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KEARSNEY COLLEGE TRIAL EXAMINATION

9 SEPTEMBER 2019

MATHEMATICS: PAPER 2

Time: 3 hours 150 marks

EXAMINATION NUMBER 1 9 1 0 6 8 0 2

PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY

1. This question paper consists of 18 pages and an Information Sheet of 2 pages (i–ii). Please

check that your question paper is complete.

2. This paper has 4 sections. Please write your examination number in the space provided in

each section

3. Read the questions carefully.

4. Answer ALL the questions on the question paper and hand it in at the end of the examination.

5. Diagrams are not necessarily drawn to scale.

6. You may use an approved non-programmable and non-graphical calculator, unless

otherwise stated.

7. Ensure that your calculator is in DEGREE mode.

8. All the necessary working details must be clearly shown. Answers only will not necessarily

be awarded full marks.

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

10. Round off to one decimal place unless otherwise stated.

Mathematics: Paper 2 Page 1 of 18

SECTION A


QUESTION 1Marshell fell ill after his choir performance and his temperature was taken every hour between 12h00 and 18h00. His temperature was recorded in the table below:

x Time 12h00 13h00 14h00 15h00 16h00 17h00 18h00

y Temperature ( ) 37,0 39,5 40,0 39,0 38,2 37,7 37,2

Round off your answers to 2 decimal digits.

(a) Determine the equation of the line of best fit in the form . (2)

(b) Use the line of best fit to estimate Marshell’s temperature at 15h30. (2)

(c) Determine Marshell’s temperature at 02h00 the next morning. Discuss the reliability of your answer. (4)

[8]

Kearsney College Copyright © 2019 Trial Examination

E

T

P

Q

RS


QUESTION 2PQR is a triangle with ST || PR and ET || PQ.

If determine the value of:

(a) (2)

(b)

(2)

(c)

(2)

[6]


O

y

C

A (6; 7)

B (8; 2)


QUESTION 3

In the diagram, AB AC and C lies on the y – axis.

(a) Show that the equation of AC is

. (4)

(b) The area of . (2)

(c) The size of . (6)

[12]


22°

21

3 2 1

B

DO C

A

x

150°

y

F

E D

A B

C


QUESTION 4O is the centre of the circle. AB produced and DO meet at C.

BC OA and

Calculate the size of .

[5]QUESTION 5In circle ABCDE, AB || ED. AD and BE intersect at F.

Determine x and y.

[4]



QUESTION 6Charlene produced these three scatter diagrams based on data from different surveys.

Diagram A Diagram B Diagram C

The titles for each scatter diagram are presented in the table below. Complete the table by matching the diagram to its title and describing the type of correlation.

Title Diagram Letter Type of Correlation

Number of shirts bought and the total cost.

The age of a car and its estimated value

Time taken to run cross country and the number of people in their family

[3]



SECTION B


QUESTION 7

The commission earned, in thousands of rands, by salesmen at Hyundai in a certain month is shown in the table below

Commission Earned Frequency868

104

(a) Calculate the estimated mean amount of commission earned. (2)

(b) Sketch a cumulative frequency curve below to represent the data above. (3)


Commission Earned

Cum

ulat

ive

Freq

uenc

y


(c) The CFO decides to award a bonus to salesmen who are earning commission in excess of R90 000. Use your graph to determine the percentage of salesmen in this category. (2)

(d) Indicate on your graph where you would read off the values of the first and third quartiles. Write down their values below. (2)

(e) It was discovered that an error in the finance department’s calculations placed 5 of the 10 salesmen in the category when they should have been in the category of . How would this change the standard deviation and mean of the data? (2)

[11]


153,435°

y

xQ (5;0)O

P


QUESTION 8Circle O is centred at the origin

with Q on the circumference.

(a) Show that the coordinates of

P are (6)

(b) Determine the equation of the tangent to the circle at point P. (4)

[10]


C

A

B E

D


QUESTION 9In the diagram, ABCD is a trapezium with

and AB || CD and

(a) Show that . (2)

(b) Prove that . (3)

(c) Given that . Find the length of CD. (4)

[9]


2

1

2 1

21

432

1

E

F

A

D

B

C


QUESTION 10In the diagram, two circles intersect at B and D.AB is a straight line such that it intersects circle

BCD at E. FC FD and

(a) Determine the following in terms of x:

(1) (3)

(2) (2)

(b) Prove ED || BC. (4)

[9]



SECTION C


QUESTION 11

The coordinates E , F and G lie in the Cartesian plane. A circle centred at G passes through E.

(a) Determine the equation of the circle. (3)

(b) Prove that F lies outside the circle. (2)

[5]



QUESTION 12

(a) Solve for x if (6)

(b)Evaluate:

(6)



(c) Prove that (6)

[18]



QUESTION 13

Sketched below is the graph of with

(a)On the set of axes shown above, sketch the graph of with

(4)

(b) Write down the value of x where if (2)

(c)Determine the value(s) of x for which if .

(4)

(d) For what values of k will have no real solutions. (2)


2132

4

1

32

12

1

2

1

S

P5 T

OYR

Q

X


[12]SECTION D


QUESTION 14In the diagram, O is the centre of the circle with PX = PY and XY is a tangent to the circle at Y. XPQ, YOR and YST are straight lines.

(a) Prove that . (5)

(b) Prove that SORT is a cyclic quadrilateral. (3)


x

3cm

8cm

5cm

5cm

D

A

B

C


[8]QUESTION 15The diagram shows a circle with points A, B, C and D on the circumference of the circle.

(a) Show that (3)

(b) Determine another equation for in terms of . (3)

(c) Determine the size of . (3)

(d) Determine the value of x. (2)


y

xO

P

A

N

BQ


[11]QUESTION 16The diagram shows the circle with centre N

and equation .

Chord AB is drawn parallel to the x – axisand is 12cm long. NP AB. AP and BP are tangents to the circle at A and B respectively.

(a) Write down the length of the radius and the centre of the circle. (2)

(b) Determine the coordinates of A. (5)

(c) Determine the length of the tangents. (4)


21

3

2 1

2

1

O

S

R

Q

P


[11] QUESTION 17In the diagram alongside, O is the centre of the circle

with RS ,

Prove:

[8]


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