Pearson Edexcel Level 3
GCE Mathematics
Advanced
Paper 2: Pure Mathematics
Mock paper Spring 2018 Paper Reference(s)
Time: 2 hours 9MA0/02
You must have:
Mathematical Formulae and Statistical Tables, calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators must not
have the facility for algebraic manipulation, differentiation and integration, or have
retrievable mathematical formulae stored in them.
Instructions
∙ Use black ink or ball-point pen.
∙ If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
∙ Answer all questions and ensure that your answers to parts of questions are clearly
labelled.
∙ Answer the questions in the spaces provided – there may be more space than you need.
∙ You should show sufficient working to make your methods clear. Answers without
working may not gain full credit.
∙ Inexact answers should be given to three significant figures unless otherwise stated.
Information
∙ A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
∙ There are 14 questions in this paper. The total mark is 100.
∙ The marks for each question are shown in brackets – use this as a guide as to how much
time to spend on each question.
Advice
∙ Read each question carefully before you start to answer it.
∙ Try to answer every question.
∙ Check your answers if you have time at the end.
∙ If you change your mind about an answer, cross it out and put your new answer and any
working underneath.
1
, Answer ALL questions.
1.
Figure 1
Figure 1 shows a circle with centre O. The points A and B lie on the circumference of the
circle.
The area of the major sector, shown shaded in Figure 1, is 135 cm2. The reflex angle AOB is
4.8 radians.
Find the exact length, in cm, of the minor arc AB, giving your answer in the form aπ + b,
where a and b are integers to be found.
(Total for Question 1 is 4 marks)
___________________________________________________________________________
2. (a) Given that θ is small, use the small angle approximation for cos θ to show that
1 + 4 cos θ + 3 cos2 θ ≈ 8 – 5θ 2.
(3)
Adele uses θ = 5° to test the approximation in part (a).
Adele’s working is shown below.
Using my calculator, 1 + 4 cos (5°) + 3 cos2 (5°) = 7.962, to 3 decimal places.
Using the approximation 8 – 5θ 2 gives 8 – 5(5)2 = –117
Therefore, 1 + 4 cos θ + 3 cos2 θ ≈ 8 – 5θ 2 is not true for θ = 5°.
(b) (i) Identify the mistake made by Adele in her working.
(ii) Show that 8 – 5θ 2 can be used to give a good approximation to 1 + 4 cos θ + 3 cos2θ
for an angle of size 5°.
(2)
(Total for Question 2 is 5 marks)
___________________________________________________________________________
2
GCE Mathematics
Advanced
Paper 2: Pure Mathematics
Mock paper Spring 2018 Paper Reference(s)
Time: 2 hours 9MA0/02
You must have:
Mathematical Formulae and Statistical Tables, calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators must not
have the facility for algebraic manipulation, differentiation and integration, or have
retrievable mathematical formulae stored in them.
Instructions
∙ Use black ink or ball-point pen.
∙ If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
∙ Answer all questions and ensure that your answers to parts of questions are clearly
labelled.
∙ Answer the questions in the spaces provided – there may be more space than you need.
∙ You should show sufficient working to make your methods clear. Answers without
working may not gain full credit.
∙ Inexact answers should be given to three significant figures unless otherwise stated.
Information
∙ A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
∙ There are 14 questions in this paper. The total mark is 100.
∙ The marks for each question are shown in brackets – use this as a guide as to how much
time to spend on each question.
Advice
∙ Read each question carefully before you start to answer it.
∙ Try to answer every question.
∙ Check your answers if you have time at the end.
∙ If you change your mind about an answer, cross it out and put your new answer and any
working underneath.
1
, Answer ALL questions.
1.
Figure 1
Figure 1 shows a circle with centre O. The points A and B lie on the circumference of the
circle.
The area of the major sector, shown shaded in Figure 1, is 135 cm2. The reflex angle AOB is
4.8 radians.
Find the exact length, in cm, of the minor arc AB, giving your answer in the form aπ + b,
where a and b are integers to be found.
(Total for Question 1 is 4 marks)
___________________________________________________________________________
2. (a) Given that θ is small, use the small angle approximation for cos θ to show that
1 + 4 cos θ + 3 cos2 θ ≈ 8 – 5θ 2.
(3)
Adele uses θ = 5° to test the approximation in part (a).
Adele’s working is shown below.
Using my calculator, 1 + 4 cos (5°) + 3 cos2 (5°) = 7.962, to 3 decimal places.
Using the approximation 8 – 5θ 2 gives 8 – 5(5)2 = –117
Therefore, 1 + 4 cos θ + 3 cos2 θ ≈ 8 – 5θ 2 is not true for θ = 5°.
(b) (i) Identify the mistake made by Adele in her working.
(ii) Show that 8 – 5θ 2 can be used to give a good approximation to 1 + 4 cos θ + 3 cos2θ
for an angle of size 5°.
(2)
(Total for Question 2 is 5 marks)
___________________________________________________________________________
2
