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Difficult C1 paper

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Paper Reference(s)
6663/01
Edexcel GCE
Core Mathematics C1Gold Level G3
Time: 1 hour 30 minutes
Materials required for examination tems included !ith question a ers
Mathematical Formulae (Green)
Nil
Candidates may use any calculator allowed by theregulations of the JointCouncil for Qualications. Calculators must not have thefacility for symbolicalgebra manipulation, dierentiation and integration, orhave retrievablemathematical formulas stored in them.
nstructions to Candidates
Write the name of the examining body (Edexcel) your centre number candidate number the unit title (!ore Mathematics ! ) the paper reference (###$) your surname initials and signature%
nformation for Candidates
& boo'let Mathematical Formulae and tatistical *ables+ is pro,ided%Full mar's may be obtained for ans-ers to &.. /uestions%*here are 0 /uestions in this /uestion paper% *he total mar' for this paper is 12%
#dvice to Candidates
3ou must ensure that your ans-ers to parts of /uestions are clearly labelled%3ou must sho- sufficient -or'ing to ma'e your methods clear to the Examiner% &ns-ers-ithout -or'ing may gain no credit%
$u%%ested %rade &oundaries for this a er:
#'#(C)E
61*3+*36,-1.Gold 3
*his publication may only be reproduced in accordance -ith Edexcel .imited copyright policy%45001650 $ Edexcel .imited%
1
Factorise completely
x
7 8
x
$
%
32anuar ,013,
Express 9
5
x
: $
in the form 5
y
stating
y
in terms of
x
%
,2anuar ,0133
(
a
) ho- that
x
5
: #
x
: can be -ritten as(
x
:
p
)
5
:
q
-here
p
and
q
are integers to be found%
,
(
b
) 'etch the cur,e -ith e/uation
y
;
x
5
: #
x
: sho-ing clearly any intersections -iththe coordinate axes%
,
(
c
) Find the ,alue of the discriminant of
x
5
: #
x
: %
,Ma ,010+
.
*he cur,e
C
has e/uation
y
;
x
(2 7
x
) and the line
L
has e/uation 5
y
; 2
x
: 8%(
a
) <se algebra to sho- that
C
and
L
do not intersect%
+
(
b
) 'etch
C
and
L
on the same diagram sho-ing the coordinates of the points at -hich
C
and
L
meet the axes%
+2anuar ,01,
Gold $= > 5
5
*4i%ure 1
Figure sho-s a s'etch of the cur,e -ith e/uation
y
;
x
5
x
? 0%*he cur,e
C
has e/uation
y
;
x
5
7 2
x
? 0 and the line
l
has e/uation
y
; 8
x
: 5%(
a
) 'etch and clearly label the graphs of
C
and
l
on a single diagram%@n your diagram sho- clearly the coordinates of the points -here
C
and
l
cross thecoordinate axes%
*
(
b
) Write do-n the e/uations of the asymptotes of the cur,e
C
%
,
(
c
) Find the coordinates of the points of intersection of
y
;
x
5
7 2 and
y
; 8
x
: 5%
*2anuar ,013
Gold $= > 5
$
6
& company -hich is ma'ing 500 mobile phones each -ee' plans to increase its production%*he number of mobile phones produced is to be increased by 50 each -ee' from 500 in -ee' to 550 in -ee' 5 to 580 in -ee' $ and so on until it is producing #00 in -ee'
N
%(
a
) Find the ,alue of
N
%
,
*he company then plans to continue to ma'e #00 mobile phones each -ee'%(
b
) Find the total number of mobile phones that -ill be made in the first 25 -ee's startingfrom and including -ee' %
*Ma
20!
5
*he e/uation
x
5
:
kx
: 9 ;
k
has no real solutions for
x
%(
a
)ho- that
k
satisfies
k
5
: 8
k
6 $5 A 0%
3
(
b
)Bence find the set of possible ,alues of
k
%
+2anuar
200
Gold $= > 5
8

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