| Exam Board | Edexcel |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 10 |
| 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 question testing basic understanding of sine graph transformations (amplitude 5, frequency 3). Part (a) requires sketching with standard x-intercepts, part (b) involves reading off max/min coordinates from the sketch, and part (c) is a routine equation solving exercise using inverse sine. All parts follow standard textbook procedures with no problem-solving 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 |
| Correct shape of graph | B1 | |
| \(60, 120, 180\) on \(x\)-axis | B1 | |
| \(5, -5\) on \(y\)-axis (may be implied by part (b)) | B1 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \((30°, 5)\); \((150°, 5)\); \((90°, -5)\) — one \(x\)-coordinate correct | B1 | |
| All \(x\)-coordinates correct | B1 | |
| All correct | B1 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(f(x) = 2.5 \Rightarrow \sin 3x° = \frac{1}{2}\) | ||
| \(3x = 30\) \((150, 390, 510)\) — one correct value | B1 | |
| \(3x = (\alpha),\ 180-\alpha,\ 360+\alpha,\ (540-\alpha)\) | M1, M1 | |
| \(x = 10, 50, 130, 170\) | A1 | Ignore extras out of range (4) |
## Question 4:
### Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Correct shape of graph | B1 | |
| $60, 120, 180$ on $x$-axis | B1 | |
| $5, -5$ on $y$-axis (may be implied by part (b)) | B1 | (3) |
### Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $(30°, 5)$; $(150°, 5)$; $(90°, -5)$ — one $x$-coordinate correct | B1 | |
| All $x$-coordinates correct | B1 | |
| All correct | B1 | (3) |
### Part (c)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $f(x) = 2.5 \Rightarrow \sin 3x° = \frac{1}{2}$ | | |
| $3x = 30$ $(150, 390, 510)$ — one correct value | B1 | |
| $3x = (\alpha),\ 180-\alpha,\ 360+\alpha,\ (540-\alpha)$ | M1, M1 | |
| $x = 10, 50, 130, 170$ | A1 | Ignore extras out of range (4) |
---4.
$$\mathrm { f } ( x ) = 5 \sin 3 x ^ { \circ } , \quad 0 \leq x \leq 180$$
\begin{enumerate}[label=(\alph*)]
\item Sketch the graph of $\mathrm { f } ( x )$, indicating the value of $x$ at each point where the graph intersects the $x$ axis.
\item Write down the coordinates of all the maximum and minimum points of $\mathrm { f } ( x )$.
\item Calculate the values of $x$ for which $\mathrm { f } ( x ) = 2.5$\\[0pt]
[P1 June 2002 Question 5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C2 Q4 [10]}}