• Mathematical Methods
  • Year 12

Logarithmic and Exponential Functions

approx. 17 hrs

7 topics

43 concepts

Develop your skills in Logarithmic and Exponential Functions to approach your examinations with confidence.

Available in
ACT NT QLD SA TAS VIC WA

Overview

The Logarithmic and Exponential Functions program of learning covers the essential components of the Year 12 Mathematical Methods course and addresses learning outcomes from the Australian Curriculum. Students studying Year 12 Logarithmic and Exponential Functions apply mathematical techniques to solve fluency style questions based on logarithmic and exponential equations. They also connect ideas of calculus with algebraic, deductive and modelling skills to successfully solve more complex problems.

Topics & Concepts We Cover

This learning program is made up of the following 7 topics, broken down into 43 concepts.

  • Calculus and the Logarithmic Function 11 concepts

    1. Differentiate logarithmic functions with linear arguments

    2. Differentiate logarithmic functions involving the chain rule

    3. Differentiate logarithmic functions involving the product rule

    4. Differentiate logarithmic functions involving the quotient rule

    5. Application of the derivative of the logarithmic function

    6. Integrating functions in the form 1/(ax+b)

    7. Using the reverse chain rule to integrate functions in the form f'(x)/f(x)

    8. Finding the area of regions using techniques of integration involving the logarithmic function

    9. Finding the volume of solids of revolution using techniques of integration involving the logarithmic function

    10. Product rule of differentiation

    11. Quotient rule of differentiation

  • Calculus and the Exponential Function 12 concepts

    1. Differentiate exponential functions with linear arguments

    2. Differentiate exponential functions involving the chain rule

    3. Differentiate exponential functions involving the product rule

    4. Differentiate exponential functions involving the quotient rule

    5. Differentiate exponential functions with different bases

    6. Application of the derivative of the exponential function

    7. Integrating functions in the form e^(ax+b)

    8. Finding the anti-derivative of an exponential function by considering a derivative

    9. Finding the area of regions using techniques of integration involving the exponential function

    10. Finding the volume of solids of revolution using techniques of integration involving the exponential function

    11. Integrating exponential functions with different bases

    12. Reverse chain rule

  • Sketching Exponential and Logarithmic Functions 3 concepts

    1. Sketching curves involving the exponential function

    2. Sketching curves involving the logarithmic function

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

  • Exponential and Logarithmic Form 3 concepts

    1. Converting logarithmic form to exponential form

    2. Converting exponential form to logarithmic form

    3. Solve simple equations that involve logarithms

  • Laws of Logarithms 7 concepts

    1. Change of base formula

    2. Log of a product

    3. Log of a quotient

    4. Log of a power

    5. Log of a reciprocal

    6. Log of a base

    7. Log of 1

  • Equations and Logarithms 4 concepts

    1. Solving equations involving the logarithmic function

    2. Proving identities using the logarithmic laws

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

    4. Simplify expressions using the laws of logarithms

  • Solving Exponential Functions using Index Laws 3 concepts

    1. Fractional indices

    2. Simplify algebraic expressions by applying index laws

    3. Solving exponential equations by equating the power

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 Logarithmic and Exponential Functions

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

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Starting at

$49(inc. GST)

per session

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