2025 OCR AS Level Further Mathematics A Y532/01 Statistics
Combined Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 16 May 2025 – Afternoon
AS Level Further Mathematics A
Y532/01 Statistics
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for AS Level Further
QP
Mathematics A
• 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 non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• 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 4 pages.
ADVICE
• Read each question carefully before you start your answer.
, © OCR 2025 [M/508/5498] OCR is an exempt Charity
DC (PQ) 356310/3 Turn over
*1919957079*
, 2
1 A six-sided dice may or may not be equally likely to land on any one of its faces. It has two faces
numbered 5 and the other four faces are numbered 1, 2, 3 and 4. The dice is thrown 60 times, and
the outcome on each throw is recorded. The results are shown in the table.
Outcome 1 2 3 4 5
Frequency 7 13 11 15 14
It is required to carry out a test at the 5% significance level of whether the probabilities of the
outcomes 1, 2, 3, 4 and 5 are in the ratio 1 : 1 : 1 : 1 : 2.
(a) State suitable hypotheses for the test. [1]
(b) Carry out the test. [6]
2 On any day, flights of helicopters and aeroplanes pass within sight of a certain building only
during a daytime period of 12 hours, from 7.00 am to 7.00 pm.
The random variable H is the number of helicopters that pass within sight of the building during a
randomly chosen daytime period of 12 hours.
(a) State two assumptions needed for H to be well modelled by a Poisson distribution. [2]
Assume now that H can be well modelled by the distribution Po(1.8).
(b) Find the probability that, during a randomly chosen daytime period of 12 hours, the number
of helicopters that pass within sight of the building is 2, 3 or 4. [2]
(c) During a period of t hours (within the daytime period of 12 hours), the probability that no
helicopters pass within sight of the building is 0.95.
Use an algebraic method to determine the value of t. [3]
(d) During a randomly chosen daytime period of t hours (where t is the value found in part (c))
two helicopters pass within sight of the building.
Explain whether this casts doubt on the validity of the model. You do not need to carry out
any calculations. [1]
Throughout the daytime period of 12 hours on any day, aeroplanes pass within sight of the
building at a fixed constant rate of 1 aeroplane every 4 minutes.
(e) Explain whether the number of aeroplanes that pass within sight of the building on any day is
likely to be well modelled by a Poisson distribution. [1]
(f) Find the expected value of the total number of helicopters and aeroplanes that pass within
sight of the building on a randomly chosen day. [1]
© OCR 2025 Y532/01 Jun25
Combined Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Friday 16 May 2025 – Afternoon
AS Level Further Mathematics A
Y532/01 Statistics
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for AS Level Further
QP
Mathematics A
• 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 non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• 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 4 pages.
ADVICE
• Read each question carefully before you start your answer.
, © OCR 2025 [M/508/5498] OCR is an exempt Charity
DC (PQ) 356310/3 Turn over
*1919957079*
, 2
1 A six-sided dice may or may not be equally likely to land on any one of its faces. It has two faces
numbered 5 and the other four faces are numbered 1, 2, 3 and 4. The dice is thrown 60 times, and
the outcome on each throw is recorded. The results are shown in the table.
Outcome 1 2 3 4 5
Frequency 7 13 11 15 14
It is required to carry out a test at the 5% significance level of whether the probabilities of the
outcomes 1, 2, 3, 4 and 5 are in the ratio 1 : 1 : 1 : 1 : 2.
(a) State suitable hypotheses for the test. [1]
(b) Carry out the test. [6]
2 On any day, flights of helicopters and aeroplanes pass within sight of a certain building only
during a daytime period of 12 hours, from 7.00 am to 7.00 pm.
The random variable H is the number of helicopters that pass within sight of the building during a
randomly chosen daytime period of 12 hours.
(a) State two assumptions needed for H to be well modelled by a Poisson distribution. [2]
Assume now that H can be well modelled by the distribution Po(1.8).
(b) Find the probability that, during a randomly chosen daytime period of 12 hours, the number
of helicopters that pass within sight of the building is 2, 3 or 4. [2]
(c) During a period of t hours (within the daytime period of 12 hours), the probability that no
helicopters pass within sight of the building is 0.95.
Use an algebraic method to determine the value of t. [3]
(d) During a randomly chosen daytime period of t hours (where t is the value found in part (c))
two helicopters pass within sight of the building.
Explain whether this casts doubt on the validity of the model. You do not need to carry out
any calculations. [1]
Throughout the daytime period of 12 hours on any day, aeroplanes pass within sight of the
building at a fixed constant rate of 1 aeroplane every 4 minutes.
(e) Explain whether the number of aeroplanes that pass within sight of the building on any day is
likely to be well modelled by a Poisson distribution. [1]
(f) Find the expected value of the total number of helicopters and aeroplanes that pass within
sight of the building on a randomly chosen day. [1]
© OCR 2025 Y532/01 Jun25
