Assessment Cover Sheet
Academic integrity
Academic Integrity is defined in the Taylors College Policy on Academic Conduct as “acting with the values of
honesty, trust, fairness, respect and responsibility in learning, teaching and research”. Taylors College expects
the highest degree of academic conduct from all students.
Penalties for breach of academic conduct vary according to seriousness of the case, and may include the
requirement to do further work or repeat work; deduction of marks; the award of zero marks for the
assessment; failure of one or more units; suspension from a course of study or exclusion from the College.
For more information about academic conduct and the levels of breach of academic conduct please see the
Taylors College Policy on Academic Conduct in your Handbook and on your StudySmart Pages.
Use of text matching software
All text-based summative assessments will be passed through text-matching software. “Passing” an automated
checking program does not in itself confirm that a breach of academic conduct has not occurred, and markers
may make other checks as appropriate.
Declaration
In accordance with the Taylors College Policy, I certify that:
• The attached work submitted for assessment is my own and that all material drawn from other
sources has been fully acknowledged, and
• I retain a copy of my submitted work
Signed _______________________________________ Date
________________
STUDENT ID. NUMBER DUE DATE
UNIT NAME
UNIT CODE
TITLE/TOPIC OF ASSIGNMENT NAME OF UNIT FACILITATOR/TEACHER
1. You are writing code for the opening credits of an upcoming movie and need the following word
to be written on the screen by an animated character:
Do Io Yo
Space constraints mean that you only have an area of 3 ⇥ 12 (pixels) and writing must be
completed in 10 seconds.
(a) (4 marks) Parametrise this word. Hint: Draw the word on grid paper. vfill
(b) (1 mark) The director decides you need to halve the time dedicated to your opening scene
and so D.I.Y. must now be written twice as fast. How does your code change? vfill
(c) (2 marks) Mr. Director would now like the font written in italics. Create a coordinate
transform. that achieves this and preserves the amount of pixels used. vfill
(d) (1 mark) At the end of movie the opening credits are run backwards. How does your code
change? vfill
(e) (2 marks) Mr. Director would now like the font written in italics. Create a coordinate
transform. that achieves this and preserves the amount of pixels used. vfill
Page 2
2. (10 marks) What examples would you use to teach vector fields and their properties to other
students? Create a tutorial question with worked solution using your method (maximum 500
words). vfill
Page 3
3. Don’t ever trust the formulas people give you!
(a) (6 marks) Prove the Jacobian given in class for polar, cylindrical and spherical coordinate
systems. vfill
(b) (4 marks) What does the Jacobian mean physically? Show this with a small illustration
of a circle in a Cartesian coordinate system being transformed to the image in a polar
coordinate system. vfill
Page 4
4. The Nike swoosh can be approximated as a set of functions:
(a) (3 marks) Describe the swoosh in cartesian coordinates as the union of many small parts.
vfill
(b) (4 marks) Calculate the area of the swoosh shown. vfill
(c) (3 marks) Explain how you would calculate the perimeter of the swoosh. Write down the
appropriate equations but do not solve (unless you really want to!). vfill
Page 5
5. You are completing a home renovation and need to drill a hole through the middle of a concrete
sphere of radius b. The drill has a radius a and (0