| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Finding maximum n for P(X=0) threshold |
| Difficulty | Moderate -0.8 This is a straightforward Poisson distribution application requiring only standard procedures: stating conditions for Poisson modeling, calculating a single probability with adjusted rate parameter, and using tables to find a time interval. All parts are routine A-level statistics exercises with no problem-solving insight required, making it easier than average but not trivial due to the multi-step nature and table work in part (c). |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | 17 | 22 |
| Answer | Marks | Guidance |
|---|---|---|
| of single | N | Mean |
| deviation | Minimum | Lower |
| quartile | Median | Upper |
| quartile | Maximum | |
| 49 | 3.57 | 0.393 |
| Answer | Marks | Guidance |
|---|---|---|
| of single | N | Mean |
| deviation | Minimum | Lower |
| quartile | Median | Upper |
| quartile | Maximum | |
| 30 | 3.13 | 0.364 |
Question 3:
3 | 17 | 22 | 7 | 0 | 0 | 0 | 0 | 0 | 1
Summary statistics
Length of single for top 50 UK Official Singles Chart (minutes)
Length
of single | N | Mean | Standard
deviation | Minimum | Lower
quartile | Median | Upper
quartile | Maximum
49 | 3.57 | 0.393 | 2.77 | 3.26 | 3.60 | 3.89 | 4.38
Summary statistics
Length of single for Gareth's random sample of 30 singles (minutes)
Length
of single | N | Mean | Standard
deviation | Minimum | Lower
quartile | Median | Upper
quartile | Maximum
30 | 3.13 | 0.364 | 2.58 | 2.73 | 2.92 | 3.22 | 3.95
PMT
GCE AS and A LEVEL MATHEMATICS Sample Assessment Materials 24
SECTION B – Mechanics
6. A small object, of mass 0.02 kg, is dropped from rest from the top of a building which
is160 m high.
(a) Calculate the speed of the object as it hits the ground. [3]
(b) Determine the time taken for the object to reach the ground. [3]
(c) State one assumption you have made in your solution. [1]
7. The diagram below shows two particles A and B, of mass 2 kg and 5 kg respectively,
which are connected by a light inextensible string passing over a fixed smooth pulley.
Initially, B is held at rest with the string just taut. It is then released.
A
B
(a) Calculate the magnitude of the acceleration of A and the tension in the string.
[6]
(b) What assumption does the word 'light' in the description of the string enable
you to make in your solution? [1]
8. A particle P, of mass 3 kg, moves along the horizontal x-axis under the action of a
resultant force F N. Its velocity v ms-1 at time t seconds is given by
v = 12t – 3t2 .
(a) Given that the particle is at the origin O when t = 1, find an expression for the
displacement of the particle from O at time t s. [3]
(b) Find an expression for the acceleration of the particle at time t s. [2]
© WJEC CBAC Ltd.
PMT
GCE AS and A LEVEL MATHEMATICS Sample Assessment Materials 25
9. A truck of mass 180 kg runs on smooth horizontal rails. A light inextensible rope is
attached to the front of the truck. The rope runs parallel to the rails until it passes
over a light smooth pulley. The rest of the rope hangs down a vertical shaft. When
the truck is required to move, a load of M kg is attached to the end of the rope in the
shaft and the brakes are then released.
(a) Find the tension in the rope when the truck and the load move with an
acceleration of magnitude 0.8 ms-2 and calculate the corresponding
value of M. [5]
(b) In addition to the assumptions given in the question, write down one
further assumption that you have made in your solution to this problem
and explain how that assumption affects both of your answers. [3]
10. Two forces F and G acting on an object are such that
F = i – 8j,
G = 3i + 11j.
The object has a mass of 3 kg. Calculate the magnitude and direction of the
acceleration of the object. [7]
© WJEC CBAC Ltd.Cars arrive at random at a toll bridge at a mean rate of 15 per hour.
\begin{enumerate}[label=(\alph*)]
\item Explain briefly why the Poisson distribution could be used to model the number of cars arriving in a particular time interval. [1]
\item Phil stands at the bridge for 20 minutes. Determine the probability that he sees exactly 6 cars arrive. [3]
\item Using the statistical tables provided, find the time interval (in minutes) for which the probability of more than 10 cars arriving is approximately 0.3. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 Q3 [7]}}