MATH 23801a A level Mathematics Practice Paper A - Pure Mathematics
Pearson Edexcel Level 3
GCE Mathematics
Advanced Level
Paper 1 or 2: Pure Mathematics
Practice Paper Paper Reference(s)
A Time: 2 hours 9MA0/01 or 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 15 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.
This study source was downloaded by 100000824374170 from CourseHero.com on 06-09-2021 14:12:02 GMT -05:00
1
https://www.coursehero.com/file/51818558/01a-A-level-Mathematics-Practice-Paper-A-Pure-Mathematicsdocx/
, Answer ALL questions.
k
1. It is suggested that the sequence ak =2 +1, k … produces only prime numbers.
a1 a2 a
(a) Show that , and 4 produce prime numbers.
(2 marks)
(b) Prove by counter example that the sequence does not always produce a prime number.
(2 marks)
a =4i - j + 3k
2. Find the angle that the vector makes with the positive y-axis.
(3 marks)
æ xö 3
g(x) =3sin 1
- x- 1
∣ 6 10
3. è , –40 < x < 20, x is in radians.
∣
𝖩
æ æ 11 öö∣
x =6∣ 3 arcsin ∣è 3 + 30 x∣𝖩
∣è ∣
(a) Show that the equation g(x) = 0 can be written �
(3 marks)
�
as
æ æ1 1 x öö
xn+1 =6∣ 3 arcsin∣ n∣ ∣
∣
+
(b) Using the formula è 3 30 𝖩 ∣ =4
, , find, to 3 decimal places, the values of x1,
x0
è (2 marks)
x2 and x3.
2
k + 2, 4k, 2k
4. The first 3 terms of a geometric sequence are , k > 0 . Find the value of k.
(4 marks)
x4 + 2x3 - 29x2 - 47x + 77
f (x)
= x2 - 2x - 15
5.
V W
Px2 + Qx+ R + +
Show that f (x) can be written as x+ 3 x- 5 and find the values of P, Q, R, V and W.
(7 marks)
This study source was downloaded by 100000824374170 from CourseHero.com on 06-09-2021 14:12:02 GMT -05:00
2
https://www.coursehero.com/file/51818558/01a-A-level-Mathematics-Practice-Paper-A-Pure-Mathematicsdocx/
Pearson Edexcel Level 3
GCE Mathematics
Advanced Level
Paper 1 or 2: Pure Mathematics
Practice Paper Paper Reference(s)
A Time: 2 hours 9MA0/01 or 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 15 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.
This study source was downloaded by 100000824374170 from CourseHero.com on 06-09-2021 14:12:02 GMT -05:00
1
https://www.coursehero.com/file/51818558/01a-A-level-Mathematics-Practice-Paper-A-Pure-Mathematicsdocx/
, Answer ALL questions.
k
1. It is suggested that the sequence ak =2 +1, k … produces only prime numbers.
a1 a2 a
(a) Show that , and 4 produce prime numbers.
(2 marks)
(b) Prove by counter example that the sequence does not always produce a prime number.
(2 marks)
a =4i - j + 3k
2. Find the angle that the vector makes with the positive y-axis.
(3 marks)
æ xö 3
g(x) =3sin 1
- x- 1
∣ 6 10
3. è , –40 < x < 20, x is in radians.
∣
𝖩
æ æ 11 öö∣
x =6∣ 3 arcsin ∣è 3 + 30 x∣𝖩
∣è ∣
(a) Show that the equation g(x) = 0 can be written �
(3 marks)
�
as
æ æ1 1 x öö
xn+1 =6∣ 3 arcsin∣ n∣ ∣
∣
+
(b) Using the formula è 3 30 𝖩 ∣ =4
, , find, to 3 decimal places, the values of x1,
x0
è (2 marks)
x2 and x3.
2
k + 2, 4k, 2k
4. The first 3 terms of a geometric sequence are , k > 0 . Find the value of k.
(4 marks)
x4 + 2x3 - 29x2 - 47x + 77
f (x)
= x2 - 2x - 15
5.
V W
Px2 + Qx+ R + +
Show that f (x) can be written as x+ 3 x- 5 and find the values of P, Q, R, V and W.
(7 marks)
This study source was downloaded by 100000824374170 from CourseHero.com on 06-09-2021 14:12:02 GMT -05:00
2
https://www.coursehero.com/file/51818558/01a-A-level-Mathematics-Practice-Paper-A-Pure-Mathematicsdocx/
