# Ib Matme Sl1 2010

Topics: Critical point, Analytic geometry, Stationary point Pages: 9 (1117 words) Published: May 5, 2013
ıM10/5/MATME/SP1/ENG/TZ1/XX

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mathematics staNDaRD level PaPeR 1 Wednesday 5 May 2010 (afternoon) 1 hour 30 minutes iNSTrucTioNS To cANdidATES  Write your session number in the boxes above.  not open this examination paper until instructed to do so. do  are not permitted access to any calculator for this paper. You  Section A: answer all of Section A in the spaces provided.  Section B: answer all of Section B on the answer sheets provided. Write your session number on each answer sheet, and attach them to this examination paper and your cover sheet using the tag provided.  At the end of the examination, indicate the number of sheets used in the appropriate box on your cover sheet.  unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. 0 0 candidate session number

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11 pages © international Baccalaureate organization 2010

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Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. Where an answer is incorrect, some marks may be given for a correct method, provided this is shown by written working. You are therefore advised to show all working. Section a Answer all the questions in the spaces provided. Working may be continued below the lines, if necessary. 1. [Maximum mark: 7] Let f ( x) = 8 x − 2 x 2 . Part of the graph of f is shown below.

(a) (b)

Find the x-intercepts of the graph. (i) (ii) Write down the equation of the axis of symmetry. Find the y-coordinate of the vertex.

[4 marks]

[3 marks]

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–3– 2. [Maximum mark: 6]  2 1 3 2   and P =  3  . Let W =  2 0 1    1  0 1 3     (a) (b) Find WP.  26    Given that 2WP + S =  12  , find S.  10   

M10/5/MATME/SP1/ENG/TZ1/XX

[3 marks] [3 marks]

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–4– 3. [Maximum mark: 6] (a) (b) Expand (2 + x) 4 and simplify your result. 1   Hence, find the term in x 2 in (2 + x) 4 1 + 2  .  x 

M10/5/MATME/SP1/ENG/TZ1/XX

[3 marks] [3 marks]

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