1MA0 Higher November 2012 Paper 2 Q25
*25 The diagram shows the triangle \(PQR\).
Diagram NOT accurately drawn
\(PQ = x\) cm
\(PR = 2x\) cm
Angle \(QPR = 30^\circ\)
The area of triangle \(PQR = A\) cm\(^2\)
Show that \(x = \sqrt{2A}\) (3)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(A = \frac{1}{2} \times x \times 2x \times \sin 30^\circ\) \(A = \frac{1}{2} \times 2x^2 \times 0.5\) OR Height \(= 2x\sin 30^\circ = x\) \(A = \dfrac{x \times x}{2} = \dfrac{x^2}{2}\) OR Height \(= x\sin 30 = \dfrac{x}{2}\) \(A = \frac{1}{2} \times 2x \times \dfrac{x}{2} = \dfrac{x^2}{2}\) | \(x = \sqrt{2A}\) shown | 3 | M1 (\(A =\)) \(\frac{1}{2} \times x \times 2x \times \sin 30^\circ\) A1 \(A = x^2 \times 0.5\) or \(A = \dfrac{x^2}{2}\) C1 for completion with all steps shown OR M1 height \(= 2x\sin 30\) (\(= x\)) A1 \(A = x^2 \times 0.5\) or \(A = \dfrac{x^2}{2}\) C1 for completion with all steps shown OR M1 for height \(= x\sin 30\) (\(= \frac{x}{2}\)) A1 \(A = x^2 \times 0.5\) or \(A = \dfrac{x^2}{2}\) C1 for completion with all steps shown |