Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships

Steve Howard
Passionate about Mathematics
A comprehensive guide to the knowledge and techniques needed to teach Combinatorics and Graphical Relationships from the new Mathematics Extension 1 Year 11 syllabus.
Target Audience
Mathematics teachers of any experience level who are preparing to teach the new Extension 1 syllabus.
2 reviews

Learning Areas

Teaching Standards

General Description

I created this course to provide teachers with a comprehensive guide to the knowledge and techniques required to teach the new NSW Mathematics Extension I Year 11 syllabus. The course covers every dot point from the new NSW Year 11 Mathematics Extension 1 syllabus, both old and new content. Please note that only Extension 1 content is covered, not Mathematics Advanced.

The course goes into greater detail than the textbooks, so teachers are more comfortable in their ability to deliver the content. All 127 examples have been recorded, so that you can watch an experienced maths teacher talk through the examples and any important points to note.

Part I covers ME-A1 Working with Combinatorics and ME-F1 Further Work with Functions (Part A) F1.1: Graphical relationships, two topics that can be taught without prerequisites from the Advanced course. Teachers of classes that include Extension and Advanced students may choose to start their Extension students with one of these topics.

New and existing content is explored in detail, including interesting and more efficient techniques that experienced teachers may not have seen before. Important points to be covered with students are noted, and the limits of the syllabus are discussed. As more detail on the syllabus is released by NESA any changes required will be made. Also included are related skills that are beyond the syllabus that you can use to extend more capable students.

The course includes 127 recorded examples, with a 139 page course handout. There are also 127 optional practice questions matching the examples from the course, with fully worked solutions. A suggested scope and sequence for Year 11 Advanced and Extension 1 for combined classes is provided, plus a lesson by lesson breakdown of the Advanced, Extension 1 and Extension 2 courses for Year 11 and 12 to help you create your own scope and sequences.

Part II of the series will cover the remainder of ME-F1 Further Work with Functions plus ME-F2 Polynomials.
Part III of the series will cover ME-T1 Inverse Trigonometric Functions, ME-T2 Further Trigonometric Identities & ME-C1 Rates of Change.


Mathematics teachers of any experience level who are preparing to teach the new Extension 1 syllabus.

Available Delivery Formats

Format Description

Course Access - This course is available 24/7. Once your enrolment is complete you will be emailed with details to give you course access. You can complete the course when it suits you, and you will have ongoing access to revisit the course at any time.

Have you considered a TTA subscription? - Unlimited online PD from $199 + GST per year.
Click here to learn more

Did you know that online courses are 50% off with TTA School Membership? - Click here to learn more

Did you know with a School Membership you can buy this course for all teachers for $850 + GST? - See the ‘WHOLE SCHOOL ONLINE’ tab above

Money Back Guarantee - If you complete less than 25% of an online course and aren’t impressed, simply visit to let us know what happened, and we will cancel your enrolment and provide a full refund.

Teaching Standards
2.1.2 Proficient Level – Content and teaching strategies of the teaching area
6.2.2 Proficient Level – Engage in professional learning and improve practice
Are you in NSW? If so, this is relevant for you
Completing this course will contribute 6 hours of NESA Registered PD addressing 2.1.2 & 6.2.2 from the Australian Professional Standards for Teachers towards maintaining Proficient Teacher Accreditation in NSW.

This course contributes to 5.0 professional development hours.


  Start Date Location Availability Price    
Enrol Now Now Online Places available $269 + GST Enrol Now



5 minutes

• Course Administration
• Introduction to the Mathematics Extension 1 In Depth Year 11 Series
• Introduction to Part I


5 minutes

• Introduction to Combinatorics
• Syllabus

Combinatorics 1: Fundamental Counting Principle and Background Information

15 minutes

• Lesson 1 Overview
• Listing and Counting the Ways an Event can Occur
• Fundamental Counting Principle (multiplication principle)
• Factorial Notation
• Distinct or Identical?
• Choosing Between Methods
• Combinatorics 1 Quiz

Combinatorics Lesson 2 - Basic Permutations

25 minutes

• Lesson 2 Overview
• All items arranged in a line
• All items arranged in a line (identical ends)
• All items arranged in a line (some items identical)
• All items arranged around a circle
• All items arranged around a bangle
• All items arranged around a circle (some items identical) - outside syllabus
• Some items in a Line
• Some items in a Circle
• Combinatorics 2 Quiz

