Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel
Level 3 GCE
Wednesday 5 June 2019
Morning (Time: 2 hours) Paper Reference 9MA0/01
Mathematics
Advanced
Paper 1: Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistical Tables, calculator
Candidates may use any calculator allowed by Pearson regulations.
Calculators must not have the facility for symbolic algebra
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).
• Fill in the boxes at the top of this page with your name,
centre number and candidate number.
• are
Answer all questions and ensure that your answers to parts of questions
clearly labelled.
• – there may
Answer the questions in the spaces provided
be more space than you need.
• You should show sufficient working to make your methods clear. Answers
without working may not gain full credit.
• Answers should be given to three significant figures unless otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 14 questions in this question paper. The total mark for this paper is 100.
• – use this asfora guide
The marks each question are shown in brackets
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.
Turn over
P58353A
©2019 Pearson Education Ltd.
1/1/1/1/1/1/C2/C2/
*P58353A0144*
, Answer ALL questions. Write your answers in the spaces provided.
1. f(x) = 3x3 + 2ax2 – 4x + 5a
DO NOT WRITE IN THIS AREA
Given that (x + 3) is a factor of f(x), find the value of the constant a.
(3)
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2
*P58353A0244*
, Question 1 continued
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(Total for Question 1 is 3 marks)
3
*P58353A0344* Turn over
, 2. y
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O x
Figure 1
Figure 1 shows a plot of part of the curve with equation y = cos x where x is measured in radians.
Diagram 1, on the opposite page, is a copy of Figure 1.
(a) Use Diagram 1 to show why the equation
DO NOT WRITE IN THIS AREA
1
cos x − 2 x − =0
2
has only one real root, giving a reason for your answer.
(2)
Given that the root of the equation is Į, and that Įis small,
(b) use the small angle approximation for cos x to estimate the value of Įto 3 decimal places.
(3)
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DO NOT WRITE IN THIS AREA
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4
*P58353A0444*
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel
Level 3 GCE
Wednesday 5 June 2019
Morning (Time: 2 hours) Paper Reference 9MA0/01
Mathematics
Advanced
Paper 1: Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistical Tables, calculator
Candidates may use any calculator allowed by Pearson regulations.
Calculators must not have the facility for symbolic algebra
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).
• Fill in the boxes at the top of this page with your name,
centre number and candidate number.
• are
Answer all questions and ensure that your answers to parts of questions
clearly labelled.
• – there may
Answer the questions in the spaces provided
be more space than you need.
• You should show sufficient working to make your methods clear. Answers
without working may not gain full credit.
• Answers should be given to three significant figures unless otherwise stated.
Information
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 14 questions in this question paper. The total mark for this paper is 100.
• – use this asfora guide
The marks each question are shown in brackets
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.
Turn over
P58353A
©2019 Pearson Education Ltd.
1/1/1/1/1/1/C2/C2/
*P58353A0144*
, Answer ALL questions. Write your answers in the spaces provided.
1. f(x) = 3x3 + 2ax2 – 4x + 5a
DO NOT WRITE IN THIS AREA
Given that (x + 3) is a factor of f(x), find the value of the constant a.
(3)
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
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DO NOT WRITE IN THIS AREA
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2
*P58353A0244*
, Question 1 continued
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DO NOT WRITE IN THIS AREA
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(Total for Question 1 is 3 marks)
3
*P58353A0344* Turn over
, 2. y
DO NOT WRITE IN THIS AREA
O x
Figure 1
Figure 1 shows a plot of part of the curve with equation y = cos x where x is measured in radians.
Diagram 1, on the opposite page, is a copy of Figure 1.
(a) Use Diagram 1 to show why the equation
DO NOT WRITE IN THIS AREA
1
cos x − 2 x − =0
2
has only one real root, giving a reason for your answer.
(2)
Given that the root of the equation is Į, and that Įis small,
(b) use the small angle approximation for cos x to estimate the value of Įto 3 decimal places.
(3)
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_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
DO NOT WRITE IN THIS AREA
_____________________________________________________________________________________
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4
*P58353A0444*
