City and Guilds Work Sheets
City and Guilds Work Sheets
City and Guilds Work Sheets
Engineering (8030-2000)
Level 5 IVQ Advanced Technician Diploma in
Electrical and Electronic Engineering
Electrical Engineering
Electronic Engineering
(8030-23) (500/5805/8)
Qualification handbook for centres
www.cityandguilds.com
September 2009
Version 2.0
ST00029395/09.09/PO4500055974
Contents
05 Important notice
06 Levels of City & Guilds qualifications
13 Syllabus
IVQ in Electrical and Electronic Engineering 8030
20 Assessment
07 Certificate
07 Diploma
26 Assessment
07 Advanced diploma
30 Assessment
07 Internal candidates
34 Assessment
07 External candidates
07 Resources
39 Assessment
07 Summary of assessment
07 Advanced Diplomas
43 Assessment
07 Award number
08 Component numbers
47 Assessment
49 Appendix A
Practical assignments
49 Practical assignments
49 Instructor notes
49 Marking
49 Candidate instructions
49 Supervision
49 Records, results and certification
49 Visiting verifier
Important notice
Following the accreditation of the Technician IVQs in Electrical and
Electronic Engineering (8030-2000) on the National Qualifications
Framework of England, Wales and Northern Ireland (NQF), some
changes have been made to the qualification, at the request of
the Office of the Qualifications and Examinations Regulator
(Ofqual), the qualifications regulator in England.
These changes took effect on 1 June 2009 and are outlined
on this page.
Note: the content of the qualifications has not changed
following accreditation.
Changes to the qualification titles
The qualification titles have changed as follows:
Advanced Technician Diploma in Applied Electrical Engineering
(8030-23)
changed to
Level 5 IVQ Advanced Technician Diploma in Electrical and
Electronic Engineering (Electrical Engineering) (8030-23)
Accreditation number: 500/5805/8
Advanced Technician Diploma in Applied Electronic Engineering
(8030-23)
changed to
Level 5 IVQ Advanced Technician Diploma in Electrical and
Electronic Engineering (Electronic Engineering) (8030-23)
Accreditation number: 500/5805/8
Changes to the unit titles
Following the accreditation of the Technician IVQs in Electrical and
Electronic Engineering, each unit has been given an accreditation
reference number which will appear on the Certificate of Unit Credit.
05
Other qualifications*
Fellowship (FCGI)
Doctorate
Membership (MCGI)
Master Professional Diploma
Level 5 vocational awards
NVQ/SVQ Level 5
Masters Degree
Postgraduate Diploma
Postgraduate Certificate
Graduateship (GCGI)
Associateship (ACGI)**
Bachelors Degree
Graduate Certificate and Diploma
Licentiateship (LCGI)
Higher Professional Diploma
Level 4 vocational awards
NVQ/SVQ Level 4
A Level
Scottish Higher
Advanced National Certificate in Education
BTEC National Certificate/Diploma
#
*
**
06
Resources
If you want to use this programme as the basis for a course, you
must read this booklet and make sure that you have the staff and
equipment to carry out all parts of the programme. If there are no
facilities for realistic practical work, we strongly recommend that
you develop links with local industry to provide opportunities for
hands-on experience.
Advanced diploma
The advanced diploma (about 600 guided learning hours) takes
these skills to the level appropriate for a person preparing for
or working in first-level management. It is also appropriate for
someone who wants to receive specialised training at a high level.
Summary of assessment
Award number
8030-23 Advanced Technician Diploma in Applied
Electrical Engineering
Advanced Technician Diploma in Applied
Electronic Engineering
We use award numbers to describe the number and level
of the award.
