2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
2025 OCR A Level Further Mathematics B (MEI)
Y432/01 Statistics Minor
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Friday 13 June 2025 – Afternoon A
Level Further Mathematics B (MEI) Y432/01
Statistics Minor
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(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 pages 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.
© OCR 2025 [M/508/5596] OCR is an exempt Charity
DC (SL) 354112/3 Turn over
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
,2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
2
1 A discrete random variable, X, has a Poisson distribution with mean 4.
(a) Write down the value of Var (X ). [1]
(b) Find P(X = 3). [1]
(c) Find P(X 2 3). [2]
Another discrete random variable, Y, which is independent of X, has a Poisson distribution with
mean 5.
(d) Find P(X + Y G 9). [2]
2 In an experiment, the speed of an object, v ms -1 , at time t seconds, is recorded at intervals
of 10 seconds from t = 0 to t = 80.
The summary statistics are as follows.
n = 8, Rt = 280, Rt2 = 14000, Rv = 876.28, Rv2 = 133310.2, Rtv = 43190
A linear function of t is used as a model for v.
(a) By first determining the equation of an appropriate regression line, estimate the value of v
when t = 45. [3]
(b) Comment on the reliability of your estimate in part (a). [1]
(c) Explain why in this scenario it would be inappropriate to use a value of v to estimate a value
of t using any regression line. [1]
© OCR 2025 Y432/01 Jun25
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
,2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
3
3 An archer fires arrows one by one at a target until an arrow hits the target. The number of
arrows fired up to and including the arrow that hits the target is denoted by X. The archer
considers using a geometric model for the distribution of X.
(a) State two assumptions required for such a model to be appropriate. [2]
For the remainder of this question you may assume that a geometric model is appropriate for the
distribution of X.
The archer keeps records of the values of X. He collects a sample of these values and uses them to
estimate the variance of X.
(b) Give two features that the sample should have. [2]
The estimate of the variance of X calculated from the sample is 12.
(c) Determine an estimate of the probability that when the archer fires a single arrow at the
target, the arrow hits the target. [3]
(d) Use your answer to part (c) to write down an estimate of the expected number of arrows
that the archer must fire at the target up to and including the first arrow that hits the target.
[1]
4 The discrete random variable, X, has a uniform distribution over the values {5, 6, ..., n}.
(a) In this question you must show detailed reasoning.
In part (a) you should assume that n = 24.
(i) Using the formula E(X) = / xi pi , determine the value of E(X) by direct calculation. [3]
(ii) Use the substitution Y = X - 4 and the given formula in the formulae booklet to
determine Var (X ). [2]
1
(iii) Show that P(X 2 E(X )) = . [1]
2
1
(b) A student states that P(X 2 E(X )) = for all n H 24.
2
Explain whether the student is correct. [1]
© OCR 2025 Y432/01 Jun25 Turn over
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
, 2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
4
5 Long-term data collected at a certain farm indicates that 30% of eggs that it produces are large
and the rest are categorised as medium.
Eggs are collected in batches of 4 and the number of large eggs in each batch, X, is recorded.
It is suggested that a binomial distribution might be appropriate to model X.
(a) (i) State two reasons, within the context of this question, why a binomial model might be
appropriate to model X. [2]
(ii) State two assumptions, within the context of this question, that must be made for a
binomial model to be appropriate to model X. You should not refer to the reasons given
in part (a)(i). [2]
(iii) Write down the binomial distribution which might be a suitable model for the
distribution of X. [1]
The farm manager investigates whether the distribution in part (a)(iii) is a good model for X.
(b) State one reason why taking data from a sample of 6 batches would not be appropriate to
carry out the investigation. [1]
The farm manager takes a random sample of 100 batches. The results are summarised in
Table 5.1.
Table 5.1
x 0 1 2 H3
Frequency 31 36 30 3
Table 5.2, shows expected frequencies for the values of X in 100 batches, assuming that X has the
distribution from part (a)(iii). The table is incomplete.
Table 5.2
x 0 1 2 H3
Expected frequency 24.01
(c) Complete the copy of Table 5.2 in the Printed Answer Booklet. Give the expected
frequencies to 2 decimal places. [2]
(d) Carry out a χ2 test, at the 5% significance level, for goodness of fit of the model in
part (a)(iii). [5]
© OCR 2025 Y432/01 Jun25
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
2025 OCR A Level Further Mathematics B (MEI)
Y432/01 Statistics Minor
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Friday 13 June 2025 – Afternoon A
Level Further Mathematics B (MEI) Y432/01
Statistics Minor
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(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 pages 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.
