| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Read parameters from graph of transformed trig function |
| Difficulty | Moderate -0.8 This is a straightforward graph reading exercise requiring students to identify amplitude (a), frequency (b), and vertical shift (c) from a sine curve, then solve a basic equation. It tests standard transformations of trig functions with minimal problem-solving—easier than average A-level questions which typically require multi-step calculations or integration of multiple concepts. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(a = 6\) | B1 | co |
| \(b = 2\) | B1 | co |
| \(c = 3\) | B1 [3] | co |
| (ii) \(6\sin 2x + 3 = 0\) | M1 | Setting to 0 and attempt at making \(\sin bx\) the subject |
| \(\rightarrow \sin 2x = -\frac{1}{2}\) | M1 | Must be evidence of \(÷ b\) |
| Works with "\(2x\)" first | ||
| \(x = \frac{7\pi}{12}\) or \(1.83\) | A1 [3] | Co (radians only) |
(i) $a = 6$ | B1 | co
$b = 2$ | B1 | co
$c = 3$ | B1 [3] | co
(ii) $6\sin 2x + 3 = 0$ | M1 | Setting to 0 and attempt at making $\sin bx$ the subject
$\rightarrow \sin 2x = -\frac{1}{2}$ | M1 | Must be evidence of $÷ b$
Works with "$2x$" first | |
$x = \frac{7\pi}{12}$ or $1.83$ | A1 [3] | Co (radians only)4\\
\includegraphics[max width=\textwidth, alt={}, center]{3b527397-7781-41e9-8218-57277cc977bf-2_561_1210_895_465}
The diagram shows the graph of $y = a \sin ( b x ) + c$ for $0 \leqslant x \leqslant 2 \pi$.\\
(i) Find the values of $a , b$ and $c$.\\
(ii) Find the smallest value of $x$ in the interval $0 \leqslant x \leqslant 2 \pi$ for which $y = 0$.
\hfill \mbox{\textit{CAIE P1 2009 Q4 [6]}}