4MA0 Higher January 2012 Paper 4 Q9
9
Diagram NOT accurately drawn
\(ABCD\) is a rhombus.
The diagonals \(AC\) and \(BD\) cross at the point \(E\).
\(AE = CE\) = 6 cm.
\(BE = DE\) = 4 cm.
Angle \(AEB = 90^\circ\)
(a) Work out the area of the rhombus. (3)
(b) Work out the length of \(AB\).
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
| Scheme | Marks |
|---|---|
| Complete, correct expression which, if correctly evaluated, gives 48 eg \(4 \times \frac{1}{2} \times 6 \times 4\), \(2 \times \frac{1}{2} \times 12 \times 4\), \(\frac{1}{2} \times 12 \times 8\) | M2 |
| 48 | A1 |
| (3) |
Notes
M2: M1 for correct expression for area of one relevant triangle
eg \(\frac{1}{2} \times 6 \times 4\), \(\frac{1}{2} \times 6 \times 4 \sin 90^\circ\), \(\frac{1}{2} \times 8 \times 6\), \(\frac{1}{2} \times 12 \times 4\)
A1: cao
Apart from Questions 3, 13(b) and 17(f) (where the mark scheme states otherwise), the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
| Scheme | Marks |
|---|---|
| \(4^2 + 6^2 = 16 + 36 = 52\) | M1 |
| \(\sqrt{4^2 + 6^2}\) | M1 |
| 7.21 | A1 |
| (3) | |
| (Total 6 marks) |
Notes
M1: for squaring and adding
M1: (dep) for square root
A1: for answer which rounds to 7.21 (7.211102…)