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.
|Task||Description and Link||Quiz ID||Due Week||Workload
|4||Errors. Error Analysis||11104||6||5||Y||here|
|5||Algebra Simplification, substitution||11105
|6||Algebra 2 Simultaneous, transposition||11106
|10||Trigonometry. Summary and Sine Rule, Cosine Rule||11110||12||10||Y||10, here|
|13||Statistics Basic Statistics||11113||15||10||Y||here|
|14||Unseen question test / paper test (verification)||-||18||-||Y||All|
CBT = Computer Based Testing: Typically consists of practice mode (iTester) and assessment mode (Moodle).
Exam = Written test submitted on paper, all working shown neatly.
(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.
tasks: Computer based learning and assessment using the
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.
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!
Mathematics for Technicians 5th ed
ISBN 007 4711571
RRP $72 (June 2009)
MEM30012A UNIT INFORMATION
Elements of Competency and Performance Criteria
1. Use concepts of arithmetic in the solution of engineering problems
2. Solve engineering problems involving algebraic expressions with one independent variable
3. Use two-dimensional 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)
Include arithmetic, algebraic expressions with one independent variable, two-dimensional geometry, trigonometry, linear functions, basic quadratic functions, basic statistical methods
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.
May include cones, pyramids, spheres, frustums and intersections of figures singularly or in combination
Knowledge and Skills
|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
- Two-dimensional figures: area, length and angles
- Complex figures: volume and surface area
- Cartesian coordinates: identifying points, conversion to and from polar coordinates
|- 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
Comparison with 7759Q: Engineering Maths ASection 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
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
Section 16: Verbally formulated problems
* Mathematical expression of problems involving linear equations
* Solution and expression of answers
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
Section 3: Exponential and logarithmic functions
* Laws of indices.
* Graphs of exponential functions.
* Solution of exponential and logarithmic functions using indices, logs,
* 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