01 scheme of work nd[1]

7/28/2019 01 Scheme of Work ND[1]

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Scheme of Work

Qualification: BETC National Diploma

in Mechanical Engineering/Year (2),Class (A)Unit No:

Unit Title:

REF. CONTENT POSSIBLE ACTIVITIES RESOURCES

Week1 introduction to unit content, scheme of work and

assessment requirements.

plotting of straight line graphs, choice of axesand explain how to rearrange equations intostraight line form.

tutor-led demonstration of plotting of straightline graphs with a minimum of three points toobtain point of intersection

discuss the shape of the graphical plot of aquadratic equation and the effects of thevarious parameters.

explain the formation of a table of values withpossible use of computer to assist and thendemonstrate how to plot smooth curves and theapplication to find the roots of a quadraticequation.

Whole class teaching

Introduction to unit

Interactive white board.

PowerPoint presentation

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Week2 explain how by plotting a quadratic and lineargraph simultaneously the intersection can beprojected onto thex-axis to give the roots of an

equation, eg Plot the graph 22xy = of and use

the graph to solve the equation

0432 2 =+ xx .

explain how laws which are not apparentlylinear can be reduced to give a straight linerelationship and then demonstrate the reductionof typical examples, eg

baxy +=2 , plotyagainst 2x .

revise the laws of logarithms and explain howlogarithms can be used to reduce laws of the

type naxy = to a straight line form.

Week3 to review the previous weeks work and

demonstration of solution of laws of the typey= axn but using logarithmic graph paper

explain and demonstrate the differing type ofcubic equation, eg 1 root, 2 roots, 3 roots

show how a table can be built up manually andcomputer generated and demonstrate plotting

of a cubic equation. summarize all the previous weeks work using

manual and graphical techniques.

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Week4 define an arithmetic progression and express anarithmetic progression in terms of the first term(a) and the common difference (d)

explain the expression for the nth term and the

sum to n terms define a geometric progress andexpress a geometric progression in terms of thefirst term (a) and the common ratio (r).

explain the expression for the nth term, the sum

to n terms and the sum to infinity.

Week5 introduce the idea of a complex number andexplain the Argand diagram

demonstration of the algebra of complex

numbers in Cartesian form

introduce the polar form of a complex number

and demonstrate the algebra of complexnumbers in polar form.

Week6 discuss the relationship between the two formsof complex number and demonstrate the use ofa calculator to interchange between the twoforms of a complex number

explain the application of complex numbers in

practical situations, eg alternating currenttheory and mechanical vector analysis

review the evaluation of the mean, median andmode for discrete and grouped data

explain the significance of standard deviationand variance and demonstrate the evaluation ofstandard deviation and variance for ungroupeddata.

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Week7 demonstrate the evaluation of standard

deviation and variance for grouped data andshow how to use the statistical functions on

calculators to obtain the mean, standarddeviation and variance.

Week8 Eid Al-Adha Holiday

Week9 to revise the relationship between degrees andradians.

explain amplitude, periodic time and frequencyand demonstrate the concept of graphsketching for periodic functions.

discuss shapes ofsinx, 2 sinx, sinx, sin 2x

for values ofxbetween 0 and 360 by usingPowerpoint demonstration.

Week10 using Powerpoint to demonstrate the concepts ofphase angle and phase difference followed by ademonstration of how a single wave results from acombination of two waves of the same frequency usinggraphs and phasor additionintroduce the compound angle formulae anddemonstrate its use followed by an explanation of the

expansion ofR sin (wt +????) in the form a cos wt + b

sin wt and then lead learners in solution of simpleproblems

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Week11 revise the concept of differentiation and reviewof standard derivatives

demonstration of the differentiation of differentfunctions, including polynomial, exponential andtrigonometrical differentiation of variouscombinations of sums.

demonstrate methods of differentiation offunctions using function of a function, productand quotient rules.

Week12 demonstrate the evaluation of differentialcoefficients and introduce the concept ofsuccessive differentiationand application, eg velocity and acceleration.

Week13 introduce the idea of stationary points and showhow to evaluate maximum and minimum valuesfor a rangeof functions

demonstrate calculation of maximum/minimumvalues for practical applications.

Week14 revise the concept of integration and review ofstandard integrals, indefinite integration,constant ofintegration and definite integration

demonstrate evaluation of definite integrals and

application eg area under a curve.Week15 demonstrate the application of integration to

calculate the mean (average) values

demonstrate the application of integration to

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calculate the root mean square (rms) values.

Week16 explain the three methods for finding areas ofirregular shapes

discuss the idea of linking the three methods

and comparing with integration to find the areaunder a curve.

Week17

Week18

Week19

Week20

Week21

Week22

Week23

Week24

Week25

Week26

Week27

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Week28

Week29

Week30

Be able to use advanced graphical techniquesAdvanced graphical techniques: graphical solution eg of a pair of simultaneous equations with twounknowns, to find the real roots of a quadratic equation, for the intersection of a linear and a quadratic

equation, non-linear laws such as (y ax b y a bx

= 2 + , = + ), by the use of logarithms to reduce laws of

typey = axn

to straight line form, of a cubic equation such as 2x3

7x2

+ 3x+ 8 = 0, recording, evaluatingand plotting eg manual, computerised2 Be able to apply algebraic techniques

Arithmetic progression (AP): first term (a), common difference (d), nth term eg a + (n 1)d; arithmetic

series eg sum to n terms, S n a n d n = { + ( ) } 22 1Geometric progression (GP): first term (a), common ratio (r), nth term eg a rn 1; geometric serieseg sum to n terms, Sa rn rn

=

( )

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11, sum to infinity S a

r=

1 ; solution of practical problemseg compound interest, range of speeds on a drilling machineComplex numbers: addition, subtraction, multiplication of a complex number in Cartesian form, vectorrepresentation of complex numbers, modulus and argument, polar representation of complex numbers,multiplication and division of complex numbers in polar form, polar to Cartesian form and vice versa, useof calculatorStatistical techniques: review of measure of central tendency, mean, standard deviation for ungrouped andgrouped data (equal intervals only), variance

3 Be able to manipulate trigonometric expressions and apply trigonometric techniques

Trigonometrical graphs: amplitude, period and frequency, graph sketching eg sinx, 2 sinx, sinx,sin 2x, sin xfor values ofxbetween 0 and 360; phase angle, phase difference; combination of twowaves of the same frequencyTrigonometrical formulae and equations: the compound angle formulae for the addition of sine and cosine

functions eg sin (A B); expansion ofR sin (wt + ) in the form a cos wt + b sin wt and vice versa

4 Be able to apply calculusDifferentiation: review of standard derivatives, differentiation of a sum, function of a function, product andquotient rules, numerical values of differential coefficients, second derivatives, turning points (maximumand minimum) eg volume of a rectangular boxIntegration: review of standard integrals, indefinite integrals, definite integrals eg area under a curve, meanand RMS values; numerical eg trapezoidal, mid-ordinate and Simpsons rule

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01 scheme of work nd[1]

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