C1 June 05
C1 June 05
C1 June 05
6663/01
Edexcel GCE
Core Mathematics C1
Advanced Subsidiary
Monday 23 May 2005 − Morning
Time: 1 hour 30 minutes
Instructions to Candidates
Write the name of the examining body (Edexcel), your centre number, candidate number, the
unit title (Core Mathematics C1), the paper reference (6663), your surname, initials and
signature.
Advice to Candidates
You must ensure that your answers to parts of questions are clearly labelled.
You must show sufficient working to make your methods clear to the Examiner. Answers
without working may gain no credit.
N23491A This publication may only be reproduced in accordance with London Qualifications copyright policy.
©2005 London Qualifications Limited.
1
1. (a) Write down the value of 8 3 .
(1)
2
(b) Find the value of 8 − 3 .
(2)
4
2. Given that y = 6x – , x ≠ 0,
x2
dy
(a) find ,
dx
(2)
⌠
(b) find y dx.
⌡
(3)
3. x2 – 8x – 29 ≡ (x + a)2 + b,
x2 – 8x – 29 = 0
(3, 5)
O (6, 0) x
Figure 1 shows a sketch of the curve with equation y = f(x). The curve passes through the
origin O and through the point (6, 0). The maximum point on the curve is (3, 5).
(a) y = 3f(x),
(2)
(b) y = f(x + 2).
(3)
On each diagram, show clearly the coordinates of the maximum point and of each point at which
the curve crosses the x-axis.
x – 2y = 1,
x2 + y2 = 29.
(6)
(3 − √ x ) 2
can be written as 9 x 2 6 x 2 .
1 1
7. (a) Show that
√x
(2)
dy (3 − √ x ) 2 2
Given that dx
= , x > 0, and that y = 3 at x = 1,
√x
1
8. The line l1 passes through the point (9, –4) and has gradient 3 .
(a) Find an equation for l1 in the form ax + by + c = 0, where a, b and c are integers.
(3)
The line l2 passes through the origin O and has gradient –2. The lines l1 and l2 intersect at the
point P.
N23491A 4
9. An arithmetic series has first term a and common difference d.
(a) Prove that the sum of the first n terms of the series is
1
2 n[2a + (n – 1)d].
(4)
Sean repays a loan over a period of n months. His monthly repayments form an arithmetic
sequence.
He repays £149 in the first month, £147 in the second month, £145 in the third month, and so on.
He makes his final repayment in the nth month, where n > 21.
(c) Form an equation in n, and show that your equation may be written as
n2 – 150n + 5000 = 0.
(3)
(d) Solve the equation in part (c).
(3)
(e) State, with a reason, which of the solutions to the equation in part (c) is not a sensible
solution to the repayment problem.
(1)