Question 4 - A-Level Maths

OCR D2 — Question 4 11 marks

Exam Board	OCR
Module	D2 (Decision Mathematics 2)
Marks	11
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Critical Path Analysis
Type	Draw cascade/Gantt chart
Difficulty	Moderate -0.3 This is a standard Critical Path Analysis question requiring routine application of well-practiced techniques (activity network, critical path identification, Gantt chart, resource histogram). While multi-part and requiring careful execution, it involves no novel problem-solving or conceptual difficulty beyond textbook exercises—slightly easier than average A-level due to its algorithmic nature.
Spec	7.05a Critical path analysis: activity on arc networks 7.05b Forward and backward pass: earliest/latest times, critical activities 7.05c Total float: calculation and interpretation 7.05d Latest start and earliest finish: independent and interfering float 7.05e Cascade charts: scheduling and effect of delays

Activity	Time	Precedence
A	12
B	5
C	10
D	8	A
E	5	A, B , C
F	9	C
G	11	D, E
H	6	G, F
I	6	H
J	2	H
K	3	I

Construct an activity network to show the tasks involved in widening a bridge over the B451.

Find those tasks which lie on the critical path and list them in order.
State the minimum length of time needed to widen the bridge.
Represent the tasks on a Gantt diagram. Tasks \(F\) and \(J\) each require 3 workers, tasks \(B\), \(D\) and \(I\) each require 2 workers and the remaining tasks each require one worker.
Draw a resource histogram showing how it is possible for a team of 4 workers to complete the project in the minimum possible time.

Show mark scheme Show mark scheme source

Question 4:

Part (a)

Answer	Marks	Guidance
Answer	Marks	Guidance
Lower figures give forward scan	M1
Upper figures give backward scan	M1 A1
Critical path is \(ADGHIK\)	A1

Part (b)

Answer	Marks	Guidance
Answer	Marks	Guidance
Minimum time is 46 days	A1

Part (c)

Answer	Marks	Guidance
Answer	Marks	Guidance
Correct Gantt chart with activities and float shown	B3

Part (d)

Answer	Marks	Guidance
Answer	Marks	Guidance
Resource histogram with max 4 workers, scheduling non-critical activities within float	M1 A2	(11 total)

# Question 4:

## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Lower figures give forward scan | M1 | |
| Upper figures give backward scan | M1 A1 | |
| Critical path is $ADGHIK$ | A1 | |

## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Minimum time is 46 days | A1 | |

## Part (c)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Correct Gantt chart with activities and float shown | B3 | |

## Part (d)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Resource histogram with max 4 workers, scheduling non-critical activities within float | M1 A2 | **(11 total)** |

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Show LaTeX source

4.

\begin{center}
\begin{tabular}{ c c c }
Activity & Time & Precedence \\
A & 12 &  \\
B & 5 &  \\
C & 10 &  \\
D & 8 & A \\
E & 5 & A, B , C \\
F & 9 & C \\
G & 11 & D, E \\
H & 6 & G, F \\
I & 6 & H \\
J & 2 & H \\
K & 3 & I \\
\end{tabular}
\end{center}

Construct an activity network to show the tasks involved in widening a bridge over the B451.
\begin{enumerate}[label=(\alph*)]
\item Find those tasks which lie on the critical path and list them in order.
\item State the minimum length of time needed to widen the bridge.
\item Represent the tasks on a Gantt diagram.

Tasks $F$ and $J$ each require 3 workers, tasks $B$, $D$ and $I$ each require 2 workers and the remaining tasks each require one worker.
\item Draw a resource histogram showing how it is possible for a team of 4 workers to complete the project in the minimum possible time.
\end{enumerate}

\hfill \mbox{\textit{OCR D2  Q4 [11]}}

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