Apply technical mathematics

Nominal Hours: 36 | Diploma/Adv Dip: Elective (Group 3) | Competency Based  
Assessment Plan A: (One Semesters: 18 weeks)
Updated July 2014

Apply technical mathematics (18 weeks)

Task Topic Description and Link to Notes Quiz # Lesson
Assess schedule Skill# Know# Competency Element Must Pass
1 Binary Numbers 11601            
2 Sequences and series PDF 11602            

Logarithms and Exponentials

03-Logarithms.pdf (1.6MB)

11603     4, 5   1,2  

Trigonometrical Functions

04-Trig-Functions.pdf (2.8MB)

Excel sine/cosine graph

Formula Sheet

11604     5   1,2  
5 Vector analysis 11605            


01-Matrices.pdf (1.3MB)

11606     8   1,2  


Probability and Statistics

11607     9   1,2  

Complex Numbers

Refer Webpage

Complex Numbers Asssignment

Formula Sheet

11608     7   1,2  
- TOTAL - - - - - 100 -

Quiz = Computer Based Testing: Typically consists of practice mode (iTester) and assessment mode (Moodle).
Exam = Written test submitted on paper, all working shown neatly.
* Pre-requisite tests embedded in these subjects.

Required Texts   

Text book Subjects Picture

ACESS: Notes for Engineering Mathematics B

MS6L Educational Services Division (TAFE NSW)

  • Matrices
  • Quadratics
  • Exponentials & Logarithmic Functions
  • Trigonometric Functions



Lab Reports: Specification for lab reports. (Including error analysis where required)

  • Project Reports: Specification for project reports.
  • TESTER tasks: Computer based learning and assessment using the TESTER program.
    Procedures and rules. For most computer-based assessments, homework must be presented before Tester (exam mode) can be attempted.  In some cases, certain programs (e.g. Excel) are excluded from running with Tester during an exam. 

This unit applies basic scientific principles and techniques in mechanical and manufacturing engineering situations, covering three branches of mechanics - Dynamics, Fluids and Thermodynamics.


Elements of Competency and Performance Criteria


Determine scope of technical mathematical techniques required for an engineering application


Analyse an engineering application for required technical mathematical tasks



Develop systematic methods for layout and solution checking



Determine mathematical software required for analytical and graphical solutions and validate software using traditional solutions to simple examples


Apply technical mathematical techniques to engineering application


Use appropriate software for analytical and graphical solutions



Convert between different number systems



Use appropriate mathematical techniques required for analysis and solution



Use appropriate data representations to communicate the solution to others.



Report results and document calculations, graphs and analysis


Knowledge and Skills 

  1. solving mathematical problems using standard engineering software packages, and validating software results of simple examples analytically and/or graphically
  2. manipulating values using decimal, binary and hexadecimal number systems
  3. graphing and analysing functions for solutions:
  4. exponential and logarithmic functions
  5. trigonometric functions
  6. using the techniques of sequences and series to solve simple mathematical problems
  7. using the techniques of two dimensional vectors to solve mathematic and applied problems
  8. solving problems involving complex quantities using the properties, operations and theorems of complex numbers
  9. using determinant and matrix analysis to solve algebraic and vectorial problems
  10. using probability to assess likely occurrences
  1. software for mathematical analysis and graphical representations
  2. binomials and polynomials
  3. exponential and logarithmic functions
  4. trigonometric equations
  5. sequences and series
  6. two dimensional vectors
  7. complex numbers
  8. determinant and matrices
  9. probability
  10. stability analysis using plots


Glossary (Range Statement) 

Engineering applications related to mathematical techniques in this unit

Most engineering disciplines will have applications supported by the technical mathematics skills described in this unit, including mechanical, manufacturing, maintenance and mechatronics engineering. Examples of engineering applications requiring mathematical skills described in this unit may include:

  • vector analysis of force systems on beams and bodies
  • trigonometric plots related to waveforms for amplitude, frequency and phase shift analysis
  • matrix and determinant solutions of vector systems or simultaneous equations
  • complex plane analysis of control systems for stability analysis

Scope of technical mathematical techniques

The scope of technical mathematical techniques required for an engineering application will vary and may include:

  • standard mathematical software
  • decimal, binary and hexadecimal number systems
  • graph exponential and logarithmic functions required for the engineering application
  • solve trigonometric equations involving single and double angles
  • solve problems using simple binomials and polynomials
  • solve problems involving simple sequences and series in the engineering application
  • analyse two dimensional vectors
  • analyse complex numbers and represent graphically
  • analyse simple algebraic and vectorial problems using determinants and matrices
  • evaluate probability as a predictive tool in simple situations

Number system

Number systems may include:

  • decimal
  • binary
  • hexadecimal