UNIT Use basic mathematics in engineering Descriptor This unit unit covres elementary concepts of mathematics appropriate to engineering questions Hours 40 hours Employability skills The required outcomes described in this unit of competency contain applicable facets of Employability Skills.   The Employability Skills Summary of the qualification in which this unit of competency is packaged will assist in identifying Employability Skills requirements. Pre/co-requisite units Nil Application This unit applies to technician level work in a civil/structural engineering environment.

 ELEMENT   Elements describe the outcome of a unit of competency. PERFORMANCE CRITERIA   Performance criteria specify the level of performance required to demonstrate achievement of the Elements. Terms in italics are elaborated in the Range Statement. 1.    Use fundamental techniques in arithmetic, measurement and mensuration. 1.1.      Round numbers to a given degree of accuracy. 1.2.      Round numbers to a given number of significant figures. 1.3.      Discuss the International System of Units (SI units) 1.4.      Demonstrate an understanding of common SI units and their abbreviations. 1.5.      Convert between commonly used Si units. 1.6.      Convert number between decimal and both scientific and engineering notation. 1.7.      Determine the perimeter and area of two dimensional shapes. 1.8.      Use the Theorem of Pythagoras and apply it to area and perimeter problems. 1.9.      Determine the volume of simple three dimensional shapes. 1.10.   Solve mensuration problems including calculating costs and capacity. 1.11.   Form a ration from information in a practical problem and express the ratio in its lowest terms. 1.12.   Divide a quantity in a given ratio. 1.13.   Solve practical problems involving proportional quantities. 2.    Use fundamental techniques in geometry 2.        2.1.      Name, classify and measure angles in a given diagram using a protractor. 2.2.      Perform angle arithmetic involving angles expressed in degrees, minutes and seconds. 2.3.      Determine the size of an unknown angle in a diagram involving complementary, supplementary adjacent or vertically opposite angles, or angles formed by parallel lines. 2.4.      Classify triangles and quadrilaterals by their side and angle properties. 2.5.      Perform calculations involving angle, chord and tangent properties of a circle. 3.    Use fundamental concepts in algebra 1.         2.         3.         3.1.       Solve arithmetical problems using positive and negative numbers and the correct order of operations. 3.2.       Substitute into, and evaluate algebraic expressions. 3.3.       Simplify algebraic expressions by combining like terms and using the distributive law. 3.4.       Simplify algebraic fractions. 3.5.       Solve linear equations in one unknown, including applied problems from which an equation can be created. 3.6.       Evaluate formulae by substitution, giving actions with appropriate units. 3.7.       Transpose formulae including those where one variable is repeated. 3.8.       Develop the equation of a straight line from a graph. 3.9.       Determine the equation of a straight line from various situations, including for the line of best fit obtained graphically from empirical data. 3.10.    Use function notation. 3.11.    Solve simultaneous equations analytically and graphically. 4.    Use quadratic equations and their graphs in problem solving. 4.        4.1.      Factorise polynomial expressions involving common factor, difference in two squares and quadratic trinomial types. 4.2.      Simplify algebraic fractions requiring the factorisation of binomial and trinomial expressions. 4.3.      Recognise and define the characteristics of parabolas and sketch their graphs. 4.4.      Solve quadratic equations analytically and graphically. 4.5.      Solve applied problems involving quadratic equations analytically and graphically. 4.6.      Analytically and graphically solve a system consisting of a quadratic and linear function. 5.    Use right triangle trigonometry to solve applied problems. 5.1.      Define the trigonometric ratios sine, cosine and tangent from a right triangle. 5.2.      Use a calculator to determine the sine, cosine and tangent of angles stated in degrees, decimal degrees and in degrees, minutes and seconds. 5.3.      Use a calculator to determine the size of an angle (correct to a certain number of decimal places or correct to the nearest second) given the sine, cosine and tangent of that angle. 5.4.      Determine an unknown side of a right triangle using the sine, cosine and tangent of a known angle. 5.5.      Determine an unknown angle of a right triangle using inverse sine, inverse cosine and inverse tangent of known sides. 5.6.      Solve applied problems using Pythagoras’ theorem and the trigonometric ratios sine, cosine and tangent.