07
Component numbers
220 Engineering Project Practical Assignment
221 Advanced Electrical Principles
222 Control Systems and Applications
223 Distribution and Utilisation of Electrical Energy
224 Generation and Supply of Electrical Energy
225 Micro-electronic Circuits and Systems
226 Electrical Plant and Equipment
227 Advanced Mathematics
8030-23-222
8030-23-225
8030-23-223
8030-23-224
8030-23-226
8030-23-221
08
8030-23-223
8030-23-224
8030-23-226
8030-23-225
a Fixed date
These are assessments which are carried out on dates and
times we set. These assessments have no brackets around their
numbers.
To offer this programme you must get approval from us. There are
two categories of approval.
b Free date
These are assessments which are carried out at a college or
other training establishment on a date or over a period which
the college chooses. These assessments have brackets around
their numbers.
In this programme the written assessments are fixed date. The
practical assignments and the project are free date.
You must carry out assessments according to our International
Directory of Examinations and Assessments. If there are any
differences between information in this publication and the current
directory, the directory has the most up-to-date information.
Subject approval
We give approval to offer a teaching course based on this syllabus.
Examination centre approval
We give approval to enter candidates for examinations.
To be approved by us to offer a teaching course you must send us
the application form.
To enter candidates for examinations you must be approved by
us as an examination centre. For this programme it is possible to
act as a registered examination centre only, and accept external
candidates. Approved examination centres must provide suitable
facilities for taking examinations, secure places to keep the
examination papers and materials, and may have an appointed
visiting verifier to review practical work.
After we have received and accepted an application, we will send
an approval letter confirming this. You can then send entries in at
any time using the International Directory of Examinations and
Assessments for guidance.
Please note that in this section we have provided an
overview of centre approval procedures. Please refer
to the current issue of Delivering International
Qualifications Centre Guide for full details of each
aspect of these procedures
09
Other information
Designing courses of study
Candidates for the various Technician Awards in Engineering
will have come from different backgrounds and will have
different employment and training experiences. We recommend
the following:
carry out an assessment of the candidates achievements so
you can see what learning they already have and decide the
level of entry they will need; and
consider what learning methods and places will best suit them.
When you assess a candidates needs, you should design
teaching programmes that consider:
what, if any, previous education qualifications or training the
candidate has, especially in the various general vocational
education certificates we provide; and
what, if any, previous practical experience the candidate has
which is relevant to the aims of the programme and from which
they may have learned the relevant skills and knowledge.
When you choose learning methods and places, you should
consider the results of your assessments and whether the
following are available.
Open or distance learning material.
Workplace learning that can be carried out on site or between
you and a local workplace. This will allow the candidates access
to specialised equipment and work experience.
Working with other registered centres to share facilities.
Opportunities for co-operative learning between candidates for
different certificates who need to gain similar skills.
As long as the candidates meet the aims of this learning
programme the structures of courses of study are up to you.
So, it is possible to include extra topics that meet local needs.
You should avoid teaching theory alone. As far as possible the
practical work should be closely related to work in the classroom
so that candidates use their theory in a realistic work environment.
You can use formal lectures in the classroom with appropriate
exercises and demonstrations. Candidates should keep records
of the practical work they do so they can refer to it at a later date.
We assume that you will include core skills, such as numeracy,
communication, working with people, and organisation and
planning throughout a teaching programme.
10
Entry levels
We consider that the following programmes are relevant
preparation for this programme.
Technician Diplomas in Electrical and Electronic Engineering (8030)
We also consider that the following Pitman Qualifications award is
relevant alongside this programme.
English for Speakers of Other Languages higher intermediate level
Useful publications
We can provide a list of suggested text books covering specific
areas of this programme. We may also know about other support
materials. You should make sure that you have the latest
information. We will automatically send updated lists to centres
we have approved to offer this programme.
11
Syllabus
IVQ in Electrical and Electronic Engineering 8030
13
Introduction
The intention of this unit is to provide an opportunity for
candidates to solve a realistic engineering problem which
requires the application and integration of other modules within
the Advanced Diploma programme of study.
