chapter 02 measurement techniques

8/22/2019 Chapter 02 Measurement Techniques

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CAMBRIDGE A LEVEL

PHYSICS

MEASUREMENTTECHNIQUES


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L E A R N I N G O U T C O M E SNUMBER LEARNING OUTCOME

i U n d e r s t a n d t h e c o n c e p t o f m e a s u r e m e n t

ii B e a b l e t o m e a s u r e p h y s i c a l q u a n t i t i e s

iii U n d e r s t a n d t h e u s e o f c a l i b r a t i o n c u r v e s

iv D i f f e r e n t i a t e b e t w e e n r a n d o m a n d

s y s t e m a t i c e r r o r s

v S h o w d i s t i n c t i o n b e t w e e n a c c u r a c y a n d

p r e c i s i o n

vi L e a r n t o h a n d l e u n c e r t a i n t i e s i n

m e a s u r e m e n t s


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C O N C E P T O F

M E A S U R E M E N T

W h a t i s a m e a s u r e m e n t ?

L o o s e l y d e f i n e d , a m e a s u r e m e n t

i s t h e b e s t e s t i m a t e o f a

p h y s i c a l d i m e n s i o n .

E x a m p l e s :

T h e h e i g h t o f a p e r s o n i s a

m e a s u r e m e n t .

T h e t i m e l a p s e b e t w e e n t h e

b e g i n n i n g a n d e n d o f a 1 0 0 m r a c e

i s a l s o a m e a s u r e m e n t .


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C O N C E P T O F


W h y b e s t e s t i m a t e ?

A m e a s u r e m e n t i s t h e b e s t e s t i m a t ed u e t o p r e s e n c e o f u n c e r t a i n t i e s i nt h e m e a s u r e m e n t .

W h a t c a u s e s u n c e r t a i n t i e s ? U n c e r t a i n t i e s i n m e a s u r e m e n t sa r e d u e t o l i m i t a t i o n s i n h u m a n

o b s e r v a t i o n a n d t h em e a s u r e m e n t t o o l .


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C O N C E P T O F


H o w t o p r e s e n t a m e a s u r e m e n t ?

measurement = best estimate absolute uncertainty

=

or


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C O N C E P T O F

M E A S U R E M E N TH o w t o o b t a i n v a l u e s o f u n c e r t a i n t i e s ? :

i . u s e t h e s m a l l e s t d i v i s i o n o n t h es c a l e , i f t h e r e i s a v i s i b l e g a p

b e t w e e n d i v i s i o n s , o r i f t h e

d i v i s i o n s o f t h e s c a l e a r e t o oc l o s e , o r

i i . b y u s i n g a s c a l e o f i n t e r p o l a t i o n

i f t h e g a p b e t w e e n d i v i s i o n s i sl a r g e .


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C O N C E P T O F

M E A S U R E M E N TW h a t a b o u t s i g n i f i c a n t f i g u r e s i n

a b s o l u t e u n c e r t a i n t i e s ? : R u l e # 1 :

R u l e # 2 :

Section 2.2, page 15, AN INTRODUCTION TO ERROR ANALYSIS: THE STUDY OF

UNCERTAINTIES IN PHYSICAL MEASUREMENTS; JOHN R. TAYLOR; University Science

Books, California 1997.

U n c e r t a i n t i e s s h o u l d a l m o s t a l w a y s

b e r o u n d e d t o 1 s i g . f i g .

T h e l a s t s i g . f i g . o f t h e b e s t e s t i m a t e

m u s t b e i n t h e s a m e d e c i m a l p o s i t i o n a s

t h e u n c e r t a i n t y


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C O N C E P T O F

M E A S U R E M E N TF o r e x a m p l e , v a l i d m e a s u r e m e n t si n c l u d e :

i . 9 . 8 2 0 . 0 2 m s - 2

i i . 6 0 5 0 3 0 m s - 1

i i i . 9 0 3 0 c m - 3

b u t :

i . 9 . 8 2 0 . 0 2 3 8 5 m s - 2 ( v i o l a t e s R u l e# 1 a n d e v e n R u l e # 2 )

i i . 6 0 5 1 . 7 8 3 0 m s- 1

( v i o l a t e s R u l e# 2 )

a r e n o t v a l i d m e a s u r e m e n t s





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C O N C E P T O F






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C O N C E P T O F


E x a m p l e o f m e a s u r i n g l e n g t h :

Figure 1.2, page 8, AN INTRODUCTION TO ERROR ANALYSIS: THE STUDY OF



Q: What is the length of the pencil?


