Cambridge International Mathematics

654 Multi-Topic Questions (Chapter 33)

12 May 2007, Paper 4

The diagram shows water in a channel.

This channel has a rectangular cross-section, 1 : 2 metres by 0 : 8 metres.

a

Calculate the number of cubic metres which flow along the channel in one hour.

b When the depth of water in the channel increases to 0 : 8 metres, the water flows at 15 metres/minute.

Calculate the percentage increase in the number of cubic metres which flow along the channel in

one hour.

c The water comes from a cylindrical tank.

d

13

Quadrilaterals P and Q have diagonals which ² are unequal ² intersect at right angles.

P has two lines of symmetry, Q has one line of symmetry.

aiSketch quadrilateral P. Write down its geometrical name.

ii Sketch quadrilateral Q. Write down its geometrical name.

b In quadrilateral P, an angle between one diagonal and a side isxo.

Write down, in terms ofx, the four angles of quadrilateral P.

c The diagonals of quadrilateral Q have lengths 20 cm and 12 cm.

Calculate the area of quadrilateral Q.

d

The lengths of the diagonals and sides of quadrilateral P are all integer values.

Find the length of a side of quadrilateral P.

14 May 2005, Paper 4

OABCDE is a regular hexagon. With O as origin the position

vector of C iscand the position vector of D isd.

a Find, in terms ofcandd,

i

¡!

DC

ii

¡!

OE

iii the position vector of B.

b The sides of the hexagon are each of length 8 cm. Calculate

i the size of angle ABC ii the area of triangle ABC

iii the length of the straight line AC iv the area of the hexagon.

1.2 m

0.8 m

0.3 m

d c

A

B

E

D

O

C

When the depth of water is 03 : metres, the water flows along the channel at 3 metres/minute.

When cubic metres of water leave the tank, the level of water in the tank goes down by

millimetres. Calculate the radius of the tank, in , correct to one decimal place.

2

13 : metres

When the channel is empty, its surface is repaired. This costs per square metre.

The total cost is. Calculate the length, in metres, of the channel.

interior $0 12

$50 40

:

:

Quadrilateral P has the same area as quadrilateral Q in .c

Adapted from Nov 2004, Paper 4

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_33\654IGCSE01_33.CDR Friday, 14 November 2008 10:26:56 AM PETER