The aim of the unit is for candidates to acquire:
220.16
220.17
220.18
220.19
Practical competences
The candidate must be able to do the following:
Specification and analysis
220.1
220.2
220.3
220.4
220.5
220.6
220.9
220.10
220.13
14
1 Competence references
3 Candidates instructions
220.1-220.19
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
2 Preparation
2.1
Location of test
The training centre or other venue where supervision and
appropriate working conditions will be provided.
2.2
Requirements
Paper, pens, pencils and ruler or a computer system
running appropriate software (eg word processing,
computer aided draughting software) and a printer
connected to the system, with paper loaded and set
up ready to print.
Manuals for software.
Copy of section 3 and section 6.
2.3
Instructor notes
Candidates are required to select and solve individually an
engineering problem which can be realistically achieved
(see section 6 for suitable suggestions) within 60 hours.
The project must be agreed between candidate and
instructor and must take into account the amount and level
of work required and the resources available. The nature of
the work must demonstrate the candidates ability at
advanced diploma level.
The project is generally considered to be a student centred
activity. The instructors main responsibility is to create an
effective learning environment. In particular the instructor
should check the project objectives, monitor the candidates
progress, advise on project progression, exercise leadership
if needed, assist in development of the candidates skills and
knowledge and counsel as appropriate.
Candidates may carry out research and produce materials
during the allocated time but the report must be produced
at the centre under supervision.
It is recommended that candidates should be allowed
adequate time to produce the final report. Candidates may
use word processors to produce their report provided they
have sufficient word processing skills to do so efficiently.
On completion of the report, candidates are required to
carry out an oral presentation of their work to the
instructor and peer group. It is envisaged that such a
presentation will take between 15-30 minutes.
15
4 Marking
5 Assignment completion
4.1
4.2
4.3
4.4
6 Assignment documentation
6.1
4.7
4.8
4.5
4.6
4.9
4.10
4.11
4.11.1
4.11.2
4.12
4.13
4.14
].
Choosing a project
The theme of the project is to investigate a particular
section of a company and to improve the section in terms
of costs or procedures (manufacturing, maintenance,
marketing, management). Possible areas for project work
are listed below:
improvement of the efficiency or effectiveness of an
existing process
introduction and commissioning of new plant
modification of existing equipment to perform new or
additional operations
improvement of maintenance procedures on selected
plant or equipment
introduction of new procedures for measuring, testing
and calibrating products or equipment
standardisation of component parts for product
assembly.
6.2
16
221.10
221.11
221.12
221.13
221.14
221.15
221.16
221.17
221.18
221.19
Introduction
This unit builds on the electrical principles previously studied in
the diploma level. It aims to cover a variety of fundamental
aspects of circuit and network theory. In addition, a section on
reliability is included. Much of the work in this unit requires a
compatible level of supporting mathematics to assist the
candidates to put into practice the various theoretical concepts. It
is not intended that the mathematics is separately examined.
Knowledge requirements
Instructors must ensure that candidates are able to:
Circuits and networks
221.1
Calculate steady state current and voltage conditions in
ac circuits using symbolic notation (j-operator).
Ac circuits: resistors, capacitors and inductors in series
and parallel circuits
221.2
221.3
221.4
221.5
221.6
221.7
221.20
221.8
221.21
is kc = 1/ QpQs
221.9
221.22
221.23
17
221.24
221.25
221.26
Filters
221.27 Sketch the ideal frequency response characteristics
of a range of filters.
Filters: low pass, high pass, band pass, band stop
221.28
221.29
221.30
221.40
221.41
221.42
Np2
Rp
=
that the
Ns
Rs
221.31
221.44
221.32
221.45
221.33
221.34
221.35
221.36
221.37
18
Reliability
221.46 Explain the importance of high reliability in typical
electrical and electronic applications.
