MATHEMATICS Learner’s Study and Revision Guide for Grade 12
DATA HANDLING Part 2
Revision Notes, Exercises and Solution Hints by
Roseinnes Phahle
Examination Questions by the Department of Basic Education
Preparation for the Mathematics examination brought to you by Kagiso Trust
Contents
Unit 19 Part 2 More questions from past examination papers
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Answers – the answers have much to teach you about statistical analysis
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How to use this revision and study guide (in conjunction with Part 1) 1. Study the revision notes given in Part 1. The notes are interactive in that in some parts you are required to make a response based on your prior learning of the topic from your teacher in class or from a textbook. Furthermore, the notes cover all the Mathematics from Grade 10 to Grade 12. 2. “Warm-up” exercises follow the notes in Part 1. Some exercises carry solution HINTS in the answer section. Do not read the answer or hints until you have tried to work out a question and are having difficulty. 3. The notes and exercises in Part 1 are followed by questions from past examination papers. 4. The examination questions are followed by blank spaces or boxes inside a table. Do the working out of the question inside these spaces or boxes. 5. Alongside the blank boxes are HINTS in case you have difficulty solving a part of the question. Do not read the hints until you have tried to work out the question and are having difficulty. 6. What follows in Part 2 are more questions taken from past examination papers. 7. Answers to the extra past examination questions appear at the end. Some answers carry notes to enrich your knowledge. 8. Finally, don’t be a loner. Work through this guide in a team with your classmates.
Data Handling – Part 2
MORE QUESTIONS FROM PAST EXAMINATION PAPERS Exemplar 2008
DIAGRAM
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DIAGRAM
Data Handling – Part 2
DIAGRAM
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Question 12
Data Handling – Part 2
Preparatory Examination 2008
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DIAGRAM SHEET 2
Data Handling – Part 2
DIAGRAM SHEET 2
DIAGRAM SHEET 3
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Feb – March 2009
Data Handling – Part 2
DIAGRAM SHEET 2 Question 11.1
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DIAGRAM SHEET 2
Data Handling – Part 2
DIAGRAM SHEET 3
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November 2009 (Unused paper)
DIAGRAM SHEET 2
Data Handling – Part 2
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DIAGRAM SHEET 2
Data Handling – Part 2
12.1
Use the above cumulative frequency curve to determine the following: 12.1.1 How many light bulbs were tested
(1)
12.1.2 The median lifetime of the electric light bulbs tested
(2)
12.1.3 The interquartile range
(2)
12.1.4 The number of electric light bulbs with a lifetime of between 1 750 and 2 000 hours (2) 12.2
If the cost of one light bulb is R5,00, determine the amount spent on purchasing the light bulbs that lasted longer than 2 500 hours. (2)[9]
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November 2009 (1)
DIAGRAM SHEET 1
Data Handling – Part 2
{Diagram Sheet 1 is the same as the one in the question above}
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3.1
How many students took the test?
(1)
3.2
Only the top 25% of the students are allowed to do an advanced course in programming. Determine the cut off-off mark to determine the top 25%.
(1)
3.3
Construct a frequency table for the information given in the ogive on DIAGRAM SHEET 2. Complete the table with the information. (3)[5]
Data Handling – Part 2
DIAGRAM SHEET 2 Marks (out of 100)
Frequency ( f )
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Feb – March 2010
Data Handling – Part 2
DIAGRAM SHEET 1
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QUESTION 3 The time taken (to the nearest minute) for a certain task to be completed was recorded on 48 occasions and the following data was obtained. Time (in minutes)
11 ≤ t < 15 15 ≤ t < 19 19 ≤ t < 23 23 ≤ t < 27 27 ≤ t ≤ 30
Frequency 6 9 13 12 8
3.1
Complete the cumulative frequency table on DIAGRAM SHEET 2.
(1)
3.2
Draw an ogive (cumulative frequency curve) for the given data on DIAGRAM SHEET 2.
(4)
3.3
Determine, from the ogive, the median, lower quartile and upper quartile for the data.
(3)
3.4
Draw a box and whisker diagram of the data on DIAGRAM SHEET 3.
(2)
3.5
Comment on the spread of the time taken to complete the task.
