Higher June 2025 Paper 2 Q18
18 Lines \(AB\), \(BC\), \(CD\) and \(AD\) form two triangles.
Not drawn accurately
Work out the length of \(AD\). [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| 116 | B1 | may be seen in \(CXB\) or \(AXD\), where \(X\) is the common vertex |
| \(9.6^2 + 2.8^2 - 2 \times 9.6 \times 2.8 \times \cos\) (their 116) or [123.5, 123.7] | M1 | oe \(0 \lt\) their \(116 \lt 180\) eg \(92.16 + 7.84 - 53.76 \cos\) (their 116) accept [−0.44, −0.438] for cos 116 |
| \(\sqrt{\text{their } [123.5, 123.7]}\) | M1dep | oe eg \(\sqrt{9.6^2 + 2.8^2 - 2 \times 9.6 \times 2.8 \times \cos(\text{their } 116)}\) accept [−0.44, −0.438] for cos 116 |
| [11.1, 11.1221] | A1 | accept 11 with B1M2 awarded |
Additional guidance
Up to B1M1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts