| Exam Board | Edexcel |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Session | Specimen |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Conditional or compound probability scenarios |
| Difficulty | Moderate -0.3 This is a standard AS-level probability question involving Venn diagrams, mutual exclusivity, and independence. Part (a) requires reading the diagram, (b) involves using probability axioms and independence definition with straightforward algebra, and (c)-(d) test understanding of independence. All techniques are routine for AS Statistics with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space |
| Paper Reference(s) | ||
| \(\mathbf { 8 M A 0 } / \mathbf { 0 2 }\) | |||
| |||
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(s = \int_0^1 16 - 3t^2 \, dt\) | M1 | 1.1a — Attempt to integrate, one power going up |
| \(= \left[16t - t^3\right]_0^1\) | A1 | 1.1b — Correct integral and limits, or indefinite integral with \(C=0\) and \(t=1\) |
| \(= 15\) (m) | A1 | 1.1b |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(16 - 3t^2 = 0\) | M1 | 3.1b — Equate \(v\) to 0 and solve for \(t\) |
| \(t = \sqrt{\frac{16}{3}}\) oe | A1 | 1.1b — Any surd or decimal equivalent to at least 2 s.f. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(16t - t^3 = 0\) | M1 | 3.1b — Use \(s=0\), equate integral to 0 |
| \(t(16 - t^2) = 0\) | M1 | 1.1b — Attempt to solve |
| \(t = 4\) | A1 | 1.1b |
## Question 4:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $s = \int_0^1 16 - 3t^2 \, dt$ | M1 | 1.1a — Attempt to integrate, one power going up |
| $= \left[16t - t^3\right]_0^1$ | A1 | 1.1b — Correct integral and limits, or indefinite integral with $C=0$ and $t=1$ |
| $= 15$ (m) | A1 | 1.1b |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $16 - 3t^2 = 0$ | M1 | 3.1b — Equate $v$ to 0 and solve for $t$ |
| $t = \sqrt{\frac{16}{3}}$ oe | A1 | 1.1b — Any surd or decimal equivalent to at least 2 s.f. |
### Part (c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $16t - t^3 = 0$ | M1 | 3.1b — Use $s=0$, equate integral to 0 |
| $t(16 - t^2) = 0$ | M1 | 1.1b — Attempt to solve |
| $t = 4$ | A1 | 1.1b |4. Alyona, Dawn and Sergei are sometimes late for school.
The events $A , D$ and $S$ are as follows:\\
A Alyona is late for school\\
D Dawn is late for school\\
S Sergei is late for school
The Venn diagram below shows the three events $A , D$ and $S$ and the probabilities associated with each region of $D$. The constants $p , q$ and $r$ each represent probabilities associated with the three separate regions outside $D$.\\
\includegraphics[max width=\textwidth, alt={}, center]{b29b0411-8401-420b-9227-befe25c245d8-06_624_1068_845_479}
\begin{enumerate}[label=(\alph*)]
\item Write down 2 of the events $A , D$ and $S$ that are mutually exclusive. Give a reason for your answer.
The probability that Sergei is late for school is 0.2 . The events $A$ and $D$ are independent.
\item Find the value of $r$.\\
(4)
Dawn and Sergei's teacher believes that when Sergei is late for school, Dawn tends to be late for school.
\item State whether or not $D$ and $S$ are independent, giving a reason for your answer.\\
(1)
\item Comment on the teacher's belief in the light of your answer to part (c).\\
(1)\\
(Total for Question 4 is 7 marks)
\section*{Pearson Edexcel Level 3}
\section*{GCE Mathematics}
\section*{Paper 2: Mechanics}
\begin{center}
\begin{tabular}{ | l | l | }
\hline
\begin{tabular}{ l }
Specimen paper \\
Time: $\mathbf { 3 5 }$ minutes \\
\end{tabular} & Paper Reference(s) \\
\hline
& $\mathbf { 8 M A 0 } / \mathbf { 0 2 }$ \\
\hline
\multicolumn{2}{|l|}{\begin{tabular}{ l }
You must have: \\
Mathematical Formulae and Statistical Tables, calculator \\
\end{tabular}} \\
\hline
\end{tabular}
\end{center}
Candidates may use any calculator permitted by Pearson regulations. Calculators must not have the facility for algebraic manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them.
\section*{Instructions}
\begin{itemize}
\item Use black ink or ball-point pen.
\item If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
\item Fill in the boxes at the top of this page with your name, centre number and candidate number.
\item Answer all the questions in Section B.
\item Answer the questions in the spaces provided - there may be more space than you need.
\item You should show sufficient working to make your methods clear. Answers without working may not gain full credit.
\item Inexact answers should be given to three significant figures unless otherwise stated.
\end{itemize}
\section*{Information}
\begin{itemize}
\item A booklet 'Mathematical Formulae and Statistical Tables' is provided.
\item There are 4 questions in this section. The total mark for Part B of this paper is 30.
\item The marks for each question are shown in brackets - use this as a guide as to how much time to spend on each question.
\end{itemize}
\section*{Advice}
\begin{itemize}
\item Read each question carefully before you start to answer it.
\item Try to answer every question.
\item Check your answers if you have time at the end.
\item If you change your mind about an answer, cross it out and put your new answer and any working underneath.
\end{itemize}
\end{enumerate}
\hfill \mbox{\textit{Edexcel AS Paper 2 Q4 [7]}}