GRADE 11 MATHEMATICS P2 11 NOVEMBER 2019 MORNING SESSION
WYNBERG BOYS' HIGH SCHOOL
Department of Mathematics End of year examination
GRADE 11
MATHEMATICS P2 11 NOVEMBER 2019 MORNING SESSION
MARKS: 150 TIME: 3 hours EXAMINER: Hu MODERATOR: Vz
This question paper consists of 16 printed pages, including this cover page.
11 Mathematics/P2
Page 2 of 16
INSTRUCTIONS AND INFORMATION
WBHS/Nov 2019
Read the following instructions carefully before answering the questions.
1. This question paper consists of 12 questions. 2. Answer ALL the questions in BLUE or BLACK ink only. Graphs must be drawn in
pencil when required. 3. Circle your teacher's monogram on your answer book. 4. Clearly show ALL calculations, diagrams, graphs, etc. that you have used in determining
your answers. Use the ADDITONAL SPACES in your ANSWER BOOK if you need to. 5. In QUESTIONS 3 ? 12, you are required to provide reasons for statements you make
arising from your use of any/all known geometry. 6. Answers only will not necessarily be awarded full marks. 7. You may use an approved scientific calculator (non-programmable and non-graphical) unless
stated otherwise. 8. If necessary, round off answers to TWO decimal places, unless stated otherwise. 9. Number the answers correctly according to the numbering system used in this question paper. 10. Write neatly and legibly. 11. The mark allocation by topic is as follows:
Question
Data Handling/ Statistics
Analytical Geometry
Trigonometry
Measure
1 2 3 4 567
8
Euclidean Geometry 9 10 11 12
Maximum 7 15 19 11 29 9 16
5
9 14 10 6
11 Mathematics/P2
Page 3 of 16
WBHS/Nov 2019
QUESTION 1
A tyre manufacturer recorded how far a selection of minibus taxis travel before they needed new tyres. The distances, in 1000's of kilometres, covered by taxis that travelled the same route are shown in the cumulative frequency graph (ogive) below.
Cumulative frequency curve showing the distances travelled by minibus taxis before they needed new tyres
110 105 100
95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10
5 0
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72
Distance travelled in 1000's of kilometres
Cumulative frequency
1.1. How many taxis were sampled?
(1)
1.2. Write down the modal class of the data.
(1)
1.3. Estimate the median number of kilometres travelled before new tyres were required. (1)
1.4. Estimate the inter-quartile range.
(3)
1.5. Provide a sensible reason why some taxis required a tyre change far sooner than others. (1) [7]
11 Mathematics/P2
Page 4 of 16
WBHS/Nov 2019
QUESTION 2
2.1. The table below shows the distances, sorted by stage length in kilometres, of the 21 stages of the 106th Tour de France, held during July 2019 ().
Stage 13 2 14 19 21 20 6 11 9 5 16
Dist. (km) 27,2 27,6 117,5 126,5 128 130 160,5 167,0 170,5 175,5 177
Stage 15 1 8 17 18 12 4 3 10 7
Dist. (km) 185 194,5 200,0 200 208 209,5 213,5 215,0 217,5 230,0
2.1.1. Calculate the mean stage distance.
(2)
2.1.2. Calculate the standard deviation of the stage distances.
(2)
2.1.3. The box-and-whisker for the data above is shown below. Write down the values for each of A to E.
A
B
C
D E
(4)
2.1.4. Explain why this data is negatively skewed.
(1)
2.1.5. What percentage of the data lies between the values A and D?
(1)
11 Mathematics/P2
Page 5 of 16
WBHS/Nov 2019
QUESTION 2 (continued)
2.2. The table and scatter plot below show the Life Sciences and English marks for 15 Grade 11 students in the June examinations. The least squares regression line has the equation y^ = a + bx .
Life Sci % 32 39 47 48 48 57 62 67 74 75 77 82 84 90 94 English % 47 49 64 62 53 59 54 53 71 69 73 78 89 95 87
English %
100
90
80
70
60
50
40
30
20
30
40
50
60
70
80
90 100
Life Sciences %
2.2.1. Determine the values of a and b.
(2)
2.2.2. A student missed both examinations due to illness. If they were assigned a
Life Sciences mark of 54%, what would their predicted English mark be?
(2)
2.2.3. What feature of the regression line indicates that increased performance in Life
Sciences is generally better than any accompanying increase in performance in
English.
(1)
[15]
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