Mathematics IM
Resources for Mathematics IM - for more information about the course, please see course outlines.
Preparation and study skills
We have revision worksheets on a number of topics, that will help you revise topics from high-school maths. These are available in print form from the MLC room in Hub Central, but you can also download them here: High School revision worksheets.
There are also mini textbooks and lecture videos covering much of the content from high school Maths Methods here: bridging course resources.
Also, this seminar page has two seminars giving advice on studying for a course like Maths IM that has lots of maths and an exam.
Topics in Maths IM
The following resources are mainly revision seminars given to Maths IM students over the years, organised by topic. At the bottom you can find them organised in order of time.
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Sets and mathematical notation
The MLC's seminar on Understanding Maths Notation will be useful for this topic in Maths 1M. It talks about how to understand a maths notation and discusses most of the notations mentioned in this section of the course.
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Functions
This playlist on YouTube has several worked examples on the topic of functions.
In 2014, David gave this revision seminar where he talked about finding domains and ranges for functions, as well as finding inverse functions.
- Revision seminar: domains and ranges 2014 (YouTube)
- Revision seminar: domains and ranges 2014 (Echo360)
- Revision seminar notes: domains and ranges 2014 (PDF)
In Semester 1 2018, David gave this revision seminar with a section about some special kinds of functions (starting at 1h22m). He talked about piecewise functions and composing them to make new functions. He also talked about how to compose trig functions and inverse trig functions.
- Revision seminar section: special functions, Sem 1 2018 (YouTube)
- Revision seminar section: special functions, Sem 1 2018 (Echo360)
- Revision seminar notes: special functions, Sem 1 2018 (PDF)
In Semester 2 2019 David gave this revision seminar with a section on inverse functions (starting at 1h17m16s).
- Revision seminar section: inverse functions, Sem 2 2019 (YouTube)
- Revision seminar section: inverse functions, Sem 2 2019 (Echo360)
- Revision seminar notes: inverse functions, Sem 2 2019 (PDF)
In Semester 2 2020, David gave a revision seminar with a section on the fundamental trig limit (starting at 28m20s).
- Revision seminar section: fundamental trig limit, Sem 2 2020 (YouTube)
- Revision seminar section: fundamental trig limit, Sem 2 2020 (Echo360)
In Semester 1 2022, David gave a revision seminar with two sections relating to functions. First, at 1h5m36s, he discussed graphs of polynomials and circles, and then, at 1h57m50s, he talked about the modulus function in both real numbers and complex numbers.
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Trigonometric functions
This handout has a list of useful trigonometric identities.
This 2015 seminar covered calculations of trig functions for large angles using the unit circle, solving equations involving trig functions, using and proving trig identities, and graphing trig functions (The part on trig identities is more comprehensive in this seminar than in the 2013 or 2017 seminar.)
- Revision seminar: trig functions 2015 (YouTube)
- Revision seminar: trig functions 2015 (Echo360)
- Revision seminar notes: trig functions 2015 (PDF)
This 2013 seminar covered calculations of trig functions for large angles using the unit circle, solving equations involving trig functions, graphing trig functions, and using and proving trig identities. (The part on graphing trig functions is better in this seminar than the 2015 seminar.)
- Revision seminar: trig functions 2013 (YouTube)
- Revision seminar: trig functions 2013 (Echo360)
- Revision seminar notes: trig functions 2013 (PDF)
This seminar for Semester 1 2022 started with a section on trig functions including calculating values of large angles and solving equations.
- Revision seminar video: trig functions Sem 1 2022 (YouTube)
- Revision seminar video: trig functions Sem 1 2022 (Echo360)
- Revision seminar notes: trig functions Sem 1 2022 (PDF)
This seminar in Semester 1 2023 had a short section at the end (starting at 1h38m10s) on solving trig equations and other ideas related to trig functions.
