| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2015 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trigonometric equations in context |
| Type | Sketch transformed/compound trig graph and identify features |
| Difficulty | Moderate -0.8 This is a straightforward C2 trigonometry question requiring basic transformations and solving a simple trig equation. Part (a) involves substituting x=0 and y=0 into a phase-shifted sine function. Part (b) requires isolating sin, finding the principal value, then using CAST diagram to find all solutions in the given range—all standard textbook procedures with no novel insight required. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\left(0, -\frac{\sqrt{3}}{2}\right)\) | B1 | Correct exact \(y\)-intercept; allow \(y=-\frac{\sqrt{3}}{2}\) |
| \((60°, 0)\) and \((240°, 0)\) | B1 | Two correct \(x\)-intercepts |
| \((-120°, 0)\) and \((-300°, 0)\) | B1 | All four correct \(x\)-intercepts; extra answers in range lose third B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\sin(x-60°) = \frac{\sqrt{6}-\sqrt{2}}{4}\) \((= 0.2588)\) | M1 | Divides by 4 first giving correct statement; \(\sin x - \sin60° = \frac{\sqrt{6}-\sqrt{2}}{4}\) is M0 |
| \(x - 60° = 15°\) (or \(165°\) or \(-195°\) or \(-345°\)) | A1 | |
| So \(x = 75°\) or \(225°\) or \(-135°\) or \(-285°\) (allow awrt) | M1 A1 A1 | Adds \(60°\) to previous answer; two correct answers then all four correct answers |
## Question 11:
### Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\left(0, -\frac{\sqrt{3}}{2}\right)$ | B1 | Correct exact $y$-intercept; allow $y=-\frac{\sqrt{3}}{2}$ |
| $(60°, 0)$ and $(240°, 0)$ | B1 | Two correct $x$-intercepts |
| $(-120°, 0)$ and $(-300°, 0)$ | B1 | All four correct $x$-intercepts; extra answers in range lose third B1 |
### Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\sin(x-60°) = \frac{\sqrt{6}-\sqrt{2}}{4}$ $(= 0.2588)$ | M1 | Divides by 4 first giving correct statement; $\sin x - \sin60° = \frac{\sqrt{6}-\sqrt{2}}{4}$ is M0 |
| $x - 60° = 15°$ (or $165°$ or $-195°$ or $-345°$) | A1 | |
| So $x = 75°$ or $225°$ or $-135°$ or $-285°$ (allow awrt) | M1 A1 A1 | Adds $60°$ to previous answer; two correct answers then all four correct answers |
---11.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{3b99072a-cd16-4c1d-9e44-085926a3ba24-16_608_952_267_495}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{center}
\end{figure}
Figure 4 shows a sketch of the curve $C$ with equation $y = \sin \left( x - 60 ^ { \circ } \right) , - 360 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }$
\begin{enumerate}[label=(\alph*)]
\item Write down the exact coordinates of the points at which $C$ meets the two coordinate axes.
\item Solve, for $- 360 ^ { \circ } \leqslant x \leqslant 360 ^ { \circ }$,
$$4 \sin \left( x - 60 ^ { \circ } \right) = \sqrt { 6 } - \sqrt { 2 }$$
showing each stage of your working.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2015 Q11 [8]}}