4MA0 Higher June 2014 Paper 3 Q18
18 A trapezium ABCD has an area of \(5\sqrt{6}\) cm2.
Diagram NOT accurately drawn
\(AB = 4\) cm.
\(BC = \sqrt{3}\) cm.
\(DC = k\) cm.
Calculate the value of \(k\), giving your answer in the form \(a\sqrt{b} - c\) where \(a\), \(b\) and \(c\) are positive integers.
Show each step in your working.
(3)
| Scheme | Marks |
|---|---|
| \((A =)\ 0.5 \times (4 + k) \times \sqrt{3}\ (= 5\sqrt{6})\) oe | M1 |
\(k + 4 = \dfrac{10\sqrt{6}}{\sqrt{3}}\) \((k =)\ 2 \times \dfrac{5\sqrt{6}}{\sqrt{3}} - 4\) or \((k =)\ \dfrac{5\sqrt{6} - 2\sqrt{3}}{0.5\sqrt{3}}\) oe | M1 |
| \((k =)\ 10\sqrt{2} - 4\) | A1 |
| (3 marks) |
Notes
M1: \(4\sqrt{3} + 0.5(k - 4) \times \sqrt{3}\) oe
M1: correctly isolating k
A1: Accept \(2(5\sqrt{2} - 2)\) but don’t accept \(10\sqrt{2} - 4\) followed by \(5\sqrt{2} - 2\)