1MA0 Higher November 2012 Paper 2 Q15
15 \(ABCD\) is a trapezium.
Diagram NOT accurately drawn
\(AD = 10\) cm
\(AB = 9\) cm
\(DC = 3\) cm
Angle \(ABC\) = angle \(BCD = 90^\circ\)
Calculate the length of \(AC\).
Give your answer correct to 3 significant figures. (5)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(9 - 3 = 6\) \(10^2 - 6^2 = 64\) \(BC = 8\) \(AC^2 = 9^2 + 8^2 = 145\) | 12.0 | 5 | M2 \(10^2 - (9 - 3)^2\) (=64) or \(BC = 8\) (M1 \(9 - 3\) (= 6) may be seen on diagram) M1 (indep) \(9^2 + \)‘\(BC\)’\(^2\) where \(BC\) is a numerical value M1 (dep on previous M1) \(\sqrt{81 + \text{‘64’}}\) A1 12.0 – 12.042 |