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C O N C E P T O F


Q: What is the length of the pencil?

indicates presence of uncertainty

37.0best estimate

1.0 mm

value of uncertainty


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C O N C E P T O F


E x a m p l e o f m e a s u r i n g v o l t a g e :

Figure 1.3, page 8, AN INTRODUCTION TO ERROR ANALYSIS: THE STUDY OF



Q: What is the value of the reading?


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C O N C E P T O F


Reading on voltmeter: 5.5 1.0 V

Q: What is the value of the reading?

Use interpolation; obtaining values between scale values; to get 5.5 V

The uncertainty of 1.0 V is the size of the divisions.


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M E A S U R I N G L E N G T H S W e w i l l l o o k a t t w o o t h e r

a p p a r a t u s u s e d t o m e a s u r el e n g t h s :

i . t h e v e r n i e r s c a l ei i . t h e m i c r o m e t e r s c r e w g a u g e


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M E A S U R I N G L E N G T H S

A VERNIER SCALE

Source:

http://teachers.cie.org.uk/community/resources/pt_view_resource?id=1474


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M E A S U R I N G L E N G T H S E X A M P L E S :

Source:


I. LOOK FOR ZERO VALUE ON VERNIER SCALE

Here ZERO VALUE is between 3.0 and 4.0 mm on

main scale. Take lower value of 3.0 mm.

II. LOOK FOR DIGIT ON VERNIERSCALE WHERE VERNIER AND

MAIN SCALES COINCIDE

Here they coincide at 0.7 mm.

The vernier scale divides the

linear scale into smaller

subdivisions

III. ADD BOTH READINGS

Here we get 3.0 + 0.7 mm = 3.7 mm


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Source:

https://changkatphysics.wikispaces.com/file/view/Worksheet+1.2_2011.pdf


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Source:

https://changkatphysics.wikispaces.com/file/view/Worksheet+1.2_2011.pdf


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Source:

http://home.vs.moe.edu.sg/imran/midyearworksheet.pdf


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Source:



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Source:



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A MICROMETER SCREW GAUGE

Source:



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III. Obtain value of measurement by adding main scale reading

with vernier scale reading. Here it is 7.72 mmSource:


II. Read value of vernier

scale where scale

coincides with line

perpendicular to

main scale. Here it is

0.22 mm.

I. Read value from main scale. Here

it is 7.5 mm.each line = 1.0 mm

each line = 0.5 mm


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Source:


What is the value of this measurement?


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Source:


What is the value of this measurement? 3.56 mm


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Source:


What is the value of this measurement?


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Source:


What is the value of this measurement? 0.29 mm


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M E A S U R I N G W E I G H T S A N D

M A S S E S A p p a r a t u s t h a t c a n b e u s e d

t o m e a s u r e w e i g h t / m a s s o f a n o b j e c t :

i . S p r i n g b a l a n c ei i . L e v e r b a l a n c e


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M A S S E S

Source:

http://images.tutorvista.com/content/forces/spring-balance.gif

The diagram on the left shows a spring

balance.

The reading of the pointer gives the

value of the gravitational force that is

exerted on the object.

To obtain the mass ofthe object, we

must divide the reading of the scale bythe local gravitational acceleration,

often taken as 9.8 m s-2


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M A S S E S

Source:

http://etc.usf.edu/clipart/67200/67265/67265_proportions.htm

The diagram on the left shows

a primitive lever balance.

The lever balance functionsusing the principle of

moments.

Weight, W to be determined is

hung on the right side offulcrum, F.

