Cambridge International Mathematics

Multi-Topic Questions (Chapter 33) 5

c Wind strength 1 2 3 4 5 6 7 8 9

Number of days 3 5 6 8 6 7 9 5 1

i State the mode and find the median wind strength.

ii Calculate the mean wind strength.

iii A ‘good wind’ has strengthxsuch that 36 x 67.

Estimate the probability of a good wind from this data.

41 Nov 1994, Paper 4

Alexis, Biatriz and Carlos are business partners.

a 60%of each week’s income is used for the business. The rest is divided between Alexis, Biatriz

and Carlos in the ratio 5:3:1.

i Calculate how much they each receive in a week when the income is$9000.

ii Calculate the income in a week when Carlos receives$420.

b Alexis buys Carlos’ share of the business for$16 000, which he borrows from the bank at a rate

of12%simple interest per year. How much interest will he have to repay in 6 months?

42

A spherical ball, radiusr, diameter AB, is floating in water

with its centre O at a depthhbelow the surface. CD is a

diameter of the circular cross-section formed at the surface.

If r=13cm and h=5cm, calculate

aithe length of CD

ii the angle COD

iii the length of the arc CBD

iv the distance from C to D round the semi-circle,

diameter CD.

biThe area of surfaceabovethe water level is given by the formula 2 ¼r(r¡h):

Find the area above the water level.

ii The total surface area of a sphere is 4 ¼r^2.

Find the area above the water level as a percentage of the total surface area of the sphere.

43

Before the Euro was introduced, France had a French franc.

aiIf$1=9: 80 French francs, calculate how much 100 francs are worth in pounds ($), giving

your answer correct to two decimal places.

ii

b A French holidaymaker toured Britain in 1989 and in 1990 .In 1990 , the exchange rate was

$1=xfrancs. In 1989 , it was $1=(x+1)francs.

The holidaymaker found that, for 100 francs, she received$ 1 more in 1990 than in 1989.

i Write down an equation inxand show that it reduces to x^2 +x¡100 = 0:

ii Use the above equation to calculate the value ofx, giving your answer correct to two decimal

places.

iii

OO

hh

CD

rr

B

A

If francs, write down an expression, in terms of , for the value in pounds of

francs.

¡$1=

100

xx¡

Use your answer to to find the value, in pounds, of francs in the year. Give

your answer correct to two decimal places.

bii ¡ 100 1990

The table shows the wind strength measured on each of 50 days.

Adapted from Nov 1994, Paper 4

Adapted from June 1992, Paper 4

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