| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2008 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trigonometric equations in context |
| Type | Solve shifted trig equation |
| Difficulty | Moderate -0.8 Both parts are routine trigonometric equation solving requiring only standard techniques: (a) involves a simple phase shift with a common exact value, (b) requires accounting for the coefficient 3 and finding multiple solutions in the range. These are textbook exercises with no problem-solving insight needed, making them easier than average A-level questions. |
| Spec | 1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | \(\alpha = 45°\) | B1 |
| \(180 - \alpha\); add 20 (for at least one angle) | M1, M1 | |
| \(65°,\ 155°\) | A1 (4) | Extra solutions in range: loses A mark; extra solutions outside range: ignore |
| (b) | \(\beta = 120°\) or \(240°\) | B1 |
| \(360 - \beta\); \(360 + \beta\) (or \(120 +\) an angle that has been divided by 3) | M1, M1 | |
| Dividing by 3 (for at least one angle) | M1 | |
| \(40°,\ 80°,\ 160°,\ 200°,\ 280°,\ 320°\) — first A1: at least 3 correct | A1 A1 (6) | Extra solutions in range: loses final A mark; extra solutions outside range: ignore |
## Question 9:
**(a)** | $\alpha = 45°$ | B1 | This mark can be implied by an answer of 65 |
| $180 - \alpha$; add 20 (for at least one angle) | M1, M1 | |
| $65°,\ 155°$ | A1 (4) | Extra solutions in range: loses A mark; extra solutions outside range: ignore |
**(b)** | $\beta = 120°$ or $240°$ | B1 | This mark can be implied by an answer of 40 or 80; could be achieved by working with 60, using $180 - 60$ and/or $180 + 60$ |
| $360 - \beta$; $360 + \beta$ (or $120 +$ an angle that has been divided by 3) | M1, M1 | |
| Dividing by 3 (for at least one angle) | M1 | |
| $40°,\ 80°,\ 160°,\ 200°,\ 280°,\ 320°$ — first A1: at least 3 correct | A1 A1 (6) | Extra solutions in range: loses final A mark; extra solutions outside range: ignore |9. Solve, for $0 \leqslant x < 360 ^ { \circ }$,
\begin{enumerate}[label=(\alph*)]
\item $\quad \sin \left( x - 20 ^ { \circ } \right) = \frac { 1 } { \sqrt { 2 } }$
\item $\cos 3 x = - \frac { 1 } { 2 }$
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 2008 Q9 [10]}}