surname names
Number Number
Paper
Further Mathematics
� �
Advanced
PAPER 1: Core 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.
Advice
Read each question carefully before you start to answer it.
• Check your answers if you have time at the end.
Turn over
,1.
3 6 0
M a 3 1 where a is a constant
2 a a
(a) Determine the values of a for which the matrix M is singular.
(3)
Given that matrix M is non-singular and that
• det(M) = −108
• a0
(b) determine the matrix M −1
(3)
2
■■■■
,Question 1 continued
(Total for Question 1 is 6 marks)
3
■■■■ Turn over
, 2. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Determine the exact values of x for which
sinh 2x 3sinh x
(5)
4
■■■■
Number Number
Paper
Further Mathematics
� �
Advanced
PAPER 1: Core 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.
Advice
Read each question carefully before you start to answer it.
• Check your answers if you have time at the end.
Turn over
,1.
3 6 0
M a 3 1 where a is a constant
2 a a
(a) Determine the values of a for which the matrix M is singular.
(3)
Given that matrix M is non-singular and that
• det(M) = −108
• a0
(b) determine the matrix M −1
(3)
2
■■■■
,Question 1 continued
(Total for Question 1 is 6 marks)
3
■■■■ Turn over
, 2. In this question you must show all stages of your working.
Solutions relying entirely on calculator technology are not acceptable.
Determine the exact values of x for which
sinh 2x 3sinh x
(5)
4
■■■■
