Homepage

Course Index

Build a Quiz

Subscriptions

Courses

NSW Y11 Maths Standard NSW Y11 Maths Advanced NSW Y11 Maths Extension 1

Topics

Functions Polynomials Inverse Trig Functions and Identities Rates of Change Permutations and Combinations

NSW Y11 Maths - Extension 1 Permutations and Combinations Pascals Triangle

Resources for Pascals Triangle

  • Questions

    24

    With Worked Solution
    Click Here
  • Video Tutorials

    1


    Click Here

Pascals Triangle Theory

NSW Syllabus Reference

NSW Syllabus Reference: ME-A1.2: The binomial expansion and Pascal’s triangle. This will require student to 

  • expand \((𝑥 +𝑦)^𝑛\) for small positive integers \(𝑛\) (ACMMM046)
  • derive and use simple identities associated with Pascal’s triangle (ACMSM009)

Ref: https://educationstandards.nsw.edu.au/

Create account

I am..

Please enter your details

I agree with your terms of service




Videos

Videos relating to Pascals Triangle.

  • Pascals Triangle - Video - Binomial Theorem Expansion, Pascal's Triangle, Finding Terms & Coefficients, Combinations

    You must be logged in to access this resource

Plans & Pricing

With all subscriptions, you will receive the below benefits and unlock all answers and fully worked solutions.

  • Teachers Tutors
    Features
    Free
    Pro
    All Content
    All courses, all topics
     
    Questions
     
    Answers
     
    Worked Solutions
    System
    Your own personal portal
     
    Quizbuilder
     
    Class Results
     
    Student Results
    Exam Revision
    Revision by Topic
     
    Practise Exams
     
    Answers
     
    Worked Solutions
  • Awesome Students
    Features
    Free
    Pro
    Content
    Any course, any topic
     
    Questions
     
    Answers
     
    Worked Solutions
    System
    Your own personal portal
     
    Basic Results
     
    Analytics
     
    Study Recommendations
    Exam Revision
    Revision by Topic
     
    Practise Exams
     
    Answers
     
    Worked Solutions

Theory

The rules for creating Pascal’s triangle:

  • The outer coefficients are unity
  • The inner coefficients come from the addition of the two adjacent numbers immediately above.
  • Each row has an extra number from the row above.

For example:

\[\begin{array}{*{20}{r}}{}&{}&{}&{}&1&{}&{}&{}&{}\\{}&{}&1&{}&2&{}&1&{}&{}\\{}&1&{}&3&{}&3&{}&1&{}\\1&{}&4&{}&6&{}&4&{}&1\end{array}\]

In the expanded form: \({\left( {1 + x} \right)^4} = 1 + 4x + 6{x^2} + 4{x^3} + {x^4}\)