Cambridge International Mathematics

2 Multi-Topic Questions (Chapter 33)

34 Nov 1996, Paper 4

Diagram 1 shows a regular

tetrahedron WXYZ with all

sides of length 6 cm. Diagram

2 shows the base XYZ of the

tetrahedron. O is the centre of

the base, M is the midpoint of

XZ, and N is the midpoint of

XY.

a Write down the size of angle OZM.

b Show that, correct to 4 significant figures, the length of OZ is 3 : 464 cm.

c Calculate the height, OW, of the tetrahedron.

d Calculate the volume of the tetrahedron. (Volume of a tetrahedron=^13 base area£height.)

e Calculate the angle between the edge WZ and the base XYZ.

35

A circular board is divided into twelve equal sectors numbered

from 1 to 12. A dart is thrown and lands on the board. Assume

that it is equally likely to land anywhere in the circle. The

score is the number in the sector where the dart lands.

a When one dart is thrown, find the probability that the

score is

i a square number

ii a prime number or less than 6 or both

b

i Listallthe possible ways of scoring 21.

ii Find the probability of scoring 21 with two darts. Give your answer as a fraction in its lowest

terms.

c The table shows the scores when a player throws one dart 30 times.

Score 1 2 3 4 5 6 7 8 9 10 11 12

Frequency 1 1 1 0 1 1 2 3 4 5 6 5

For these scores, find i the mode ii the median iii the mean.

d To prevent damage to the wall, the board, which has a

radius of 10 cm, is placed on a wooden square of side

30 cm. One dart is thrown by a beginner who is equally

likely to hit anywhere within thesquare.

i Calculate the area of the sector numbered 2.

ii Calculate the probability that the beginner scores 2 ,

giving your answer as a decimal.

X

Y

Z

M

N

3

3

(^33)
6
X O
Y
Z
W
6
6
6
6 O 6
1
2
3
4
5
(^76)
8
9
10
11
12
diagram 1 diagram 2
30 cm
30 cm
10 cm
2
When two darts are thrown, thesumof the two scores is calculated.
Adapted from June 1997, Paper 4
IGCSE01
cyan magenta yellow black
(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_33\popup\002IGCSE01_33a.CDR Friday, 14 November 2008 11:03:37 AM PETER
(Page included on the Student CD only)