221.47
221.48
221.49
221.50
221.51
221.52
221.53
221.54
221.55
221.56
221.57
221.58
221.59
221.68
221.71
221.72
221.73
221.74
Associated mathematics
The following section is intended to illustrate the topic areas and
the applications of mathematics that the candidates require in
order to complete the applications work arising from this unit.
Trigonometric functions
221.60 Represent sine, cosine and harmonic waveforms using
y = Asin (t + ) and y = Acos (t + ).
221.76
221.77
221.78
Graphical representations
221.79 Use log/linear graph paper to present frequency
response of electrical/electronic circuits in graphical
form and interpret practical results.
221.61
221.62
Calculus
221.63 Differentiate, applying standard rules, a range of functions.
Functions: a constant, xn, Acos (x), Bsin(x), ex
221.80
221.64
221.81
221.65
221.66
221.67
19
Assessment
Topic
Circuits and networks
Filters
Transients and transformers
Reliability
20
Approximate %
examination
weighting
50
15
15
20
Introduction
The aim of the unit is to provide a general background in control
theory with details of the construction and performance of the
associated practical equipment over a range of applications, using
an inter-disciplinary approach. Much of the work in this unit
requires a compatible level of supporting mathematics to assist the
candidates to put into practice the various theoretical concepts. It
is not intended that the mathematics is separately examined.
Knowledge requirements
Instructors must ensure that candidates are able to:
Control principles
222.1
222.2
222.3
222.4
222.5
222.6
Sensors (transducers)
222.7 Describe, with the aid of diagrams, the construction,
the principles of operation, and characteristics of a
range of sensors.
Sensors: diaphragm and bellows types including
capacity, inductive and piezoelectric transducers for
pressure measurement; load cells and strain gauges,
including bridges techniques for measurement of
weight; thermistors, thermocouples and resistance
thermometers for temperature measurement; linear
variable differential transformer and resistance potential
divider for linear displacement; digital optical encoders
for rotational displacement; tacho generators and pulse
counting techniques with magnetic induction for
measurement of angular velocity; venturi with pressure
transducers, turbine meters and doppler frequency shift
meters for measurement of liquid flow
222.8
222.9
222.12
222.13
222.14
21
222.15
222.16
22
Nyquist diagrams
222.42 Explain that mathematical expressions such as
G(j ) = 1/ (1 + j T) where T is the time constant of the
system in seconds can also be represented in the form of
a single polar plot, (magnitude in dB for each phase
angle), known as a Nyquist diagram.
Digital systems
222.53 Explain how open and closed loop control systems can
incorporate signal sampling rather than continuous
control, thus providing a means of controlling a process
by means of digital computers with suitable interfacing,
eg digital to analogue and analogue to digital converters.
23
24
Associated mathematics
This section of the syllabus is intended as a guide to the
mathematics that candidates are likely to find helpful in carrying
out practical calculations arising from the topics in the main body
of this unit.
Exponential functions
222.76 Solve equations involving exponential functions arising
from electrical problems.
Equations:
i = I(1 e t/CR), V = E(1 e tR/L) for electrical circuits.
Complex numbers
222.77 Represent ac quantities using operator jw.
222.78 Perform addition, subtraction, multiplication and
division of complex numbers.
222.79 Use polar form in calculations involving jw.
222.80 Convert polar to cartesian form and cartesian to
polar form.
222.81 Solve series and parallel ac linear circuit problems.
222.82 Solve problems involving amplitude and phase shift in
simple RC networks.
Differential equations
222.83 Apply simple modelling techniques to represent the
performance of mechanical and electrical systems
based on differential equations.
Systems: electrical L, C and R series and parallel
circuits, mechanical spring mass and damper systems,
closed loop position and speed control systems
222.84 Determine transient and steady state solutions of
first and second order differential equations arising
from 222.83.
Laplace transforms
222.85 Explain the general use of Laplace transforms and their
application to the solution of electrical and electronic
circuit problems.
