Cambridge International Mathematics

Investigation and modelling questions (Chapter 34) 663

5

a

b

c

d

6 June 1988, Specimen Paper 6

The diagram shows 3 squares, the sides of which are 1 cm, 2 cm and 3 cm respectively. Each of the

small squares on the diagram has a side of length 1 cm and alternate squares are coloured black and

white.

a The number of small squares of each colour used is shown in the following table. Copy and

complete the table.

Length of side of given square L 1 2 3 4 5

Number of black squares B 1 2 5

Number of white squares W 0 2 4

Total number of squares T 1 4 9

biHow many small white squares will there be when a square of side 11 cm is drawn?

ii Find the length of the side of a square when 1681 small black and white squares are needed

to cover it.

c Write down a formula connectingTandL.

d Write down a formula connectingTandBwhen

i Bis an even number ii Bis an odd number.

P

4

8

Q

6

6

R

8

T 6

p

12

1cm 2cm 3cm

Consider the figures P to T:

All five figures have something important in common. What is it?

Calculate the area of a regular hexagon (H) of side 4 centimetres.

Using the letters P, Q, R, S, T and H, list the areas in order of size, starting with the smallest.

Explain any conclusions you arrive at.

Adapted from June 1989, Paper 6

S

3

2

4

6

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Y:\HAESE\IGCSE01\IG01_34\663IGCSE01_34.CDR Friday, 14 November 2008 11:59:25 AM PETER