## REQUIRED SKILLS AND KNOWLEDGE

This describes the essential skills and knowledge and their level required to complete the unit.

## Essential knowledge:

• Estimation and rounding
• Scientific and engineering notation
• Ratio and percentages
• Mensuration techniques
• Definitions in geometry
• Basic problem solving in geometry
• Fundamental algebraic concepts
• Linear equations and graphs
• Graphing and function notation
• Translating English into Algebra
• Formulae substitution and transposition
• Factorisation techniques
• The methods for solving quadratic equations
• Definitions in right angle triangle trigonometry
• The use of scientific calculator in finding trigonometric values and inverse trigonometric values
• Angles relevant to trigonometric problems and an understanding of compass bearings

## Essential skills:

#### Ability to:

• Estimate and round off
• Use a scientific calculator
• Convert between ordinary decimal notation, scientific and engineering notation
• Use ratios and percentage
• Calculate perimeter, area and volume
• Apply the Theorem of Pythagoras
• Apply circle theorems
• Use signed numbers
• Substitute values in algebraic equations and formulae
• Simplify algebraic expressions
• Use brackets
• Solve linear equations
• Use function notation
• Draw and interpret linear graphs
• Solve simultaneous equations and formulae
• Convert word problems to algebraic equations
• Classify polynomials
• Factorize algebraic expressions using the common factor method
• Factorize difference of squares
• Factorize trinomials
• Solve quadratic equations using factorization and using the formula
• Draw the parabola
• Determine the trigonometric and inverse trigonometric values
• Solve right triangles
• Solve applied problems involving right triangles
• Solve problems involving right angles of elevation and depression
• Solve problems involving bearings

 RANGE STATEMENT The Range Statement relates to the unit of competency as a whole. It allows for different work environments and situations that may affect performance. Add any essential operating conditions that may be present with training and assessment depending on the work situation, needs of the candidate, accessibility of the item, and local industry and regional contexts. Simple three dimensional shapes may include More complex shapes composed of more simple shapes Given ratio may include Three part ratios Arithmetic problems may include Word problems Quadratic equations may include Equations that don’t usually look like quadratic equations but become quadratic after simplification

 EVIDENCE GUIDE The Evidence Guide provides advice on assessment and must be read in conjunction with the Performance Criteria, Required Skills and Knowledge, the Range Statement and the Assessment Guidelines for this course. Critical aspects of assessment and evidence required to demonstrate this competency unit: ·         Correct units are used for all quantities. ·         Answers must be given correctly to the appropriate degree of accuracy. ·         Credit is given for correct methods of solution in problem solving. ·         Logical supporting evidence must be given in solution to problems. ·         Axes and graphs must be labelled and presented correctly. Access and equity considerations: The assessment environment should not disadvantage the candidate. Context of and specific resources for assessment: This unit may be assessed on the job, off the job or a combination of both on and off the job, that is the candidate is not in productive work, then an appropriate simulation must be used where the range of conditions reflects realistic workplace situations. The competencies covered by this unit would be demonstrated by an individual working alone or as a part of a team. Method of assessment: Assessors must a gather a range of evidence that is valid, sufficient, current and authentic. Evidence can be gathered in a variety of ways including direct observation, supervisor’s report, project work, samples, questioning, workplace-supervised practicals, remote labs, simulations, video, assignments, quizzes, scenario participation, e-portfolios and other techniques as required. Questioning should not require language, literacy or numeracy skills beyond those required in this unit. The candidate must have access to all tools, equipment, materials and documentation required and must be permitted to refer to any relevant workplace procedures, product and manufacturing specifications, code, standards, manuals and reference materials.

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