Ib Diploma

Only available on StudyMode
  • Topic: Cumulative distribution function, Function, Inverse function
  • Pages : 12 (1337 words )
  • Download(s) : 108
  • Published : April 20, 2013
Open Document
Text Preview
M09/5/MATHL/HP1/ENG/TZ2/XX

22097205

mathematics higher level PaPer 1 Thursday 7 May 2009 (afternoon) 2 hours iNsTrucTioNs To cANdidATEs Write your session number in the boxes above. do not open this examination paper until instructed to do so. You are not permitted access to any calculator for this paper. 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

2209-7205

13 pages © international Baccalaureate organization 2009

0113

–2–

M09/5/MATHL/HP1/ENG/TZ2/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 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 . ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... .....................................................................

2209-7205

0213

–– 2. [Maximum mark: 5]

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

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]

..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... ..................................................................... 2209-7205

turn over
0313

–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]

..................................................................... ........................................................................
tracking img