| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2009 |
| Session | November |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Sketch trig curve and straight line, count intersections |
| Difficulty | Easy -1.2 This is a straightforward sketching question requiring knowledge of cosine transformations (amplitude 3, period π) and plotting a simple linear equation. Both are routine A-level skills with no problem-solving or novel insight required, making it easier than average. |
| Spec | 1.02m Graphs of functions: difference between plotting and sketching1.03a Straight lines: equation forms y=mx+c, ax+by+c=01.05f Trigonometric function graphs: symmetries and periodicities |
B1: 1 complete oscillation $0 \to \pi$
B1: Range from $-3$ to $3$
B1: All correct (V shape B0)
B1: Line correct.
[4]2 The equation of a curve is $y = 3 \cos 2 x$. The equation of a line is $x + 2 y = \pi$. On the same diagram, sketch the curve and the line for $0 \leqslant x \leqslant \pi$.
\hfill \mbox{\textit{CAIE P1 2009 Q2 [4]}}