Year 12 Mathematics Advanced
Transformed trigonometric graphs and modelling, sequences and series, and differentiating exponential, logarithmic and trigonometric functions.
- Each week
- One 3-hour lesson · 30-minute break
- In person · St Leonards
- Weekly from Saturday 17 October, decide by Saturday 24 October · 10:00am or 2:00pm
- Online · live from home
- Weekly from Sunday 18 October, decide by Sunday 25 October · 10:00am or 2:00pm
- Price
- $1,000 instead of $1,500 for all 10 lessons, for the first 5 students to sign up. Try 2 lessons before you pay
The term price covers all 10 lessons, the first 2 included. Pay up front, after the first lesson or after the second; if the class is not right by then, there is nothing to pay.
The term, lesson by lesson
In person Saturday 17 October to Saturday 19 December, online Sunday 18 October to Sunday 20 December. Follows the new NESA Mathematics Advanced 11–12 Syllabus (2024), which this cohort is the first to sit in the 2027 HSC, in the order most schools teach it.
The term at a glance
| Lesson | Topic | In person | Online |
|---|---|---|---|
| Lesson 1 | Further graph transformations and modellingThe Year 11 toolkit for Year 12 | Sat 17 Oct | Sun 18 Oct |
| Lesson 2 | Further graph transformations and modellingTransforming trigonometric graphs | Sat 24 Oct | Sun 25 Oct |
| Lesson 3 | Further graph transformations and modellingTrigonometric equations and graphical solutions | Sat 31 Oct | Sun 1 Nov |
| Lesson 4 | Further graph transformations and modellingModelling with functions | Sat 7 Nov | Sun 8 Nov |
| Lesson 5 | Sequences and seriesSequences, sigma notation and arithmetic series | Sat 14 Nov | Sun 15 Nov |
| Lesson 6 | Sequences and seriesGeometric series and limiting sums | Sat 21 Nov | Sun 22 Nov |
| Lesson 7 | Differential calculusDifferentiating exponential functions | Sat 28 Nov | Sun 29 Nov |
| Lesson 8 | Differential calculusDifferentiating logarithmic functions | Sat 5 Dec | Sun 6 Dec |
| Lesson 9 | Differential calculusDifferentiating trigonometric functions | Sat 12 Dec | Sun 13 Dec |
| Lesson 10 | Term reviewConsolidation and term test | Sat 19 Dec | Sun 20 Dec |
Further graph transformations and modelling
The Year 11 toolkit for Year 12
- Year 11 review
- MAV-12-01
- Radians and exact trigonometric values
- Solving trigonometric equations within a given domain
- Transformations of y = f(x): shifts, stretches and reflections
- The sine and cosine curves drawn in radians
Key skill: Describing a transformation both in words and in function notation.
Transforming trigonometric graphs
- Graph transformations
- MAV-12-01
- Amplitude, period, phase shift and vertical shift in y = a sin(b(x − c)) + d
- The same transformations applied to cosine and tangent
- Domain and range of a transformed function
- Sketching accurately over a set domain
Key skill: Reading the amplitude and period straight from an equation.
Trigonometric equations and graphical solutions
- Graph transformations
- MAV-12-01
- Solving equations such as 2 sin 2x = 1 within a domain
- Adjusting the domain when the angle is ax + b
- Counting solutions by sketching two graphs on the same axes
- Checking solutions with graphing technology
Key skill: Finding every solution in a domain, not just the first one.
Modelling with functions
- Modelling
- MAV-12-02
- Modelling tides, daylight hours and other repeating data with trigonometric functions
- Choosing a suitable Year 11 function to model a practical problem
- Logarithmic scales: decibels, earthquakes, pH and star magnitude
Key skill: Building a model from a real situation and interpreting what it predicts.
Sequences and series
Sequences, sigma notation and arithmetic series
- Sequences and series
- MAV-12-03
- Sequence notation and partial sums
- Writing and evaluating sums in sigma notation
- The nth term and the sum of an arithmetic series
- Problems involving linear growth
Key skill: Choosing the right arithmetic series formula for the information given.
Geometric series and limiting sums
- Sequences and series
- MAV-12-03
- The nth term and the sum of a geometric series
- When a limiting sum exists, and finding it
- Writing recurring decimals as fractions
Key skill: Testing whether a series has a limiting sum before using the formula.
