GRADE 11 MATHEMATICS P2 11 NOVEMBER 2019 MORNING SESSION

[Pages:16]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.

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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

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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]

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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)

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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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WBHS/Nov 2019

QUESTION 3 In the diagram below, ABCD is a parallelogram. E and H are the x- and y-intercepts respectively of diagonal AC and AC DG . BE is perpendicular to the x-axis and AD = 4 13 units.

A (-12; 10)

y B (8; 8)

H J

E D (-4; -2)

G

x C (16; -4)

3.1. Calculate the gradient of diagonal AC.

(2)

3.2. Calculate the coordinates of J, the midpoint of AC.

(2)

3.3. Show that AC has the equation y = - 1 x + 4 .

(3)

2

3.4. Write down the coordinates of E.

(1)

3.5. Determine the equation of DG, in the form y = mx + c .

(3)

( ) 3.6. Show that the perimeter of ABCD is 4 101 + 8 13 units.

(4)

3.7. Prove that BEGH is a parallelogram.

(4)

[19]

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WBHS/Nov 2019

QUESTION 4

In the diagram below, S and P are the x- and y-intercepts respectively of the line passing through S, T

and P. SP has the equation y = 1 x +1. PS^O = .

3

y

P

T

S

O

x

R (0; -4)

4.1. Determine the coordinates of S.

(2)

4.2. Determine the equation of the line RT.

(3)

4.3. Calculate the size of .

(2)

4.4. Hence calculate the size of .

(2)

4.5. Determine the radius of the circle passing through P, T and R.

(2)

[11]

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QUESTION 5

5.1. In the diagram below, OA = 4, OB = 8 and XO^ B = . OA OB .

y 4

A (x; 2)

O

8

WBHS/Nov 2019 x

B (4; q)

5.1.1. Calculate the value of x (express your answer in simplest surd form).

(2)

5.1.2. Determine the value of .

(2)

5.1.3. Determine the value of q (express your answer in simplest surd form).

(2)

5.2. Given sin 36 = t , express each of the following in terms of t by making use of a suitable diagram.

5.2.1. sin144

(3)

5.2.2. cos 234

(2)

5.3. Simplify the following to a single trig ratio of :

sin (180 - ) - 2cos(90 - ) cos

(8)

2cos2 (360 + ) - cos(-)

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