Unit 12: Integrated Science
CHAPTER 1
Important Notes and Tables
Some important prefixes
The SI allows the sizes of units to be made bigger or smaller by the use of appropriate prefixes. For
example, the electrical unit of a watt is not a big unit even in terms of ordinary household use, so it is
generally used in terms of 1000 watts at a time. The prefix for 1000 is kilo so we use kilowatts[kW] as
our unit of measurement. For makers of electricity, or bigger users such as industry, it is common to
use megawatts[MW] or even gigawatts [GW]. The full range of prefixes with their [symbols or
abbreviations] and their multiplying factors which are also given in other forms is
tera [T] 1 000 000 000 000 = 10^12
giga [G] 1 000 000 000 (a thousand millions = a billion)
mega [M] 1 000 000 (a million)
kilo [k] 1 000 (a thousand)
hecto [h] 100 (a hundred)
deca [da]10 (ten) 1
deci [d] 0.1 (a tenth)
centi [c] 0.01 (a hundredth)
milli [m] 0.001 (a thousandth)
micro [µ] 0.000 001 (a millionth)
nano [n] 0.000 000 001 (a thousand millionth)
pico [p] 0.000 000 000 001 = 10^-12
Mr. J.Agius Personal Notes
Page 1
Unit 12: Integrated Science
SI base units
Base quantity
length
mass
time
electric current
thermodynamic temperature
amount of substance
luminous intensity
SI base unit
Name
metre
kilogram
second
ampere
kelvin
mole
candela
Symbol
m
kg
s
A
K
mol
cd
You may find that some resources also refer to fundamental units as
“basic” units or “base” units.
SI derived units
Derived Quantity
area (L × B)
volume (L × B × H)
speed, velocity (Distance/time)
acceleration (Dist./time squared)
wave number ( = 1/m)
mass density (D = Mass/Volume)
specific volume ( = Volume/Mass)
Electrical Charge (coulomb) (Q = It)
current density
magnetic field strength
amount-of-substance concentration
Mr. J.Agius Personal Notes
Name
square metre
cubic metre
metre per second
metre per second squared
reciprocal metre
kiolgram per cubic metre
cubic metre per kilogram
Current multiplied by time
ampere per square metre
ampere per metre
mole per cubic metre
Symbol
m2
m3
m/s
m/s2
m-1
kg/m3
m3/kg
As
A/m2
A/m
mol/m3
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Unit 12: Integrated Science
Expression in
terms of other
SI units
Expression in
terms of SI base
units
Derived quantity
Name
Symbol
frequency (f = 1/t)
hertz
Hz
s-1
force (F = ma)
newton
N
m kg s-2
pressure, stress (P = F/A)
pascal
energy, work, quantity of heat
(W = Fd)
joule
Work done in terms of
Electricity (W = Pt)
joule
Pa
N/m2
m-1 kg s-2
J
Nm
m2 kg s-2
J
CV or AVs
m2 kg s-2
power, radiant flux (P = W/t) watt
electric potential difference,
electromotive force (V = P/I or
V = IR)
volt
W
J/s
m2 kg s-3
V
W/A
m2 kg s-3 A-1
capacitance (C = Q/V)
farad
F
C/V
m-2 kg-1 s4 A2
electric resistance (R = V/I)
W
V/A
m2 kg s-3 A-2
Celcius temperature
ohm
degree
Celcius
dose equivalent (d)
Conductance
Inductance
Magnetic flux
Magnetic flux density
Luminous Flux
illuminance
Sievert
Siemens
Henry
Weber
Tesla
Lumen
lux
Mr. J.Agius Personal Notes
o
C
Sv
S
H
wb
T
lm
lx
K
J/kg
m2 s-2
Ω-1
wb/A
Vs
wb m-2
cd sr
lm m-2
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Unit 12: Integrated Science
Q1: What are the seven SI base units? List also from where they
originated where possible.