Differential calculus
Differentiating exponential functions
- Differential calculus
- MAV-12-04
- The derivatives of eˣ and of e raised to a linear function
- The derivative of aˣ for any base
- Using the chain rule on e raised to a function
- Tangents to exponential curves
Key skill: Differentiating exponential functions quickly and without errors.
Differentiating logarithmic functions
- Differential calculus
- MAV-12-04
- The derivative of ln x, and of logarithms to other bases
- Differentiating the logarithm of a function
- Using the log laws to simplify before differentiating
Key skill: Simplifying with the log laws first, so the derivative is short.
Differentiating trigonometric functions
- Differential calculus
- MAV-12-04
- The derivatives of sin x, cos x and tan x
- The chain rule with trigonometric functions
- Products and quotients that mix exponential, logarithmic and trigonometric functions
- Equations of tangents and normals
Key skill: Deciding which of the product, quotient and chain rules a question needs.
Term review
Consolidation and term test
- MAV-12-01 to MAV-12-04
- Mixed HSC-style questions on graph transformations, sequences and series, and calculus, including the mistakes that cost marks most often
- A short test under exam conditions, marked with written feedback
- A plan for the summer holidays, built around the integration work that opens Term 1
Key skill: Working accurately under time pressure.
How every lesson runs
3 hours of teaching with a 30-minute break, following the same pattern every week.
Check in
A short quiz on last week’s content, and the homework questions that caused trouble worked through on the board before anything new is taught.
Teach
The new content taught at the whiteboard, with worked examples that build from the first idea up to the standard of an HSC question.
Practise
Questions at four levels: Assimilate, Consolidate, Integrate and Extend. Everyone starts together and moves up as they are ready, with written work checked as they go.
Exam practice
Past HSC questions on the week’s topic, answered under time and marked against the NESA marking guidelines, so students learn what earns the marks.
Take home
Session notes and homework set at each student’s level, so the week’s work is secure before the next lesson builds on it.
What your child receives
Every student in the class gets all of this, week by week and across the term.
- Every week
A check-in quiz
A short quiz on last week’s content opens every lesson, so a gap is found and fixed before new work is built on top of it.
- Every week
Session notes
Notes on what the lesson covered, to revise from at home. They are sent even when a lesson is missed.
- Every week
Homework at their level
Questions set at one of four levels, Assimilate, Consolidate, Integrate or Extend, so the work stretches each student without losing them.
- Every week
Marked HSC questions
Past HSC questions on the week’s topic, answered under time and marked against the NESA marking guidelines.
- End of term
A term test with written feedback
A short test under exam conditions in the final lesson, marked and returned with written feedback on where the marks were won and lost.
- End of term
A holiday plan
A plan for the holidays that follow, built around the work that opens the next term.
The rest of Year 12
Where the course goes next, in the order schools teach it.
- Term 1, 2027
Integral calculus: primitives, definite integrals, the fundamental theorem, and areas under and between curves.
- Term 2, 2027
Applications of calculus to curve sketching, optimisation, growth and decay, and motion in a straight line. Then financial mathematics, with loans and annuities.
- Term 3, 2027
Random variables, continuous distributions and the normal distribution. Then trial exams and revision for the HSC.
Questions about this class
Which syllabus does the Mathematics Advanced class follow?
The class follows the new NESA Mathematics Advanced 11–12 Syllabus (2024), which this cohort is the first to sit in the 2027 HSC, in the order most schools teach it.
What if my school teaches Mathematics Advanced in a different order?
The class follows the plan on this page, which uses the order most schools teach Mathematics Advanced in. Where your school takes a topic earlier or later, that week’s lesson is either revision of work already done or a head start on what is coming. You keep the session notes from every lesson, so they are on hand when school reaches the topic.
Can I join partway through the term?
Yes. Classes run every week through the term, so you can start whenever suits and still have two lessons to decide before you pay. Tell us which course you are in and we will let you know what the class has covered so far.
What if I miss a week?
Tell us as early as you can. Where there is room, you can sit that week with the other day’s group. The Saturday and Sunday classes cover the same material and we will send the session notes either way.
Do I pay for the first two lessons?
Only if you stay. The term price covers every lesson, the first two included. Pay up front, after the first lesson or after the second. If the class is not right after two lessons, you pay nothing.
Sitting more than one?
Every course runs as its own class, each with its own plan.
Join the Mathematics Advanced class
Try 2 lessons before you pay. Tell us whether Saturdays in person or Sundays online suit, and we will confirm your session.