| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Trig Graphs & Exact Values |
| Type | Real-world modelling (tides, daylight, etc.) |
| Difficulty | Moderate -0.3 This is a straightforward application of trigonometric modeling with standard techniques: finding amplitude from a cosine function (part i), using period formula to find k (part ii), and solving a basic trigonometric inequality (part iii). While it requires multiple steps and understanding of transformations, each individual step is routine for A-level students and requires no novel insight—slightly easier than average due to the guided structure and standard methods. |
| Spec | 1.05f Trigonometric function graphs: symmetries and periodicities1.05o Trigonometric equations: solve in given intervals |
A tourist attraction in a city centre is a big vertical wheel on which passengers can ride. The wheel turns in such a way that the height, $h$ m, of a passenger above the ground is given by the formula $h = 60(1 - \cos kt)$. In this formula, $k$ is a constant, $t$ is the time in minutes that has elapsed since the passenger started the ride at ground level and $kt$ is measured in radians.
\begin{enumerate}[label=(\roman*)]
\item Find the greatest height of the passenger above the ground. [1]
\end{enumerate}
One complete revolution of the wheel takes 30 minutes.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Show that $k = \frac{\pi}{15}\pi$. [2]
\item Find the time for which the passenger is above a height of 90 m. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2015 Q6 [6]}}