Answer
metre [m]
The metre is the basic unit of length. It is the distance light travels, in a vacuum, in 1/299 792 458 th
of a second.
kilogram [kg]
The kilogram is the basic unit of mass. It is the mass of an international prototype in the form of a
platinum-iridium cylinder kept at Sevres in France. It is now the only basic unit still defined in terms
of a material object, and also the only one with a prefix [kilo] already in place.
second [s]
The second is the basic unit of time. It is the length of time taken for 9 192 631 770 periods of
vibration of the caesium-133 atom to occur.
ampere [A]
The ampere is the basic unit of electric current. It is that current which produces a specified force
between two parallel wires which are 1 metre apart in a vacuum. It is named after the French
physicist Andre Ampere (1775-1836).
kelvin [K]
The kelvin is the basic unit of temperature. It is 1/273.16th of the thermodynamic temperature of the
triple point of water. It is named after the Scottish mathematician and physicist William Thomson
1st Lord Kelvin (1824-1907).
mole [mol]
The mole is the basic unit of substance. It is the amount of substance that contains as many
elementary units as there are atoms in 0.012 kg of carbon-12.
candela [cd]
The candela is the basic unit of luminous intensity. It is the intensity of a source of light of a
specified frequency, which gives a specified amount of power in a given direction.
Mr. J.Agius Personal Notes
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Unit 12: Integrated Science
Q2: Name 6 common derived SI units and state from where they
originate.
farad [F]
The farad is the SI unit of the capacitance of an electrical system, that is, its capacity to store
electricity. It is a rather large unit as defined and is more often used as a microfarad. It is named
after the English chemist and physicist Michael Faraday (1791-1867).
hertz [Hz]
The hertz is the SI unit of the frequency of a periodic phenomenon. One hertz indicates that 1 cycle
of the phenomenon occurs every second. For most work much higher frequencies are needed
such as the kilohertz [kHz] and megahertz [MHz]. It is named after the German physicist Heinrich
Rudolph Hertz (1857-94).
joule [J]
The joule is the SI unit of work or energy. One joule is the amount of work done when an applied
force of 1 newton moves through a distance of 1 metre in the direction of the force. It is named
after the English physicist James Prescott Joule (1818-89).
newton [N]
The newton is the SI unit of force. One newton is the force required to give a mass of 1 kilogram
an acceleration of 1 metre per second per second. It is named after the English mathematician
and physicist Sir Isaac Newton (1642-1727).
ohm [Ω ]
The ohm is the SI unit of resistance of an electrical conductor. Its symbol, is the capital Greek letter
'omega'. It is named after the German physicist Georg Simon Ohm (1789-1854).
pascal [Pa]
The pascal is the SI unit of pressure. One pascal is the pressure generated by a force of 1 newton
acting on an area of 1 square metre. It is a rather small unit as defined and is more often used as a
kilopascal [kPa]. It is named after the French mathematician, physicist and philosopher Blaise
Pascal (1623-62).
volt [V]
The volt is the SI unit of electric potential. One volt is the difference of potential between two points
of an electical conductor when a current of 1 ampere flowing between those points dissipates a
power of 1 watt. It is named after the Italian physicist Count Alessandro Giuseppe Anastasio Volta
(1745-1827).
watt [W]
The watt is used to measure power or the rate of doing work. One watt is a power of 1 joule per
second. It is named after the Scottish engineer James Watt (1736-1819).
Mr. J.Agius Personal Notes
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Unit 12: Integrated Science
Quiz
Q1: Match the SI unit to the quantity it measures. Choose from the following.
Metre, Kelvin mole, radian, ampere, kilogram, second, candela
plane angle
time
luminous intensity
length
thermodynamic temperature
mass
amount of substance
electric current
Q2: SI units and their symbols. Write the matching SI symbol.
1
metre
2
kilogram
3
second
4
ampere
5
kelvin
6
candela
7
mole
Q3: What quantity do each of these SI units measure? Choose from the following.
