Cambridge International Mathematics

Multi-Topic Questions (Chapter 33) 651

4 Nov 2006, Paper 4

Maria, Carolina and Pedro receive$800from their grandmother in the ratio

Maria : Carolina : Pedro=7:5:4.

a Calculate how much money each receives.

b Maria spends^27 of her money and then invests the rest for two years at5%per year simple interest.

How much money does Maria have at the end of the two years?

c Carolina spends all of her money on a hi-fi set and two years later sells it at a loss of20%.

How much money does Carolina have at the end of the two years?

d Pedro spends some of his money and at the end of the two years he has$100. Write down and

simplify the ratio of the amounts of money Maria, Carolina and Pedro have at the end of the two

years.

e

5

The table shows some terms

of several sequences.

Term 1 2 3 4 ...... 8 ......

SequenceP 7 5 3 1 ...... p ......

SequenceQ 1 8 27 64 ...... q ......

SequenceR^12233445 ...... r ......

SequenceS 4 9 16 25 ...... s ......

SequenceT 1 3 9 27 ...... t ......

SequenceU 3 6 7 ¡ 2 ...... u ......

a Find the values ofp,q,r,s,tandu.

b Find thenth term of sequence

i P ii Q iii R iv S v T vi U

c Which term in sequencePis equal to¡ 777?

d Which term in sequenceTis equal to177 147?

6

OBCD is a rhombus with sides of 25 cm. The length of the diagonal OC is 14 cm.

a

b Calculate, correct to the nearest degree,

i angle BCD ii angle OBC.

c

¡!

DB=2p and

¡!

OC=2q.

Find, in terms ofpandq, i

¡!

OB ii

¡!

OD

d BE is parallel to OC and DCE is a straight line.

Find, in its simplest form,

¡!

OE in terms ofpandq.

e M is the midpoint of CE.

Find, in its simplest form,

¡¡!

OM in terms ofpandq.

f q=

¡ 7

0

¢

.

(

¡!

DB is vertical and j

¡!

DBj=48). Write down as column vectors i p ii

¡!

BC

g Write down the value of j

¡!

DEj:

Pedro invests his for two years at a rate of per year. Calculate how

much money he has at the end of these two years.

$100 5% compound interest

Show,by calculation, that the length of the diagonal BD is 48 cm.

O is the origin of a coordinate grid. OC lies along the -axis andx

Adapted from Nov 2007, Paper 4

Adapted from May 2007, Paper 4

25 cm

14 cm

M

B E

C

D

O

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Y:\HAESE\IGCSE01\IG01_33\651IGCSE01_33.CDR Friday, 14 November 2008 10:24:26 AM PETER