surname names
Number Number
Further Mathematics
■ ■
Advanced
PAPER 3A: Further Pure Mathematics 1
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebraic 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 10 questions in this question paper. The total mark for this paper is 75.
– 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. (a) Given that
y ln 3 x2
complete the table with the value of y corresponding to x = 3, giving your answer to
4 significant figures.
x 2 2.5 3 3.5 4 4.5 5
y 1.946 2.225 2.725 2.944 3.146 3.332
(1)
In part (b) you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
(b) Use Simpson’s rule with all the values of y in the completed table to estimate, to 3
significant figures, the value of
5ln 3 x2 dx
2
(3)
(c) Using your answer to part (b) and making your method clear, estimate the value of
ln 3 x dx
5
2
2
(1)
,Question 1 continued
(Total for Question 1 is 5 marks)
, 2. Use algebra to determine the values of x for which
x2 2x x
(4)
Number Number
Further Mathematics
■ ■
Advanced
PAPER 3A: Further Pure Mathematics 1
Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebraic 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 10 questions in this question paper. The total mark for this paper is 75.
– 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. (a) Given that
y ln 3 x2
complete the table with the value of y corresponding to x = 3, giving your answer to
4 significant figures.
x 2 2.5 3 3.5 4 4.5 5
y 1.946 2.225 2.725 2.944 3.146 3.332
(1)
In part (b) you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
(b) Use Simpson’s rule with all the values of y in the completed table to estimate, to 3
significant figures, the value of
5ln 3 x2 dx
2
(3)
(c) Using your answer to part (b) and making your method clear, estimate the value of
ln 3 x dx
5
2
2
(1)
,Question 1 continued
(Total for Question 1 is 5 marks)
, 2. Use algebra to determine the values of x for which
x2 2x x
(4)