DIAGRAM SHEET 2
(1)[11]
Data Handling – Part 2
DIAGRAM SHEET 2
DIAGRAM SHEET 3
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ANSWERS Exemplar 2008 9.1 Median = 21 9.2 Lower quartile = 17 Upper quartile = 26 9.3 & 9.4
Preparatory Examination 2008 9.1.1 & 9.1.2
9.1.3 kms. 9.1.4 10.1 & 10.2
10.1
10.2
10.3
R2,47 or
R2,48
11.1 11.2
Mean = 32,7
12.1 12.2
Supplier B I would choose Supplier A because their bulbs with the smaller standard deviation means that they have a more consistent life time. Whereas some bulbs from Supplier B have a longer life time than Supplier A’s there are also some that have a shorter life time.
σ =2
VO 2 max ≈ 60 units if an athlete runs 19 Yes. The more kms run the more VO 2 used.
Data Handling – Part 2
10.3 10.4
Median = 63km/h Majority of drivers are driving above the speed limit.
11.1 11.2 11.3
Minimum and maximum marks. 23rd learner. The learner is correct because Q2 − Q1 ≠ Q3 − Q2 . 15 results lie outside 1 sd of the mean.
11.4
11.4
11.5 Heights of players are spread fairly evenly. 11.6 6100 players fall within this interval. 12.1
Feb/March 2009 10.1 Mean = 550 kilocalories 10.2 σ = 69,03 kilocalories 10.3 Variation is greater in snack foods. So energy levels of breakfast cereals are spread closer to the mean thanthose of the snack foods sd’s 28 and 69,03 respectively). 11.1
12.2 Quadratic. 12.3 Minimum value of the quadratic is approximately 110 km/h. At this speed fuel consumption per 100km is at its lowest. Drivers should be advised to drive at this
11.2
11.3 Q1 ≈ 138 cms Median = Q2 ≈ 148 cms
Q3 ≈ 158 cms
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November 2009 (Unused paper) 9.1
November 2009(1) 1.1 x = 43,5 1.2 9,3; 19,3; 30,3; 68,8; 98,2 The following is also an acceptable 5 number summary: 9,3; 17,2; 30,3; 70,4; 98,2 1.3
9.2
There is a negative linear trend suggesting a decrease in the number of new infections year after year. 9.3 Give an answer that is valid in the context of this situation. Discuss your answer with the teacher to find out if it is acceptable. 10.1 Mean = 26 10.2 Standard deviation = 8,34 10.3 The teacherâ&#x20AC;&#x2122;s conclusion is reasonable because 13 out of the 20 travelling times fall within one standard deviation of the mean.
1.4
1.5 2.1 2.2
11.1 Lower quartile = 691 Median = 716 Upper quartile = 825 11.2
Or 11.3 There are 9 data points between 600 and 800. 12.1.1 500 12.1.2 About 2050 12.1.3 IQR = 675 12.2
Cost = R400
Data is positively skewed suggesting a large interval between the median and maximum rainfall because of some months having very heavy rainfall.
Ď&#x192; = 28,19
Linear or exponential.
Data Handling – Part 2
2.3 The trend is an overall decreasing one.
2.1.1
2.4 It is left to you to give an answer. The answer must be reasonable within the context of the given situation. Check your reason with the teacher or classmates. 2.5 It is left to you to give an answer. The answer must be reasonable within the context of the given situation. Check your reason with the teacher or class mates. 2.6 Approximately 47,6 seconds or an answer that is consistent with your diagram will be acceptable. 2.2
x = 29
3.1 50 3.2 Any answer in the interval 55% to 60% is acceptable. 3.3
2.1.2 Indicated on the graph. 2.1.3 8 goals. 2.2 x = 29 3.1
3.2
Feb/March 2010 1.1 Range = 22 1.2 x = 15,25 1.3 σ = 7,6 1.4.1 Increase in mean = 2 C per month. 1.4.2 Write your own description and check its reasonableness with your teacher or classmates.
3.3 Median = 22 minutes Lower quartile ≈ 18 minutes Upper quartile ≈ 25,5 minutes 3.4
3.5 Times are skewed to the left. Implies a small number of people finished the task very quickly whilst others took more time.
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