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: (Based on Alldis textbook)
MEM30012A Mathematical Techniques  

Description  Quiz ID  Competency Element and the Link to IXL Maths $13/month or $99/year 
Competency Element and the Link to BBC Bitesize Edexcel* 
Alldis Chapter 
1.Numbers  11101 
1.2 Decimals D 1.2 Fractions, decimals and percentages F, G, L 1.3 Scientific Notation A.9, T 1.4 Estimation N 
1.2 Whole numbers 1.2 Decimals 1.2 Fractions, decimals and percentages 1.4 Estimation Excel maths notation 
Alldis Ch1 Part 1.1, 1.2, 1.3 
2.Ratios  11102  1.2 Fractions F, G 1.2 Ratio in context J 1.2 Percentages L 1.2 Direct and inverse proportion K 
1.2 Fractions 1.2 Ratio in context 1.2 Percentages 
Alldis Ch2 
3.Measurement  11103  1.1 Units of measure O 1.4 Approximate Measurements O1, O7 3.3 3dimensional shapes S 4.1 Pythagoras' theorem Q 
1.1 Units of measure 
Alldis Ch3 
5.Algebra Simplification, substitution  11105 
2.1 Algebraic fractions, expressions, formulae J 2.1 Solving linear equations K 
Alldis Ch4,5 

6.Algebra 2 Simultaneous, transposition  11106 
6.2 Solving simultaneous equations R, H 6.1 Solving quadratic equations Q 2.1 Inequalities Q 
6.2 Solving simultaneous equations 6.1 Solving quadratic equations 2.1 Inequalities 
Alldis Ch4,5 
7.Triangles  11107  3.1 Angles, lines, polygons N 3.1 Loci and constructions M 4.1 Pythagoras' theorem Q 
Alldis Ch6,7 Part 3.1  3.32 

8.Circles  11108  Circles, sectors and arcs GG Circle theorems GG 
Alldis Ch8 Part 3.33  3.37 

9.Cartesian Geometry  11109  5.1, 5.3 Straight line graphs M 5.2 Using and interpreting graphs Q 5.2 Solving simultaneous equations (#1) H2, H3, H4 3.4 Polar/Cartesian conversion page 
5.1, 5.3 Straight line graphs 5.2 Using and interpreting graphs 5.2 Solving simultaneous equations (#1) 3.4 Polar/Cartesian conversion page 
Alldis Ch9 Part 3.413.44 
10.Trigonometry. Summary and Sine Rule, Cosine Rule  11110  4.1,2,3,4 Trigonometry EE See also Sine/Cosine Rule page 
4.1,2,3,4 Trigonometry See also Sine/Cosine Rule page 
Alldis Ch10, here Part 3.413.44 
11.Indices  11111  2.1 Laws of Indices K 2.1 Surds V 
2.1 Laws of Indices 2.1 Surds 
Alldis Ch11 Part 1.2 
12.Polynomials  11112  2.1 Polynomials V  Other graphs  Alldis Ch12 
13.Statistics Basic Statistics  11113  7.1 Collecting, Representing, Analysing data FF.2 7.1 Basic statistics KK.1 7.2 Standard Deviation: KK.4 See also Basic Statistics page 
7.1 Collecting data 7.1 Analysing data 7.2 Standard Deviation (#4): See also Basic Statistics page 
here 
Unseen question test / paper test (verification)    All  
TOTAL     
*Do all sections in the BBC Bitesize Edexcel unless stated otherwise. E.g. (#4) means only do section 4 of that set.
ASSESSMENT
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 twodimensional 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 36hour 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 McGrawHill. 2003 ISBN 007 4711571 RRP $72 (June 2009) 


Calculator: CASIO FX 82 AU (Around $25 at Officeworks etc) This is the Australian HSC certified calculator which means it is allowed in HSC exams, so it is popular. There are fancier graphing calculators, but they are not allowed during exams in this subject. These notes will be based on this calculator. 

Formula Sheet
Full size version here: MathsFormulas11Full.png (3508 x 4961 pixels)
Updates: 20200511 Added Casio instructions for Sample Standard Deviation
MEM30012A UNIT INFORMATION
Elements of Competency and Performance Criteria
Competency  Competency Elements 
1. Use concepts of arithmetic in the solution of engineering problems 

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

3. Use twodimensional geometry to solve practical problems 

4. Use trigonometry to solve practical problems


5. Graph linear functions 

6. Solve quadratic equations 

7. Perform basic statistical calculations 

Glossary (Range Statement)
Concepts of
mathematics

Include arithmetic, algebraic expressions with one independent variable, twodimensional 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 

Knowledge 

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. Twodimensional geometry   Angles: degrees and
radians, conversion  Twodimensional 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 midpoint 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, McGrawHill
(Old version based on TAFE Engineering Maths A notes)
A  Mathematical Techniques  

Task  Description and Link  Notes  New Notes 
1  Numbers: Indices of base 10 /1.2 SI units, eng & sci notation / 1.3 Approximations, errors  Section01.pdf (1MB) 
(no surds) 
2  Algebra: 2.1 Basic / 2.2 Indices and linear eqns / 2.3 Factors and trinomials / 2.4 Harder terms / 2.5 Transposition and evaluation  Section02.pdf (2.3MB)  
3  Geometry: 3.1 Angles / 3.2 Triangles / 3.3 Quadrilaterals / 3.4 Trigonometry  Section03.pdf (2.5MB)  
4  Coordinate Geometry: 4.1 Number plane / 4.2 Eqn of a line / 4.3 Funstion notation / 4.4 Simultaneous  
5  Substitution in algebraic formulas  
6  Simplification of algebraic formulas 6.1 Addition of like terms / 6.2Removal of brackets / 6.3 Mutliplying and dividing terms / 6.4 Algebraic fractions / 6.5 Applying the laws of indices 

7  Solution of linear equations  
8  Factorising: 8.1 Common factors / 8.2 Difference of two squares / 8.3 Quadratic expressions  
9  Transposition of algebraic formulas  
10  Angles: 10.1 Radian measure / 10.2 Parallel lines  
11  Triangles: 11.1 Angles in a triangle / 11.2 Isosceles and equilateral triangles / 11.3 Congruent triangles / 11.4 Pythagoras' theorem / 11.5 Similar triangles / 11.6 Area of traingles  
12  Quadrilaterals and circles : 12.1 Types and properties of quadrilaterals / 12.2 Areas and perimeters of regular quadrileterals / 12.3 Lengths of arcs / 12.4 Angles in a circle / 12.5 Lengths of chord segments / 12.6 Tangents to circles / 12.7 Circumference and area of circles  
13  Trigonometry: 13.1 Basic trigonometry functions / 13.2 Inverse trig func~ions / 13.3 Sine and cosine rules  
14  Graphs of linear functions: 14.1 The number plane / 14.2 Gradient and x and y intercepts of a straight line / 14.3 Equation of a straight line / 14.4 Length and midpoint of a straight line segment / 14.5 Function notation  
15  Simultaneous equations: 15.1 Graphical solutions / 15.2 Substitution / 15.3 Elimination  
16  Verbally formulated problems : 16.1 Mathematical expression of problems involving linear equations / 16.2 Solution and expression of answers  
Final Exam  
  TOTAL   