| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trigonometric equations in context |
| Type | Solve shifted trig equation |
| Difficulty | Moderate -0.8 This is a straightforward C2 trigonometry question requiring basic equation solving with standard techniques: (a) uses exact values and angle shifts, (b) uses double angles and calculator work. Both are routine applications with no problem-solving insight needed, making it easier than average but not trivial since students must handle the domain restrictions and find all solutions correctly. |
| Spec | 1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((x + 10 =)\ 60\ \alpha\) | B1 | |
| \(120\) | M1 | \(180 - \alpha\) or \(\pi - \alpha\); must subtract from 180 before subtracting 10 |
| \(x = 50\), \(x = 110\) (or 50.0 and 110.0) | M1 A1 | M: subtract 10. Total: 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((2x =)\ 154.2\ \beta\) (allow a.w.r.t. 154 or a.w.r.t. 2.69 radians) | B1 | |
| \(205.8\) | M1 | \(360 - \beta\) or \(2\pi - \beta\); must subtract from 360 before dividing by 2 |
| \(x = 77.1\), \(x = 102.9\) | M1 A1 | M: divide by 2. Total: 4 |
## Question 5:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(x + 10 =)\ 60\ \alpha$ | B1 | |
| $120$ | M1 | $180 - \alpha$ or $\pi - \alpha$; must subtract from 180 before subtracting 10 |
| $x = 50$, $x = 110$ (or 50.0 and 110.0) | M1 A1 | M: subtract 10. **Total: 4** |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(2x =)\ 154.2\ \beta$ (allow a.w.r.t. 154 or a.w.r.t. 2.69 radians) | B1 | |
| $205.8$ | M1 | $360 - \beta$ or $2\pi - \beta$; must subtract from 360 before dividing by 2 |
| $x = 77.1$, $x = 102.9$ | M1 A1 | M: divide by 2. **Total: 4** |5. Solve, for $0 \leqslant x \leqslant 180 ^ { \circ }$, the equation
\begin{enumerate}[label=(\alph*)]
\item $\quad \sin \left( x + 10 ^ { \circ } \right) = \frac { \sqrt { } 3 } { 2 }$,
\item $\cos 2 x = - 0.9$, giving your answers to 1 decimal place.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2005 Q5 [8]}}