Mathematics: analysis and approaches
Higher level
Paper 2
Friday 7 May 2021 (morning)
Candidate session number
2 hours
Instructions to candidates
y Write your session number in the boxes above.
y Do not open this examination paper until instructed to do so.
y A graphic display calculator is required for this paper.
y Section A: answer all questions. Answers must be written within the answer boxes provided.
y Section B: answer all questions in the answer booklet provided. Fill in your session number
on the front of the answer booklet, and attach it to this examination paper and your
cover sheet using the tag provided.
y Unless otherwise stated in the question, all numerical answers should be given exactly or
correct to three significant figures.
y A clean copy of the mathematics: analysis and approaches formula booklet is required for
this paper.
y The maximum mark for this examination paper is [110 marks].
2221 – 7112
13 pages © International Baccalaureate Organization 2021
16EP01
, –2– 2221 – 7112
Full marks are not necessarily awarded for a correct answer with no working. Answers must be
supported by working and/or explanations. 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.
Section A
Answer all questions. Answers must be written within the answer boxes provided. Working may be
continued below the lines, if necessary.
1. [Maximum mark: 6]
At a café, the waiting time between ordering and receiving a cup of coffee is dependent upon
the number of customers who have already ordered their coffee and are waiting to receive it.
Sarah, a regular customer, visited the café on five consecutive days. The following table
shows the number of customers, x , ahead of Sarah who have already ordered and are
waiting to receive their coffee and Sarah’s waiting time, y minutes.
Number of customers (x) 3 9 11 10 5
Sarah’s waiting time (y) 6 10 12 11 6
The relationship between x and y can be modelled by the regression line of y on x with
equation y = ax + b .
(a) (i) Find the value of a and the value of b .
(ii) Write down the value of Pearson’s product-moment correlation coefficient, r . [3]
(b) Interpret, in context, the value of a found in part (a)(i). [1]
On another day, Sarah visits the café to order a coffee. Seven customers have already
ordered their coffee and are waiting to receive it.
(c) Use the result from part (a)(i) to estimate Sarah’s waiting time to receive her coffee. [2]
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16EP02
, –3– 2221 – 7112
2. [Maximum mark: 5]
An arithmetic sequence has first term 60 and common difference -2.5.
(a) Given that the k th term of the sequence is zero, find the value of k . [2]
Let Sn denote the sum of the first n terms of the sequence.
(b) Find the maximum value of Sn . [3]
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Turn over
16EP03
Higher level
Paper 2
Friday 7 May 2021 (morning)
Candidate session number
2 hours
Instructions to candidates
y Write your session number in the boxes above.
y Do not open this examination paper until instructed to do so.
y A graphic display calculator is required for this paper.
y Section A: answer all questions. Answers must be written within the answer boxes provided.
y Section B: answer all questions in the answer booklet provided. Fill in your session number
on the front of the answer booklet, and attach it to this examination paper and your
cover sheet using the tag provided.
y Unless otherwise stated in the question, all numerical answers should be given exactly or
correct to three significant figures.
y A clean copy of the mathematics: analysis and approaches formula booklet is required for
this paper.
y The maximum mark for this examination paper is [110 marks].
2221 – 7112
13 pages © International Baccalaureate Organization 2021
16EP01
, –2– 2221 – 7112
Full marks are not necessarily awarded for a correct answer with no working. Answers must be
supported by working and/or explanations. 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.
Section A
Answer all questions. Answers must be written within the answer boxes provided. Working may be
continued below the lines, if necessary.
1. [Maximum mark: 6]
At a café, the waiting time between ordering and receiving a cup of coffee is dependent upon
the number of customers who have already ordered their coffee and are waiting to receive it.
Sarah, a regular customer, visited the café on five consecutive days. The following table
shows the number of customers, x , ahead of Sarah who have already ordered and are
waiting to receive their coffee and Sarah’s waiting time, y minutes.
Number of customers (x) 3 9 11 10 5
Sarah’s waiting time (y) 6 10 12 11 6
The relationship between x and y can be modelled by the regression line of y on x with
equation y = ax + b .
(a) (i) Find the value of a and the value of b .
(ii) Write down the value of Pearson’s product-moment correlation coefficient, r . [3]
(b) Interpret, in context, the value of a found in part (a)(i). [1]
On another day, Sarah visits the café to order a coffee. Seven customers have already
ordered their coffee and are waiting to receive it.
(c) Use the result from part (a)(i) to estimate Sarah’s waiting time to receive her coffee. [2]
..........................................................................
..........................................................................
..........................................................................
..........................................................................
..........................................................................
..........................................................................
16EP02
, –3– 2221 – 7112
2. [Maximum mark: 5]
An arithmetic sequence has first term 60 and common difference -2.5.
(a) Given that the k th term of the sequence is zero, find the value of k . [2]
Let Sn denote the sum of the first n terms of the sequence.
(b) Find the maximum value of Sn . [3]
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..........................................................................
..........................................................................
..........................................................................
..........................................................................
..........................................................................
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Turn over
16EP03