Force, acceleration, density of mass, volume, current density, velocity/speed
kilogram metre per second squared
Ampere per square metre
cubic metre
Mr. J.Agius Personal Notes
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Unit 12: Integrated Science
metre per second
kilogram per cubic metre
metre per second squared
Q4: Enter the SI unit which measures each quantity.
siemens volt coulomb newton lumen ohm joule henry farad lux weber hertz watt pascal
sla
force, weight, tension, thrust:
work, energy, heat:
power, heat flow rate:
capacitance:
conductance:
inductance:
magnetic flux density:
illuminance:
te
pressure, stress:
frequency:
electric charge:
resistance:
electric potential, electromotive force:
magnetic flux:
luminous flux:
Q5: Type the SI unit which matches each symbol.
1
lx
2
Wb
3
W
4
Hz
5
Pa
6
N
7
C
8
F
9
V
Mr. J.Agius Personal Notes
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Unit 12: Integrated Science
Q6: Prove that the derived unit of force is kg m s-2 (kg m/s2)
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Q7: Prove that the derived unit of speed (or velocity) is m s-1 (m/s). Recall that
speed = distance over time.
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Q8: Prove that the derived unit of acceleration is m s-2 (m/s2). Recall that
acceleration = distance over velocity.
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Mr. J.Agius Personal Notes
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Unit 12: Integrated Science
Q6: Prove that the derived unit of Pressure is kg m-1 s-2 (kg m/s2)
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Q7: How many metres does 12 feet equal? (Note: 1 feet = 0.3048 metres)
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Q8: How many feet does 3 metres equal?
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Mr. J.Agius Personal Notes
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Unit 12: Integrated Science
Q9: What is 55 mph in terms of metres/sec?
(Note: 1 mile = 1609.344 metres and 1 hour = 60  60 = 3600 seconds.)
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Q10: Convert 10 metres/sec to miles/hour
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Mr. J.Agius Personal Notes
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Unit 12: Integrated Science
Standard Units
1)
In the table below, write down the standard unit for each of the quantities.
Quantity
Potential
Difference
Power
Force
Velocity Frequency
Current
Standard Unit
2)
In the table below, write down the quantity for each of the standard units.
Standard Unit
Quantity
ohms
joules
kilogram
pascals
candela
seconds
3)
Physics units can be combined to give new units.
For the following combinations a) to j), write down the correct unit if we:
a)
multiply amps by ohms.
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b)
multiply amps by seconds.
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c)
multiply kilograms by metres/(sec)2 _______________________________________________
d)
divide newtons by (metres)2
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e)
multiply hertz by metres
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f)
multiply coulombs by volts
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g)
divide volts by amps
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h)
multiply newtons by metres
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i)
multiply pascals by (metres)2
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j)
divide joules by seconds
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Mr. J.Agius Personal Notes
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Unit 12: Integrated Science
Derived Units
A derived unit is just a multiple or sub-multiple of a unit, and it can sometimes be written by adding a
prefix before the unit.
4)
In the following, calculate how many: (the first one has been done for you)
a)
seconds in 3 minutes
b)
hours in 23 days
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c)
metres in 3.2 km
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d)
kilograms in 7200g
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e)
newtons in 0.034 kilonewtons
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f)
watts in 1.2 MW
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g)
milliohms in 32 ohms
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h)
coulombs in 6200000 microcoulombs______________________________________________
i)
miiliseconds in 9.6 seconds
5)
Write down the name and symbol of the derived unit for: (the first one has been done for you)
a)
one thousand metres
b)
one thousandth of a watt.
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c)
one million joules
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d)
one millionth of an ohm
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e)
one millionth of a kilonewton
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f)
one million millivolts
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6)
Give the prefix we would put in front of a unit if we wanted to multiply it by the following
numbers: (the first one has been done for you)
a)
103
Ans: kilo (k)
b)
106
_________________
c)
10-3
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d)
10-6
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e)
109
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f)
0.000 000 000 1________________
g)
1/10
_________________
h)
1/1 000 000
i)
0.000 000 000 001
Mr. J.Agius Personal Notes
Ans:
3  60 = 180s
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Ans:
kilometres (km)
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Page 12
Unit 12: Integrated Science
7)
Work out the following.
a)
Convert 7.5 metres to feet
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b)
Convert 55miles to metres
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c)
Convert 55 miles/hour to metres/second
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d)
Convert 25 metres/second to miles/hour
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Mr. J.Agius Personal Notes
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Unit 12: Integrated Science
Making Sense of your Readings
8)
A student carries out an experiment with a resistor. An ammeter and voltmeter are used to
measure the current through the resistor and the voltage across it.
a) What current does the meter read?
