Foundation November 2020 Paper 2R Q26
26 The diagram shows four congruent right-angled triangles \(ABJ\), \(BCI\), \(CDH\) and \(DEG\).
The diagram also shows the straight line \(ABCDEF\).
Diagram NOT accurately drawn
\(AJ\) = 15 cm
Angle \(BAJ\) = 35°
\(AF\) = 80 cm
Work out the length of \(EF\).
Give your answer correct to 3 significant figures.
(5)
| Scheme | Marks |
|---|---|
| \(\cos 35^\circ = \dfrac{15}{AB}\) or \(\sin 55^\circ = \dfrac{15}{AB}\) | M1 |
| \((AB =) \dfrac{15}{\cos 35^\circ }\) (= 18.3) or \((AB =) \dfrac{15}{\sin 55^\circ }\) (= 18.3) | M1 |
| ‘18.3’ × 4 (= 73.2) | M1 |
| 80 − ‘18.3’ × 4 or 80 – ‘73.2’ | M1 |
| 6.75 | A1 |
| (5) | |
| (5 marks) |
Notes
M1: NB 18.3(116...)
M1: dep 1st M1
A1: accept 6.75 – 6.8
Alternative [do not mix and match with above MS]
| Scheme | Marks |
|---|---|
| 15 × 4 (= 60) | M1 |
| \(\cos 35^\circ = \dfrac{\text{‘}60\text{’}}{AE}\) or \(\sin 55^\circ = \dfrac{\text{‘}60\text{’}}{AE}\) | M1 |
| \((AE =) \dfrac{\text{‘}60\text{’}}{\cos 35^\circ }\) (= 73.2) or \((AE =) \dfrac{\text{‘}60\text{’}}{\sin 55^\circ }\) (= 73.2) | M1 |
| 80 – ‘73.2’ | M1 |
| Answer: 6.75 | A1 |
M1 (3rd): dep 1st M1
A1: accept 6.75 – 6.8