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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: (Based on Alldis textbook)

MEM30012A Mathematical Techniques
Description Quiz ID

Competency Element and the

\$13/month or \$99/year

Competency Element and the

Alldis
Chapter
1.Numbers  11101

1.2 Whole numbers A.8, B.1

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 Decimals

1.4 Estimation

Excel maths notation

Alldis Ch1

Section01.pdf

Part 1.1, 1.2, 1.3

2.Ratios 11102

1.2 Fractions F, G

1.2 Multiples and Factors

1.2 Ratio in context J

1.2 Percentages L

1.2 Direct and inverse proportion K

1.2 Fractions

1.2 Percentages

Alldis Ch2

2-ratios.pdf

2-ratios.one

3.Measurement 11103

1.1 Units of measure O

1.4 Approximate Measurements O1, O7

3.2 2-dimensional shapes U, V

3.3 3-dimensional shapes S

4.1 Pythagoras' theorem Q

Alldis Ch3
5.Algebra    Simplification, substitution 11105

2.1 Algebraic fractions, expressions, formulae J

2.1 Solving linear equations K

Alldis Ch4,5

5-algebra-1.pdf

5-algebra-1.one

Section02.pdf

6.Algebra 2  Simultaneous, transposition 11106

6.2 Solving simultaneous equations R, H

2.1 Inequalities Q

2.1 Inequalities

Alldis Ch4,5

5-algebra-1.pdf

5-algebra-1.one

Section02.pdf

7.Triangles 11107

3.1 Angles, lines, polygons N

3.1 Loci and constructions M

4.1 Pythagoras' theorem Q

Alldis Ch6,7

Section03.pdf

Part 3.1 - 3.32

8.Circles 11108

Circles, sectors and arcs GG

Circle theorems GG

Alldis Ch8

Section03.pdf

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

3.4 Polar/Cartesian conversion page

Alldis Ch9

Section04.pdf

Part 3.41-3.44

10.Trigonometry.  Summary and Sine Rule, Cosine Rule 11110

4.1,2,3,4 Trigonometry EE

4.1,2,3,4 Trigonometry

Alldis Ch10, here

Section03.pdf

Part 3.41-3.44

11.Indices 11111

2.1 Laws of Indices K

2.1 Surds V

2.1 Surds

Alldis Ch11

Section01.pdf

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

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 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 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. All subjects

#### Formula Sheet

Full size version here: Maths-Formulas-11-Full.png (3508 x 4961 pixels)

## MEM30012A UNIT INFORMATION

#### Elements of Competency and Performance Criteria

 Competency Competency Elements 1. Use concepts of arithmetic in the solution of engineering problems Units of physical quantities are converted to facilitate engineering calculations.  Calculations are performed to solve problems involving rational and irrational numbers. Scientific notation is used to represent numbers. Calculations are checked for reasonableness using estimating and approximating techniques. 2. Solve engineering problems involving algebraic expressions with one independent variable Algebraic expressions are manipulated using mathematical operations in their correct order. 3. Use two-dimensional geometry to solve practical problems Angles expressed in degrees are correctly converted to radians and vice versa. The perimeter, area, length and angles of a range of two-dimensional figures are correctly calculated. The volume and surface area of complex figures are correctly calculated. Points identified in terms of cartesian coordinates can be converted to polar coordinates and vice versa. 4. Use trigonometry to solve practical problems Basic trigonometry functions are used to calculate the lengths of the sides of right-angled triangles. Inverse trigonometry functions are used to determine angles in a right-angled triangle given the lengths of two sides. The sine rule is used to determine the lengths of the sides of acute and obtuse angled triangles given one side and two angles. 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 Linear functions are solved graphically and equations of straight lines are determined from the slope and one point, or two points. Two linear functions are solved simultaneously both algebraically and geometrically.  The length and mid point of a line segment are determined. 6. Solve quadratic equations Quadratic equations are solved. Simultaneous linear and quadratic equations are solved. 7. Perform basic statistical calculations Mean, median and mode are calculated from given data. 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
*  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

Section 9:  Transposition of algebraic formulas

Section 10: Angles
*  Parallel lines

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

*  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.

*  Graphs of quadratic functions represented by parabolas and the
*  Zeros represented graphically.
*  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.
*  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

(Old version based on TAFE Engineering Maths A notes)