MATHEMATICS EXAMINATION PAPER 2 GRADE 11 10 …

[Pages:24]ST DAVID'S MARIST INANDA

MATHEMATICS EXAMINATION PAPER 2 GRADE 11

10 NOVEMBER 2018

EXAMINER: MRS N GOEMANS MODERATOR: MRS S RICHARD

MARKS: 125 TIME: 2 hours

NAME:_____________________________________________________________

PLEASE PUT A CROSS NEXT TO YOUR TEACHER'S NAME:

Mrs Kennedy Mrs Richard Ms de Villiers Mrs Nagy

Mrs Dyer Mrs Goemans

INSTRUCTIONS:

This paper consists of 24 pages. Please check that your paper is complete. Please answer all questions on the Question Paper. Answers must be rounded off to two decimal places, unless otherwise stated. It is in your interest to show all your working details. Work neatly. Do NOT answer in pencil. Diagrams are not drawn to scale. Please ensure that your calculator is on DEGREE mode.

QUESTION

Q1

Q2

Q3 Q4 Q5 Q6 Q7 Q8

[13] [13] [10] [16] [8] [12] [23] [8]

LEARNER'S MARKS

Q9 Q10 Q11 TOTAL

[9]

[5]

[8]

[125]

Page 2 of 24

QUESTION 1

[13 marks]

The cumulative frequency curve (ogive) below shows the heights (in inches) of a sample of 50 randomly-selected females between the ages of 20 and 29.

a) What percentage of women are shorter than 62 inches?

(1)

b) Write down the median height of the sample.

(1)

c) Estimate the interquartile range of the sample heights.

(3)

d) i) Use the ogive to complete the following table:

Height (inches)

58 < 60 60 < 62 62 < 64 64 < 66 66 < 68 68 < 70 70 < 72 72 < 74

Frequency

3 6

11 7 5 2

Cumulative frequency

2

11

36 43 48 50

Mid-Point

59 61 63 65 67 69 71 73

Page 3 of 24 (4)

ii) Use the completed table to calculate the estimated mean of the data. (2)

iii) Hence, comment on the symmetry (skewness) of the data set.

(2)

Page 4 of 24

QUESTION 2

[13 marks]

The following data was collected from 6 separate farms in KZN: the amount of fertilizer used by the farm (measured in kilograms per hectare), as well as the associated grain yield of the farm (measured in tons per hectare). The collected data is displayed in the following table:

Fertilizer used (kg/ha) Grain yield (tons/ha)

0

24

53

77

a

123

4,27

4,67

5,00

5,03

5,28

5,67

a) Given that the mean amount of fertilizer used per farm is 62,5 kg/ha, calculate the

value of a.

(1)

b) i) Use your calculator to determine the mean and standard deviation of the grain yield

of the 6 farms. Give your answers to 2 decimal places.

(2)

ii) The following statement is given: Based on the sample data, 68% of farms in

KZN have a grain yield of between 4,55 tons/ha and 5,99 tons/ha.

Comment on the validity of this statement, using numerical evidence.

(2)

Page 5 of 24

c) The data is represented in the scatter plot that follows. The least-squares regression line has been drawn onto the scatter plot.

Grain yield (t/ha)

Scatterplot of Grain yield (t/ha) vs Fertilizer used (kg/ha)

5,8

5,6

5,4

5,2

5,0

4,8

4,6

4,4

4,2 0

20

40

60

80

100

120

140

Fertilizer used (kg/ha)

i) Explain why "Grain yield" is represented on the vertical axis.

(2)

ii) 1) Determine the equation of the regression line.

(2)

Page 6 of 24

2) Use the equation of the regression line to predict the amount of fertilizer

required to produce a grain yield of 4,8 tons/ha.

(2)

iii) Given that the correlation coefficient of the data is 0,98, comment on the

relationship between the two variables. Use a real-life explanation to

support your answer.

(2)

QUESTION 3

[10 marks]

a) In the diagram below, P is the point (; 5). = . = 13 units. y

P (x; 5) 13

O

Determine, without the use of a calculator: i) the value of x.

Page 7 of 24

S

x

(1)

ii) 29 cos(360? - ) - 3 sin( + 90?)

(4)

b) Simplify, without the use of a calculator. Show all calculations.

3 cos 150?.sin 270? tan(-45?)+cos 600?

Page 8 of 24 (5)

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