Foundation November 2023 Paper 1 Q21
21
(a) A student is using trigonometry to work out an angle, \(B\), in a right-angled triangle.
They tell the teacher that \(\sin B = \dfrac{5}{4}\).
Explain why this student must be wrong. [1]
(b) Here is a right-angled triangle.
Not to scale
Work out the value of \(x\). [3]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Eg sin must be \(\leqslant 1\) their opp is \(\gt\) than their hyp | 1 | See appendix | |
Appendix
Exemplar responses for Q21a
| Response | Mark |
|---|---|
| The fraction cannot be bigger than 1 | 1 |
| The numerator cannot be bigger than the denominator | 1 |
| Not using degrees with sin and putting B in the wrong place | 0 |
| The student must be wrong because the question said so | 0 |
| That is upside down \(\frac{4}{5}\) | 0 |
| It’s the wrong calculation | 0 |
| The fraction cannot be bigger than 1 otherwise it’s a reflex angle in a triangle which is not possible | 0 |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 53.1[3…] | 3 | M2 for \(\cos^{-1} \frac{24}{40}\) or M1 for \(\cos\) [\(x\)] [=] \(\frac{24}{40}\) or 0.6 | Accept 53 after M1 or M2 scored Accept full methods using Pythagoras or sin or tan |