surname names
Number Number
Mathematics
■ ■
Advanced Subsidiary
PAPER 1: Pure Mathematics
Candidates may use any calculator allowed by the regulations of the Joint Council for
Qualifications. Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae stored in them.
Instructions
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). centre number
and candidate number.
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.
• There are 14 questions in this question paper. The total mark for this paper is 100. – use this as a guide
as to how much time to spend on each question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. Find
2 x 3 2
dx x
giving your answer in simplest form.
(4)
,Question 1 continued
(Total for Question 1 is 4 marks)
, 2. In this question you must show all stages of your working. Solutions
relying entirely on calculator technology are not acceptable.
f (x) = 2x3 – 3ax2 + bx + 8a
where a and b are constants.
Given that (x – 4) is a factor of f (x),
(a) use the factor theorem to show that
10a = 32 + b
(2)
Given also that (x – 2) is a factor of f (x),
(b) express f (x) in the form
f (x) = (2x + k)(x – 4) (x – 2)
where k is a constant to be found.
(4)
(c) Hence,
(i) state the number of real roots of the equation f (x) = 0
1
(ii) write down the largest root of the equation f x = 0
3
(2)
Number Number
Mathematics
■ ■
Advanced Subsidiary
PAPER 1: Pure Mathematics
Candidates may use any calculator allowed by the regulations of the Joint Council for
Qualifications. Calculators must not have the facility for symbolic algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae stored in them.
Instructions
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). centre number
and candidate number.
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.
• There are 14 questions in this question paper. The total mark for this paper is 100. – use this as a guide
as to how much time to spend on each question.
• Read each question carefully before you start to answer it.
• Check your answers if you have time at the end. Turn over
,1. Find
2 x 3 2
dx x
giving your answer in simplest form.
(4)
,Question 1 continued
(Total for Question 1 is 4 marks)
, 2. In this question you must show all stages of your working. Solutions
relying entirely on calculator technology are not acceptable.
f (x) = 2x3 – 3ax2 + bx + 8a
where a and b are constants.
Given that (x – 4) is a factor of f (x),
(a) use the factor theorem to show that
10a = 32 + b
(2)
Given also that (x – 2) is a factor of f (x),
(b) express f (x) in the form
f (x) = (2x + k)(x – 4) (x – 2)
where k is a constant to be found.
(4)
(c) Hence,
(i) state the number of real roots of the equation f (x) = 0
1
(ii) write down the largest root of the equation f x = 0
3
(2)