- Revision seminar video: solving trig equations Sem 1 2023 (YouTube)
- Revision seminar video: solving trig equations Sem 1 2023 (Echo360)
- Revision seminar notes: solving trig equations Sem 1 2023 (PDF)
This 2016 seminar was just a few examples of shifting and stretching the graphs of trig functions and how it relates to the equations.
- Revision seminar: trig graphs 2016 (Echo360)
- Revision seminar: trig graphs 2016 (Echo360)
- Revision seminar notes: trig graphs 2016 (PDF)
This 2017 seminar covered calculating exact values of trig functions using the unit circle and also using the trig identities to calculate exact values; it also covered drawing transformations of trig functions. (I used a very different way to explain the transformation of trig functions than in the other videos, so if the other ways haven't been working for you, check out this video.)
- Revision seminar: trig functions 2017 (YouTube)
- Revision seminar: trig functions 2017 (Echo360)
- Revision seminar notes: trig functions 2017 (PDF)
In this revision seminar from Semester 2 2020, there was a section on finding exact values of trig functions (starting at 50m30s).
- Revision seminar section: trig exact values, Sem 2 2020 (YouTube)
- Revision seminar section: trig exact values, Sem 2 2020 (Echo360)
In Semester 2 2019 David gave a seminar with a short section on the calculus of trig functions (starting at 1h39m18s).
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Techniques of integration
This revision seminar from Semester 2, 2012, is about integration techniques. (It is for a course called AQMF but the content is the same as Maths 1M.) David covered the basic formulas, substitution and integration by parts.
- Revision seminar: integration techniques 2012 (YouTube)
- Revision seminar: integration techniques 2012 (Echo360)
- Revision seminar notes: integration techniques 2012 (PDF)
This revision seminar from Semester 1 2020 had a section on integration techniques (starting at 53m26s).
- Revision seminar section: integration techniques Sem 1 2020 (YouTube)
- Revision seminar section: integration techniques Sem 1 2020 (Echo360)
This lecture from the old MLC bridging course MathTrackX is about techniques of integration, and the content is similar to that in Maths IM.
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Differential equations
In this revision seminar from Semester 2 2019, the beginning was on differential equations, including the ways to solve them and Euler's method.
- Revision seminar section: differential equations, Semester 2 2019 (YouTube)
- Revision seminar section: differential equations, Semester 2 2019 (Echo360)
- Revision seminar notes: differential equations, Sem 2 2019 (PDF)
In this seminar from Semester 2 2023, Nicholas started by talking about separable differential equations and Euler's method.
- Revision seminar section: separable differential equations and Euler's method, Semester 2 2023 (YouTube)
- Revision seminar section: separable differential equations and Euler's method, Semester 2 2023 (Echo360)
- Revision seminar notes: separable differential equations and Euler's method, Sem 2 2013 (PDF)
This seminar from Semester 1 2012, covered differential equations. David discussed briefly the basic kinds of differential equations in Maths 1M, Newton's law of cooling, and Euler's method. (Note that the second hour of this seminar covered miscellaneous topics. Note also that the seminar covered the logistic equation, which is no longer a topic in Maths 1M.)
- Revision seminar: differential equations 2012 (YouTube)
- Revision seminar: differential equations 2012 (Echo360)
- Revision seminar notes: differential equations 2012 (PDF)
This revision seminar from Semester 1 2016, was on differential equations. David discussed separable differential equations, and also various rules of integration used in Maths 1M.
- Revision seminar: differential equations 2016 (YouTube)
- Revision seminar: differential equations 2016 (Echo360)
- Revision seminar notes: differential equations 2016 (PDF)
In this revision seminar from Semester 2 2018, there was a short section on Newton's law of cooling (starting at 1h40m25s).
- Revision seminar section: Newton's law of cooling Sem 2 2018 (YouTube)
- Revision seminar section: Newton's law of cooling Sem 2 2018 (Echo360)
- Revision seminar notes: Newton's law of cooling Sem 2 2018 (PDF)
In this revision seminar from Semester 2 2020, there was a section on Euler's method (starting at 35m).
