Calculus and Probability Online is designed to substitute for the Victorian Certificate of Education (VCE) Mathematical Methods 3/4 (MM3/4) prerequisite for entry to the Bachelor of Science, Bachelor of Commerce, Bachelor of Biomedicine, and Bachelor of Agriculture at the University of Melbourne. It also substitutes for individual MM3/4 prerequisites within particular subjects in those degree programs.
Calculus and Probability Online comprises two modules - a Calculus module and a Probability module. Students may enrol in one or both of the modules, depending on their prior study. Note that Calculus and Probability Online does not count for credit towards any degree program offered by The University of Melbourne.
The Calculus module covers fundamental concepts about functions and their inverses including linear, quadratic, cubic, logarithmic, exponential and trigonometric functions and their graphs; differentiation (including product, quotient and chain rules) and its applications (stationary points, tangents, normals, optimisation, related rates); integration (including definite and indefinite integrals and their properties) and its applications (areas under and between curves); limits and continuity; binomial expansion; polynomial division, and transformation of graphs.
The Probability module covers sets and Venn diagrams; factorials and counting methods; conditional probability and tree diagrams; discrete and continuous random variables (including Binomial and Normal distributions); cumulative distribution functions and simple discrete Markov Chains.
NB: This course does NOT use calculators either during the course or in the Exam. There are NO multiple choice questions in the course or Exam.
Additional fee information
- Subject fees are not covered by Australian HECS - the full fee is payable on registration;
- Withdrawals prior to course commencement receive a refund of fees less 10%;
- Withdrawals before the end of week 2 receive a refund of fees less 20%;
- Students who are unable to attend the examination at the University of Melbourne will be required to make arrangements to sit the examination at an appropriate venue at their own cost. See guidelines.
This wholly online course is open to anyone, worldwide, and has no formal prerequisites. However, it assumes knowledge equivalent to the Victorian Certificate of Education (VCE) subject Mathematical Methods 1/2 (MM1/2). You are strongly recommended to have completed that subject, or a subject equivalent to it, before attempting Calculus and Probability Online.
MM1/2 covers the following topics:
- Algebra (factorisation, expansion, solving equations, simplification, simultaneous equations, equation of a straight line);
- Functions and Graphs (domain and range; graphs of parabolas, general cubics and trigonometric functions; trigonometric exact values, unit circle & symmetry; transformation of graphs; logarithmic & exponential rules;
- Probability (simple and compound events; Venn diagrams; conditional probability and tree diagrams);
- Calculus (derivatives and anti-derivatives of simple algebraic functions and simple related applications).
You can test your MM1/2 knowledge by completing this test. You can see the answers, but try and do the test without looking at these first. A more comprehensive list of the content of MM1/2 is here: VCE Mathematical Methods 1/2.
It is the responsibility of each student to decide if their knowledge of the MM1/2 content is adequate to undertake Calculus and Probability Online.
This course is fully online. Course content is provided through the Learning Management System (LMS). Online consultations require Skype or Zoom, so access to a computer with internet access and webcam (video and audio) is essential.
Choice of modules
Students must know the content of both the Calculus and Probability Modules to meet the MM3/4 prerequisite, but it is possible to enrol in just a single Module if you have appropriate prior study covering the other.
For students who are hoping to study at the University of Melbourne, if you believe you have already studied the material in either Module as described above, then please email firstname.lastname@example.org attaching copies of the relevant prior study and results. You will be advised about your appropriate choice of Modules. Students completing Calculus and Probability Online for entry at other Institutions should seek advice from them.
Just before the course starts you will receive a Student Course Booklet and be given access to the University of Melbourne Learning Management System (LMS) course site.
Each week of the course (6 in Summer and 9 in Autumn/Spring), course material will be released at the start of the week. Typically students will need to:
- Watch lecture videos and take appropriate notes (depending on your experience with the topic)
- Complete practice sheet questions. The practice sheets given are the absolute MINIMUM you would need to do for each topic
- Check your answers and watch the corresponding solution video if necessary
- Do extra follow up questions from the additional material, located in Extra Resources on LMS, if you need extra practice. Your prior experience will determine how much you need to do to learn each technique
- Initiate online consultations with the Course Coordinator as necessary.
We estimate the subject will require approximately 8 to 12 hours time commitment per week, including watching all the videos and doing problems. However, this will depend on the student and is only an estimate.
Assignments will need to be completed by hand and submitted via the Turnitin system on the LMS. You will need to either save your work as a single pdf or scan it as a pdf in order to submit it. There are strict deadlines for the submission of assignments for them to count towards your assessment. Assessment of the assignments will count for 24% of your final mark. An examination for each module will be held in the examination week and will constitute 76% of your final mark.
This subject is not a technology-based subject, so no calculator is required, nor will it be permitted to use a calculator in the examination. The examination is a handwritten examination, which must be properly supervised either at the University of Melbourne (Parkville) or at a supervised location that you must arrange yourself and have approved by the Subject Coordinator (see guidelines).
Students will be issued with an original Certificate certifying completion of the Course with an overall mark and stating which Modules have been successfully completed. Students must obtain a mark of at least 50% for a Module for it to count towards the MM3/4 prerequisite at the University of Melbourne.