Higher June 2025 Paper 2 Q10
10
Not drawn accurately
Use trigonometry to work out the value of \(x\).
You must show your working. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1: uses or states tan | ||
| tan stated or used | M1 | implied by [0.726, 0.73] or [1.376, 1.4] |
| \(\tan 36 = \dfrac{x}{4}\) or \(4 \times \tan 36\) or \(\tan 54 = \dfrac{4}{x}\) or \(\dfrac{4}{\tan 54}\) | M1dep | oe accept [0.726, 0.73] for tan 36 accept [1.376, 1.4] for tan 54 |
| [2.9, 2.91] with M2 awarded | A1 | accept 3 with M2 awarded |
| Alternative method 2: works out hypotenuse first | ||
| (hypotenuse \(=\)) \(\dfrac{4}{\sin 54}\) or \(\dfrac{4}{\cos 36}\) or 4.9(…) | M1 | oe accept [0.8, 0.81] for sin 54 or cos 36 |
| \(\sqrt{(\text{their } 4.9(\ldots))^2 - 4^2}\) or \(\sqrt{[8, 8.45]}\) or their 4.9(…) \(\times \sin 36\) or their 4.9(…) \(\times \cos 54\) | M1dep | oe |
| [2.9, 2.91] with M2 awarded | A1 | accept 3 with M2 awarded |
Additional guidance
| Alt 1 SOHCAHTOA with TOA selected (eg circled) | M1 |
| [2.9, 2.91] with no working | M0M0A0 |
| [2.9, 2.91] from accurate/scale drawing only | M0M0A0 |