• Mathematics Advanced
  • Year 10

Polynomials

approx. 8 hrs

7 topics

22 concepts

Gain proficiency when working with polynomials.

Available in
ACT NSW NT QLD SA TAS VIC WA

Overview

The principal focus of polynomials is to explore the behaviour of polynomials algebraically and graphically. Students will investigate the concept of a polynomial and apply the remainder and factor theorems to solve problems. Students will learn to apply an understanding of polynomials to sketch a range of curves and describe the features of these curves from their equation.

Topics & Concepts We Cover

This learning program is made up of the following 7 topics, broken down into 22 concepts.

  • Logarithmic Laws 7 concepts

    1. Log of a product

    2. Log of a quotient

    3. Log of a power

    4. Log of a reciprocal

    5. Log of a base

    6. Log of 1

    7. Simplify expressions using the laws of logarithms

  • Solving Exponential Equations 2 concepts

    1. Solving exponential equations by taking the logarithm of both sides.

    2. Solving exponential equations by equating the power

  • Relationship between Exponentials and Logarithms 4 concepts

    1. Converting logarithmic form to exponential form

    2. Converting exponential form to logarithmic form

    3. Solve simple equations that involve logarithms

    4. Draw and compare the graphs of the inverse functions y=a^x and y=logax

  • Remainder and Factor Theorem 2 concepts

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

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

  • Sketch 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

  • Simplify Linear Expressions uing Polynomials 3 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

  • Identify Polynomials 2 concepts

    1. Use the notation P(x) for polynomials and P(c) to indicate the value of P(x) for x=c

    2. 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

Reporting

  • 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?

Simply pick a time that works for you

Add your payment details securely online

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

Not sure if this program is right for you?

Ask us, we'll help you find the right program.

Enquire now