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Paper Reference
6 6 6 3 0 1Paper Reference(s)
6663/01
Edexcel GCECore Mathematics C1
Advanced Subsidiary
Wednesday 9 January 2008 Afternoon
Time: 1 hour 30 minutes
Materials required for examination Items included with question
papers
Mathematical Formulae (Green) Nil
Instructions to Candidates
In the boxes above, write your centre number, candidate number,
your surname, initials and signature.Check that you have the
correct question paper.Answer ALL the questions.You must write your
answer for each question in the space following the question.
Information for Candidates
A booklet Mathematical Formulae and Statist ical Tables is
provided.Full marks may be obtained for answers to ALL
questions.The marks for individual questions and the parts of
questions are shown in round brackets: e.g. (2).There are 11
questions in this question paper. The total mark for this paper is
75.There are 24 pages in this question paper. Any blank pages are
indicated.
Advice to Candidates
You must ensure that your answers to parts of questions are
clearly labelled.
You should show sufficient working to make your methods clear to
the Examiner.Answers without working may not gain full credit.
Examiners use only
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No.
*N25561A0124*Turn over
Candidate
No.
This publication may be reproduced only in accordance
withEdexcel Limited copyright policy.
2008 Edexcel Limited.
Printers Log. No.
N25561AW850/R6663/57570 3/3/3/3/3/3
Calculators may NOT be used in this examination.
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1. Find 3 4 72 5x x x+ d( ) .(4)
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Q1
(Total 4 marks)
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2. (a) Write down the value of161
4 .
(1)
(b) Simplify 16 123
4x( ) .
(2)
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3. Simplify
5 3
2 3
+,
giving your answer in the form a + b3, where a and b are
integers.(4)
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Q3
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4. The pointA (6, 4) and the pointB (8, 3) lie on the lineL.
(a) Find an equation forL in the form ax + by + c = 0, where a,
b and c are integers.
(4)
(b) Find the distanceAB, giving your answer in the form k5,
where kis an integer.(3)
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Q4
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5. (a) Write2 3x
x
+in the form wherep and q areconstants.
(2)
Given thaty = 5 72 3
xx
x +
+, x > 0,
(b) findd
d
y
x, simplifying the coefficient of each term.
(4)
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Question 5 continued
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Q5
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6.
Figure 1
Figure 1 shows a sketch of the curve with equation y = f(x). The
curve crosses thex-axis
at the points (1, 0) and (4, 0). The maximum point on the curve
is (2, 5).
In separate diagrams sketch the curves with the following
equations.
On each diagram show clearly the coordinates of the maximum
point and of each point at
which the curve crosses thex-axis.
(a) y = 2f(x),
(3)
(b) y = f(x).
(3)
The maximum point on the curve with equationy = f(x + a) is on
they-axis.
(c) Write down the value of the constant a.
(1)
x1 4
(2, 5)
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Q6
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7. A sequence is given by:
x
x x p xn n n
1
1
1=
= ++
,
( ),
wherep is a constant p .
(a) Find x2 in terms ofp.
(1)
(b) Show that x p p321 3 2= + + .
(2)
Given that x3 1= ,
(c) find the value ofp,
(3)
(d) write down the value ofx2008 .
(2)
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Question 7 continued
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Q7
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8. The equation
x kx k2 8+ + =
has no real solutions forx.
(a) Show that ksatisfies .
(3)
(b) Hence find the set of possible values ofk.
(4)
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Question 8 continued
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9. The curve Chas equationy = f(x),x > 0, and .
Given that the pointP(4, 1) lies on C,
(a) find f(x) and simplify your answer.
(6)
(b) Find an equation of the normal to Cat the pointP(4, 1).
(4)
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Question 9 continued
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(Total 10 marks)
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10. The curve Chas equation
y x x= + ( )( )3 1 2 .
(a) Sketch C showing clearly the coordinates of the points where
the curve meets the
coordinate axes.
(4)
(b) Show that the equation ofCcan be written in the form
y x x x k= + +3 2 5 ,
where kis a positive integer, and state the value ofk.
(2)
There are two points on Cwhere the gradient of the tangent to
Cis equal to 3.
(c) Find thex-coordinates of these two points.
(6)
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Question 10 continued
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Question 10 continued
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Q10
(Total 12 marks)
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11. The first term of an arithmetic sequence is 30 and the
common difference is 1.5
(a) Find the value of the 25th term.
(2)
The rth term of the sequence is 0.
(b) Find the value ofr.
(2)
The sum of the first n terms of the sequence is Sn .
(c) Find the largest positive value of Sn .
(3)
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Question 11 continued
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Question 11 continued
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Question 11 continued
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TOTAL FOR PAPER: 75 MARKS
END
Q11
(Total 7 marks)
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