Question 1 (30 marks)

Given the sets and

set

(i) List the first 10 elements of set A. [5 marks]

(ii) List the first 10 elements of set B. [5 marks]

(iii) List the elements of set *C*. [5 marks]

(iii) Draw a Venn diagram to illustrate . [5 marks]

(iv) Insert any common elements in the Venn diagram of part (iii). [10 marks]

[Note: elements in a Venn diagram has to be indicated by a dot, together with the element, as shown, ” ]

Question 2 (30 marks)

Follow the instructions below …..

- Draw an equilateral triangle of sides about 4 cm, naming the vertices as A, B and C.

[You may use MS Word to ‘draw’, no need to be exactly equilateral, but close to one.] - Copy and paste triangle in (i) and draw an inverted equilateral triangle inside it using the mid-points of AB, BC and CA as vertices. Name this triangle PQR.
- Copy and paste the result shape in (ii) and draw another equilateral triangle inside triangle PQR, naming this triangle LMN where L, M and N are the mid-points of the sides of triangle PQR.
- Now, count the number of triangles in each of the diagrams in (i), (ii) and (iii) and write down the answers next to the diagrams.
- Can you predict the number of triangles in the next 2 diagrams if you were to continue the process of drawing equilateral triangle within the inner most triangle.

- List the five numbers in a horizontal manner; what type of sequence does the 5 numbers above constitute?

Use the information to find the number of triangles after adding the 10^{th} triangle.