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MEM30012A

Apply mathematical techniques in a manufacturing engineering or related environment (36 HRS)

Nominal Hours: 72 | Diploma/Adv Dip: Compulsory (Group 1) | Competency Based  
Assessment Plan A: (One Semester: 18 weeks x 2 hrs/wk)
Updated Mar 2017

 

Assessment Task Schedules: Note: Content follows the textbook rather than the CIDO delivery plan.

A  Mathematical Techniques
Task Description and Link Quiz ID Due Week  Workload
%
Must
Pass 
Alldis
Chapter
1 Numbers  11101 3 5 Y 1
2 Ratios 11102 4 5 Y 2
3 Measurement 11103 5 5 Y 3
4 Errors.  Error Analysis 11104 6 5 Y here
5 Algebra    Simplification, substitution 11105
7 10 Y 4,5
6 Algebra 2  Simultaneous, transposition 11106
8 10 Y 4,5
7 Triangles 11107 9 10 Y 6,7
8 Circles 11108 10 10 Y 8
9 Cartesian Geometry 11109 11 10 Y 9
10 Trigonometry.  Summary and Sine Rule, Cosine Rule 11110 12 10 Y 10, here
11 Indices 11111 13 10 Y 11
12 Polynomials 11112 14 10 Y 12
13 Statistics  Basic Statistics 11113 15 10 Y here
14 Unseen question test / paper test (verification) - 18 - Y All
- TOTAL - - 100 - -

CBT = Computer Based Testing: Typically consists of practice mode (iTester) and assessment mode (Moodle).
Exam = Written test submitted on paper, all working shown neatly.

*Where applicable.

 

 

ASSESSMENT

(CAUTION: This subject contains most of MEM30006A Stresses, so you should do both together) Assessment is a combination of multiple choice tests, written tests, and submitted reports (print/email).

  • 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. 

When you have completed this unit of competency you will have developed the knowledge and skills to use concepts of arithmetic in the solution of engineering problems; solve engineering problems involving algebraic expressions with one independent variable; use two-dimensional geometry to solve practical problems; use trigonometry to solve practical problems; graph linear functions; solve quadratic equations and finally, perform basic statistical calculations. 

Comment: 

This maths subject includes the entire content of the previous 7759Q Maths A (below), plus additional content (statistics), but still remains at 36 hours. This makes it a fairly large 36-hour subject for students without good high school mathematics.

This subject (unit) covers the first 12 chapters of the textboox (Alldis), leaving Chapters 13 to 21 for the next Maths subject. (which is comparitively easy, especially since the topics are not nearly as essential to engineering). In other words, THIS is the maths subject! 



 

Required Texts  

Text book Subjects Picture
Alldis, Blair
Mathematics for Technicians 5th ed
McGraw-Hill. 
2003
ISBN 007 4711571
RRP $72 (June 2009)

  • MEM30012A s



MEM30012A UNIT INFORMATION

Elements of Competency and Performance Criteria

Competency Competency Elements

1. Use concepts of arithmetic in the solution of engineering problems

  1. Units of physical quantities are converted to facilitate engineering calculations. 

  2. Calculations are performed to solve problems involving rational and irrational numbers.

  3. Scientific notation is used to represent numbers.

  4. Calculations are checked for reasonableness using estimating and approximating techniques.

2. Solve engineering problems involving algebraic expressions with one independent variable

  1. Algebraic expressions are manipulated using mathematical operations in their correct order.

3. Use two-dimensional geometry to solve practical problems

  1. Angles expressed in degrees are correctly converted to radians and vice versa.

  2. The perimeter, area, length and angles of a range of two-dimensional figures are correctly calculated.

     

  3. The volume and surface area of complex figures are correctly calculated.

  4. Points identified in terms of cartesian coordinates can be converted to polar coordinates and vice versa.

4. Use trigonometry to solve practical problems

 

  1. Basic trigonometry functions are used to calculate the lengths of the sides of right-angled triangles.

  2. Inverse trigonometry functions are used to determine angles in a right-angled triangle given the lengths of two sides.

  3. The sine rule is used to determine the lengths of the sides of acute and obtuse angled triangles given one side and two angles.

  4. The cosine rule is used to determine the lengths of the sides of acute and obtuse angled triangles given two sides and one angle.

5. Graph linear functions

  1. Linear functions are solved graphically and equations of straight lines are determined from the slope and one point, or two points.
  2. Two linear functions are solved simultaneously both algebraically and geometrically. 
  3. The length and mid point of a line segment are determined.

6. Solve quadratic equations

 
  1. Quadratic equations are solved.
  2. Simultaneous linear and quadratic equations are solved.

7. Perform basic statistical calculations

  1. Mean, median and mode are calculated from given data.
  2. Standard deviation is calculated and interpreted employing graphical representation.

Glossary (Range Statement) 

Concepts of mathematics

 

Include arithmetic, algebraic expressions with one independent variable, two-dimensional geometry, trigonometry, linear functions, basic quadratic functions, basic statistical methods

Correct order

Refers to the correct procedure when expanding brackets, factorising algebraic expressions, factorising quadratic expressions, simplifying algebraic fractions, transposing formulae, solving simple one variable equations, finding the quotient and remainder given a linear division.

