The ellipse E has equation
x + y2 = 1
36 20
Find
(a) the coordinates of the foci of E,
(3)
(b) the equations of the directrices of E.
(2)
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Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel
Level 3 GCE
Time 1 hour 30 minutes
Paper
reference 9FM0/3A
Further Mathematics
Advanced
PAPER 3A: Further Pure Mathematics 1
You must have: Total Marks
Mathematical Formulae and Statistical Tables (Green), 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).
• Fill in the boxes at the top of this page with your name,
centre number and candidate number.
• clearly
Answer all questions and ensure that your answers to parts of questions are
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.
•Information
Inexact answers should be given to three significant figures unless otherwise stated.
•• AThere
booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
are 8 questions in this question paper. The total mark for this paper is 75.
• 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.
Good luck with your examination.
Turn over
Find
(a) the coordinates of the foci of E,
(3)
(b) the equations of the directrices of E.
(2)
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, x
2. (i) Use the substitution t = tan to prove the identity
2
sin x − cos x + 1 nπ
≡ sec x + tan x x≠ n
sin x + cos x − 1 2
(5)
θ
(ii) Use the substitution t = tan to determine the exact value of
2
π
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