Cambridge International Mathematics

Multi-Topic Questions (Chapter 33) 653

e

f The plane took 3 hours 15 minutes to return to Spain. The length of this journey was 2350 km.

Calculate the average speed of the plane in

i kilometres per hour ii metres per second.

10

The diagram shows a pyramid on a horizontal rectangular

base ABCD. The diagonals of ABCD meet at E. P is

vertically above E. AB=8cm, BC=6cm and

PC=13cm.

a Calculate PE, the height of the pyramid.

b Calculate the volume of the pyramid.

(The volume of a pyramid is given by^13 £area of base£height.)

c Calculate angle PCA.

d M is the midpoint of AD and N is the midpoint of BC.

eiCalculate angle PBC.

ii K lies on PB so that BK=4cm. Calculate the length of KC.

11

a The numbers 0 , 1 , 1 , 1 , 2 ,k,m, 6 , 9 , 9 are in order (k 6 =m).

Their median is 2 : 5 and their mean is 3 : 6.

i Write down the mode.

ii Find the value ofk.

iii Find the value ofm.

iv Maria chooses a number at random from the list.

The probability of choosing this number is^15. Which number does she choose?

b 100 students are given a question to answer.

The time taken (tseconds) by each student is recorded and the results are shown in the table.

t 0 <t 62020 <t 63030 <t 63535 <t 64040 <t 65050 <t 66060 <t 680

Frequency 10 10 15 28 22 7 8

i Calculate an estimate of the mean time taken.

ii Two students are picked at random. What is the probability that they both took more than 50

seconds? Give your answer as a fraction in its lowest terms.

c Answer this part on a sheet of graph paper.

The data in partbis re-grouped to give the following table.

t 0 <t 630 30 <t 660 60 <t 680

Frequency p q 8

i Write down the values ofpandq.

ii Draw an accurate histogram to show these results. Use a scale of 1 cm to represent 5 seconds

on the horizontal time axis. Use a scale of 1 cm to 0 : 2 units of frequency density (so that

1 cm^2 on your histogram represents 1 student).

A

B

C

D

P

E

8cm

6cm

13 cm

Theoriginalcost of the holiday wasreducedby10% 4347 00toE :. Calculate the original cost.

Adapted from May 2006, Paper 4

Adapted from May 2006, Paper 4

Calculate angle MPN.

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Y:\HAESE\IGCSE01\IG01_33\653IGCSE01_33.CDR Friday, 14 November 2008 10:26:14 AM PETER