 

Complex figures

May include cones, pyramids, spheres, frustums and intersections of figures singularly or in combination

Knowledge and Skills

Skills
  • using and applying mathematical formulas:
  • logical thinking
  • problem solving
  • calculating
  • applying statistics
  • using computer numerical methods
  • drawing graphs
Knowledge
  • transposing and evaluating formulae
  • polynomials
  • straight line coordinate geometry
  • introduction to indices
  • introduction to trigonometry
  • circular functions
  • trigonometry of oblique triangles
  • trigonometric identities
  • introduction to functions and their graphs

Delivery Plan

1.  Concepts of arithmetic - Units of physical quantities for length , mass, area, volume, time, velocity, density
    - basic units and derived units, conversion of units
- Rational and irrational numbers: problem solving
- Scientific and engineering notations
- Estimation and approximation

 

2. Algebraic expressions - Correct order for applying mathematical operations
- Solving of engineering problems involving algebraic
   expressions with one independent variable.

 

3. Two-dimensional geometry - Angles: degrees and radians, conversion
- Two-dimensional figures: area, length and angles
- Complex figures: volume and surface area
- Cartesian coordinates: identifying points, conversion to and from polar coordinates

 

4. Trigonometry

 

- Basic trig functions: calculation of sides of right angled triangle
- Inverse trig functions: calculation of angles in right angled triangles
- Sine rule:calculation of lengths of acute and obtuse angled triangles
- Cosine rule: calculation of lengths of acute and obtuse angled triangles

 

5.  Graphing linear functions - Solving linear functions graphically
- Determining the equations of straight lines
- Solving two linear functions algebraically
- Solving two linear functions geometrically
- Determining the length and midpoint of a line segment

6.  Quadratic equations

 

- Solving quadratic equations
- Solving simultaneous and quadratic equations
7.  Statistical calculations - Calculation of mean, median and mode
- Calculation of standard deviation
- Interpretation of standard deviation employing
  graphical representation 

 

 

Comparison with 7759Q: Engineering Maths A

Section 1:  Rational and irrational numbers
    *  Simplification of expressions involving square roots and cube roots
    *  Evaluation of expressions using a calculator

Section 2:  SI units
    *  Conversion of physical quatities in SI units

Section 3:  Laws of indices
    *  Laws of indices using base 10
    *  Conversion between decimal notation, scientific notation and engineering
        notation

Section 4:  Estimations, errors and approximations
    *  Errors in measurement
    *  Maximum probable error
    *  Significant figures
    *  Estimations and approximations

Section 5:  Substitution in algebraic formulas

Section 6:  Simplification of algebraic formulas
    *  Addition of like terms
    *  Removal of brackets
    *  Mutliplying and dividing terms
    *  Algebraic fractions
    *  Applying the laws of indices

Section 7:  Solution of linear equations

Section 8:  Factorising
    *  Common factors
    *  Difference of two squares
    *  Quadratic expressions

Section 9:  Transposition of algebraic formulas

Section 10: Angles
    *  Radian measure
    *  Parallel lines

Section 11: Triangles
    *  Angles in a triangle
    *  Isosceles and equilateral triangles
    *  Congruent triangles
    *  Pythagoras' theorem
    *  Similar triangles
    *  Area of traingles

Section 12: Quadrilaterals and circles
    *  Types and properties of quadrilaterals
    *  Areas and perimeters of regular quadrileterals
    *  Lengths of arcs
    *  Angles in a circle
    *  Lengths of chord segments
    *  Tangents to circles
    *  Circumference and area of circles

Section 13: Trigonometry
    *  Basic trigonometry functions
    *  Inverse trig functions
    *  Sine and cosine rules

Section 14: Graphs of linear functions
    *  The number plane
    *  Gradient and x and y intercepts of a straight line
    *  Equation of a straight line
    *  Length and mid-point of a straight line segment
    *  Function notation

Section 15: Simultaneous equations
    *  Graphical solutions
    *  Substitution
    *  Elimination

Section 16: Verbally formulated problems
    *  Mathematical expression of problems involving linear equations
    *  Solution and expression of answers

Comparison with 7759R: Engineering Maths B
Section 1:  Matrices
    *  The operations: addition, subtraction, scalar multiplication, matrix
        multiplication up to 3 x 3 matrices.
    *  Identity matrix, inverse matrix.
    *  Elementary algebraic manipulation of matrices.
    *  Solution of up to three linear equations in three unknowns using inverse
        matrices and determinants.

Section 2:  Quadratic functions
    *  Graphs of quadratic functions represented by parabolas and the
        significance of the leading coefficient.
    *  Zeros represented graphically.
    *  Solution of quadratic equations by factoring and the quadratic formula.
    *  Solution of simultaneous linear and quadratic equations algebraically
        and geometrically.

Section 3:  Exponential and logarithmic functions
    *  Laws of indices.
    *  Graphs of exponential functions.
    *  Solution of exponential and logarithmic functions using indices, logs,
        calculator, graphically.
    *  Change of log base, emphasising 10 and e.
    *  Growth and decay.

Section 4:  Trigonometric functions
    *  The ratios: sin, cos, tan, cosec, sec, cot.
    *  Degrees, radians.
    *  Graphs of trigonometric functions.
    *  Trigonometric identities.
    *  Solution of trigonometric equations.

Teaching and Learning Resources

  • Unit Resource Manual for this unit of competency.  
  • Textbook:  Aldis, B; Mathematics for Technicians, McGraw-Hill