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Vectors, planes and parametic curves
This seminar in Semester 1 2015 was on vectors. The seminar covered the major things you can calculate with vectors (such as dot and cross product, projections and angles), and doing geometry proofs with vectors, and also briefly discussed equations of lines and planes. Note I mentioned a list of versions of the right hand rule, which is linked below.
- Revision seminar: vectors 2015 (YouTube)
- Revision seminar: vectors 2015 (Echo360)
- Revision seminar notes: vectors 2015 (PDF)
- The right hand rules blog post
This seminar in Semester 2 2021 covered various concepts about vectors in 2D and 3D, including equations of lines and planes, and vector proofs.
This seminar in Semester 1 2016, had two separate parts on vectors. David discussed geometrical proofs using vectors, and also finding the equations of planes in 3D.
- Revision seminar: vector proofs 2016 (YouTube)
- Revision seminar: vector proofs 2016 (Echo360)
- Revision seminar notes: vector proofs 2016 (PDF)
- Revision seminar: vectors and planes 2016 (YouTube)
- Revision seminar: vectors and planes 2016 (Echo360)
- Revision seminar notes: vectors and planes 2016 (PDF)
In this seminar in Semester 1 2023, David discussed vectors, lines, planes and curves.
- Revision seminar video: vectors, lines, planes and curves Sem 1 2023 (YouTube)
- Revision seminar video: vectors, lines, planes and curves Sem 1 2023 (Echo360)
- Revision seminar notes: vectors, lines, planes and curves Sem 1 2023 (PDF)
In this seminar in Semester 2 2018, there was a section on vectors (starting at 40m6s), including using them in geometrical proofs and the equations of planes.
- Revision seminar section: vectors Sem 2 2018 (YouTube)
- Revision seminar section: vectors Sem 2 2018 (Echo360)
- Revision seminar notes: vectors Sem 2 2018 (PDF)
This seminar in Semester 2 2023 had a section where Nicholas talked about unit vectors and projection (starting at 40m10s). The section of the PDF notes begins on page 5.
- Revision seminar section: unit vectors and projection Sem 2 2023 (YouTube)
- Revision seminar section: unit vectors and projection Sem 2 2023 (Echo360)
- Revision seminar notes: unit vectors and projection Sem 2 2023 (PDF)
This seminar in Semester 1 2016 was on curves. David discussed what a curve is, converting between parametric and Cartesian form, and finding tangents to curves.
- Revision seminar: curves 2016 (YouTube)
- Revision seminar: curves 2016 (Echo360)
- Revision seminar notes: curves 2016 (PDF)
In this seminar in Semester 1 2019, the middle section (starting at 36m30s) was about curves. David discussed what a curve is, the various classic curve formulas, finding slopes and tangent lines, and converting to Cartesian form.
- Revision seminar section: curves Sem 1 2019 (YouTube)
- Revision seminar section: curves Sem 1 2019 (YouTube)
- Revision seminar notes: curves Sem 1 2019 (PDF)
This seminar in Semester 2 2020 started with a section on dot and cross products of vectors in 3D.
- Revision seminar section: dot and cross products, Sem 2 2020 (YouTube)
- Revision seminar section: dot and cross products, Sem 2 2020 (Echo360)
In this seminar in Semester 1 2021, the second part (starting at 1h5m) was about lines and curves in 2D and 3D.
- Revision seminar section: lines and curves, Sem 1 2021 (YouTube)
- Revision seminar section: lines and curves, Sem 1 2021 (Echo360)
This seminar in Semester 2 2022 was about visualising lines and planes in 3D space.
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Related rates
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Complex numbers and polynomials
This revision seminar from 2013 covered polynomials.
- Revision seminar: polynomials 2013 (YouTube)
- Revision seminar: polynomials 2013 (Echo360)
- Revision seminar notes: polynomials 2013 (PDF)
This lecture on polynomials was done for the MLC's old bridging course MathsTrack, and covers similar content to what is in Maths 1M.
