The encyclopedia of NSW Mathematics
- Standard 1 & 2, Advanced, Extension 1 and Extension 2 -
- 2017 and 2024 syllabuses -
Latest news
October 28 2026: The next chapter of my Extension 2 textbook has just been released, covering The nature of proof. I have had to release the chapter without the 100 revision questions at the moment, as HSC marking has just started. I will add the revision questions over the next couple of weeks as time allows, but those who will soon start the focus area can get a head start.
Check below for all published PD courses and textbook chapters.
The 2017 Extension 2 student course is free until the 2027 HSC. I won’t have time to update the course for the 2024 syllabus until next year, so opened it up for free rather than closing students out from so many great resources. I have added a few videos summarising the differences in the whole course, and chapter by chapter, then a short note at the start of each lesson explaining the differences, if any, for the content of that lesson. Follow the link below to sign up for free.
The next Mathematics In Depth course to be created will cover Extension 2 The nature of proof.
For Extension 2, I will be finishing the revision exercise from The nature of proof, then later in Term 4 start on Further work with vectors, probably to be released during the summer holidays, as there is no rush there.
New Mathematics In Depth courses are released at a rate of approximately one per fortnight, with some taking less time than others!
2024 Syllabus resources
HSC Mathematics Extension 2 (2024) textbook (FREE)
The 2024 version of the textbook will be much larger than the 2017 version, as I am combining the 1000 Revision Questions into the textbook, rather than having two separate documents.
The current download (below) includes Chapter 1 Introduction to complex numbers, Chapter 2 The nature of proof and Chapter 4 Further integration, at 598 pages just for three chapters, including fully worked solutions. The other chapters will be produced in the order 3 then 5.
The chapters are:
- Chapter 1 Introduction to complex numbers (COMPLETE)
- Chapter 2 The nature of proof (COMPLETE)
- Chapter 3 Further work with vectors (COMING SOON)
- Chapter 4 Further integration (COMPLETE)
- Chapter 5 Applications of calculus to mechanics
I will start working on Chapter 3 later in the term, which should be ready duing the summer holidays.
Use the big red button below to download the current chapters and solutions available, for FREE.
Mathematics in Depth online professional development courses for the 2024 syllabuses (PAID)
The following online courses have been updated for the 2024 syllabus – the list will be updated as I complete each new course.
For a summary of the changes to all of the syllabuses, see the course ‘2024 Stage 6 Mathematics Syllabuses in detail’.
Use the big yellow button below for a direct link to all the courses at stevehoward.tta.edu.au.
The Standard courses available are:
Standard Course 1 – Year 11
Formulas and equations
Linear relationshipsStandard Course 2 – Year 11
Earning money
Managing moneyStandard Course 3 – Year 11
Applications of measurement
Time and locationStandard Course 4 – Year 11
Networks, paths and treesStandard Course 5 – Year 11
Data analysis- Standard Course 6 – Year 12
STD1: Algebraic relationships
STD2: Algebraic relationships
The Advanced courses available are:
Advanced Course 1 – Year 11
Working with functions (Part A)Advanced Course 2 – Year 11
Working with functions (Part B)Advanced Course 3 – Year 11
Trigonometry and measure of angles
Trigonometric identities and equationsAdvanced Course 4 – Year 11
Introduction to differentiationAdvanced Course 5 – Year 11
Exponential and logarithmic functions
Graph transformationsAdvanced Course 6 – Year 11
Probability and data- Advanced Course 7 – Year 12
Further graph transformations and modelling - Advanced Course 8 – Year 12
Sequences and series
Financial mathematics - Advanced Course 9 – Year 12
Differential calculus
Integral calculus
The Extension 1 courses available are:
Extension 1 Course 1 – Year 11
Permutations and combinations
The binomial theoremExtension 1 Course 2 – Year 11
Polynomials
Further work with functionsExtension 1 Course 3 – Year 11
Further trigonometry- Extension 1 Course 4 – Year 12
Proof by mathematical induction
Inverse trigonometric functions - Extension 1 Course 5 – Year 12
Introduction to vectors
The Extension 2 courses available are:
Extension 2 Course 1 – Year 12
Introduction to complex numbers
TTA Trial HSCs and Year 11 Final Examinations (PAID)
The Year 12 Trial HSCs and Year 11 Final Examinations are now available from TTA at stevehoward.tta.edu.au.
Use the big green button below to go straight to the correct page of the website.
2017 Syllabus resources
Extension 2 textbook and 1000 Revision Questions (2017) (FREE)
Here is the full version of the Extension 2 textbook for the 2017 syllabus for the 2017 syllabus, plus the 1000 Revison Questions, for FREE.
These resources are only suitable if you are sitting the HSC in 2026.
They will be replaced by the updated version of the textbook, available at the top of the page.
Mathematics Extension 2 – Student Course (2017) (FREE UNTIL THE 2027 HSC with the updated version PAID once it is ready)
The 2017 version of my Extension 2 Students Course is being made available to everyone completely free until after the 2027 HSC. Because of all the other courses I need to complete, I won’t get a chance to update this course for the 2024 syllabus until Term 3 2027. There are over 950 videos in this course, and the updated course will have well over 1000!
