| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch two trig curves and count intersections/solutions |
| Difficulty | Moderate -0.3 This is a straightforward C2 graphical question requiring sketches of two standard trigonometric functions with simple transformations (horizontal stretch/compression), then counting intersections. The sketching is routine for C2 level, and identifying solutions from a graph requires minimal problem-solving beyond visual inspection. Slightly easier than average due to its procedural nature. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05k Further identities: sec^2=1+tan^2 and cosec^2=1+cot^2 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Sketch showing \(y = \tan \frac{x}{2}\) | B2 | |
| Sketch showing \(y = \sin 2x\) | B2 | |
| (b) 4 solutions | B1 | |
| the graphs intersect at 4 points | B1 | (6) |
**(a)** Sketch showing $y = \tan \frac{x}{2}$ | B2 |
Sketch showing $y = \sin 2x$ | B2 |
**(b)** 4 solutions | B1 |
the graphs intersect at 4 points | B1 | (6)\begin{enumerate}[label=(\alph*)]
\item Sketch on the same diagram the graphs of $y = \sin 2x$ and $y = \tan \frac{x}{2}$ for $x$ in the interval $0 \leq x \leq 360°$. [4]
\item Hence state how many solutions exist to the equation
$$\sin 2x = \tan \frac{x}{2},$$
for $x$ in the interval $0 \leq x \leq 360°$ and give a reason for your answer. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [6]}}