In Semester 1 2017, the MLC gave a revision seminar on Complex Numbers to Maths 1M students. In this seminar, David covered where the complex numbers fit in the families of number, and how the various operations relate to the three main representations of complex numbers. It is quite similar to the 2012 seminar, but there are some differences, so I have put the old seminar further down in case you want to see both.
- Revision seminar: complex numbers 2017 (YouTube)
- Revision seminar: complex numbers 2017 (Echo360)
- Revision seminar notes: complex numbers 2017 (PDF)
The MLC gave a revision seminar on Complex Numbers to Maths IM students in Semester 1 2012. In this seminar, we covered most of the topic 'complex numbers', particularly focussing on organising the information about the different representations of complex numbers (x+yi, graph and polar).
- Revision seminar: complex numbers 2012 (YouTube)
- Revision seminar: complex numbers 2012 (Echo360)
- Revision seminar notes: complex numbers 2012 (PDF)
In Semester 1 2018, the MLC gave a revision seminar with some Complex Number ideas to Maths 1M students. In this seminar, David covered the relationship between polar form and Cartesian form, choosing the principal argument, drawing sets of complex numbers defined by equations/inequalities, and factorising complex polynomials.
- Revision seminar section: complex numbers Sem 1 2018 (YouTube)
- Revision seminar section: complex numbers Sem 1 2018 (Echo360)
- Revision seminar notes: complex numbers Sem 1 2018 (PDF)
In Semester 2 2018, the MLC gave a revision seminar with a short section on Complex Number ideas (starting at 1h12m). Nicholas discussed representations of complex numbers and drawing sets of complex numbers.
- Revision seminar: complex numbers Sem 2 2018 (YouTube)
- Revision seminar: complex numbers Sem 2 2018 (Echo360)
- Revision seminar notes: complex numbers Sem 2 2018 (PDF)
In Semester 2 2023, Nicholas gave a revision seminar whose last section (starting at 1h13m40s) was on the polar form of complex numbers. In the notes, this section begins on page 8.
- Revision seminar: complex numbers polar form Sem 2 2023 (YouTube)
- Revision seminar: complex numbers polar form Sem 2 2023 (Echo360)
- Revision seminar notes: complex numbers polar form Sem 2 2023 (PDF)
In Semester 1 2019 David gave a revision seminar with a section on complex roots and De Moivre's theorem (starting at 1h16m35s).
- Revision seminar section: complex roots and De Moivre's theorem Sem 1 2019 (YouTube)
- Revision seminar section: complex roots and De Moivre's theorem Sem 1 2019 (Echo360)
- Revision seminar notes: complex roots and De Moivre's theorem Sem 1 2019 (PDF)
In Semester 1 2022, David gave a revision seminar with a section on the modulus function for both real and complex numbers (starting at 1h57m50s).
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Reasoning, proofs and induction
The MLC gave a revision seminar on logic and proofs in 2015. The first part covered constructions such as negation, the converse and the contrapositive. The second part covered mathematical induction.
- Revision seminar: logical constructions 2015 (YouTube)
- Revision seminar: logical constructions 2015 (Echo360)
- Revision seminar notes: logical constructions 2015 (PDF)
- Revision seminar: mathematical induction 2015 (YouTube)
- Revision seminar: mathematical induction 2015 (Echo360)
- Revision seminar notes: mathematical induction 2015 (PDF)
In Semester 1 2020, David gave a revision seminar where the first section was about mathematical induction.
- Revision seminar section: mathematical induction Sem 1 2020 (YouTube)
- Revision seminar section: mathematical induction Sem 1 2020 (Echo360)
In Semester 1 2021, David gave another revision seminar where the first section was about mathematical induction.
- Revision seminar section: mathematical induction Sem 1 2021 (YouTube)
- Revision seminar section: mathematical induction Sem 1 2021 (Echo360)
In Semester 2 2023, Nicholas gave a seminar with a section on mathematical induction (starting at 51m30s). The part of the notes on mathematical induction starts on page 6.
