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Paper Reference(s) 6663/01 Edexcel GCE Core Mathematics C1

Advanced Subsidiary

Monday 23 May 2005 ( Morning Time: 1 hour 30 minutes

Materials required for examination Items included with question papers Mathematical Formulae (Green) Nil

Calculators may NOT be used in this examination.

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.

Information for Candidates
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
Full marks may be obtained for answers to ALL questions.
There are 10 questions in this question paper. The total mark for this paper is 75.

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.

1. (a) Write down the value of [pic].
(b) Find the value of [pic].

2. Given that y = 6x – [pic], x ≠ 0,

(a) find [pic],
(b) find [pic] dx.

3. x2 – 8x – 29 ( (x + a)2 + b,

where a and b are constants.

(a) Find the value of a and the value of b.
(b) Hence, or otherwise, show that the roots of

x2 – 8x – 29 = 0

are c ( d(5, where c and d are integers to be found. (3)

4. Figure 1

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).

On separate diagrams, sketch the curve with equation

(a) y = 3f(x),
(b) y =…...

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