20 marks....Maths

1. A supercomputer can perform 12,300,000,000,000 calculations per second. If 1 nanosecond= 10^-9 seconds. Work out the time, in nanoseconds, this computer takes to perform one calculation.

The time that this computer takes to perform one calculation
= 1/12,300,000,000,000
= 1/(1.23 x 1013) s
= 8.13 x 10-14 s
= 8.13 x 10-5 x 10-9 s
= 8.13 x 10-5 ns
(or 0.0000813 ns)


2. 1 litre of paint covers an area of 12m^2. Work out the thickness, in centimetres, of the coat of paint.

1 L = 1000 cm3
1 m2 = (100 cm)2 = 10000 cm2

Thickness of the coat of paint
= volume/area
= (1 L)/(12 m2)
= (1000 cm3)/(12 x 10000 cm2)
= 1/120 cm
= 0.00833 cm


3. The mass of the The Earth= 5.97*10^21 tonnes. The mass of the Moon =7.36*10^19 tonnes. The mass of Mars is 11% of the mass of the Earth. Work out the difference in mass, in tonnes, between Mars and Moon.

Difference in mass between Mars and Moon
= [(5.97 x 1021 x 11%) - (7.36 x 1019)] tones
= 5.83 x 1020 tonnes


4. Factorize 9x^2 -1. Hence express as a product of its prime factors i)899 ii)8.99*10^4.

9x2 - 1
= (3x)2 - (1)2
= (3x + 1)(3x - 1)

i)
When x = 10:
899 = 9(10)2 - 1
899 = [3(10) - 1] x [3(10) + 1]
899 = (30 - 1) x (30 + 1)
899 = 29 x 31

ii)
8.99 x 104
= 899 x 102
= 29 x 31 x (2 x 5)2
= 22 x 52 x 29 x 31