The mass, P is moved until the

the scale is horizontal.

rd


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M E A S U R I N G A N G L E S

Source:

http://www.mathsisfun.com/geometry/images/protractor-2-angles.gif

The diagram on the left

shows a protractor.

Protractors can be usedto measure angles

between 0 to 180 .

The absolute uncertainty

of a protractor = 1.0 . You will use protractors

later during the practical

sessions.


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M E A S U R I N G T I M E T i m e i s u s u a l l y m e a s u r e d u s i n g :

W e w i l l l o o k a t t h e s e i n a l i t t l e

b i t m o r e d e t a i l i n t h e n e x t f e ws l i d e s .

i . a c l o c k ,i i . a s t o p w a t c h ,

i i i . a c a l i b r a t e d t i m e b a s e

s e t t i n g o f a C R O .


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M E A S U R I N G T I M E

C l o c k / s t o p w a t c h :

C l o c k s a n d s t o p w a t c h e s a r et i m e m e a s u r i n g d e v i c e s .

C l o c k s a n d s t o p w a t c h e s c a n b ee i t h e r a n a l o g u e o r d i g i t a l .

T h e u n c e r t a i n t i e s o f d i g i t a l

s t o p w a t c h / c l o c k a r e . .


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U S I N G A C R OC a t h o d e R a y O s c i l l o s c o p e ( C R O ) :

V e r y g o o d e x p l a n a t i o n s o f t h eC R O u s e i s p r o v i d e d i n t h e

l i n k s b e l o w :

I. http://www.antonine-

education.co.uk/Pages/Physics_1/Electricity

/EL_10/Electricity_10.htmII. http://www.doctronics.co.uk/scope.htm


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U S I N G A C R O

Source:

http://www.antonine-education.co.uk/Pages/Physics_1/Electricity/EL_10/Electricity_10.htm

The diagram below shows a sinusoidal trace on the screen of a CRO


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OT H E R M E A S U R E M E N T S O t h e r m e a s u r e m e n t s d o n e i n

t h e l a b i n c l u d e :i . m e a s u r i n g t e m p e r a t u r e s

u s i n g t h e r m o m e t e r s ,

i i . m e a s u r i n g c u r r e n t s u s i n g

a m m e t e r s / g a l v a n o m e t e r s ,

i i i . m e a s u r i n g p o t e n t i a ld i f f e r e n c e u s i n g v o l t m e t e r s .


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E X A M P L E SMay/Jun 2009, Paper 1, question 3.


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E X A M P L E SOct/Nov 2010, Paper 12, question 4.


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H O M E W O R K Q U E S T I O N SHomework:

1. Question 4, Paper 1, May/Jun 2009.2. Question 4, Paper 11, Oct/Nov 2009.

3. Question 1, Paper 11, Oct/Nov 2010.



6. Question 4, Paper 11, May/Jun 2011.7. Question 5, Paper 12, May/Jun 2011.


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C A L I B R AT I O N C U R V E S Calibration curves are functions of an

instrument's responses to a range of factor

levels. (*) A factor level could be current, potential

difference, or some other measurable quantity.

A calibration curve is used to give readings ofvalues for analogue meters that have:

i. non linear scales, or

ii. are not properly calibrated, or

iii. are faulty.

(*) Source:

http://www.aerosols.eas.gatech.edu/EAS%20Graduate%20Lab/Class%20Notes%20Uncertainty.p

df


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C A L I B R AT I O N C U R V E S The gradient of a calibration curve

gives the sensitivity of the measuringdevice.

The sensitivity of a measuring devicegives amount of change in

measurement output for a given

measurement input change.


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C A L I B R AT I O N C U R V E S A more sensitive measurement tool

will give a larger range of response to asmaller input change.

e.g. the needle of a sensitive analoguemeter will deflect more for a smaller

change in input.


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E X A M P L E SMay/June 2008, Paper 1, question 5.

