| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Curve Sketching |
| Type | Trigonometric curve intersections |
| Difficulty | Moderate -0.8 This is a straightforward curve sketching question requiring students to sketch two sine curves (one a horizontal translation of the other) and identify intersection points graphically. The transformations are basic, and finding intersections from a sketch requires minimal problem-solving beyond recognizing symmetry and periodicity. This is easier than average for A-level, being a routine C2 exercise with clear visual guidance. |
| Spec | 1.02q Use intersection points: of graphs to solve equations1.02w Graph transformations: simple transformations of f(x)1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
\begin{enumerate}
\item (i) Sketch the curve $y = \sin x ^ { \circ }$ for $x$ in the interval $- 180 \leq x \leq 180$.\\
(ii) Sketch on the same diagram the curve $y = \sin ( x - 30 ) ^ { \circ }$ for $x$ in the interval $- 180 \leq x \leq 180$.\\
(iii) Use your diagram to solve the equation
\end{enumerate}
$$\sin x ^ { \circ } = \sin ( x - 30 ) ^ { \circ }$$
for $x$ in the interval $- 180 \leq x \leq 180$.\\
\hfill \mbox{\textit{OCR C2 Q3 [6]}}