GRADE 12 - MATHEMATICS PAPER 2 - St Stithians College

A World of Education…an Education for the World! 

GRADE 12 - MATHEMATICS PAPER 2 

EXAMINER: Mrs R Pike DATE: 19 th July 2011 

MODERATOR: Ms B Maganbhai TOTAL: 150 

TIME: 3 hours 

CANDIDATE’S NAME: 

CANDIDATE’S MATHS TEACHER: 

______________________________________________________________ 

______________________________________________________________ 

INSTRUCTIONS TO CANDIDATES: 

1. Answer all questions in the answer book provided. 

2. Diagrams have been reproduced in the answer booklet for ease of use. 

3. Rule a right hand margin on each page and rule off after each question. 

4. All written work must be done using blue or black ink. Diagrams and graphs must be 

drawn neatly using pencil. 

5. No correction fluids may be used 

6. Non-programmable calculators may be used unless otherwise stated. 

7. Round off to TWO decimal places unless otherwise stated. 

8. It is in your own interests to work neatly and to show all necessary steps in calculations. 

THIS EXAMINATION CONSISTS OF 10 PAGES 

Dainfern College 

Grade 12 Mathematics 

July Exam Paper 2 

Page 1 of 10

SECTION A 

QUESTION 1 

a) Complete the table below. It has been reproduced in your answer booklet. 

Question 

Co-ordinate(s) 

of point(s) 

before 

transformation 

Transformation in words 

Co-ordinate(s) of 

point(s) after 

transformation 

Eg. 

Reflection about the -axis 

i) 

Reflection about the line 

ii) 

iii) Translation of 5 units right and 4 

units down. 

iv) 

Reduce by a scale factor of 2 with 

centre of enlargement at the origin 

v) Rotate 

 

90 anti-clockwise about 

the origin. 

vi) 

vii) 

Rotate 

 

90 clockwise about the 

origin and then translate 3 units to 

the left 

Reflect about the line 

then rotate 

and 

 

90 anti-clockwise 

about the origin 

(9) 




Page 2 of 10

) Refer to the diagram. is a parallelogram. The following transformations occur on 

in the given order: 

D 

C 

A 

B 

1. Reflection in the -axis 

2. Rotation through the origin by in a clockwise direction 

3. Reflection in the line 

The end result is quadrilateral 

i) Write down the coordinates of and (5) 

ii) Give a single transformation that will return to in the form 

(2) 

[16] 

QUESTION 2 

y 

Z 

R 

θ 

x 

X 1 

Y 

Using the given diagram determine: 




Page 3 of 10

a) Distance (simplest surd form). (2) 

b) Midpoint of . (2) 

c) The gradient of . (2) 

d) The magnitude of angle . (2) 

e) The magnitude of angle . (3) 

f) The equation of line parallel to and passing through (3) 

[14] 

QUESTION 3 

In the diagram line passes through the midpoint of at , and the midpoint of at , 

the origin. 

M 

L 

T 

O 

K 1 1 

P 

W 

If is further given that the co-ordinates of , and are as follows: 1 1 ; 

and 

a) Show that is the midpoint of . (5) 

b) Write down two possible pairs of coordinates for and if the equation of is given 

by: (4) 

[9] 




Page 4 of 10

QUESTION 4 

a) Simplify to a single trigonometric ratio: 

(5) 

b) Simplify without a calculator, showing all your working : 

1 1 

1 1 1 

(6) 

[11] 

QUESTION 5 

Given, in the sketch below and where 1 1 

E 

A 1 

g 

D 

f 

C B 1 ½ 

a) Find the values of and (2) 

b) What is the period of ? (1) 

c) is a turning point on g; determine the coordinates of . (2) 

d) Determine the coordinates of and . (4) 




Page 5 of 10

m 

e) For which values of is if 1 ? (3) 

f) Determine the equation of if the – axis is moved to the left. (2) 

g) Without solving the following equation, explain how you would use the graph to solve: 

√ (3) 

[17] 

QUESTION 6 

a) Give the general solution for : (2) 

b) Hence, give the values for if (3) 

QUESTION 7 

[5] 

The diagram represents a playground slide ( ). This is attached at points , and to the 

tops of vertical struts , and . is the ladder used to reach the top of the slide. 

is the horizontal base used to stabilize the structure. 

