WJEC Unit 1 2024 June — Question 10 6 marks

Exam BoardWJEC
ModuleUnit 1 (Unit 1)
Year2024
SessionJune
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicTangents, normals and gradients
TypeVelocity and acceleration problems
DifficultyModerate -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.
Spec1.02f 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 $$y = t^2 - 14t + 49 \quad\quad 0 \leqslant t \leqslant 7.$$
  1. Find the value of \(t\) when the depth of water is 25cm. [3]
  2. Find the rate of decrease of the depth of water when \(t = 3\). [3]

Question 10:
AnswerMarks
106
Question 10:
10 | 6
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]}}