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New draft syllabuses will be available for consultation from 24 February 2025 to 7 April 2025, as part of the NSW Curriculum Reform.

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11–12Mathematics Extension 1 11–12 Syllabus

Record of changes
Implementation from 2026
Expand for detailed implementation advice
OverviewRationaleAimOutcomesContentAssessmentGlossaryTeaching and learning support

Content

Year 11

Polynomials
  • MAO-WM-01

    develops understanding and fluency in mathematics through exploring and connecting mathematical concepts, choosing and applying mathematical techniques to solve problems, and communicating their thinking and reasoning coherently and clearly

  • ME1-11-02

    applies the remainder and factor theorem and sums and products of zeroes to solve problems involving polynomials

Polynomials
Language and graphs of polynomials
  • Define a polynomial function of degree , where is a non-negative integer, to be a function that can be expressed in the form , for real and
  • Define the leading term of to be the term of highest degree and define the leading coefficient of to be the coefficient of the leading term
  • Define the constant term of to be

  • Define a polynomial to be monic if its leading coefficient is 1

  • Define the zero polynomial to be to be the polynomial with all the coefficients equal to zero and recognise that the zero polynomial has no leading term, no leading coefficient, no degree and constant term 0

  • Determine the degree of when two non-zero polynomials and , of degrees and respectively, are added
  • Explain how the leading coefficient and the degree determine whether or as and as  
  • Define the zeroes of to be the numbers such that , and define the roots of the polynomial equation to be its solutions, and recognise that every real number is a zero of the zero polynomial

  • Define as a repeated zero or multiple zero of a non-zero polynomial when is a factor of , and as a single zero of when  is not a factor of , for  

  • Define as a zero of of multiplicity  if , where  is a positive integer and

  • State the multiplicity of each root of a polynomial equation given in factored form

  • Find the zeroes of a polynomial that is expressed as a product of linear factors, determine their multiplicity and graph the polynomial

Remainder and factor theorems

  • Examine the process of division of polynomials by comparing with the process of division with remainders for whole numbers, and use the terms dividend, divisor, quotient and remainder

  • Express in the form the result of dividing by a divisor , that is not the zero polynomial, with quotient and remainder , and explain why either or
  • Express the result of the division also in the form
  • Explain why division by yields , where is a constant, and why is a factor if and only if
  • Prove and apply the remainder theorem for polynomials: when is divided by , the remainder is , and solve related polynomial problems
  • Prove and apply the factor theorem for polynomials: if and only if is a factor of , and solve related polynomial problems
  • Use the factor theorem to find all factors of of the form , where is an integer, and use division to find the remaining factor of the polynomial
Sums and products of zeroes of polynomials
  • Prove that if a quadratic has zeroes and then , the sum of the zeroes, and , the product of the zeroes
  • Prove that if a cubic has three zeroes , , , then , and
  • Prove that if a quartic has four zeroes , , , then , , and

  • Use the formulas for the sums and products of zeroes to solve problems involving zeroes and coefficients of quadratic, cubic and quartic polynomials

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