Unit Number:
6
Unit Title:
Using mathematical tools for science
Unit Code:
M/502/5009
Outcomes Covered:
(1) Be able to use mathematical tools in science
Instructions:
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All necessary working must be shown.
The use of scientific calculators is allowed.
The use of electronic graph plotting tools is allowed.
All questions must be read carefully before attempted.
Question 1: This question covers grading criterion P1.
P1.1
A junior scientist is about to purchase a consignment of volumetric
cylinders through an online website. The seller is advertising the
cylinders as 12 inches long and holds 100 ml of liquid. The
company is registered in the United States of America from
where the consignment is to be delivered, 4750 miles away from
Malta.
Convert:
P1.2
(i) the length of the cylinder from inches to cm;
(ii) the capacity of the cylinder from ml to pints (2d.p.);
(iii) the distance between the seller and the scientist from miles to km.
(All working must be shown)
The following three readings are printed on the volumetric cylinder. Write down
these decimals correct to the specified number of decimal places in brackets.
(i) 2.1567 (1)
(ii) 45.6792 (2)
(iii) 99.0015 (3)
P1.3
Re-write the given decimals in P1.2 correct to three significant figures.
P1.4
If VAT at 20% is included, the price of a bottle of methanol is €40. What is the price
exclusive of VAT to the nearest eurocent?
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Question 2: This question covers grading criterion P2.
P2.1
Expand and simplify 5(6s + 9) - 3(4d +7)
P2.2
Where v = u + at, find v when u = 0, a = 3 and t = 10
P2.3
One of Newton’s laws of motion states that v2 = u2 + 2as. Make the initial velocity u,
the subject of the formula.
P2.4
Solve 8(5x - 10) = 40
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Unit 6: Using Mathematical Tools for Science (M/502/5009)
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Question 3: This question covers grading criterion M1.
M1.1 It is estimated that light takes 100,000 years to travel across our galaxy, the Milky
Way. If light travels at 3x108ms-1, how long is the Milky Way? Give your answer in
standard form correct to 2d.p.
M1.2 During a practical session in a chemistry laboratory, the water molecule was
discussed. As a matter of fact, the diameter of a water molecule is similar to that of a
hydrogen bond and approximately equal to 0.29 nanometers. Using a standard form,
re-write this figure in meters.
M1.3 While studying for his biology test, in his biology textbook Jacob read that the width
of an influenza virus particle is about 0.00000008m. Giving your answer in standard
form, work out the width of a cluster of five of these particles stuck together in line.
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Question 4: This question covers grading criterion M2.
M2.1 The given diagram represents an octagonal nut
with a hole drilled through its centre. This nut is
produced from a block of metal 9cm by 9cm by
2cm from which the four equal corners were
removed. The hole in the middle has a radius of
2cm. The density of the metal is 8.7g/cm3.
(i) Find the volume of the nut in cm3 correct to 2d.p.
(ii)Find the mass of the nut in kg correct to 2d.p.
M2.2 A milling machine produces spacing collars for a spindle of a production machine in
a pharmaceutical factory. It is in the form of a solid metal cylinder of diameter 8mm
with a cylindrical hole of radius 2mm drilled through the centre. The collar is 11cm
long.
Use the given dimensions to find to 2d.p:
(i) the volume of metal removed by the drill in cm3;
(ii) the volume of metal in the collar in cm3;
(iii) the density of the metal, in gcm-3, given that the collar has a
mass of 3.32g.
Unit 6: Using Mathematical Tools for Science (M/502/5009)
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Question 5: This question covers grading criterion D1.
D1.1
Simplify the ratios:
(i) 60c : €1.40
(ii) 1.25kg : 850g
(iii) 45min : 60min : 2h
D1.2
A clinical chemist in charge of the testing of urine samples is required to mix a
sodium chloride solution with water in the ratio of 3:8. Starting with 110ml of the
sodium chloride solution, how much water needs to be added?
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Question 6: This question covers grading criterion D2.
D2.1
One tin of sulphur granules weighs W grams and n of these tins are packed into a
carton that weighs C grams. Find a formula for K where K kg is the weight of the
carton when full of tins.
D2.2
The periodic time for one swing of a pendulum, used in a grandfather clock, can be
approximated using the equation:
𝑇=√
4𝜋 2 𝐿
𝑔
(i)Correct to 2d.p, calculate the periodic time T in seconds of a pendulum placed on
the surface of the earth, if the length L of the pendulum is 100cm and g = 9.81ms-2.
(ii) How longer would the periodic time of the same pendulum be if it was placed
swinging on the moon, assuming that the acceleration due to gravity on the moon, g,
is one sixth that on planet earth? (Give your answer correct to 2d.p.)
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Unit 6: Using Mathematical Tools for Science (M/502/5009)
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