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Revision seminars in order of time since 2018
Over the years, the MLC has given many revision seminars for Maths 1M, and most of these cover several different topics. Links to relevant sections of the seminars are under the headings above, but you may find it useful to watch each seminar as a whole. Here are the seminars in order of time from 2018, with the newest ones at the top.
Semester 2 2023
Various problems from across the course including first order separable differential equations (at the start), Euler's method (starting at 28m55s), unit vectors and projections (starting at 40m10s), mathematical induction (starting at 51m30s), and the polar form of complex numbers (starting at 1h13m40s).
- Revision seminar video: various problems Sem 2 2023 (YouTube)
- Revision seminar video: various problems Sem 2 2023 (Echo360)
- Revision seminar notes: various problems Sem 2 2023 (PDF)
Semester 1 2023
Vectors, lines, planes and curves, as well as solving equations with a trig function (starting at 1h38m10s).
- Revision seminar video: vectors, lines, planes and curves Sem 1 2023 (YouTube)
- Revision seminar video: vectors, lines, planes and curves Sem 1 2023 (Echo360)
- Revision seminar notes: vectors, lines, planes and curves Sem 1 2023 (PDF)
- Revision seminar notes: solving trig equations Sem 1 2023 (PDF)
Semester 2 2022
Study skills and problem-solving skills for maths especially in preparation for an exam.
- Seminar video: Study skills Sem 2 2022 (YouTube)
- Seminar video: Study skills Sem 2 2022 (Echo360)
- Seminar notes: Study skills Sem 2 2022 (PDF)
- Handout: Solving problems (PDF)
Visualising lines and planes in 3D.
- Revision seminar video: visualising 3D, Sem 2 2022 (YouTube)
- Revision seminar video: visualising 3D, Sem 2 2022 (Echo360)
- Revision seminar notes: visualising 3D, Sem 2 2022 (PDF)
Semester 1 2022
Trig functions including solving equations , recognising the graphs of polynomial functions and circles (at 1h5m36s ), the modulus function in both real numbers and complex numbers (at 1h57m50s)
- Revision seminar video: Sem 1 2022 (YouTube)
- Revision seminar video: Sem 1 2022 (Echo360)
- Revision seminar notes: trig functions Sem 1 2022 (PDF)
- Revision seminar notes: graphs Sem 1 2022 (PDF)
- Revision seminar notes: modulus Sem 1 2022 (PDF)
Semester 2 2021
Various concepts relating to vectors, lines and planes in 2D and 3D.
Semester 1 2021
Mathematical induction, lines and curves.
Semester 2 2020
Dot and cross products, the fundamental trig limit, Euler's method, exact values of trig functions.
Semester 1 2020
Mathematical induction and techniques of integration.
Semester 2 2019
Differential equations, inverse functions, trig calculus.
- Revision seminar video: Sem 2 2019 (YouTube)
- Revision seminar video: Sem 2 2019 (Echo360)
- Revision seminar notes: differential equations, Sem 2 2019 (PDF)
- Revision seminar notes: inverse functions, Sem 2 2019 (PDF)
- Revision seminar notes: trig calculus, Sem 2 2019 (PDF)
Semester 1 2019
Related rates, parametric curves, complex roots and DeMoivre's theorem.
- Revision seminar video: Sem 1 2019 (YouTube)
- Revision seminar video: Sem 1 2019 (Echo360)
- Revision seminar notes: related rates, Sem 1 2019 (PDF)
- Revision seminar notes: parametric curves, Sem 1 2019 (PDF)
- Revision seminar notes: complex roots, Sem 1 2019 (PDF)
Semester 2 2018
Related rates, vector proofs, planes, complex numbers, reduced row echelon form, Newton's law of cooling.
- Revision seminar video: Sem 2 2018 (YouTube)
- Revision seminar video: Sem 2 2018 (Echo360)
- Revision seminar notes: miscellaneous problems, Sem 2 2018 (PDF)
Semester 1 2018
Polar forms of complex numbers, sketching sets of complex numbers, factorising complex polynomials, piecewise functions, composing trig functions and inverse trig functions.