M13/5/FURMA/SP2/ENG/TZ0/XX
22137102
Further mathematics
STANDARD level
Paper 2
Tuesday 21 May 2013 (morning)
2 hours
Instructions to candidates
Do not open this examination paper until instructed to do so.
Answer all questions.
Unless otherwise stated in the question, all numerical answers should be given exactly or
correct to three significant figures.
A graphic display calculator is required for this paper.
A clean copy of the Mathematics HL and Further Mathematics SL information booklet is
required for this paper.
The maximum mark for this examination paper is [120 marks].
2213-7102 7 pages
© International Baccalaureate Organization 2013
, –2– M13/5/FURMA/SP2/ENG/TZ0/XX
Please start each question on a new page. Full marks are not necessarily awarded for a correct answer
with no working. Answers must be supported by working and/or explanations. In particular, solutions
found from a graphic display calculator should be supported by suitable working, for example, if graphs
are used to find a solution, you should sketch these as part of your answer. 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.
1. [Maximum mark: 9]
The discrete random variable X follows the distribution Geo ( p).
(a) (i) Write down the mode of X .
28
(ii) Find the exact value of p if Var ( X ) = . [3 marks]
9
Arthur tosses a biased coin each morning to decide whether to walk or cycle to school;
he walks if the coin shows a head.
The probability of obtaining a head is 0.55.
(b) (i) Find the smallest value of n for which the probability of Arthur walking to
school on the next n days is less than 0.01.
(ii) Find the probability that Arthur cycles to school for the third time on the
last of eight successive days. [6 marks]
2213-7102
22137102
Further mathematics
STANDARD level
Paper 2
Tuesday 21 May 2013 (morning)
2 hours
Instructions to candidates
Do not open this examination paper until instructed to do so.
Answer all questions.
Unless otherwise stated in the question, all numerical answers should be given exactly or
correct to three significant figures.
A graphic display calculator is required for this paper.
A clean copy of the Mathematics HL and Further Mathematics SL information booklet is
required for this paper.
The maximum mark for this examination paper is [120 marks].
2213-7102 7 pages
© International Baccalaureate Organization 2013
, –2– M13/5/FURMA/SP2/ENG/TZ0/XX
Please start each question on a new page. Full marks are not necessarily awarded for a correct answer
with no working. Answers must be supported by working and/or explanations. In particular, solutions
found from a graphic display calculator should be supported by suitable working, for example, if graphs
are used to find a solution, you should sketch these as part of your answer. 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.
1. [Maximum mark: 9]
The discrete random variable X follows the distribution Geo ( p).
(a) (i) Write down the mode of X .
28
(ii) Find the exact value of p if Var ( X ) = . [3 marks]
9
Arthur tosses a biased coin each morning to decide whether to walk or cycle to school;
he walks if the coin shows a head.
The probability of obtaining a head is 0.55.
(b) (i) Find the smallest value of n for which the probability of Arthur walking to
school on the next n days is less than 0.01.
(ii) Find the probability that Arthur cycles to school for the third time on the
last of eight successive days. [6 marks]
2213-7102
