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Paper Reference
6 6 6 3 0 1
This publication may be reproduced only in accordance with
Pearson Education Ltd copyright policy.2013 Pearson Education
Ltd.
Printers Log. No.
P41488AW850/R6663/57570 4/5/5/5/
*P41488A0132*
Paper Reference(s)
6663/01Edexcel GCECore Mathematics C1
Advanced Subsidiary
Monday 14 January 2013 Morning
Time: 1 hour 30 minutes
Materials required for examination Items included with question
papers
Mathematical Formulae (Pink) Nil
Calculators may NOT be used in this examination.
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 Statistical 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
32 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.
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1. Factorise completely x x 4 3
(3)
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Q1
(Total 3 marks)
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2. Express 82 3x + in the form 2y , statingy in terms ofx.
(2)
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Q2
(Total 2 marks)
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3. (i) Express
5 8 1 2 ( ) + ( )
in the form a b+ 2, where a and b are integers.(3)
(ii) Express
+
8030
5
in the form c 5 , where c is an integer.(3)
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Q3
(Total 6 marks)
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4. A sequence u u u1 2 3, , , ... satisfies
u u nn n+ = 1 2 1 1, .
Given that u2
9= ,
(a) find the value of u 3 and the value of u 4 ,(2)
(b) evaluate ur
r
.
=
1
4
(3)
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Q4
(Total 5 marks)
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5. The line l1 has equation y x= +2 3
The line l2
is perpendicular to l1
and passes through the point (5, 6).
(a) Find an equation for l2
in the form ax by c+ + = 0, where a b, and c are
integers.(3)
The line l2
crosses thex-axis at the pointA and they-axis at the pointB.
(b) Find thex-coordinate ofA and they-coordinate ofB.
(2)
Given that O is the origin,
(c) find the area of the triangle OAB .
(2)
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Question 5 continued
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Q5
(Total 7 marks)
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6.
Figure 1 shows a sketch of the curve with equation yx
x= 2
0,
The curve Chas equationyx
x= 2
5 0, , and the line lhas equation y x= +4 2
(a) Sketch and clearly label the graphs ofCand lon a single
diagram.
On your diagram, show clearly the coordinates of the points
where Cand lcross the
coordinate axes.
(5)
(b) Write down the equations of the asymptotes of the curve
C.
(2)
(c) Find the coordinates of the points of intersection ofy
x=
2
5 and y x= +4 2 (5)
y
xO
Figure 1
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Q6
(Total 12 marks)
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7. Lewis played a game of space invaders. He scored points for
each spaceship that he
captured.
Lewis scored 140 points for capturing his first spaceship.
He scored 160 points for capturing his second spaceship, 180
points for capturing his third
spaceship, and so on.
The number of points scored for capturing each successive
spaceship formed an arithmetic
sequence.
(a) Find the number of points that Lewis scored for capturing
his 20th spaceship.
(2)
(b) Find the total number of points Lewis scored for capturing
his first 20 spaceships.
(3)
Sian played an adventure game. She scored points for each dragon
that she captured.
The number of points that Sian scored for capturing each
successive dragon formed an
arithmetic sequence.
Sian captured n dragons and the total number of points that she
scored for capturing
all n dragons was 8500.
Given that Sian scored 300 points for capturing her first dragon
and then 700 points for
capturing hern th dragon,
(c) find the value ofn.(3)
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Question 7 continued
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Question 7 continued
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(Total 8 marks)
Q7
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8.d
d
y
xx
x
xx= +
3
3
4 5
20,
Given thaty = 7 atx = 1, findy in terms ofx, giving each term in
its simplest form.
(6)
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Question 8 continued
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(Total 6 marks)
Q8
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*P41488A02232*
9. The equation
k x x k +( ) + + =3 6 52 , where kis a constant,
has two distinct real solutions forx.
(a) Show that ksatisfies
k k2 2 24 0
