or truncated to at least 3SF
Condone \(2\sqrt{7}^2\)
M1: Correct simplification as far as the first expression shown, or better.
A1: oe dep on at least M1