# Ib Diploma

Topics: Cumulative distribution function, Function, Inverse function Pages: 12 (1337 words) Published: April 20, 2013
M09/5/MATHL/HP1/ENG/TZ2/XX

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13 pages © international Baccalaureate organization 2009

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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: 5] When the function q ( x) = x + kx 2 − 7 x +  is divided by ( x +1) the remainder is seven times the remainder that is found when the function is divided by ( x + 2) . Find the value of k . ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... .....................................................................

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–– 2. [Maximum mark: 5]

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The test scores of a group of students are shown on the cumulative frequency graph below. 200 180 160 Cumulative frequency 140 120 100 80 60 40 20 0 0 10 20 0 40 50 60 70 80 90 100

Test Scores (a) (b) Estimate the median test score. The top 10 % of students receive a grade A and the next best 20 % of students receive a grade B. Estimate (i) (ii) the minimum score required to obtain a grade A; the minimum score required to obtain a grade B. [4 marks] [1 mark]

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–4– 3. [Maximum mark: 6] A random variable has a probability density function given by kx (2 − x) , 0 ≤ x ≤ 2 f ( x) =  0, elsewhere.  (a) (b) Show that k = Find E ( X ) .  . 4

M09/5/MATHL/HP1/ENG/TZ2/XX

[4 marks] [2 marks]

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