SUMMER 2026
PREDICTED PAPER
OCR
AS Level Mathematics A
H230/02 Pure Mathematics and Mechanics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
QP
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 75.
• The marks for each question are shown in brackets [ ].
Turn over
1 for more: tyrionpapers.com
, 3
1 Given that sin θ = 5
find the possible values of cos θ and tan θ .
(3 marks)
2 (a) The points A (3, 5) , B (5, 3) and C (9, 7) lie on a circle.
Show that triangle ABC is a right-angle triangle.
(2 marks)
(b) Explain why the line segment AC must be the diameter of the circle.
(1 mark)
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, (c) Hence find the equation of the circle.
(4 marks)
3 Let m be a natural number in the range 5 < m < 10 .
Use proof by exhaustion to show that all possible values of m 2 differ from a multiple of 5 by
1.
(2 marks)
1
4 (a) Sketch the graph of y= + 3 , showing clearly the points where the curve crosses the
x
coordinate axes and stating the equations of the asymptotes.
for more: tyrionpapers.com
PREDICTED PAPER
OCR
AS Level Mathematics A
H230/02 Pure Mathematics and Mechanics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
QP
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 75.
• The marks for each question are shown in brackets [ ].
Turn over
1 for more: tyrionpapers.com
, 3
1 Given that sin θ = 5
find the possible values of cos θ and tan θ .
(3 marks)
2 (a) The points A (3, 5) , B (5, 3) and C (9, 7) lie on a circle.
Show that triangle ABC is a right-angle triangle.
(2 marks)
(b) Explain why the line segment AC must be the diameter of the circle.
(1 mark)
for more: tyrionpapers.com
, (c) Hence find the equation of the circle.
(4 marks)
3 Let m be a natural number in the range 5 < m < 10 .
Use proof by exhaustion to show that all possible values of m 2 differ from a multiple of 5 by
1.
(2 marks)
1
4 (a) Sketch the graph of y= + 3 , showing clearly the points where the curve crosses the
x
coordinate axes and stating the equations of the asymptotes.
for more: tyrionpapers.com
