• Mathematical Methods
  • Year 11


approx. 9 hrs

6 topics

18 concepts

Deepen your understanding of Polynomials to optimise your performance in Mathematics.

Available in


Year 11 Mathematical Methods gives students the essential skills associated with Polynomials as specified in the Senior Mathematics Australian curriculum. In this program, we help students build on their prior learning to develop algebraic skills to manipulate polynomials and find rational factors. Also, students will learn how to apply the rational-root theorem to find all possible rational roots. This enables them to fully factorise any given polynomial. In addition, we show students how to sketch polynomials using the rational factors.

Topics & Concepts We Cover

This learning program is made up of the following 6 topics, broken down into 18 concepts.

  • Rational-Root Theorem 2 concepts

    1. Apply the rational-root theorem to find rational factors of a given polynomial

    2. Factorise a polynomial using the factor theorem or the rational-root theorem

  • Roots and Coefficients of a Polynomial 2 concepts

    1. Root-coefficient relationships for quartic equations

    2. Root-coefficient relationships for cubic equations

  • Approximation Solutions of Equations 3 concepts

    1. Approximate solutions of equations through an iterative process

    2. Approximate solutions of equations by halving the interval

    3. Approximate solutions of equations using Newton's method

  • Remainder and Factor Theorem 5 concepts

    1. Equating coefficients of a polynomial

    2. Applications of the remainder or factor theorem

    3. Use given data to find the roots of a polynomial

    4. Verify the remainder theorem and use it to find factors

    5. Use the factor theorem and long division to find all zeroes of a polynomial

  • Sketching Polynomials 2 concepts

    1. Sketch polynomials with degree no more than four by using the leading term, the roots and the x- and y-intercepts

    2. Determine the effect of single, double and triple roots of a polynomial equation on the shape of the graph

  • Operations with Polynomials 4 concepts

    1. Add and subtract polynomials and multiply polynomials by linear expressions

    2. Division of polynomials

    3. State the degree of a polynomial after adding, subtracting, multiplying or dividing of one or more polynomials

    4. Identify a polynomial expression and describe the key features using appropriate terminology

What you'll get

Learning Content

  • A customised learning plan to suit your needs, adapting to your pace as you learn, progress and achieve mastery
  • All the content required to help you master the syllabus, including theory, worked examples, exam preparation and practice questions

An Expert Tutor

  • We match you to a private, expert tutor who is right for your needs and goals
  • Our tutors are talented, tested, top ATAR achievers and subject experts
  • During each session, your tutor guides you through your learning program, providing real-time, live expert tutoring in Polynomials


  • Access information at every stage showing what's been mastered, what areas need to be worked on and what's next
  • You and your parents receive a comprehensive feedback report after every session
  • Every session is recorded and available for you to watch at any time, allowing you to review what was covered

Ready to start this program?

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We'll book in your first session and match you to an expert tutor

Starting at

$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime

Access to practice questions

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