JEPPE HIGH SCHOOL FOR BOYS

Department of Mathematics

GRADE 11

FINAL EXAMINATION – PAPER 2

DATE:

27 November 2017

TIME:

3 hours

TOPICS:

Analytical Geometry, Trigonometry, Euclidean Geometry and Statistics

TOTAL MARKS:

150

EXAMINER:

Mrs. M Marais

MODERATOR:

Mr. P Statham

NAME: __________________________________

TEACHER: __________________________________

PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY:

1. This question paper consists of 24 pages and 11 questions, as well as a green information (formula) sheet. Please check that your paper is complete.

2. Answer all the questions in the question paper booklet in the spaces provided.

3. All necessary working must be clearly shown.

4. You may use an approved scientific calculator (non-programmable and non-graphical) unless otherwise stated.

5. Please note that diagrams are not drawn to scale.

6. It is in your own interest to write legibly and to present your work neatly.

This page is left blank intentionally and may be used for rough working.

QUESTION 1:[8]

The data in the table below represents the scores in percentages obtained by 12 Mathematics learners in their Grade 12 trial examination and in their corresponding final examination respectively:

Trial Exam (x)

76

64

90

68

70

79

52

64

61

71

84

70

Final Exam (y)

82

69

94

75

80

88

56

81

76

78

90

76

1.1 Determine the equation of the least squares regression line for this set

of data correct to 4 decimal places.(3)

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1.2 Hence, predict the final exam percentage for a learner obtaining 73% in

the trial examination. Give your answer to the nearest percentage. (2)

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1.3 Calculate the correlation coefficient for the above data. (1)

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1.4 Do you think that by using the least squares regression line one can accurately predict a learner’s final exam mark from their trial exam mark? Provide mathematical justification for your answer. (2)

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QUESTION 2:[12]

The following table shows the absenteeism for 280 employees in a South African company during one particular year:

Number of Days Absent

Frequency

Cumulative Frequency

0 < d 5

32

5 < d 10

68

10 < d 15

130

15 < d 20

42

20 < d 25

8

2.1On the grid below, draw an Ogive using the information from the table:(4)

Cumulative Frequency

Number of days absent (d)

2.2From your Ogive, determine the approximate number of employees that were:

(a)absent for 13 days or less.(1)

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(b)absent for more than 17 days.(2)

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2.3From your Ogive, determine the following:

(a)the median number of days absent.(1)

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(b)the inter-quartile range of days absent.(2)

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(c)the percentage of workers absent for more than 20 days.(2)

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QUESTION 3:[21]

Refer to the sketch below, showing points , and as the vertices of on the Cartesian plane. , is the midpoint of AC and N is the point :

D

3.1Show that . (2)

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3.2Calculate the gradient of AB. (2)

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3.3Determine the equation of AB and the coordinates of D.(5)

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3.4Calculate the length of AC. (Leave your answer in simplest surd form) (2)

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3.5Find q if it is given that .(3)

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3.6 Calculate the area of . (2)

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3.7Calculate the size of angle correct to 1 decimal place.(3)

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3.8Determine the coordinates of so that the quadrilateral ABMP is a parallelogram.(2)

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QUESTION 4:[26]

4.1Simplify the following expression without the use of a calculator:

(6)

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4.2Prove the identity:(5)

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4.3Determine the general solution of:(4)

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4.4The area of triangle ABC is with and :

C

A

B

x

x

Calculate the value of x to the nearest integer.(5)

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4.5A rain gauge is in the shape of an inverted cone. Water flows into the gauge through the open top and is collected inside. The slant height of the water is 15 cm. The angle at the bottom of the cone is as shown in the following diagram:

d

15cm

(a) Determine the diameter at the surface of the water (d), correct to

two decimal places.(3)

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(b)

If the height of the water in the cone is , find the volume of

water in the rain gauge to 1 decimal place.(3)

Volume of cone

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QUESTION 5:[8]

In the diagram below, P is the point , S and PS and TR are perpendicular to the x-axis. and :

Determine the following without the use of a calculator:

5.1 (2)

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5.2 in terms of (2)

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5.3the length of OT. (4)

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QUESTION 6:[9]

The diagram shows the graphs of and for The points P and R are indicated as shown:

6.1Write down the values of . (4)

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6.2Write down the period of . (1)

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6.3If the coordinates of P are , write down the coordinates of R.(2)

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6.4

Determine the equation of , the graph of translated to the

left and 3 units down. (2)

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QUESTION 7:[16]

Refer to the diagram below. O is the centre of the circle and diameter KL is produced to meet chord NM produced at P. and :

Calculate the size of the following angles, giving reasons:

7.1 (2)

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7.2 (2)

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7.3 (2)

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7.4(2)

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7.5 (4)

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7.6Prove that (4)

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QUESTION 8: [12]

In the diagram below, EB is a tangent to the semi-circle with centre O passing through A, B, C and D. DC produced meets the tangent at E, and :

8.1Name two right angles in the figure, giving reasons.(4)

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8.2 Show that , giving reasons. (4)

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8.3Determine in terms of y, giving reasons.(4)

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QUESTION 9:[14]

In the diagram below, two circles have a common tangent TAB. PT is a tangent to the smaller circle. PAQ, QRT and NAR are straight lines. Let :

9.1 Name, with reasons, THREE other angles equal to x. (6)

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9.2Prove .(2)

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9.3 Prove APTR is a cyclic quadrilateral. (6)

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QUESTION 10:[9]

The time shown on the clock above is exactly twelve minutes past ten or 10h12.

The clock is now represented in the figure below:

10.1Show that , giving reasons. (5)

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10.2 Hence find the size of , giving reasons. Show all working. (4)

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QUESTION 11:[15]

and are two points on a circle. The perpendicular to AB through

B meets the circle again at :

11.1Show that .(4)

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11.2If the radius of the circle is , find the values of p and q with reasons.(7)

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11.3Find the size of to the nearest degree.(4)

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END OF EXAMINATION

MARK RECORD SHEET

FOR OFFICIAL USE ONLY

NAME OF LEARNER:

NAME OF TEACHER:

Statistics

Analytical

Geometry

Euclidean

Geometry

Trigonometry

1

/8

2

/12

3

/21

4

/26

5

/8

6

/9

7

/16

8

/12

9

/14

10

/9

11

/15

TOTAL

/20

/36

/51

/43

TOTAL

/150

%

11

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