We decided to open the 2017 course up to everyone for free until just after the 2027 HSC, as there is too much good content that can help students understand the course. About 95% of the content remains the same.
There is a video at the start of each chapter explaining the changes required for the 2024 syllabus for the whole chapter, and each lesson has a short summary covering the specific changes where needed, or lets you know that there are no changes.
Use this course in conjunction with my current textbook for the best results. The 2024 version of the textbook is available further up this page – look for the big red button for the most up-to-date version.
This course is based on the 2017 version of my Extension 2 textbook. Look for one of the blue buttons just above here to download it.
I will complete the 2024 course starting with Mechanics and working backwards, so that students or teachers can sign up for the updated course if they wish before the HSC.
I will send an email to everyone who is enrolled in this course when Mechanics is published.
Mathematics in Depth Professional Development online courses for the 2017 syllabuses (PAID)
All of the online courses for the 2017 syllabus will be available online until after the 2026 HSC and once the replacement course for the 2024 syllabus has been published. There are over 3100 recorded examples and over 7100 pages of handouts – a true encyclopedia of knowledge at your fingertips! Use the big yellow button below for a direct link to all the courses for both the 2017 and 2024 syllabuses at stevehoward.tta.edu.au. above
EXTENSION 2 TEXTBOOK AT NO COST TO YOU
See below for more information.
About The Mathematician, Teacher & Author
My name is Steve Howard. I am a Mathematics Teacher who taught at Cowra High School, a medium sized rural high school in Central West NSW, for 30 years, and also taught gifted and talented students online through xsel and Aurora College. I now work from home, mainly creating Mathematics resources available through TTA, but also teaching extension online through Mount View High School in the Hunter, and marking the Extension 2 HSC. This website is a portal that brings together my free and commercial Mathematics resources for students and teachers. Here you will find my passion project - my own Mathematics Extension 2 textbook and 1000 Revision Questions for Extension 2 - that are available here for free. You can also look at information about and links to the commercial online PD courses that I make for teachers through TTA, the TTA Maths Exams and the Extension 2 course for students. Get a free download of the textbook and revision book using the links above, and subscribe to the email list to keep up to date with new resources - free or commercial.
1000 EXTENSION 2 REVISION QUESTIONS AT NO COST TO YOU
TTA ONLINE PD
Extension 2 Textbook and Revision Questions
The Extension 2 textbook and matching ‘1000 Revision Questions’ will be continually changed and updated over time so that it better matches the HSC while the other textbooks stay the same.
The textbook has over 1000 questions and at 582 pages is about 50% bigger than the commercial textbooks. The two digital books work best together, but you can just use one or the other.
This textbook is mainly a passion project, but indirectly earns me a bit of pocket money through school copyright licensing and increasing traffic to my commercial online professional development courses for teachers through TTA.
Some of the features of this textbook that students and teachers may find useful:
* The questions are in the style of past HSC questions where possible, so students are learning the right type of questions throughout the course.
* The questions are graded in difficulty so students can work at their own level.
* Each exercise starts with Basic questions that match the examples, so students can ease themselves into the new concepts if they need to. More confident students can skip these first questions and start with Medium.
* All questions have fully worked solutions.
* There are lots of diagrams that help students understand concepts that would normally only be dealt with algebraically. There are many hints and tips on how to more easily answer questions, and to see the way past tricks in exam questions.
The textbook is paired with ‘1000 Revision Questions in Mathematics Extension 2’. The first 500 questions are arranged topic by topic matching the chapters from the textbook to help students study and revise, while the last 500 questions are from mixed topics to help students prepare for their Trials and the HSC.
The textbook is set out so that you can cover the course in 42 lessons. The aim is for you to be able to finish the course as soon as possible so that you can have months of revision before the HSC to master the content.
Extension 2 Textbook and Revision Questions
The Extension 2 textbook and matching ‘1000 Revision Questions’ will be continually changed and updated over time so that it better matches the HSC while the other textbooks stay the same.
The textbook has over 1000 questions and at 582 pages is about 50% bigger than the commercial textbooks. The two digital books work best together, but you can just use one or the other.
This textbook is mainly a passion project, but indirectly earns me a bit of pocket money through school copyright licensing and increasing traffic to my commercial online professional development courses for teachers through TTA.
Some of the features of this textbook that students and teachers may find useful:
* The questions are in the style of past HSC questions where possible, so students are learning the right type of questions throughout the course.
* The questions are graded in difficulty so students can work at their own level.
* Each exercise starts with Basic questions that match the examples, so students can ease themselves into the new concepts if they need to. More confident students can skip these first questions and start with Medium.
* All questions have fully worked solutions.
* There are lots of diagrams that help students understand concepts that would normally only be dealt with algebraically. There are many hints and tips on how to more easily answer questions, and to see the way past tricks in exam questions.
The textbook is paired with ‘1000 Revision Questions in Mathematics Extension 2’. The first 500 questions are arranged topic by topic matching the chapters from the textbook to help students study and revise, while the last 500 questions are from mixed topics to help students prepare for their Trials and the HSC.
The textbook is set out so that you can cover the course in 42 lessons. The aim is for you to be able to finish the course as soon as possible so that you can have months of revision before the HSC to master the content.
