1MA0 Higher June 2013 Paper 1 Q20
20
Diagram NOT accurately drawn
\(ABCD\) is a square with a side length of \(4x\)
\(M\) is the midpoint of \(DC\).
\(N\) is the point on \(AD\) where \(ND = x\)
\(BMN\) is a right-angled triangle.
Find an expression, in terms of \(x\), for the area of triangle \(BMN\).
Give your expression in its simplest form. (4)
| Answer | Mark | Notes |
|---|---|---|
| \(5x^2\) | 4 | M1 for \(4x \times 4x\) M1 for \((2x \times 4x)/2\) or \((2x \times x)/2\) or \((3x \times 4x)/2\) M1(dep M2) for \(\text{``}16x^2\text{''} - \text{``}4x^2\text{''} - \text{``}x^2\text{''} - \text{``}6x^2\text{''}\) A1 for \(5x^2\) OR M1 for \(\sqrt{(2x)^2 + (4x)^2}\) \((= \sqrt{20x^2} = \sqrt{20}\,x)\) M1 for \(\sqrt{(x)^2 + (2x)^2}\) \((= \sqrt{5x^2} = \sqrt{5}\,x)\) M1(dep M2) for \(\dfrac{\text{``}\sqrt{5}\,x\text{''} \times \text{``}\sqrt{20}\,x\text{''}}{2}\) \(\left(= \dfrac{\sqrt{100}}{2}x^2\right)\) A1 for \(5x^2\) |