Combinatorics Lesson 3 - Permutations with Restrictions

20 minutes

• Lesson 3 Overview
• Some items must be together – Bubble Method
• Some items must be apart – Gap Method
• Groups of items must alternate
• Groups around a Circle
• Combinatorics 3 Quiz

Combinatorics Lesson 4 - Combinations

20 minutes

• Lesson 4 Overview
• Combinations
• Groups
• Stars and Bars
• Combinatorics 4 Quiz

Combinatorics Lesson 5 - Harder Permutations

20 minutes

• Lesson 5 Overview
• Mixing Permutations and Combinations
• Arranging some items in a line with some identical
• Ascending/ Alphabetical order
• Combinatorics 5 Quiz

Combinatorics Lesson 6 - Probability

20 minutes

• Lesson 6 Overview
• Probability Theory
• Probability with Combinatorics
• Combinatorics 6 Quiz

Combinatorics Lesson 7 - Pigeonhole Principle

30 minutes

• Lesson 7 Overview
• Pigeonhole Principle
• Pigeonhole Principle – Generalised Form
• Combinatorics 7 Quiz

Combinatorics Lesson 8 - Binomial Expansion and Pascal's Triangle

30 minutes

• Lesson 8 Overview
• Binomial Expansions for small numbers
• Pascal’s Triangle
• Patterns in Pascal’s Triangle
• Relationships in Pascal’s Triangle
• Binomial Theorem
• Combinatorics 8 Quiz

Combinatorics 9 (Optional): Beyond the Syllabus

35 minutes

• Lesson 9 Overview
• Numbering Faces on 3D solids
• Negative Conditions
• Derangements
• Paths on a grid
• Triangles formed between points
• Diagonals of a convex polygon
• Probability that an event first occurs on the kth trial
• Miscellaneous

Graphical Relationships

5 minutes

• Introduction to Graphical Relationships
• Vertical versus Horizontal Changes
• Syllabus

Graphical Relationships 1: Reciprocal Functions

15 minutes

• Lesson 1 Overview
• Reciprocal of a Function
• Graphical Relationships 1 Quiz

Graphical Relationships 2: Square Roots of Functions

15 minutes

• Lesson 2 Overview
• Square Roots of a Function
• Y Squared Equals a Function
• Graphical Relationships 2 Quiz

Graphical Relationships 3: Absolute Values of Functions

10 minutes

• Lesson 3 Overview
• Absolute Value of a Function
• Function of the Absolute Value of x
• Graphical Relationships 3 Quiz

Graphical Relationships 4: Sums and Products of Functions

30 minutes

• Lesson 4 Overview
• Addition of Ordinates
• Multiplication of Ordinates
• Graphical Relationships 4 Quiz

Graphical Relationships 5 (Optional): Beyond the Syllabus

15 minutes

• Lesson 5 Overview
• Square of a Function
• Function of a Square
• Cube of a Function
• Higher Powers of a Function


1 minute

• Conclusion to Part I

User Rating


Latest Reviews

Please note the feedback listed here is unfiltered, and includes all comments and ratings collected.

Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard

very relevant and definitely use in class

Mathematics Extension 1 Year 11: In Depth Part I - Combinatorics & Graphical Relationships - Steve Howard

The content was very relevant and very well structured. I really enjoyed the course. Thanks.

About the team

Steve Howard


Steve is a Mathematics Teacher at Cowra High School, a medium sized rural high school in Central West NSW, where he has taught for 25 years. He has also taught gifted and talented students online through xsel and Aurora College. He has a particular love and passion for Mathematics Extension 2, writing his own textbook and study resources for the old syllabus, to be updated for the new syllabus. He also creates study resources for Mathematics and Extension 1. He loves finding more efficient techniques for solving mathematical questions, by trawling through other teachers' solutions or making up his own approaches when there must be a better way. Steve did 4 Unit Mathematics as a student, gaining a mark of 198/200 and training as an actuary. Working in an office in the city wasn’t for him, so he went back to uni to retrain as a teacher then headed to the country, where he lives in an owner built mud house, with chickens, goats and rescued native birds (which you will sometimes hear in his recordings)!!