Herzlia Senior High School

HERZLIA SENIOR HIGH SCHOOL

“If you will it, it is no legend”

MARKS:125

TIME: HOURS

This question paper consists of 11 pages and 5 diagram sheets.

INSTRUCTIONS AND INFORMATION

Read the following instructions carefully before answering the questions.

1. This question paper consists of 9 questions.

2. Answer ALL the questions.

3.Clearly show ALL calculations, diagrams and graphs that you have used in determining your answers.

4.Answers only will NOT necessarily be awarded full marks.

5.An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise.

6.If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise.

7.FIVE diagram sheets for answering QUESTION 1.2, QUESTION 2.1, QUESTION 2.2, QUESTION 5.1, QUESTION 7, QUESTION 8.1, QUESTION 8.2 and QUESTION 9are attached at the end of this question paper. Write your name on the diagram sheets in the space provided and insert the diagram sheets inside the back cover of your ANSWER BOOK.

8.Diagrams are NOT necessarily drawn to scale.

9. Number your answers correctly according to the numbering system used in this question paper.

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

QUESTION 1

The tuck shop sells cans of soft drinks. The Environmental Club decided to

have a can-collection project for three weeks to make learners aware of the

effects of litter on the environment.

The data below shows the number of cans collected on each school day of

the three-week projects.

1.1Determine the lower and upper quartiles of the data.(2)

1.2Use the scaled line on DIAGRAM SHEET 1 to draw a box and

whisker diagram to represent the data.(3)

1.3Calculate the mean number of cans collected over the three-week

period.(2)

1.4Calculate the standard deviation.(2)

1.5On how many days did the number of cans collected lie outside

ONE standard deviation of the mean? Show all calculations.(3)

[12]

PLEASE TURN OVER

QUESTION 2

The histogram below shows the time, in minutes, spent by customers

while shopping at a supermarket.

2.1Complete the frequency column and cumulative frequency

column in the table on DIAGRAM SHEET 1.(3)

2.2Use the grid on DIAGRAM SHEET 2 to draw the ogive of

the above data.(4)

2.3Use the ogive to estimate the median time that customers

spent at this supermarket.(2)

2.4Comment on the skewness of the data.(1)

[10]

QUESTION 3

In the diagram below, A(–1;–3), B and C are the vertices of a triangle.

P(2,5;1) is the midpoint of AB. CA extended cuts the y-axis at D. The

equation of CD is. . and are the angles

that AB and AC respectively make with the x-axis.

3.1Determine the value of k.(2)

3.2Determine the coordinates of B.(2)

3.3Determine the gradient of AB.(2)

3.4Calculate the size of .(5)

3.5Calculate the length of AD.(2)

3.6The point Elies in the third quadrant and has coordinates E(–3;y).

If the length of AE = ,calculate the value of y.(5)

[18]

PLEASE TURN OVER

QUESTION 4

4.1In the figure below, the point is a point in the Cartesian

plane. units and .

Determine the values of the following:

4.1.1(2)

4.1.2(4)

4.2Simplify as far as possible without the use of a calculator:

4.2.1(5)

4.2.2(8)

4.3Prove the following identity:

(5)

4.4Solve for x if :

(3)

4.5Determine the general solution of:

(6)

[33]

QUESTION 5

Given:

5.1Sketch the graph of f for on the graph paper

provided on DIAGRAM SHEET 3.(4)

5.2 Write down:

5.2.1The period of (1)

5.2.2The range of (2)

5.3The graph f is shifted horizontally to the right to obtain a

new graph h.

5.3.1Write down the equation of h in its simplest form.(1)

5.3.2Write down the value of x for which h has a minimum

value in the interval .(1)

5.4Use your graph (or otherwise) to solve for x, ,

for which .(2)

[11]

PLEASE TURN OVER

QUESTION 6

6.1The diagram below illustrates a piece of land divided into two

triangles. PS = 5,6 km, RS = 3,1 km, QR = 6,7 km,

and .

Determine the area of the piece of land, to the nearest kilometre.

Show all calculations.(8)

6.2In below, and .

Prove that .(3)

[11]

QUESTION 7

In the diagram below, OP is the diameter of the smaller circle. O is

the centreof the larger circle. Also, PTW is a chord of the larger

circle and Tlies on the smaller circle. OT is joined.

If OT = 10 cm and PW = 48 cm, calculate, giving reasons, the length

of the radius of the smaller circle.

[5]

QUESTION 8

8.1In the diagram below, O is the centre of the circle. PSRT is a cyclic quadrilateral. Prove the theorem that states .

(6)

PLEASE TURN OVER

8.2In the diagram below, O is the centre of the circle. RDS is a

tangent to the circle at D.BC = DC and .

Calculate, with reasons, the size of the following angles:

8.2.1(3)

8.2.2(3)

8.2.3(2)

[14]

QUESTION 9

In the diagram below, O is the centre of the circle. AB is a diameter

of the circle. Chord CF produced meets chord EB produced at D.

Chord EC is parallel to chord BF. CO and AC are joined.

Let .

9.1Determine, with reasons, the size of in terms of x.(4)

9.2Prove that DF = BD.(4)

9.3Prove that OCDB is a cyclic quadrilateral.(3)

[11]

TOTAL : 125

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HERZLIA SENIOR HIGH SCHOOL

DIAGRAM SHEET

GRADE 11 MATHEMATICS PAPER 2

FRIDAY 28THNOVEMBER 2014

(PLEASE PLACE IN YOUR ANSWER BOOK)

NAME:……………………………………………………..

DIAGRAM SHEET 1

QUESTION 1.2

QUESTION 2.1

DIAGRAM SHEET 2

QUESTION 2.2

DIAGRAM SHEET 3

QUESTION 5.1

QUESTION 7

DIAGRAM SHEET 4

QUESTION 8.1

QUESTION 8.2

DIAGRAM SHEET 5

QUESTION 9