222.86 Explain that in the s-domain, a transfer function of a
network is given by:
T(s) = (Laplace transform of output)/(Laplace transform
of input)
222.87 Describe the use of Laplace transform tables to obtain
the Laplace transforms of unit amplitude signals which
are functions of time.
Signals: impulse, step, ramp, exponential growth and
decay, sinewave, cosinewave.
25
Assessment
Topic
Control principles
Sensors (transducers)
Amplifiers and actuators
Feedback and performance criteria
Frequency response and system testing
System stability
Nyquist diagrams
Use of controllers and compensation
techniques
Process control
Digital systems
Programmable logic controllers (PLC)
Applications and programming
26
Approximate %
examination
weighting
10
10
10
40
30
Introduction
Many industrial processes depend on the conversion of electrical
energy into motive power, heat and light. This unit is concerned
with the fundamental engineering principles which need to be
understood to ensure that electrical installations are correctly
planned, constructed and maintained.
Knowledge requirements
223.10
223.11
223.12
223.13
223.14
223.15
223.16
223.17
223.18
223.19
223.3
223.4
223.5
223.6
223.7
27
28
29
Assessment
Topic
Distribution Systems
Protection Systems and Devices
Machines
Heating, Refrigeration and Air-Conditioning
Industrial Processes
Illumination
Testing
30
Approximate %
examination
weighting
14
14
24
14
10
14
10
Introduction
A major proportion of industry, commercial businesses and
domestic homes depend on a reliable supply of electrical energy
into which can be converted into motive power, heat and light.
This unit is concerned with the fundamental engineering principles
relating to the generation of electricity and its transmission on
overhead and underground cables supplied via transformers.
224.9
224.10
224.11
224.12
Knowledge requirements
On completion of this unit and as a result of instruction and
practical activities, the candidate should be able to:
Generating stations
224.1
Explain a load duration curve and construct typical
curves from given data relating to a supply situation.
224.2
224.3
224.4
Synchronous generators
224.13 Describe the use of gas and liquid cooling for the stator
and rotor of large generators.
224.14
224.15
224.16
224.17
224.18
224.19
224.5
224.6
224.7
Compare the use of a public supply with the use of an onsite generating plant taking into account the various
factors which may influence the choice of supply.
Factors: convenience, economic, continuity of supply,
use of waste heat
Transformers
224.21 Explain, with the aid of diagrams, how transformer
windings may be connected in different configurations.
Use standard markings to show phase and polarity.
Configurations: star, delta, interconnected star
arrangements
224.8
31
32
224.38 Describe the use of design aids to determine the sag and
tension in overhead lines.
Design aids: charts, templates, computer programs
224.39 Describe the construction used for a range of
overhead lines.
Lines: copper, aluminium, aluminium alloy, aluminium
conductor steel reinforced (ACSR), Aerial Bundled
Conductor (ABC)
224.40 Compare the suitability of different types of conductor,
in various applications, on the basis of their properties.
Properties: electrical conductivity, mechanical
strength, corrosion resistance
224.41 Describe the important physical factors to be
considered in overhead line construction.
Physical factors: conductor separation, ground
clearance, wind and ice loading, environment
224.42 Describe the construction of suspension, pin and post
type insulators.
224.43 Describe the effects of moisture and pollution on the
breakdown voltage of insulators and explain how good
design can reduce these effects.
224.44 Explain why insulation stress is a maximum adjacent to
the line and how the stress may be more evenly
distributed by grading or by rings.
224.45 Calculate the voltage distribution across an insulator
string and hence determine the string efficiency.
224.46 Explain the basic principles and operation of moving coil
and induction regulators.
Underground cables
224.47 Describe the construction of various types of cable.
Cable types: solid, gas-filled, oil-filled, screened,
polymeric
224.48 Describe for different types of cable, an appropriate
method of cable laying and jointing.
