A APPROVED
GRADE 12 EXAMINATION
NOVEMBER 2016
ADVANCED PROGRAMME MATHEMATICS: PAPER II
Time: 1 hour 100 marks
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. This question paper consists of 14 pages and an Information Booklet of 4 pages (i–iv).
Please check that your question paper is complete.
2. This question paper consists of THREE modules:
Choose ONE of the THREE modules:
MODULE 2: STATISTICS (100 marks) OR
MODULE 3: FINANCE AND MODELLING (100 marks) OR
MODULE 4: MATRICES AND GRAPH THEORY (100 marks)
3. Non-programmable and non-graphical calculators may be used.
4. All necessary calculations must be clearly shown and writing should be legible.
5. Diagrams have not been drawn to scale.
6. Rounding of final answers.
MODULE 2: Four decimal places, unless otherwise stated.
MODULE 3: Two decimal places, unless otherwise stated.
MODULE 4: Two decimal places, unless otherwise stated.
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, GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II Page 2 of 14
MODULE 2 STATISTICS
QUESTION 1
1.1 In a large city one person in five is left-handed.
(a) Calculate the probability that in a random sample of 10 people, exactly
three will be left-handed. (5)
(b) Find the most likely number of left-handed people in a random sample of
15 people. (2)
(c) In a random sample of n people, the probability that the sample contains at
least one left-handed person is greater than 0,95. Solve for n, and hence
determine the least number of people required in the sample. (8)
1.2 Bjorn saves his digital images on his computer in three separate folders, namely
'Family', 'Friends' and 'Rowing'. His Family folder contains three images, his
Friends folder contains four images and his Rowing folder contains eight images.
All the images are different.
(a) How many ways can he arrange these 15 images in a row across his
computer screen if he keeps the images from each folder together? (5)
(b) Calculate the probability that if Bjorn chooses six images at random, there
are two from each folder. (5)
(c) Calculate the number of different ways in which Bjorn can choose six of
these images if there are at least three images from the Rowing folder and at
least one image from each of the other two folders. (8)
[33]
QUESTION 2
2.1 It is known that the wind causes a 'chill factor' so that the human body experiences
the temperature to be lower than the actual temperature. The following table gives
the experienced temperature (t °C) for different wind speeds (w km/h) when the
actual temperature is 10 °C. (Work accurately to two decimal places in this
question.)
w (km/h) 0 5 10 15 20 25
t (°C) 10° 6° –6° –16° –22° –25°
(a) Determine the equation of a suitable regression line from which a value of t
can be estimated for a given value w. (4)
(b) Find the value of the correlation coefficient for the data, and state what this
indicates about the data. (2)
(c) Estimate the experienced temperature when the wind speed is 35 km/h. (2)
(d) Comment on the reliability of this estimate. (2)
IEB Copyright © 2016
GRADE 12 EXAMINATION
NOVEMBER 2016
ADVANCED PROGRAMME MATHEMATICS: PAPER II
Time: 1 hour 100 marks
PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY
1. This question paper consists of 14 pages and an Information Booklet of 4 pages (i–iv).
Please check that your question paper is complete.
2. This question paper consists of THREE modules:
Choose ONE of the THREE modules:
MODULE 2: STATISTICS (100 marks) OR
MODULE 3: FINANCE AND MODELLING (100 marks) OR
MODULE 4: MATRICES AND GRAPH THEORY (100 marks)
3. Non-programmable and non-graphical calculators may be used.
4. All necessary calculations must be clearly shown and writing should be legible.
5. Diagrams have not been drawn to scale.
6. Rounding of final answers.
MODULE 2: Four decimal places, unless otherwise stated.
MODULE 3: Two decimal places, unless otherwise stated.
MODULE 4: Two decimal places, unless otherwise stated.
IEB Copyright © 2016 PLEASE TURN OVER
, GRADE 12 EXAMINATION: ADVANCED PROGRAMME MATHEMATICS: PAPER II Page 2 of 14
MODULE 2 STATISTICS
QUESTION 1
1.1 In a large city one person in five is left-handed.
(a) Calculate the probability that in a random sample of 10 people, exactly
three will be left-handed. (5)
(b) Find the most likely number of left-handed people in a random sample of
15 people. (2)
(c) In a random sample of n people, the probability that the sample contains at
least one left-handed person is greater than 0,95. Solve for n, and hence
determine the least number of people required in the sample. (8)
1.2 Bjorn saves his digital images on his computer in three separate folders, namely
'Family', 'Friends' and 'Rowing'. His Family folder contains three images, his
Friends folder contains four images and his Rowing folder contains eight images.
All the images are different.
(a) How many ways can he arrange these 15 images in a row across his
computer screen if he keeps the images from each folder together? (5)
(b) Calculate the probability that if Bjorn chooses six images at random, there
are two from each folder. (5)
(c) Calculate the number of different ways in which Bjorn can choose six of
these images if there are at least three images from the Rowing folder and at
least one image from each of the other two folders. (8)
[33]
QUESTION 2
2.1 It is known that the wind causes a 'chill factor' so that the human body experiences
the temperature to be lower than the actual temperature. The following table gives
the experienced temperature (t °C) for different wind speeds (w km/h) when the
actual temperature is 10 °C. (Work accurately to two decimal places in this
question.)
w (km/h) 0 5 10 15 20 25
t (°C) 10° 6° –6° –16° –22° –25°
(a) Determine the equation of a suitable regression line from which a value of t
can be estimated for a given value w. (4)
(b) Find the value of the correlation coefficient for the data, and state what this
indicates about the data. (2)
(c) Estimate the experienced temperature when the wind speed is 35 km/h. (2)
(d) Comment on the reliability of this estimate. (2)
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