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Elements and Performance Criteria

1. Apply mathematical formulae to solve engineering problems
   • Proportions, variation, percentages and averages are calculated, and method of unity is applied
2. Problems involving the manipulation of indices are solved
3. Written descriptions of actual or hypothetical engineering problems are expressed in mathematical terms
4. Algebraic formulae and equations are manipulated to change subjects, as and when required
5. Index problems are converted to logarithmic problems, and vice versa, according to the Law of Logarithms
6. Calculator is used to resolve engineering problems
7. Calculate areas, volumes and masses of regular and irregular figures
   • Problems related to areas and volumes of regular geometric figures are solved using standard formulae
8. Problems relating to surface areas and volumes of circular figures are solved
9. Centres of gravity (CG) and centroids of area are found for both line figures and areas
10. Concept of density is applied to calculate masses
11. Apply trigonometry to solve problems relating to angular measurement and the resolution of vectors
    • Basic trigonometric ratios of sine, cosine and tangent, together with their reciprocals are explained with respect to the sides of a right-angled triangle
12. Pythagoras’ Theorem is proved
13. Problems associated with single angle trigonometric identities, including those derived from the application of Pythagoras’ Theorem to the basic sin, cos and tan identities, are solved
14. Derivation of multiple, double and half angle trigonometric identities are shown and used to simplify complicated trigonometric expressions and identities
15. Sine rule and cosine rule for solution of triangles are proved and applied

Range Statement

Range is restricted to essential operating conditions and any other variables essential to the work environment.

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Performance 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 on at least one occasion and include: assessing own work outcomes and maintaining knowledge of current codes, standards, regulations and industry practices explaining basic mathematical concepts and techniques relevant to engineering identifying and determining appropriate mathematical techniques and formula to solve engineering problems identifying the methods and procedures needed to select mathematical techniques and formula to solve engineering problems imparting knowledge and ideas through verbal, written and visual means performing accurate and reliable calculations performing calculations relevant to engineering, including volumes and masses of regular and irregular areas reading and interpreting written information on engineering problems and expressing this information in mathematical terms solving problems using appropriate laws and principles using a calculator to resolve engineering problems.

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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: calculations, including: algebra calculations with positive and negative integers graphs indices mensuration simplifying expressions trigonometry centre of gravity (CG), longitudinal centre of gravity (LCG) and vertical centre of gravity (VCG) centroids of area formulae for areas, volumes and masses of regular and irregular shapes indices Law of Logarithms proportions, variation, percentages, averages and method of unity Pythagoras’ Theorem.

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