Cable types: solid, gas-filled, oil-filled, screened,
polymeric
224.49 Compare the applications of different types of cable on
the basis of the conditions
Cable types: solid, gas-filled, oil-filled, screened,
polymeric
Conditions: voltage range, temperature range,
grouping, ground conditions
224.50 Sketch a diagram showing the access points, joints and
feed points for oil or gas filled cables.
33
Assessment
Topic
Generating Stations
Synchronous Generators
Transformers
Transmission circuit principles
Overhead Lines
Underground Cables
Substations
Operational Safety
Economics
34
Approximate %
examination
weighting
12
12
10
12
12
12
10
10
10
Introduction
This unit provides further study of the application of electronics.
It includes a range of topics covering devices, circuits and
systems with appropriate industrial applications. The treatment
of the topics include both descriptive and mathematical
calculations to a level where students can produce practical
circuit and system designs.
Knowledge requirements
225.10
225.11
225.12
225.13
225.14
225.15
225.2
225.3
225.4
225.5
225.6
225.7
225.17
225.18
225.19
Amplifiers
225.8 Explain briefly the terms associated with various types
of amplifier.
Terms: small-signal, large signal, negative feedback,
operational, audio frequency, video, radio frequency,
tuned frequency
225.9
Oscillators
225.16 Explain the term positive feedback and the conditions
for oscillations to be maintained.
Conditions: loop-gain positive and equal to, or greater
than, unity
35
Power supplies
225.21 Explain the need for regulated (stabilised) power
supplies in electronic equipment applications.
225.22 Describe, with the aid of circuit diagrams, the operation
of basic types of regulator.
Types: shunt, series
225.23 Explain, with the aid of circuit diagrams, how a
combination of series and shunt regulators is used to
provide the basis for a stabilised power supply and how
the system can be improved by the addition of dc
amplifiers and negative feedback
225.24 Perform calculations relating to the operation of
stabilised power supplies including the applications
of commercially available integrated circuit types
eg 7812 and 7912.
Calculations: output resistance, regulation,
output voltage
225.25 Describe, with the aid of circuit diagrams, the operation
of protection circuits in stabilised power supplies.
Circuits: over current, over voltage
225.26 Explain, with the aid of circuit diagrams, the principle of
operation of a switched mode dc voltage regulator eg
integrated circuit type L296.
Operation: pulse width modulator (PWM) operating at
high frequency followed by a smoothing circuit with
feedback controlling the pulse width and dc output voltage
225.27 Describe the advantages of switched mode
power supplies.
Advantages: greater efficiency, smaller size due to
greater efficiency, suitable for high current low voltage
supplies
Power control
225.28 Describe the features of a power MOSFET and perform
simple calculations of current and voltage levels in dc
load control.
Features: high input resistance, low saturation
resistance, low saturation voltage, high saturation current
225.29 Describe, with the aid of current/voltage characteristics,
the operation of semiconductor power switching devices.
Devices: thyristor, diac, triac, unijunction transistor
225.30 Explain, with the aid of a circuit diagram, the operation of
a unijunction transistor relaxation oscillator.
225.31 Describe, with the aid of circuit and waveform diagrams,
typical applications of the power switching devices
listed in 225.29.
Applications: half bridge and full bridge control of ac
motor speed using thyristors, control of ac lighting
using a triac
36
37
38
Assessment
Topic
Information transmission, signals and noise
Amplifiers
Oscillators
Power supplies
Power control
Introduction to Microcomputers
Logic Systems
Display Devices
A-D and D-A Conversion
Approximate %
examination
weighting
10
10
10
10
10
10
20
10
10
39
Introduction
This unit is intended for candidates who are involved with
industrial plant. It provides a detailed approach to the
construction, design and performance characteristics and
industrial applications of electric motors and transformers.
Calculations relating to design and performance of plant are
included in the relevant sections.
