Evidence shall show that knowledge has been acquired of safe working practices and providing computational solutions to basic engineering problems. All knowledge and skills detailed in this unit should be contextualised to current industry practices and technologies. KS01-EE126A Electrotechnology engineering maths Evidence shall show an understanding of electrotechnology engineering maths to an extent indicated by the following aspects: T1 Rational, irrational numbers and basic algebra simplification of expressions involving square roots and cube roots scientific and engineering notation evaluation of expressions using a calculator convert units of physical quantities using unity brackets substitute given values into formulae to find physical quantities manipulate algebraic expressions using mathematical operations in their correct order, the laws of indices, expansion of brackets and collecting like terms T2 Algebraic manipulation Factorise algebraic expressions using common factors Factorise quadratic expressions using trial and error on the factors of the coefficients Simplify algebraic fractions using common denominators and cancelling Solve simple one variable equations including algebraic fractions Find the quotient and remainder given a linear divisor. Transpose formulae to find a required variable. T3 Laws of indices Conversion between decimal notation, scientific notation and engineering notation Laws of indices: positive /negative values, multiplication/division, fractional values, index equals zero Logarithmic laws: multiply/divide solution of exponential equations using logarithms, substitution and solution of relevant formulae involving exponents or logarithms Graphs of exponential functions, 10x and ex and the inverses log10(x) and loge(x) functions on log-linear graphs Convert numbers into scientific and engineering notation using the laws of indices Manipulate and simplify arithmetic and algebraic expressions using the laws of indices and logarithms Express logarithms as indices. Perform logarithmic operations. Determine logarithms and antilogarithms to base 10, using a scientific calculator. Determine logarithms and antilogarithms to base e, using a scientific calculator. Convert logarithmic values from base 10 to base e and vice versa. Sketch given functions on log-linear graphs T4 Estimations, errors and approximations Errors in measurement Maximum probable error Show awareness of errors in measurement and of giving results in appropriate number of significant figures Use estimations and approximations to check the reasonableness of results. T5 Plane figures – triangles and basic trigonometry Angles in a triangle Isosceles and equilateral triangles Congruent triangles Similar triangles Pythagoras' theorem Area of triangles Basic trigonometry functions Degrees, radians The ratios: sin, cos, tan, cosec, sec, cot. Inverse trig functions Sine and cosine rules T6 Plane figures - quadrilaterals and circles Types and properties of quadrilaterals Areas and perimeters of regular quadrilaterals Lengths of arcs Angles in a circle - degrees Angles in a circle - radians Lengths of chord segments Tangents to circles Circumference and area of circles Names and characteristics of common polygons T7 Graphs of Trigonometric functions Graph trigonometric functions and solve trigonometric equations. Simplify trigonometric expressions using trigonometric identities Convert angular measure in degrees to radians and vice versa Graph trigonometric functions including graphs of y = sin x and y = cos x Using vocational applications of current or voltage as a function of time, consider changes in amplitude, consider changes in frequency. Examine relationships of frequency, period and angular velocity. Sketch graphs of the form f(t) = a sin φt and f(t) = a cos φt, where a is the peak voltage or current, and φ is the angular velocity Solve graphically equations of the form f(t) = a sin φt and f(t) = a cos φt Show a positive or negative angle on the unit circle. Use symmetry properties to find trigonometric ratios for angles greater than π/2. Solve simple vocational problems relating period, frequency and angular velocity. T8 Graphs of linear functions The number plane Gradient and x and y intercepts of a straight line Equation of a straight line length and mid-point of a straight line segment Function notation T9 Simultaneous equations Graphical solutions Substitution Elimination Solve 2 linear simultaneous equations both algebraically and graphically. T10 Matrices Perform the basic operations on matrices up to 3 x 3 Manipulate matrix equations and expressions Recognise inverse and identity matrices up to 3 x 3 and use to solve systems of linear equations. Find determinants up to 3 x 3 and use to solve systems of linear equations. Solve problems involving more than two simultaneous equations. State the limitations of graphical methods of solution. Distinguish between a matrix and an array. Describe the null, diagonal and unit matrix Describe and identify a singular/non-singular matrix T11 Quadratic functions Graphs of quadratic functions represented by parabolas and the significance of the leading coefficient. Graph quadratic functions and solve quadratic equations. Sketch and interpret the graphs of quadratic functions showing the significance of the leading coefficient and the zeros Solve quadratic equations by factoring or using quadratic formula Solve simultaneously linear and quadratic equations algebraically and geometrically Interpret verbally formulated problems involving quadratic and linear equations and solve. T12 Exponential and logarithmic functions Transform non-linear functions (including exponential) to linear forms and plot data. Draw curves of best fit, interpolate data and estimate constants in suggested relationships. Interpret verbally formulated problems involving growth and decay, and solve. Graph exponential and logarithmic functions and solve exponential and logarithmic equations. Sketch the graphs of simple exponential and logarithmic functions showing behaviour for large and small values T13 Vectors and Phasors The vector as an expression of magnitude and direction The vector sum of x and y values in terms of magnitude and direction Rectangular components of vectors in the form x = r cos θ and y = r sin θ Rectangular-polar and polar-rectangular conversion Vector addition and subtraction Express rectangular components of vectors in the form x = r cos θ and y = r sin θ T14 Complex numbers Definitions and notation of complex numbers Complex numbers as vectors on an Argand diagram laws of complex numbers and apply the laws in suitable calculations. Plot complex numbers on the Argand plane. Express vectors as complex numbers and perform suitable calculations. Calculate the conjugate of a complex number. Using a calculator for rectangular-polar and polar-rectangular conversions. |