June 2022 Paper 2 Q11
11 Here is a right-angled triangle.
Not drawn accurately
You are given that \(\quad a \gt 5\)
Use trigonometry to work out the range of values of \(x\). [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \((0 \lt)\; x \lt 60\) or \((0 \leqslant)\; x \lt 60\) | B2 | B1 \(\cos x \gt \dfrac{5 - 3}{4}\) or \(\cos x \gt \dfrac{2}{4}\) or \(\cos x \gt \dfrac{1}{2}\) or \(x \lt \cos^{-1}\dfrac{1}{2}\) or \(a \lt x \lt 60\) where \(a\) is a non-zero value less than 60 or \(b \leqslant x \lt 60\) where \(b\) is a value less than 60 SC1 \((0 \lt)\; x \leqslant 60\) or \((0 \leqslant)\; x \leqslant 60\) |
Additional guidance
| Answer \((0 \lt)\; x \lt 60\) (can ignore working lines) | B2 |
| \(60 \gt x \gt 0\) is equivalent to \(0 \lt x \lt 60\) etc | |
| \(0 \lt x \lt 60\) is equivalent to the two inequalities \(x \gt 0 \quad x \lt 60\) etc | B2 |
| Allow decimals for B1 responses eg \(\cos x \gt 0.5\) | B1 |
| For B1 condone \(\cos x = \gt \dfrac{1}{2}\) for \(\cos x \gt \dfrac{1}{2}\) | |
| \(\cos x \gt \dfrac{1}{2}\) followed by \(x \gt \cos^{-1}\dfrac{1}{2}\) | B1 |
| Only \(x \gt \cos^{-1}\dfrac{1}{2}\) | B0 |
| (0, 60) | B2 |
| [0, 60) | B2 |
| (0, 60] | SC1 |
| [0, 60] | SC1 |