OCR A Level Further Mathematics B Y433/01
Modelling with Algorithms Combined Question
paper & Marking Scheme A+ June 2025
Oxford Cambridge and RSA
Tuesday 3 June 2025 – Afternoon A Level
Further Mathematics B (MEI) Y433/01 Modelling
with Algorithms
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
(MEI)
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined page at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
Turn over
, 32
1 Four workers, Ali (A), Beth (B), Casey (C) and Dev (D), are available to complete three tasks,
P, Q and R. Each worker can only be assigned to at most one task, and each task must be done by
at most one worker.
The table in Fig. 1.1 shows the average time, in minutes, that each worker takes to complete each
task.
Fig. 1.1
P Q R
A 32 39 37
B 29 28 32
C 35 36 39
D 38 39 34
The four workers need to know, based on the times in the table, who should be allocated to each
task so that the total time to complete all three tasks is minimised.
(a) Formulate this allocation problem as an LP. [4]
The LP was run in an LP solver and the output is shown in the table in Fig. 1.2.
Fig. 1.2
Variable Value
AP 1.000 000
AQ 0.000 000
AR 0.000 000
BP 0.000 000
BQ 1.000 000
BR 0.000 000
CP 0.000 000
CQ 0.000 000
CR 0.000 000
DP 0.000 000
DQ 0.000 000
DR 1.000 000
(b) (i) State which worker will not be assigned to a task according to the output given in Fig. 1.2.
[1]
(ii) Find the predicted total time for the three assigned workers to complete the three
tasks, according to the output given in Fig. 1.2. [1]
© OCR 2025 Y433/01 Jun25
, 3
2 Consider the following algorithm.
Line 10 Let A = 5, B = 6, C = 150
Line 20 Calculate D = (A +B) ' 2
Line 30 Calculate E = C - D3
Line 40 If E2 1 0.1 go to Line 100
Line 50 If E 2 0 go to Line 80
Line 60 Let B = D
Line 70 Go to Line 20
Line 80 Let A = D
Line 90 Go to Line 20
Line 100 Output D
Line 110 Stop
(a) Work through the algorithm, recording the values of A, B, D and E every time they change.
You should record the exact values of A, B and D, and the value of E correct to 3 decimal
places. Give the final output to 2 decimal places. [4]
The algorithm gives the cube root of 150 correct to 2 decimal places.
A student adapts the algorithm to try to find the cube root of 1500 correct to 2 decimal places by
changing only Line 10 to ‘Let A = 5, B = 6, C = 1500’.
(b) Explain why this change will not give the output of the cube root of 1500 correct to
2 decimal places. [1]
© OCR 2025 Y433/01 Jun25 Turn over
, 34
3 The table lists the duration (in hours) and immediate predecessors for each activity in a project.
Duration Immediate
Activity
(hours) predecessors
A 3 –
B 5 A
C 6 –
D 6 B
E 4 B, C
F 2 B
G 5 B
H 4 C
I 7 C
J 4 E, H
K 2 G, I, J
L 4 I
(a) Draw an activity network, using activity on arc, to represent the project. [3]
(b) (i) Carry out a forward pass and a backward pass through the activity network, showing
the early event time and the late event time at each vertex of your network. [3]
(ii) State the minimum project completion time. [1]
(iii) List the critical activities. [1]
Each activity requires one worker. When an activity is started it must be completed without
interruption.
(c) Use the diagram in the Printed Answer Booklet to show how four workers can complete
the project in the minimum time found in part (b)(ii). Each column in the diagram
represents
1 hour. For each worker, write the letter of the activity they are doing in each box, or leave
the box blank if the person is resting for that 1 hour. [3]
(d) Explain why it is not possible for only three people to complete the project in the minimum
time found in part (b)(ii). [1]
© OCR 2025 Y433/01 Jun25
Modelling with Algorithms Combined Question
paper & Marking Scheme A+ June 2025
Oxford Cambridge and RSA
Tuesday 3 June 2025 – Afternoon A Level
Further Mathematics B (MEI) Y433/01 Modelling
with Algorithms
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
(MEI)
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined page at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
Turn over
, 32
1 Four workers, Ali (A), Beth (B), Casey (C) and Dev (D), are available to complete three tasks,
P, Q and R. Each worker can only be assigned to at most one task, and each task must be done by
at most one worker.
The table in Fig. 1.1 shows the average time, in minutes, that each worker takes to complete each
task.
Fig. 1.1
P Q R
A 32 39 37
B 29 28 32
C 35 36 39
D 38 39 34
The four workers need to know, based on the times in the table, who should be allocated to each
task so that the total time to complete all three tasks is minimised.
(a) Formulate this allocation problem as an LP. [4]
The LP was run in an LP solver and the output is shown in the table in Fig. 1.2.
Fig. 1.2
Variable Value
AP 1.000 000
AQ 0.000 000
AR 0.000 000
BP 0.000 000
BQ 1.000 000
BR 0.000 000
CP 0.000 000
CQ 0.000 000
CR 0.000 000
DP 0.000 000
DQ 0.000 000
DR 1.000 000
(b) (i) State which worker will not be assigned to a task according to the output given in Fig. 1.2.
[1]
(ii) Find the predicted total time for the three assigned workers to complete the three
tasks, according to the output given in Fig. 1.2. [1]
© OCR 2025 Y433/01 Jun25
, 3
2 Consider the following algorithm.
Line 10 Let A = 5, B = 6, C = 150
Line 20 Calculate D = (A +B) ' 2
Line 30 Calculate E = C - D3
Line 40 If E2 1 0.1 go to Line 100
Line 50 If E 2 0 go to Line 80
Line 60 Let B = D
Line 70 Go to Line 20
Line 80 Let A = D
Line 90 Go to Line 20
Line 100 Output D
Line 110 Stop
(a) Work through the algorithm, recording the values of A, B, D and E every time they change.
You should record the exact values of A, B and D, and the value of E correct to 3 decimal
places. Give the final output to 2 decimal places. [4]
The algorithm gives the cube root of 150 correct to 2 decimal places.
A student adapts the algorithm to try to find the cube root of 1500 correct to 2 decimal places by
changing only Line 10 to ‘Let A = 5, B = 6, C = 1500’.
(b) Explain why this change will not give the output of the cube root of 1500 correct to
2 decimal places. [1]
© OCR 2025 Y433/01 Jun25 Turn over
, 34
3 The table lists the duration (in hours) and immediate predecessors for each activity in a project.
Duration Immediate
Activity
(hours) predecessors
A 3 –
B 5 A
C 6 –
D 6 B
E 4 B, C
F 2 B
G 5 B
H 4 C
I 7 C
J 4 E, H
K 2 G, I, J
L 4 I
(a) Draw an activity network, using activity on arc, to represent the project. [3]
(b) (i) Carry out a forward pass and a backward pass through the activity network, showing
the early event time and the late event time at each vertex of your network. [3]
(ii) State the minimum project completion time. [1]
(iii) List the critical activities. [1]
Each activity requires one worker. When an activity is started it must be completed without
interruption.
(c) Use the diagram in the Printed Answer Booklet to show how four workers can complete
the project in the minimum time found in part (b)(ii). Each column in the diagram
represents
1 hour. For each worker, write the letter of the activity they are doing in each box, or leave
the box blank if the person is resting for that 1 hour. [3]
(d) Explain why it is not possible for only three people to complete the project in the minimum
time found in part (b)(ii). [1]
© OCR 2025 Y433/01 Jun25
