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Elements and Performance Criteria

1. Apply mathematical formulae to solve marine engineering problems
   • Proportions, variation, percentages and averages are calculated, and method of unity is applied
   • Problems involving the manipulation of indices are solved
   • Written descriptions of actual or hypothetical marine engineering problems are expressed in mathematical terms
   • Algebraic formulae and equations are manipulated to change subjects, as and when required
   • Index problems are converted to logarithmic problems, and vice versa, according to the Law of Logarithms
   • Calculator is used to resolve marine engineering problems
2. 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
   • Problems relating to surface areas and volumes of circular figures are solved
   • Centres of gravity and centroids of area are found for both line figures and areas
   • Concept of density is applied to calculate masses
3. 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
   • Pythagoras’ Theorem is proved
   • 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
   • Derivation of multiple, double and half angle trigonometric identities are shown and used to simplify complicated trigonometric expressions and identities
   • Sine Rule and Cosine Rule for solution of triangles are proved and applied

Range Statement

Specifies different work environments and conditions that may affect performance. Essential operating conditions that may be present (depending on the work situation, needs of the candidate, accessibility of the item, and local industry and regional contexts) are included. Range is restricted to essential operating conditions and any other variables essential to the work environment.

Not Applicable.

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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 marine engineering, and

identifying and determining appropriate mathematical techniques and formula to solve marine engineering problems

identifying the methods and procedures needed to select mathematical techniques and formula to solve marine engineering problems

imparting knowledge and ideas through verbal, written and visual means

performing accurate and reliable calculations

performing calculations relevant to marine engineering, including volumes and masses of regular and irregular areas

reading and interpreting written information on marine engineering problems and express this information in mathematical terms

solving problems using appropriate laws and principles

using a calculator to resolve marine 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:

centre of gravity (CG), longitudinal centre of gravity (LCG), 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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