Updated TL: July 2009. Nominal Hours: 36 | 9154 Dip / 9163 Adv Dip: Compulsory (Group 1) | Competency
Mathematics for Technicians 5th ed
ISBN 007 4711571
RRP $72 (June 2009)
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 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!
Assessment is a combination of multiple choice tests and hand-in reports.
|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||8||10||Y||4,5|
|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|
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
variable equations, finding the quotient and remainder given a linear
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
|- 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
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.