Calculus and Probability Online is an online course which covers similar material to the Victorian Certificate of Education (VCE) subject Mathematical Methods 3/4, and provides a firm foundation for tertiary mathematics study. Calculus and Probability Online will satisfy the Mathematical Methods units 3/4 entry requirement for entry to the Bachelor of Science, Bachelor of Commerce, Bachelor of Biomedicine and Bachelor of Agriculture at the University of Melbourne, as well as satisfying the Mathematical Methods 3/4 prerequisite for particular subjects within those degree programs.

**This subject will not count for credit towards any degree program offered by The University of Melbourne.**

## Overview

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.

## Annual intakes

This course runs three times a year:

- Summer intensive - January to February (6 week intensive)
***** - Autumn (Semester 1) - March to May (9 week course)
- Spring (Semester 2) - August to October (9 week course)

Please see the generic course timetables for an overview of how each intake is structured.

*****Students completing this subject in the Summer intensive period are unable to use their results to be considered for a Bachelor of Agriculture, Bachelor of Biomedicine, Bachelor of Commerce or Bachelor of Science Semester 1/Start Year Intake offer in the same year. Students will need to consider applying for admission to their preferred undergraduate degree in the mid-year intake.

## Key dates

Dates for the Spring 2023 offering:

- Registration opens 10am AEST on
**Monday 17 July 2023** - Spring 2023 course commences
**Monday 14 August 2023** - Registration closes
**Monday 14 August 2023**at**11:59 pm AEST** - Course runs for 9 teaching weeks
- Non-teaching week
**Monday 25 September to Friday 29 September 2023** - Course finishes
**Friday 20 October 2023** - Swot-vac (study) week
**Monday 23 October to Friday 27 October 2023** - Exam on
**Monday 30 October 2023** - Some results can be prioritised for return by
**Wednesday 1 November 2023** - Most results returned by
**Monday 6 November 2023**

For VTAC (and international direct) applicants using this subject to meet a prerequisite for course admission: Students completing this subject in the Summer intensive period are unable to use their results to be considered for a Bachelor of Agriculture, Bachelor of Biomedicine, Bachelor of Commerce or Bachelor of Science Semester 1/Start Year Intake offer in the same year. Students will need to consider applying for admission to their preferred undergraduate degree in the mid-year intake.

## Fee information

Calculus module: $660

Probability module: $330

Both modules: $990

Note:

- Payment can only be made using the booking link at the bottom of this page, and must be paid in full up-front.
- No discounts or payment plans are available. In particular, subject fees are not covered by Australian HECS - the full fee is payable on registration.
- Registrants who withdraw from the course before the start of the course will receive a refund of fees less 10% for administration.
- Registrants who withdraw from the course before the end of week 2 will receive refund of fees less 20% for administration.
- After the end of week 2, no refund of fees is available.
- Refunds will be made to the credit/debit card used for payment. We recommend that the credit/debit card used for payment remain valid until at least 3 weeks after the start of the course in case a refund is required.
- There are no course expenses additional to the module fees (e.g. no book or note purchases).
- Students will need to attend an online examination via Zoom, at the end of the course.

## Entry requirements

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.

## Delivery mode

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

Your choice of modules in Calculus and Probability Online will depend on your previous studies. The table below shows appropriate module choices for the main University of Melbourne degrees for students coming from the most frequent previous study backgrounds. For advice on choice of modules for other previous studies, you should contact mslc-approvals@unimelb.edu.au. If you are uncertain about your mathematical background, we recommend that you take both modules. Students completing Calculus and Probability Online for entry at other Institutions should seek advice from them.

Previous Studies | Module(s) required for Bachelor of Science, Commerce or Biomedicine |

VCE Mathematical Methods 1/2 | Both |

VCE Further Mathematics 3/4
(with a study score of at least 30) | Calculus |

VCE General Mathematics 3/4 (with a study score of at least 30) | Calculus |

HKDSE Mathematics Compulsory Part only | Both |

HKDSE Extension 1 (Calculus and Statistics) | Calculus |

HKDSE Extension 2 (Calculus and Algebra) | Probability |

IB Mathematical Studies (SL) | Calculus |

IB Applications and Interpretations (SL) | Calculus |

VCE Mathematical Methods 3/4 (with study score < 25) | Both |

GCE O-Level Mathematics | Both |

WACE Mathematics Methods 1/2 | Both |

SACE Mathematics Methods 1/2 | Both |

## Course process

The day after registration, you will receive an email containing the student course guide and instructions to gain 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 an online examination via Zoom. Supervisors will be provided to invigilate students, during the zoom examination.

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.

## Contact details

Phone: +61 3 8344 0010 *Office hours are Monday-Friday 9am-5pm Melbourne (Australia) time*

Email: online-calcprob@unimelb.edu.au