Module: EA002
Engineering Mathematics A
Module Purpose:
This module aims to provide students with the essential core skills in basic algebra
and geometry common to all engineering disciplines.
Relationship to competency standards:
This module will be modified in line with the requirements of the National Metals and
Engineering Standard when they become available.
The module contains the knowledge and skills identified and agreed by all
states/territories. It has been developed on the assumption that these will be reflected
in the Standards.
Prerequisites and/or corequisites:
Before attempting this module, the participants should have knowledge of:
Basic arithmetic, including fractions.
Summary of content:
Arithmetic:
Rational and irrational numbers, surds SI units, conversion using unity brackets.
Laws of indices (base 10), scientific and engineering notation Estimations, errors and
approximations, signification figures.
Algebra:
Substitution +, -, x on simple polynomials. Simple indices expanding brackets
Factorising quadratics. Common factors, difference of two squares. Simplifying algebraic
fractions. Transposition of engineering formulae. Solving one variable equations. Simple
algebraic division.
Geometry:
Pythagoras Theorem Angles: degrees, radians. Parallel lines cut by a transverse.
Triangles: sum of angles, propitious of equilateral and isosceles triangles equilateral
and isosceles triangles. Congruent triangles. Similar triangles. Similar triangles: ratio
of corresponding sides.
Sin, cos, tan: ratios of a right angled triangles.
Sine and cosine rules.
Circles: circumference, arcs, chords, and tangents, circle theorems.
Area and perimeter mensuration on above figures.
Co-ordinate Geometry:
2D plane; x-y axes, s-t axes.
Graph of linear function, y = axe + b.
Functional notation, y = f(x)
Straight line given slope and one point or given to points
Linear equations: solving algebriacally and geometrically
Solving 2 linear functions simultaneously, algebriacally and geometrically
Line segment: length and mid point
Delivery:
The sequential nature of mathematics requires regular and consistent assessment to
demonstrate the mastery of mathematical skills and techniques. Regular marked assignments
(homework) will form 20% of the total assessment, the four 1 hour tests applicable to the
learning outcomes making up the balance.
Learning Outcomes:
On completion of this module the learner will be able to:
Learning Outcome 1
Manipulate surd expressions, use engineering notation, convert units of measure and
demonstrate an awareness errors and estimations.
Assessment Criteria:
Simplify and evaluate square roots and cube roots of rational numbers
Convert units of physical quantities using unity brackets
Convert numbers into scientific and engineering notation using the laws of indices
Show awareness of errors in measurement and of giving results in appropriate number of
significant figures and use estimations and approximations to check the reasonableness of
results.
Use 2D geometry to solve practical problems
Assessment Criteria:
Convert angular measure in degrees toradians and vice versa
Solve right angled triangle and Pythagoras Theorem
Solve mensuration problems using the properties of angles and triangles
Solve similar triangles problems using the ratios of corresponding sides
Solve acute and obtuse angled triangle problems using the sine and cosine rules
Find perimeters and areas of simple figures.
Conditions:
Assessment method
Assignments and 1 hour test
Learning Outcome 4
Graph linear functions
Assessment Criteria
Sketch the graphs of linear functions showing the significance of slope and y intercept
Find equations of straight lines given slope and one point or given 2 points
Solve linear equations both algebraically and geometrically
Solve 2 linear functions simultaneously both algebraically and geometrically
Calculate the length and mid point of line segment
Interpret verbally formulated problems involving linear functions and linear equations and
solve.
Conditions:
Assessment method:
Assignments and 1 hour test
Suggested learning resources:
