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PAPER 2

TOTAL: 75

TIME: 2 hours

QUESTION 1 [6]

Complete the following:

1.1 The supplement of 70° is ………. . (1)

1.2 If two lines intersect, the ……… angles are equal. (1)

1.3 The exterior angle of a triangle is equal to the ……… . (1)

1.4 Corresponding angles ar equal if ……... . (1)

1.5 The base angles of a …….. are always equal. (1)

1.6 The complement of 𝑥° is ………. . (1)

QUESTION 2 [6]

Are the following statements true or false:

2.1 30° and 60° are supplements of one another. (1)

2.2 The longest side of a right angled triangle is opposite the right angle. (1)

2.3 Two corresponding angles always add up to 180°. (1)

2.4 Co-interior angles are always equal. (1)

2.5 The sum of the interior angles of a triangle always add up to 360°. (1)

2.6 The sum of two acute angles is always smaller than 90°. (1)

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QUESTION 3 [11]

3.1 Calculate, with reasons:

3.1.1 𝑥 + 𝑦 (3)

3.1.2 < 𝑂! (2)

3.2 Examine the figure below: AB//CD, EF = EG and 𝐺! = 30°.

Calculate the following, with reasons:

3.2.1 < 𝐹! (2)

3.2.2 < 𝐹! (2)

3.2.3 < 𝐸! (2)

QUESTION 4 [10]

Examine the following and prove (in full): Δ𝐷𝐸𝐹 ≡ ∆𝐺𝐸𝐻.

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QUESTION 3 [5]

3.1 Calculate the value of !. Give a reason.

(2)

3.2 Examine the figure below: AB//CD , EF = EG and < !! = 30∘. Calculate the following, with reasons :

3.2.1 < !! (1)

3.2.2 < !! (1)

3.2.3 < !! (1)

QUESTION 4 [20]

5.1 Examine the sketch and answer the questions:

3! 66°

5,6

8x

B

C

A B

C DG

12E F

1 2 3

1 2

B

C AD

O

xx

y y

1

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(5)

4.2 Below 𝐶𝐷 = 35𝑐𝑚,𝐵𝐶 = 20𝑐𝑚 𝑎𝑛𝑑 𝐷𝐸 = 45𝑐𝑚. 𝐴𝐵 ∥ 𝐷𝐸.

4.2.1 Complete: Δ𝐷𝐸𝐶 /// Δ ….. ( ….. ). (2)

4.2.2 Calculate the length of AB. (3)

QUESTION 5 [19]

5.1 Examine the sketch and answer the questions:

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QUESTION 3 [5]

3.1 Calculate the value of !. Give a reason.

(2)

3.2 Examine the figure below: AB//CD , EF = EG and < !! = 30∘. Calculate the following, with reasons :

3.2.1 < !! (1)

3.2.2 < !! (1)

3.2.3 < !! (1)

QUESTION 4 [20]

5.1 Examine the sketch and answer the questions:

3! 66°

5,6

8x

B

C

A B

C DG

12E F

1 2 3

1 2

F G

D H

E

A B

D E

C35cm

45cm

20cm

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5.1.1 Calculate the length of 𝑥, with reasons. (3)

5.1.2 Calculate the area of the triangle. (3)

5.1.3 What will the area be of the remaining part of the circle, if you cut the

triangle away? (3)

5.2 The figure below is an old window.

5.2.1 Determine the circumference of the window. (2)

5.2.2 Calculate the area of the remaining part of the window if you cut a

circle with a radius of 2cm out of the window. (8)

QUESTION 6 [13]

6.1 Complete the following:

6.1.1 1 350 000 000 𝑚𝑚! = ………. 𝑚!. (2)

6.1.2 313 𝑘𝑙 = …….. 𝑙. (2)

6.1.3 6,5 𝑚! = ………. 𝑙. (2)

6.2 Calculate the total surface area of a rectangular prism with a length

of 31cm, breadth of 24cm and height of 12cm. (3)

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4.1.1 Calculate the lenge of ! , with reasons. (3)

4.1.2 Calculate the area of the triangle. (3)

4.1.3 What will the area be of the remaining part of the circle, if you cut the

triangle away? (3)

4.2 The figure below is an old window.

4.2.1 Determine the circumference of the window? (2)

4.2.2 Calculate the area of the remaining part of the window if you cut a

circle with a radius of 2cm out of the window. (9)

QUESTION 5 [13]

5.1 Complete the following:

5.1.1 1 350 000 000 !!! = ………. !! (2)

5.1.2 313 !" = ……… ! (2)

5.1.3 6,5 !! = ………. ! (2)

5.2 Calculate the total surface area of a rectangular prism with a length of

31cm, breadth of 24cm and height of 12cm. (3)

5cm

8cm

2

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6.3 The cylinder below has a volume of 400𝑐𝑚!.

Calculate the height of the cylinder.

(4)

QUESTION 7 [5]

The mass of 12 people are:

41 ; 43 ; 45 ; 45 ; 50 ; 52 ; 54 ; 56 ; 60 ; 62 ; 62 ; 62

7.1 What is the range of the data? (1)

7.2 Calculate the median of the data. (1)

7.3 Calculate the average of the data. (3)

QUESTION 8 [5]

There are 6 yellow balls and 4 red balls in a bag.

One ball is taken out of the bag and the colour is written down. The ball is

put back in the bag, and another ball is taken out of which the colour is also

written down.

8.1 Draw a tree diagram to illustrate the information. (3)

8.2 What is the probability that both balls taken from the bag are the

same colour? (2)

TOTAL: 75 marks

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5.3 The cylinder below has a volume of 400 cm2 .

Calculate the height of the cylinder.

(4)

QUESTION 6 [5]

The mass of 12 people are:

41 ; 43 ; 45 ; 45 ; 50 ; 52 ; 54 ; 56 ; 60 ; 62 ; 62 ; 62

6.1 What is the range of the data? (1)

6.2 Calculate the median of the data. (1)

6.3 Calculate the average of the data. (3)

QUESTION 7 [5]

There are 6 yellow balls and 4 red balls in a bag.

One ball is taken out of the bag and the colour is written down.

The ball is put back in the back, and another ball is taken out.

7.1 Draw a tree diagram to illustrate the information. (3)

7.2 What is the probability that both balls taken out of bag are the same

colour? (2)

TOTAL: 60 marks

H

9cm