Higher January 2022 Paper 1R Q22
22 The diagram shows triangle \(ABC\)
Diagram NOT accurately drawn
| \(c = 11.5\) | correct to one decimal place |
| \(x = 80\) | correct to the nearest whole number |
| \(y = 75\) | correct to the nearest whole number |
Calculate the upper bound for the value of \(b\)
Show your working clearly.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
| 11.45 or 11.55 or 79.5 or 80.5 or 74.5 or 75.5 | B1 |
| 180 – (74.5 + 79.5) (= 26) | M1 |
\(\dfrac{(AC)}{\sin(26)} = \dfrac{11.55}{\sin(74.5)}\) oe or \(\dfrac{(AC)}{\sin(180 - 74.5 - 79.5)} = \dfrac{11.55}{\sin(74.5)}\) | M1 |
| Working required Answer: 5.25 | A1 |
| (4) | |
| (4 marks) |
Notes
B1: Accept
\(11.54\dot{9}\) for 11.55
\(80.4\dot{9}\) for 80.5
\(75.4\dot{9}\) for 75.5
M1: for a correct calculation to find the upper bound of angle \(B\)
NB 180° – (\(LB\) of 75° + \(LB\) of 80°)
M1: for substituting the correct bounds into the sine rule
\(\dfrac{(YZ)}{\sin(\text{``}{26}\text{''})} = \dfrac{UB_1}{\sin(LB_2)}\) oe where
\(11.5 \lt UB_1 \leqslant 11.55\) and
\(74.5 \leqslant LB_2 \lt 75\)
A1: awrt 5.25 from correct working