© OCR 2025 [M/508/5596] OCR is an exempt Charity
DC (SL) 354112/3 Turn over
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
,2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
2
1 A discrete random variable, X, has a Poisson distribution with mean 4.
(a) Write down the value of Var (X ). [1]
(b) Find P(X = 3). [1]
(c) Find P(X 2 3). [2]
Another discrete random variable, Y, which is independent of X, has a Poisson distribution with
mean 5.
(d) Find P(X + Y G 9). [2]
2 In an experiment, the speed of an object, v ms -1 , at time t seconds, is recorded at intervals
of 10 seconds from t = 0 to t = 80.
The summary statistics are as follows.
n = 8, Rt = 280, Rt2 = 14000, Rv = 876.28, Rv2 = 133310.2, Rtv = 43190
A linear function of t is used as a model for v.
(a) By first determining the equation of an appropriate regression line, estimate the value of v
when t = 45. [3]
(b) Comment on the reliability of your estimate in part (a). [1]
(c) Explain why in this scenario it would be inappropriate to use a value of v to estimate a value
of t using any regression line. [1]
© OCR 2025 Y432/01 Jun25
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
,2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
3
3 An archer fires arrows one by one at a target until an arrow hits the target. The number of
arrows fired up to and including the arrow that hits the target is denoted by X. The archer
considers using a geometric model for the distribution of X.
(a) State two assumptions required for such a model to be appropriate. [2]
For the remainder of this question you may assume that a geometric model is appropriate for the
distribution of X.
The archer keeps records of the values of X. He collects a sample of these values and uses them to
estimate the variance of X.
(b) Give two features that the sample should have. [2]
The estimate of the variance of X calculated from the sample is 12.
(c) Determine an estimate of the probability that when the archer fires a single arrow at the
target, the arrow hits the target. [3]
(d) Use your answer to part (c) to write down an estimate of the expected number of arrows
that the archer must fire at the target up to and including the first arrow that hits the target.
[1]
4 The discrete random variable, X, has a uniform distribution over the values {5, 6, ..., n}.
(a) In this question you must show detailed reasoning.
In part (a) you should assume that n = 24.
(i) Using the formula E(X) = / xi pi , determine the value of E(X) by direct calculation. [3]
(ii) Use the substitution Y = X - 4 and the given formula in the formulae booklet to
determine Var (X ). [2]
1
(iii) Show that P(X 2 E(X )) = . [1]
2
1
(b) A student states that P(X 2 E(X )) = for all n H 24.
2
Explain whether the student is correct. [1]
© OCR 2025 Y432/01 Jun25 Turn over
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
, 2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
4
5 Long-term data collected at a certain farm indicates that 30% of eggs that it produces are large
and the rest are categorised as medium.
Eggs are collected in batches of 4 and the number of large eggs in each batch, X, is recorded.
It is suggested that a binomial distribution might be appropriate to model X.
(a) (i) State two reasons, within the context of this question, why a binomial model might be
appropriate to model X. [2]
(ii) State two assumptions, within the context of this question, that must be made for a
binomial model to be appropriate to model X. You should not refer to the reasons given
in part (a)(i). [2]
(iii) Write down the binomial distribution which might be a suitable model for the
distribution of X. [1]
The farm manager investigates whether the distribution in part (a)(iii) is a good model for X.
(b) State one reason why taking data from a sample of 6 batches would not be appropriate to
carry out the investigation. [1]
The farm manager takes a random sample of 100 batches. The results are summarised in
Table 5.1.
Table 5.1
x 0 1 2 H3
Frequency 31 36 30 3
Table 5.2, shows expected frequencies for the values of X in 100 batches, assuming that X has the
distribution from part (a)(iii). The table is incomplete.
Table 5.2
x 0 1 2 H3
Expected frequency 24.01
(c) Complete the copy of Table 5.2 in the Printed Answer Booklet. Give the expected
frequencies to 2 decimal places. [2]
(d) Carry out a χ2 test, at the 5% significance level, for goodness of fit of the model in
part (a)(iii). [5]
© OCR 2025 Y432/01 Jun25
2025 OCR
2025
A Level
OCR
2025
Further
A Level
OCRMathematics
Further
A LevelMathematics
Further
B (MEI)
Mathematics
Y432-01
B (MEI) Y432-01
B
Statistics
(MEI) Y432-01
Statistics
Minor Verified
Statistics
Minor Question
Verified
Minor Question
Verified
paper with
Question
paper
Marking
with
paper
Marking
Scheme
with Marking
Scheme
Attached.pdf
Scheme
Attached.pdf
Attached.pdf