Knowledge requirements
Transformers
226.12 Describe types of construction of transformers.
Types: core, shell, Berry
226.13
226.14
226.15
226.16
226.17
226.18
226.19
226.3
226.4
226.5
226.6
226.7
226.8
226.9
226.10
226.11
40
Synchronous machines
226.25 Describe the construction of synchronous machines
Machines: cylindrical rotor, salient pole
226.26 Describe methods of supplying excitation power to
synchronous machines.
Methods: direct coupled ac and dc generators,
permanent magnet generators
226.27 Sketch an equivalent circuit of a synchronous machine.
226.28 Perform calculations from given data.
Calculations: excitation , load power, power/load
angle relationship
Data: terminal voltage, load current, power factor,
excitation current
226.29 Describe the conditions necessary for synchronising an
ac generator.
226.30 Describe the synchronisation of an ac machine with a
similar machine or an infinite busbar.
226.31 Explain the effects of varying the power input or
excitation on a synchronous machine.
Effects: open circuit terminal emf, short current, on
load terminal voltage
226.32 Calculate the synchronising power from given data.
Data: open circuit terminal voltage, on load power
and power factor, winding resistance, synchronous
reactance
226.33 Construct an operating chart for a motor or generator
connected to an infinite busbar.
226.34 Indicate on the operating chart and explain the
operating limits.
226.35 Explain typical applications for synchronous motors.
Applications: constant speed drives, power
factor correction
226.36 Describe methods of starting synchronous motors.
Methods: using a separate motor, starting as an
induction motor
226.37 Explain the use of synchronous motors for power factor
improvement.
Induction machines
226.38 Describe the construction of types of rotor used in
induction motors.
Types: cage, wound
41
42
Assessment
Topic
General Machine Theory
Transformers
Synchronous machines
Induction machines
DC machines
Protection of machines
Special purpose machines and supplies
Approximate %
examination
weighting
15
15
15
15
15
10
15
43
Introduction
Much of the study of the technical units at the diploma and
advanced diploma levels has integrated the mathematical
content in with the applied technology. This unit, at the higher
diploma level, provides additional mathematics to both advance
and broaden a candidates understanding of mathematics to
supplement other studies at this level and to also provide a sound
foundation for further study. Where possible, it is expected that
worked examples will be selected to represent relevant
engineering problems.
227.13
f(x)
(x-a)3
f(x)
ax2+bx+c
Complex Numbers
227.14 Define a complex quantity as a number which has real
and imaginary parts.
227.15
Use the definition j = 1 to identify the imaginary parts
of a complex number.
227.16
Trigonometry
227.1
Prove simple trigonometrical identities involving
sinA, cosA, tanA, cosecA, secA and cotA.
227.17
227.2
227.18
227.3
227.19
227.4
Knowledge requirements
Instructors must ensure that candidates are able to:
227.5
227.6
Geometry
227.7 Create a diagram from given data to a suitable scale.
227.8
227.9
227.10
Algebra
227.11 Sketch graphs of the type yaebx and a(1 ebx) for given
values of a and b.
227.12
44
Differential Calculus
227.30 Derive, from first principles, the differential coefficients
for function such as y = axn+b.
227.31 Use the notations dy/dx, and d2y/dx2 or f'(x) and f''(x)
for derived expressions noting that other variables, such
as V, A, h and r, may be used for Volume, Area, height
and radius.
227.32 Differentiate, by rule, a range of functions and
combinations of functions noting that the constants may
be positive, negative or fractional numbers.
Range of functions:
i
yaxn b xma xb
-where a,b,m, and n
are constants
ii y + a sin (b + a)
-similarly for other
trigonometric functions
iii y = aln (bx)
-similarly for functions
involving log10x and ex
iv y = abx
227.33 Differentiate, by rule, functions of functions, products
and quotients of functions for the range given in 227.32.
227.34 Obtain the first and second derivatives for the range of
functions given in 227.32.
227.35 Determine turning points for the range of functions
given in 227.32 and identify these as local maxima, local
minima or points of inflection.
