| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch single standard trig graph (sin/cos/tan) |
| Difficulty | Moderate -0.8 This is a straightforward C2 trigonometry question requiring basic graph sketching, finding intercepts by substituting x=0 and y=0, and solving a standard cosine equation using the CAST diagram. All parts use routine techniques with no problem-solving insight needed, making it easier than average. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Shape | B1 | (2 marks) |
| Position | B1 | |
| (b) \((0, \frac{1}{\sqrt{2}})\), \((\frac{\pi}{4}, 0)\), \((\frac{5\pi}{4}, 0)\) | B1, B1, B1 | (3 marks) |
| (c) \((x + \frac{\pi}{4}) = \frac{\pi}{3}\) | B1 | |
| Other value \((2\pi - \frac{\pi}{3} - \frac{\pi}{4})\) \(\frac{5\pi}{3}\) | M1 | |
| Subtract \(\frac{\pi}{4}\) \(x = \frac{\pi}{12}, x = \frac{17\pi}{12}\) | M1, A1 | (4 marks) |
**(a)** Shape | B1 | (2 marks)
Position | B1 |
**(b)** $(0, \frac{1}{\sqrt{2}})$, $(\frac{\pi}{4}, 0)$, $(\frac{5\pi}{4}, 0)$ | B1, B1, B1 | (3 marks)
**(c)** $(x + \frac{\pi}{4}) = \frac{\pi}{3}$ | B1 |
Other value $(2\pi - \frac{\pi}{3} - \frac{\pi}{4})$ $\frac{5\pi}{3}$ | M1 |
Subtract $\frac{\pi}{4}$ $x = \frac{\pi}{12}, x = \frac{17\pi}{12}$ | M1, A1 | (4 marks)The curve $C$ has equation $y = \cos \left( x + \frac{\pi}{4} \right)$, $0 \leq x \leq 2\pi$.
\begin{enumerate}[label=(\alph*)]
\item Sketch $C$. [2]
\item Write down the exact coordinates of the points at which $C$ meets the coordinate axes. [3]
\item Solve, for $x$ in the interval $0 \leq x \leq 2\pi$, $\cos \left( x + \frac{\pi}{4} \right) = 0.5$, giving your answers in terms of $\pi$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q3 [9]}}