A 

60° 

G 

m 

B 

H 

D 

̂ 

E 

̂ 

F 

C 

Calculate: 

a) The length of (3) 

b) The total distance travelled down the slide from to (5) 

[8] 




Page 6 of 10

QUESTION 8 

A South African swimmer is competing in the Olympics. His coach kept a record of the times 

that he took to swim the 100m freestyle during twelve practice sessions in the Olympic pool. 

Below is a record of the times (in seconds) for this training period. 

62, 56, 59, 64, 57, 59, 61, 60, 58, 61, 56, 55 

a) Find the five number summary for the information above. (5) 

b) Draw a box and whisker plot for this data. (4) 

c) Comment on the distribution of his times. (2) 

[11] 

SECTION B 

QUESTION 9 

a) Any point with coordinates can be located using the coordinates ; where the 

distance of the point from the origin is and is the angle that is being made with the - 

axis. When is given can be determined (and vice-versa) using the following: 

√ 

and 

After rotation through an angle , the image of is where 

and . 

Examine the figure below. If A has co-ordinates (4; 2), determine the co-ordinates of B to 

3 decimal places. (5) 

B 

A 4 2 




Page 7 of 10

) XYZ 

is enlarged by a scale factor of 3, with the centre of enlargement at the origin, to 

produce X ' Y' 

Z' 

. The area of XYZ 

is 

2 

20cm . 

i) True or False: (1) 

ii) Determine the area of X ' Y' 

Z' 

. (3) 

[9] 

QUESTION 10 

a) 

i) Determine the general solution of the above equation. (8) 

ii) Hence determine the value of if (2) 

b) If 1 express the following in terms of : 

i) 1 (1) 

ii) 1 (1) 

iii) (2) 

iv) (2) 

c) Without using a calculator, and showing sufficient working, evaluate the following: 

i) 1 (2) 

ii) 1 (2) 

iii) 1 (3) 

[23] 




Page 8 of 10

QUESTION 11 

is a straight line with units. is the centre of the semicircle with radius 2 

units. is a point on the semi-circle. The following is also given: 

Q 

̂ 

1 

P 

̂ 

A B C 

1 

a) Express in terms of a trigonometric ratio of . (2) 

b) Write Pˆ 1 

in terms of and θ . (1) 

c) Express ̂ in terms of sine and cosine ratios of and θ . (2) 

d) Hence show that (7) 

QUESTION 12 

[12] 

In the figure AB is a diameter of the circle with centre M and radius r. It is further given that 

^ 

CD = DE = AE and AME . It is also given that BC = r. 

E 

D 

C 

r 

B 

M 

A 

1 

Prove by using the cosine rule in triangles AME and CME, that cos . [8] 

4 




Page 9 of 10

QUESTION 13 

The Dainfern College tuck shop sells three kinds of pizzas; Hawaiian, Salami and Tikka Chicken. 

Mr Atteridge, who has a passion for statistics (and pizzas), produces the following report: 

“During the past month, the Hawaiian pizzas were most popular and accounted for 40% of the 

total number of pizzas sold. Of the remainder, 40% were salami. The range of the total number 

of pizza sold was 128. The popularity of the Hawaiian pizzas was exaggerated because of the 

Derby Day on which 59 more Hawaiian pizzas were sold than any other kind. This was probably 

due to the Hawaiian pizzas being sold half-price.” 

a) How many Tikka Chicken pizzas were sold? (4) 

b) If you ignore the 59 pizzas sold at half-price, what is the range of the total number of 

each kind of pizza sold? (3) 

[7] 




Page 10 of 10

GRADE 12 - MATHEMATICS PAPER 2 - St Stithians College

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