| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Tangents, normals and gradients |
| Type | Velocity and acceleration problems |
| Difficulty | Moderate -0.8 This is a straightforward AS-level calculus application question. Part (a) requires solving a simple quadratic equation (which factorises as (t-7)²), and part (b) requires differentiating a quadratic and substituting a value. Both parts are routine procedures with no problem-solving insight needed, making this easier than average but not trivial since it requires correct application of basic techniques. |
| Spec | 1.02f Solve quadratic equations: including in a function of unknown1.07b Gradient as rate of change: dy/dx notation |
Water is being emptied out of a sink. The depth of water, $y$cm, at time $t$ seconds, may be modelled by
$$y = t^2 - 14t + 49 \quad\quad 0 \leqslant t \leqslant 7.$$
\begin{enumerate}[label=(\alph*)]
\item Find the value of $t$ when the depth of water is 25cm. [3]
\item Find the rate of decrease of the depth of water when $t = 3$. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2024 Q10 [6]}}