227.36 Solve problems involving maximum and minimum values.
227.37 Identify and use the first and second derivatives of a
displacement / time function as velocity and acceleration
respectively, for linear and angular motions.
Integral calculus
227.38 Determine the indefinite integrals of functions for the
range given in 227.32 including integrals of the form
f'(x) / f(x), f'(x)[f(x)]'', integration by substitution and
integration by parts.
227.39 Evaluate definite integrals of functions for the range
given in 227.32 between various limits.
227.40 Solve problems involving definite integration by partial
fractions of functions of the type given in 227.32.
227.41 Evaluate the area under a curve from the range in 227.32
as the integral between given limits.
227.42 Express and evaluate, by integration, the area between
two curves from the range in 227.32.
227.43 Define and calculate the mean and root mean square
values of the functions in 227.32 ii).
227.44 Calculate the centroid, first and second moments of area
of plane figures.
Differential equations and Laplace transforms
dy
227.45 Solve, by direct integration, equations of the form
dx
+ bx + c = 0.
227.46 Solve, by assuming a solution of the form -Aebt, an
d
equation of the form
= k.
dt
227.47 Solve differential equations arising from practical
situations.
227.48 Define Laplace transformation and inverse transformation.
227.49 Use Laplace transforms and inverse transforms to solve
first and second order differential equations for
functions of t when f(t) = k, tn, ekt,sin t, cos t, sinh t,
cosh t, and combinations of these.
Progressions and series
227.50 Define arithmetic progressions (APs) and geometric
progressions (GPs) as progressions having a common
difference and common ratio between successive terms
respectively.
227.51 Evaluate the sum of n terms of an arithmetic progression
using the formula
n[2a+d(n1)]
Sn =
where a is the first term, d is the
2
common difference and n is the number of terms.
227.52 Evaluate the sum of n terms in a geometric progression
using the formula
a(1r n )
Sn =
, where a is the first term, d is the common
(1r)
ratio and n is the number of terms.
227.53 Deduce general expressions for the nth term of simple
arithmetic and geometric progressions.
227.54 Expand the general binomial expression (a=b)n for any
positive integer value of n.
227.55 Write a single specified term from the expansion
given in 227.54.
227.56 Use the binomial series to expand expressions such as
(1+x)n for 1<x<1.
227.57 Use the binomial series to estimate the effects on the
subject of a formula, involving power laws, when there
are small percentage errors in the variables.
45
46
Assessment
Topic
Trigonometry
Geometry
Algebra
Complex numbers
Matrices and determinants
Differential calculus
Integral calculus
Differential equations and
Laplace transforms
Progressions and series
Complex waveforms
Probability
Approximate %
examination
weighting
20
10
10
30
10
10
10
47
Appendix A
Practical assignments
Instructor notes
It is essential that you read these before attempting to administer
the practical assignment. Practical assignments usually require
you to prepare material for the assignment.
Candidate instructions
Make sure every candidate has a copy of these before beginning
the practical assignment.
Marking
The marking is based on performance criteria or outcomes
related to the practical assignment, to which the answer will
always be either yes the candidate achieved this or no the
candidate did not achieve this. Credit is given for those
performance competences for which the answer is yes the
candidate achieved this.
Supervision
All assignments require supervision and you must make sure that
the results reflect only the individual candidates own work. You
must keep all assessment documentation and material in a file for
each candidate until the results have been agreed by the visiting
verifier and until confirmation of results has been received from
City & Guilds.
Records, results and certification
Successful completion of the related practical assignments for
each unit needs to be recorded and then sent to City & Guilds. We
suggest that you keep a record of each individuals achievements
which may then be transferred to the entry forms. A model is
given at the end of this section but you may use any form of
record keeping that is convenient and accessible.
Appendix A
49
50
Date completed
Instructor signature
Instructor name
Date completed
Instructor signature
Instructor name
Appendix A
51
SP-03-8030