4MA0 Higher June 2011 Paper 4 Q22
22
Diagram NOT accurately drawn
The diagram shows a cuboid \(ABCDEFGH\).
\(AB\) = 5cm
\(BC\) = 7cm
\(AE\) = 3cm
(a) Calculate the length of \(AG\).
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
(b) Calculate the size of the angle between \(AG\) and the plane \(ABCD\).
Give your answer correct to 1 decimal place. (2)
Give your answer correct to 1 decimal place. (2)
| Scheme | Marks |
|---|---|
| (\(AC^2\)=) \(5^2 + 7^2\) (=74) | M1 |
(\(AG^2\)=) “74” + \(3^2\) (=83) (\(AG\) =) \(\sqrt{\text{“}83\text{”}}\) | M1 ft |
| 9.11 | A1 |
| (3) |
Notes
M1: or \(AC\) = 8.6.. or (\(BG^2\)) = \(3^2 + 7^2\) (=58) or (\(AF^2\)) = \(3^2 + 5^2\)
M1 ft: (dep on M1) (\(AG^2\)) = “58” + \(5^2\) (=83)
M1M1 for \(\sqrt{(5^2 + 7^2 + 3^2)}\)
A1: awrt 9.11
Apart from questions 5b, 8, 15d, 20b, 21b, 23, 24b (where the mark scheme states otherwise) the correct answer, unless clearly obtained by an incorrect method, should be taken to imply correct working.
| Scheme | Marks |
|---|---|
| \(\sin\theta = 3 / \sqrt{\text{“}83\text{”}}\) | M1 |
| 19.2 | A1 |
| (2) | |
| (Total 5 marks) |
Notes
M1: or \(\cos\theta = \sqrt{\text{“}74\text{”}} / \sqrt{\text{“}83\text{”}}\) or \(\tan\theta = 3 / \sqrt{\text{“}74\text{”}}\)
or \(\cos\theta = \dfrac{\text{“}74\text{”} + \text{“}83\text{”} - 9}{2 \times \sqrt{\text{“}74\text{”}} \times \sqrt{\text{“}83\text{”}}}\)
A1: awrt 19.2 or 160.8