| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2017 |
| Session | June |
| Marks | 4 |
| Topic | Standard trigonometric equations |
| Type | Transformed argument solving |
| Difficulty | Moderate -0.8 This is a straightforward transformed argument equation requiring only inverse tan calculation and period adjustment. Students apply arctan(0.1), subtract 10°, then add 180° for the second solution—purely mechanical with no conceptual challenge beyond basic trigonometric equation solving. |
| Spec | 1.05o Trigonometric equations: solve in given intervals |
**Question 3: Solve $\tan(\theta + 10°) = 0.1$**
- $\theta = \tan^{-1}0.1 - 10°$ **M1** Attempt $\theta$ using correct order of operations
- Obtain at least one correct value **A1** inc $-4.29$
- Attempt at least one value of $\theta$ in range **M1** allow incorrect principal angle $+ 180°$
- $\theta = (-4.29°),\ 175.7°,\ 355.7°$ **A1** Obtain both angles, and no others in range
If using $\tan(A+B)$ approach:
- **B1** for correct identity
- **B1** for correct expression for $\tan\theta$
- **M1** for attempting $\theta$ (in range) from $\tan\theta = k$
- **A1** for both angles, and no others in range
**Total: 4 marks**3 Solve the equation $\tan \left( \theta + 10 ^ { \circ } \right) = 0.1$ in the range $0 ^ { \circ } \leqslant \theta \leqslant 360 ^ { \circ }$.
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2017 Q3 [4]}}