4MA0 Higher January 2018 Paper 3 Q6
6
Diagram NOT accurately drawn
(a) Work out the length of \(QR\).
Give your answer correct to 3 significant figures. (3)
Give your answer correct to 3 significant figures. (3)
(b) Work out the size of angle \(PRQ\).
Give your answer correct to 1 decimal place. (3)
Give your answer correct to 1 decimal place. (3)
The length of a line is 12.4 cm correct to one decimal place.
(c) Write down the upper bound for the length of the line. (1)
| Scheme | Marks |
|---|---|
| \((QR^2 =)\;10.6^2 - 5.9^2\;(= 77.55)\) | M1 |
| \((QR =)\sqrt{10.6^2 - 5.9^2}\) or \(\sqrt{\text{“}77.55\text{”}}\) | M1 |
| 8.81 | A1 |
| (3) |
Notes
M1: for squaring and subtracting.
M1: dep
A1: for 8.806 – 8.81
| Scheme | Marks |
|---|---|
E.g. \(\sin R = \dfrac{5.9}{10.6}\) or \(\cos R = \dfrac{\text{'}8.81\text{'}}{10.6}\) or \(\tan R = \dfrac{5.9}{\text{'}8.81\text{'}}\) | M1 |
| E.g. \(\sin^{-1}\left(\dfrac{5.9}{10.6}\right)\) or \(\cos^{-1}\left(\dfrac{\text{'}8.81\text{'}}{10.6}\right)\) or \(\tan^{-1}\left(\dfrac{5.9}{\text{'}8.81\text{'}}\right)\) | M1 |
| 33.8 | A1 |
| (3) |
Notes
M1: correct trig statement for angle \(PRQ\) or for angle \(QPR\)
M1: complete method to find angle \(PRQ\)
A1: for 33.8 – 33.82125
| Scheme | Marks |
|---|---|
| 12.45 | B1 |
| (1) |
Notes
B1: 12.45 or \(12.44\dot{9}\)