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Elements and Performance Criteria
Range Statement
Performance Evidence
Knowledge Evidence
Evidence required to demonstrate competence in this unit must be relevant to and satisfy all of the requirements of the elements and performance criteria and include knowledge of: |
energy sector applied mathematical concepts of engineering mathematics with calculus, including:mathematical linear measurement in engineering situations encompassing:precision and error in mathematical computations displaying mathematical outcomes in the correct format using the appropriate significant figures and in scientific notationperimeters of plane figures, polygons and the perimeter of shapes involving arcsPythagoras’ theorem to engineering situationsmathematical spatial measurement in engineering situations encompassing:areas of combined shapesvolume and surface areas of solidsright triangle trigonometry in engineering problem solving encompassing:problems using the six trigonometrical ratiosproblems involving compass bearings and angles of elevation/depressiontrigonometrical concepts in problems involving inclined planes, vectors and forces and electrical sinusoidal waveformssine and cosine rules in practical applications encompassing:sine rule to solve unknown dimensions/angles in trianglescosine rule to solve unknown dimensions/angles in trianglesmathematical concepts in basic surveying and computation of areas encompassing:mathematical concepts for radial and triangulation surveysSimpson’s Rule in engineering applicationsbasic algebra in engineering calculations encompassing:basic operations involving substitutions, additions, removal of brackets, multiplication and divisionssolving linear equationstransportation in non-linear equationslinear graphical techniques in engineering problem solving encompassing:graphing linear functionsderiving equations from graphs and tablessolving simulations equations algebraically and graphicallythe best line of fit graphically and determine equationmathematical computations involving polynomials encompassing:adding, subtracting and multiplying polynomialsfactorising trinomialssolving quadratic equationmathematical computations involving quadratic graphs encompassing:graphs of quadratic functionsmaxima and minimagraphical solutions of quadratic equationsproperties of a parabolaapplications of parabolas in engineering applicationstrigonometry and graphical techniques in engineering outcomes encompassing:graphs of trigonometric functions e.g.: V=VmsinV,I=Imcosaddition of equations such as: vsinA + usin( + ) graphicallySimpson’s Rule to determine the average and root mean square values of a sinusoidal waveformstatistical data presentation encompassing:appropriate presentation of frequency tables, histograms, polygons, stem and leaf plotsadvantages of different visual presentationsappropriate sampling techniques for gathering data encompassing:design of surveys and censussample data using correct techniqueuse of the measures of central tendency encompassing:estimation of percentiles and deciles from cumulative frequency polygons (ogives)interpreting data from tables and graphs, including interpolation and extrapolationanalysing misleading graphsmeasures of dispersion in statistical presentations encompassing:box-and-whisker graphsmeasures of dispersion using variance and standard deviationstandardised scores, including Z-scorescorrelation and regression techniques encompassing:interpreting scatter plotscorrelation coefficientscalculate the regression equation and use for prediction purposeselementary probability theory encompassing:probabilities in everyday situationscounting techniques: factorials; permutations and combinationsPaschal’s triangle and the normal curve encompassing:Paschal’s trianglecharacteristics of the normal curvestandard deviation and applications to everyday occurrencesprobabilities using the normal curvedifferential calculus encompassing:basic concepts - definition of the derivative of a function as the slope of a tangent line (the gradient of a curve); limits; basic examples from 1st principles; notation and results of derivative of k.f(ax + b) where f(x)=x to the power of n, sin x, cos x, tan x, e to the power of x, ln xrules - derivative of sum and difference; product rule; quotient rule; chain rule (function of a function), limited to two rules for any given functionthe 2nd derivativeapplication - equations of tangents and normals; stationary points; turning points; and curve sketching; rates of change and rectilinear motionverbally formulated problems involving related rates and maxima: minimaintegral calculus encompassing:integration as the inverse operation to differentiation - results of the integral of k.f(ax + b) where f(x) = x to the power of n, sin x, cos x, sec squared x, e to the power of xthe method of substitutionthe definite integralapplications - areas between curves; rectilinear motion, including displacement from acceleration and distance travelled; and voltage and current relationship in capacitors and inductors differential equations encompassing:first order and separable linear equationsrelevant workplace documentationrelevant workplace policies and procedures. |