Edexcel GCE Core 1 Mathematics C1 jun 2006 6663/01 question paper

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N23557AW850/R6663/57570 3/3/3/3/3/53,900

Paper Reference(s)

6663/01Edexcel GCECore Mathematics C1Advanced SubsidiaryMonday 22 May 2006 – MorningTime: 1 hour 30 minutes

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

Calculators may NOT be used in this examination.

Instructions to CandidatesIn the boxes above, write your centre number, candidate number, your surname, initial(s) andsignature.Check that you have the correct question paper.You must write your answer for each question in the space following the question.

Information for CandidatesA 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 24 pages in this question paper. Any blank pages are indicated.

Advice to CandidatesYou 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 withoutworking may gain no credit.

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1. Find , giving each term in its simplest form.(4)

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1226 2 d( )x x x−+ +∫

Q1

(Total 4 marks)

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2. Find the set of values of x for which

x2 – 7x – 18 > 0.(4)

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Q2

(Total 4 marks)

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3. On separate diagrams, sketch the graphs of

(a) y = (x + 3)2,(3)

(b) y = (x + 3)2 + k, where k is a positive constant.(2)

Show on each sketch the coordinates of each point at which the graph meets the axes.

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Question 3 continued

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Q3

(Total 5 marks)

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4. A sequence a1, a2, a3, . . . is defined by

a1 = 3,

an + 1 = 3an – 5, n 1.

(a) Find the value of a2 and the value of a3.(2)

(b) Calculate the value of (3)

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1

.rr

a=∑

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Question 4 continued

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Q4

(Total 5 marks)

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5. Differentiate with respect to x

(a) x4 + 6√x,(3)

(b)

(4)

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2( 4) .xx+

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Question 5 continued

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Q5

(Total 7 marks)

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6. (a) Expand and simplify (4 + √3)(4 – √3).(2)

(b) Express in the form a + b√3, where a and b are integers.

(2)

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264+ √3

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Question 6 continued

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Q6

(Total 4 marks)

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7. An athlete prepares for a race by completing a practice run on each of 11 consecutivedays. On each day after the first day, he runs further than he ran on the previous day. Thelengths of his 11 practice runs form an arithmetic sequence with first term a km andcommon difference d km.

He runs 9 km on the 11th day, and he runs a total of 77 km over the 11 day period.

Find the value of a and the value of d.(7)

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Question 7 continued

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Q7

(Total 7 marks)

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8. The equation x2 + 2px + (3p + 4) = 0, where p is a positive constant, has equal roots.

(a) Find the value of p.(4)

(b) For this value of p, solve the equation x2 + 2px + (3p + 4) = 0.(2)

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Question 8 continued

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Q8

(Total 6 marks)

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9. Given that f(x) = (x2 – 6x)(x – 2) + 3x,

(a) express f(x) in the form x(ax2 + bx + c), where a, b and c are constants.(3)

(b) Hence factorise f(x) completely.(2)

(c) Sketch the graph of y = f(x), showing the coordinates of each point at which the graphmeets the axes.

(3)

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Question 9 continued

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Q9

(Total 8 marks)

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10. The curve C with equation y = f(x), x ≠ 0, passes through the point (3, 7 ).

Given that f ′(x) =

(a) find f(x).(5)

(b) Verify that f(–2) = 5.(1)

(c) Find an equation for the tangent to C at the point (–2, 5), giving your answer in theform ax + by + c = 0, where a, b and c are integers.

(4)

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32 ,xx

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12

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Question 10 continued

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Q10

(Total 10 marks)

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11. The line l1 passes through the points P(–1, 2) and Q(11, 8).

(a) Find an equation for l1 in the form y = mx + c, where m and c are constants.(4)

The line l2 passes through the point R(10, 0) and is perpendicular to l1. The lines l1 and l2intersect at the point S.

(b) Calculate the coordinates of S.(5)

(c) Show that the length of RS is 3√5.(2)

(d) Hence, or otherwise, find the exact area of triangle PQR.(4)

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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

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Q11

(Total 15 marks)

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Edexcel GCE Core 1 Mathematics C1 jun 2006 6663/01 question paper

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