R A N D O M v s S Y S T E M AT I C


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R A N D O M v s . S Y S T E M AT I C

E R R O R S

MEASUREMENT ERRORS

RANDOMERRORS

SYSTEMATICERRORS



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E R R O R S

Figure 4.1, page 95, Chapter 4: Statistical Analysis of Random Uncertainties, AN INTRODUCTION TO ERROR

ANALYSIS: THE STUDY OF UNCERTAINTIES IN PHYSICAL MEASUREMENTS; JOHN R. TAYLOR; University

Science Books, California 1997.


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R A N D O M v s . S Y S T E M A T I C E R R O R S

RANDOM ERROR SYSTEMATIC ERROR

Definition: Experimental

uncertainties that can be revealed by

repeating the measurement arecalled random errors.

Definition: Experimental

uncertainties that cannot be

revealed by repeating themeasurement are called

systematic errors.

Examples of causes of this type of

error:

i. misreading of data/value on part

of data collector.

ii. variations in thickness of a wirewhen measuring its thickness.

Examples of causes of this type

of error:

i. zero error, a type of

calibration error.

ii. poorly calibrated equipment.

* Definition from page 94, Chapter 4: Statistical Analysis of Random Uncertainties, AN INTRODUCTION TO

ERROR ANALYSIS: THE STUDY OF UNCERTAINTIES IN PHYSICAL MEASUREMENTS; JOHN R. TAYLOR;

University Science Books, California 1997.** Source for examples:http://www.ibid.com.au/Uploads/English/Documents/Subject/Physics%20Ch%201.pdf

R A N D O M S Y S T E M A T I C E R R O R S


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R A N D O M v s . S Y S T E M A T I C E R R O R S

RANDOM ERROR SYSTEMATIC ERROR

Examples of causes of this type of

error (contd):

iii. reaction time errors, if reactiontimes are inconsistent.

iv. usage of less sensitive equipment

when more sensitive equipment is

available.v. effect of air currents when

reading mass.

vi. parallax error on part of observer,if inconsistent.

Examples of causes of this type

of error (contd):

iii. reaction time errors,provided consistent reaction

times.

iv. instrumental parallax error.

v. observers parallax error, ifparallax error consistent.

* Definition from page 94, Chapter 4: Statistical Analysis of Random Uncertainties, AN INTRODUCTION TO

ERROR ANALYSIS: THE STUDY OF UNCERTAINTIES IN PHYSICAL MEASUREMENTS; JOHN R. TAYLOR;

University Science Books, California 1997.** Source for examples:http://www.ibid.com.au/Uploads/English/Documents/Subject/Physics%20Ch%201.pdf



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E R R O R SRANDOM ERROR SYSTEMATIC ERROR

Effects the standarddeviation (the spread of

results) of an experiment.

Each result from experiments

with higher random error

will be spread further apart

from the mean.

Effects the mean of theexperimental results.

Results of experiments with

more significant systematic

error will have a mean

further away from actual

value.

Effect of error on average of best estimate can be reduced

by repeating the experiment.

Effect of error on average of best estimate cannot be

reduced by numerous trials


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P R E C I S I O N v s . A C C U R A C Y

PRECISION ACCURACY

For measurements:

Relates to the spread; i.e. differenceof the results from the mean value

of all the measurements.

For a particular equipment: Relates to how much resolution a

measuring tool gives.

E.g. a micrometer screw gauge is

more precise in measurement than

a vernier scale because its

resolution is to the nearest 0.01

mm.

For measurements:

Relates to how close the reading isto the actual value.

For a particular equipment: Relates to how close to the actual

value a measurement tool can

measure.

Greatly depends on the calibration

of the equipment prior to

performing experiment.


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P R E C I S I O N v s . A C C U R A C Y


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E X A M P L E SMay/June 2008, Paper 1, question 5.

H O M E W O R K


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H O M E W O R K

1. Oct/Nov 2008, Paper 1, question 4.

2. Oct/Nov 2009, Paper 11, Question 3.3. May/Jun 2010, Paper 22, question 1.

4. May/Jun 2011, Paper 23, question 1.5. Oct/Nov 2011, Paper 12, question 5.

H A N D L I N G U N C E R TA I N T I E S


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UNCERTAINTIES

ABSOLUTEe.g. 9.8 0.2 m s-2FRACTIONAL/PERCENTAGE

e.g. 9.8 .

