22117303

mathematics staNDaRD level PaPeR 1 Wednesday 4 May 2011 (afternoon) 1 hour 30 minutes iNSTrucTioNS To cANdidATES

candidate session number 0 0 Examination code 2 2 1 1 – 7 3 0 3

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 questions in the boxes provided. Section B: answer all questions 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.

11 pages © international Baccalaureate organization 2011

0112

–2–

M11/5/MATME/SP1/ENG/TZ1/XX

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 questions in the boxes provided. 1. [Maximum mark: 5] Let f ( x) = 7 − 2 x and g ( x) = x + 3 . (a) (b) (c) Find ( g f ) ( x) . Write down g −1 ( x) . Find ( f g −1 ) (5) . [2 marks] [1 mark] [2 marks]

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0212

–3– 2. [Maximum mark: 6]

M11/5/MATME/SP1/ENG/TZ1/XX

−2 1 A line L passes through A (1, − 1, 2) and is parallel to the line r = 1 + s 3 . 5 −2 (a) Write down a vector equation for L in the form r = a + tb . [2 marks]

The line L passes through point P when t = 2 . (b) Find (i) (ii) OP ; |OP| . → →

[4 marks]

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turn over

0312

–4– 3. [Maximum mark: 6] 2 −4 Let A = . −1 3 (a) (b) Find A−1 . 4 6 Solve the matrix equation AX = . 2 −2

M11/5/MATME/SP1/ENG/TZ1/XX

[2 marks] [4 marks]

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