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The MLC's seminar on Understanding Maths NotationÌýwill 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.

This playlist on YouTube has several worked examples on the topic of functions.

In 2014, David gave thisÌýrevision seminar where he talked about finding domains and ranges for functions, as well as finding inverse functions.

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.

In Semester 2 2019 David gave this revision seminar with a section on inverse functions (starting at 1h17m16s).Ìý

In Semester 2 2020, David gave a revision seminar with a section on the fundamental trig limit (starting at 28m20s).

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.

This handout has a list of useful trigonometric identities.

• Useful trig identities handout

ThisÌý2015 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.)

ThisÌý2013 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.)

This seminar for Semester 1 2022 started with a section on trig functions including calculating values of large angles and solving equations.

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.

ThisÌý2016 seminar was just a few examples of shifting and stretching the graphs of trig functions and how it relates to the equations.

ThisÌý2017 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.)

In this revision seminar from Semester 2 2020, there was a section on finding exact values of trig functions (starting at 50m30s).

In Semester 2 2019 David gave a seminar with a short section on the calculus of trig functions (starting at 1h39m18s).Ìý

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.

This revision seminar from Semester 1 2020 had a section on integration techniques (starting at 53m26s).

This lecture from the old MLC bridging course MathTrackX is about techniques of integration, and the content is similar to that in Maths IM.

In this revision seminar fromÌýSemester 2 2019,Ìýthe beginning was on differential equations, including the ways to solve them and Euler's method.

In this seminar from Semester 2 2023, Nicholas started by talking about separable differential equations and Euler's method.

This seminar fromÌýSemester 1 2012, coveredÌýdifferential 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.)Ìý

This revision seminar from Semester 1 2016, wasÌýon differential equations. David discussed separable differential equations, and also various rules of integration used in Maths 1M.

In this revision seminar from Semester 2 2018, there was a short section onÌýNewton's law of cooling (starting at 1h40m25s).

In this revision seminar from Semester 2 2020, there was a section on Euler's method (starting at 35m).

This seminar inÌýSemester 1 2015 wasÌýon 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.

• 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,Ìýhad two separate parts on vectors. David discussed geometrical proofs using vectors, and also finding the equations of planes in 3D.Ìý

In this seminar in Semester 1 2023, David discussed vectors, lines, planes and curves.

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.

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.

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.

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.

This seminar in Semester 2 2020 started with a section on dot and cross products of vectors in 3D.

In this seminar in Semester 1 2021, the second part (starting at 1h5m) was about lines and curves in 2D and 3D.

This seminar in Semester 2 2022 was about visualising lines and planesÌý in 3D space.

In this revision seminar in Semester 1 2019, the first section was about related rates, specifically on strategies to take the information presented and turn it into equations connecting the rates.

In this revision seminar in Semester 1 2016,ÌýDavid covered several examples of calculating rates in related ratesÌýsituations.

In this revision seminar in Semester 2 2018, Nicholas started with a section on related rates, including several examples of these kinds of problems.

This revision seminar from 2013 covered polynomials.

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.

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).

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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.

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.

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.

In Semester 1 2019 David gave a revision seminar with a section on complex roots and De Moivre's theorem (starting at 1h16m35s).Ìý

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).

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.

In Semester 1 2020, David gave a revision seminar where the first section was about mathematical induction.

In Semester 1 2021, David gave another revision seminar where the first section was about mathematical induction.

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.

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 2024

Nicholas discussed the following topics: Trigonometric functions (at the start), Parametric curves (at 37m46s), Composition of functions (at 53m38s), Integration (at 1h7m5s), Differential equations (at 1h16m54s), Complex numbers (at 1h26m2s).

Semester 1 2024

Nicholas discussed various topics from across the course: Euler's method (at the start), equations of planes and lines in 3D (at 10m42s), mathematical induction (at 1h9m52s) and complex number operations (at 1h28m27s). The video was cut short before the end of the complex number examples, but you can still find the end of those examples in the document camera notes.

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).

Semester 1 2023

Vectors, lines, planes and curves, as well as solving equations with a trig function (starting at 1h38m10s).

Semester 2 2022

Study skills and problem-solving skills for maths especially in preparation for an exam.

• Handout: Solving problems (PDF)

Visualising lines and planes in 3D.

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)

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.

Semester 1 2019

Related rates, parametric curves, complex roots and DeMoivre's theorem.

Semester 2 2018

Related rates, vector proofs, planes, complex numbers, reduced row echelon form, Newton's law of cooling.

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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.