.

e.g. 9.8 m s-2 2%



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CONVERTING UNCERTAINTIES

between absolute and

fractional/percentage

%

between absolute and

percentage

%



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Quick Check 2.4, Section 2.7, page 29, AN INTRODUCTION TO ERROR ANALYSIS: THE

STUDY OF UNCERTAINTIES IN PHYSICAL MEASUREMENTS; JOHN R. TAYLOR;

University Science Books, California 1997.



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Quick Check 2.4, Section 2.7, page 29, AN INTRODUCTION TO ERROR ANALYSIS: THE

STUDY OF UNCERTAINTIES IN PHYSICAL MEASUREMENTS; JOHN R. TAYLOR;

University Science Books, California 1997.

a. 55 cm/s 4%,

b. -20 cm/s 10%,

c. 4.58 0.09 J

P R O P A G A T I N G


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U N C E R T A I N T I E SUncertainties propagate when

measurements with uncertainties are:I. added, or

II. subtracted, or

III. multiplied, or

IV. divided.



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U N C E R T A I N T I E S What happens when measurements

with uncertainties areadded/subtracted?:

the measurements areadded/subtracted.

their respective absoluteuncertainties are added.



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U N C E R T A I N T I E S

Example from page 50, AN INTRODUCTION TO ERROR ANALYSIS: THE STUDY OF





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U N C E R T A I N T I E S

Example from page 50, AN INTRODUCTION TO ERROR ANALYSIS: THE STUDY OF





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U N C E R T A I N T I E S What happens when measurements

with uncertainties aremultiplied/divided?:

the measurements aremultiplied/divided.

their respective percentage orfractional uncertainties are added.

E X A M P L E S


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E X A M P L E S

May/June 2008, Paper 1, question 4.



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U N C E R T A I N T I E STWO SPECIAL CASES:

i. Constants

If a constant/exact value appears in an equation, themagnitude of the constant is multiplied by the absolute

uncertainties of the other measured variables that the

constant is multiplied by in the original equation.

e.g. Given the radius of a circle, 1.20 0.02cm, find

its circumference, with its uncertainty:

2 2

2 1.20 2 0.02

7.5 0.1cm



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U N C E R T A I N T I E STWO SPECIAL CASES:

ii. Powers

If a term is raised to a power, the magnitude of the poweris multiplied by the percentage uncertainties of the term

that is raised.

e.g. Given the length of a cube, 2.00 0.02cm, findits volume, with its uncertainty:

3 100%

2.00 3 0.02

2.00 100%

8. 00 3% 8.0 0.2

E X A M P L E S


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E X A M P L E S

Oct/Nov 2009, Paper 22, question 1.

E X A M P L E S


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E X A M P L E S

Oct/Nov 2009, Paper 22, question 1 (contd).

E X A M P L E S


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E X A M P L E S


E X A M P L E S


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E X A M P L E S


E X A M P L E S


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E X A M P L E S


E X A M P L E S


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E X A M P L E S

May/Jun 2010, Paper 23, question 1.

E X A M P L E S


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E X A M P L E S

May/Jun 2010, Paper 23, question 1 (contd).

E X A M P L E S


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May/Jun 2010, Paper 23, question 1 (contd).

E X A M P L E S


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Oct/Nov 2011, Paper 11, question 5.

H O M E W O R K


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2. May/Jun 2009, Paper 21, question 1.3. Oct/Nov 2009, Paper 21, question 1.

4. May/Jun 2010, Paper 11, question 6.



7. May/June 2011, Paper 11, question 5.8. May/June 2011, Paper 12, question 4.

H O M E W O R K


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10.May/Jun 2011, Paper 23, question 1.11.Oct/Nov 2011, Paper 12, question 4.

12.Oct/Nov 2011, Paper 12, question 5.