Cambridge International Mathematics

AB

C

E D

400 m

70 m

30 m

D

C

A

E

B

25 m

1.2 m

2m

5m

11.0 m

23.8 m

AB C D

1.4 m

1.92 m

6.4 m

U T

S

Similarity (Chapter 18) 375

4 A swimming pool is 1 : 2 m deep at one end, and 2 m deep at

the other end. The pool is 25 m long. Isaac jumps into the

pool 10 metres from the shallow end. How deep is the pool

at this point?

5 Ryan is standing on the edge of the shadow formed by a 5 m

tall building. Ryan is 4 m from the building, and is 1 : 8 m

tall. How far must Ryan walk towards the building so that he

is completely shaded from the Sun?

6 Kalev is currently at K, walking parallel to the side of a

building at a speed of 1 m/s. A flag pole is located at T.

How long will it be before Kalev will be able to see the flag

pole?

7 A, B, C and D are pegs on the bank of a canal which has

parallel straight sides. C and D are directly opposite each

other. AB=30m and BC= 140m.

When I walk from A directly away from the bank, I reach a

point E, 25 m from A, where E, B and D line up. How wide

is the canal?

8 An engineer was asked to construct a bridge across a river.

He noticed that if he started at C and walked 70 m away from

the river to D and 30 m parallel to the river to E, then C and

E formed a straight line with a statue at B.

Determine the length of the bridge to be built to span the river

if it must extend 40 m from the river bank in both directions.

Give your answer correct to the nearest metre.

9 The dimensions of a tennis court are given in the diagram

alongside.

Samantha hits a shot from the base line corner at S. The ball

passes over her service line at T such that UT=1: 92 m.

The ball then travels over the net and lands on the opposite

baseline AD.

a Find the length of SU and BC.

b A ball landing on the baseline is “in” if it lands between

points B and C.

Assuming the ball continues along the same trajectory,

will it land “in”?

10 m

2m

T

6m

K 3m

building

view

from

above

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Y:\HAESE\IGCSE01\IG01_18\375IGCSE01_18.CDR Tuesday, 21 October 2008 9:14:33 AM PETER