Ans.__________________________
b) What voltage does the meter read?
Ans.__________________________
c) Use the formula V = IR to calculate the resistance.
Ans.__________________________
9)
Angela carries out an experiment to find the electrical energy used by a light bulb. She ran the
experiment for 2 minutes.
a) Round the reading to the nearest joule.
Ans.__________________________
b) Use the equation Power = work done  time (in seconds) to find the
power of the light bulb to the nearest watt.
Ans.__________________________
c) What should she do to be more confident of her result for the power of the light bulb?
Ans._______________________________________________________________________________
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Mr. J.Agius Personal Notes
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Unit 12: Integrated Science
10)
Neville is part of a group carrying out a radioactivity experiment. They take several readings of
background count and the average count rate is found to be 14 counts/min.
They place a detector near a radioactivity source (which
they know emits beta particles).
The counter is switched on for 30 seconds and the
counter reading is shown in the picture opposite.
a) What reading does the counter show?
Ans.__________________________
b) What is the count rate in counts per minute?
Ans.__________________________
c) What is the corrected count rate due to the source alone?
Ans.__________________________
They are told that the half-life of the source is 45 minutes.
d) How many counts per minute would you expect them to record 3 hours later?
Ans.__________________________
e) Why is it necessary to take several measurements to work out the background count?
Ans._______________________________________________________________________________
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Mr. J.Agius Personal Notes
Page 15
Unit 12: Integrated Science
11)
A group of students is carrying out an experiment on pressure. They use a Bourdon gauge to
measure the pressures.
a)
What is the reading on the Bourdon gauge (shown opposite)? Give your
answer in kilopascals.
Ans.__________________________
b)
The pointer on the gauge does not return to zero when they disconnect
the gauge from the apparatus. Explain this observation.
Ans._______________________________________________________________________________
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12)
An old forcemetre is being used to measure weights.
Abbie looks at the
scale of the
forcemetre (shown
opposite) before any
weights have been
hung on.
Then the first weight
is attached …
a) Calculate the force pulling the weight downwards.
Ans.__________________________
b) What is the cause of this downward force?
Ans.__________________________
c) How would the reading change if the weight was lowered gently into a beaker of water?
Ans._______________________________________________________________________________
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Mr. J.Agius Personal Notes
Page 16
Unit 12: Integrated Science
Rounding Off
13)
Round the following numbers up or down:
a) 3645N to the nearest kN
Ans.__________________________
b) 195 seconds to the nearest minute.
Ans.__________________________
c) 13.27 cm to the nearest mm
Ans.__________________________
d) 2493 kW to the nearest MW
Ans.__________________________
e) 12.56 Nm to the nearest joule
Ans.__________________________
f) 9854399 amps to the nearest kilo amp
Ans.__________________________
14)
Work out the answers to the following calculations.
a)
Calculate the resistance of a resistor if a potential difference of 5.5V drives a current of 2.1A
through it. Give your answer to 3 significant figures. (Use the equation V = I  R)
Ans.__________________________
b)
Calculate the volume of a cylindrical barrel if it has a height of 1m and a radius of 0.32m. Give
your answer to 2 significant figures.
Ans.__________________________
c)
Calculate the speed of a skier if he travels a distance of 35.7 metres through two slalom gates in
a time of 5.2 seconds. Give your answer to 1 decimal place. (Use the equation Velocity =
Distance  Time)
Ans.__________________________
d)
Find the work done when a tractor winch pulls a weight of 34.6N a distance of 9.1m vertically
upwards. Give your answer to 2 significant figures. (Use the equation Work done = Force 
Perpendicular Distance).
Ans.__________________________
Mr. J.Agius Personal Notes
Page 17