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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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NSW Curriculum
NSW Education Standards Authority

11–12Mathematics Extension 1 11–12 Syllabus

Record of changes
Implementation from 2026
Expand for detailed implementation advice

Content

Year 11

The binomial theorem
  • 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

  • ME1-11-05

    uses the binomial theorem to solve problems and prove identities

The binomial theorem
  • Recognise that a binomial is an expression with two terms, and that a binomial expansion is an expansion of a power of a binomial

  • Examine the symmetry formed by the coefficients of decreasing powers of x in the expansion of x+yn for n=0,1, 2,3,4,5 and arrange the coefficients into Pascal’s triangle
  • Recognise the equivalence between the coefficient of xn-ryr in the expansion of x+yn and nCr, when n is a positive integer
  • Use patterns and symmetry in Pascal’s triangle to confirm the identities nCr= n-1Cr-1+ n-1Cr for 1rn-1 and  nCr= nCn-r for 0rn
  • Derive the binomial theorem: x+yn= nC0xn+ nC1xn-1y+ nC2xn-2y2++ nCn-1xyn-1+nCnyn, when n is a positive integer
  • Apply the binomial theorem to expand and simplify expressions of the form x+yn
  • Use the binomial theorem to determine the coefficient of a term with a specific power or the constant term in a binomial expansion

  • Use the identities nC0=1, nCn=1, nCr= n-1Cr-1+ n-1Cr for 1rn-1 and nCr= nCn-r for 0rn to simplify expressions involving the binomial coefficients
  • Prove identities involving binomial coefficients in binomial expansions by substituting values, comparing coefficients or applying a combinatorial argument to a specified context

  • Apply given or proven identities involving binomial coefficients to prove further identities, without the use of calculus