BlogLearnThe Ultimate Guide to QCAA Maths Methods Unit 3: Further Calculus

The Ultimate Guide to QCAA Maths Methods Unit 3: Further Calculus

Mathematical equations written in a notebook - QCE Maths Methods Unit 3

Begun working on Unit 3 of QCAA Maths Methods but aren’t sure what you’ll be covering? We’ve come up with a handy guide for you!

To simplify your learning, we’ve identified the key things you’ll be learning in each of the topics for Unit 3 of QCAA Maths Methods and the assessments you’ll have.

Ready to get started? Let’s go!

What is Unit 3 in QCAA Maths Methods all about?
Topic 1: The Logarithmic Function 2
Topic 2: Further Differentiation and Applications 2
Topic 3: Integrals
QCAA Maths Methods Unit 3 Assessments
Study Tips

What is Unit 3 in QCAA Maths Methods all about?

Unit 3 is the first of your two formative senior units for Mathematical Methods. This means that the assessments you do for this unit (IA1, 1A2 and EA) will count towards your ATAR. If that fact makes you worry, here’s how to make sure you’re in the right level for QCAA Maths or if you need to drop!

The unit is split into three topics:

  • The Logarithmic Function 2
  • Further Differentiation and Applications 2
  • Integrals

These topics cover a variety of content which involve building on previous topics as well as learning entirely new concepts. 

Topic 1

Topic 1 builds on your knowledge and application of logarithmic laws and indices laws, as well as your ability to interpret logarithmic scales. It also covers graphing logarithmic functions and understanding their features.

Developing a deep understanding of how changing each of the features of the logarithmic function can produce its translations is definitely helpful. Use Desmos to play around with the different factors of the log function and explore what happens as you change them.  

Topic 2

Topic 2 furthers your understanding of differentiation of exponential, logarithmic, and trigonometric functions through the application of a number of formulas to solve practical problems.

The key to this topic is understanding when and how to apply the appropriate formula to solve each problem. For this, it is important to be able to recall and apply each of the formulas quickly, which can best be achieved through good old practice.   

Topic 3

Topic 3 consists of a new concept: anti-differentiation. As the name suggests, anti-differentiation is the opposite of differentiation.

This means being confident with differentiation will be super helpful to getting the hang of anti-differentiation.

Similar to differentiation, knowing the formulas is key, and again, practice is the best way to get there. 

Topic 1: The Logarithmic Function 2

Logarithmic Laws and Logarithmic Functions

This subtopic covers: 

  • Understanding and effectively applying the logarithmic laws and indice laws 
  • Understanding and interpreting logarithmic scales such as decibels in acoustics and pH in chemistry 
  • Identifying contexts suitable for modelling by logarithmic functions 
  • Understanding the qualitative features of the graph y = loga(x)  (a > 1) and of its translations y = loga(x) + b and y = loga(x + c)

Indices Laws

Image sourced from OnlineMathLearning.com

Log laws

Logarithm graph

Image sourced from Jacaranda Maths Quest Mathematical Methods 12 Units 3 & 4

Still unsure what the best ATAR school is to study Maths Methods? We’ve done the research for you!

Topic 2: Further Differentiation and Applications 2

Calculus of Exponential Functions

This subtopic covers: 

  • Estimating the limit of
    Limit - QCE Maths Methods Unit 3
    using technology 
  • Understanding and applying the formula
    Applying formula - QCE Maths Methods Unit 3and
    Exponential functions - QCE Maths Methods Unit 3
  • Identifying contexts suitable for modelling by logarithmic functions and their derivatives 

Differential of an exponential

Image sourced from Jacaranda Maths Quest Mathematical Methods 12 Units 3 & 4

Calculus of Logarithmic Functions

This subtopic covers: 

  • Understanding the natural logarithm ln ln (x) = x
  • Understanding and utilising the inverse relationship of the functions:
    Inverse relationshipand
    Inverse relationships
  • Using logarithmic functions and their derivatives to solve practical problems 

Logarithm differentiation

Image sourced from Jacaranda Maths Quest Mathematical Methods 12 Units 3 & 4

Calculus of Trigonometric Functions

This subtopic covers: 

  • Understanding and applying the formulas
    Calculus of Trigonometric Functionsand
    Calculus of Trigonometric Functions
  • Identifying contexts suitable for modelling by trigonometric functions and their derivatives 
  • Using trigonometric functions and their derivatives to solve practical problems 

Trig functions

Image sourced from Jacaranda Maths Quest Mathematical Methods 12 Units 3 & 4

Special triangles

Image sourced from Educating MrMattock

Differentiation Rules

This subtopic covers: 

  • Appropriately utilising product rule, quotient rule, and chain rule to differentiate functions 

Differentiation rules

Image sourced from Maths Methods Formula Book

Topic 3: Integrals

 Anti-differentiation 

This subtopic covers: 

Anti-differentiation - QCE Maths Methods Unit 3

Anti Differentiation rules

Image sourced from Maths Methods Formula Book

Fundamental Theorem of Calculus and Definite Integrals 

This subtopic covers: 

Fundamental Theorem of Calculus and Definite Integrals

Example of an area positioned between two curves

Image sourced from The Story of Mathematics

Applications of Integration 

This subtopic covers: 

  • Calculating the area under a curve and the area between curves 
  • Calculating total change by integrating rate of change 
  • Calculating displacement given acceleration and initial values of displacement and velocity 

Applications of Integration

Image sourced from Jacaranda Maths Quest Mathematical Methods 12 Units 3 & 4

Jump over to our Maths Methods Unit 4 Summary Guide when you’re done!

QCAA Maths Methods Unit 3 Assessments

#1: IA1 – Problem solving and modelling task (PSMT)

It will assess your ability to respond to a mathematical investigative scenario and constitutes 20% of your overall grade. For a guide on how to structure your PSMT, see How to Structure Your PSMT Report for QCAA Mathematical Methods 

#2: IA2 – Internal examinations

It will assess your understanding and application of the concepts learnt in Unit 3. It constitutes 15% of your overall grade. 

#3: EA – External assessment

It is an exam that consists of both Unit 3 and 4 content and constitutes 50% of your overall grade. 

Find past papers for QCAA Maths Methods here!

Tips for Study 

#1: Manage your time well

The syllabus has a guide for how much time should be spent on each subtopic.

Although this guide is technically for teachers and their lesson planning, you as a student can also use it to help guide your study (i.e. to figure out what topics may be more important and therefore require more study time). 

QCEC Maths Methods Unit 3 - Syllabus

#2: Understand how formulas work

A deep understanding of how the different formulas function and how they can be applied is crucial to tackling complex familiar and complex unfamiliar questions.

With complex unfamiliar questions in particular, it may not immediately be evident which formulas/concepts should be applied. Therefore, having a strong understanding of each formula can help you determine the required approach for each question efficiently.

#3: Complete a range of practice question styles

If there’s a style of question you find yourself struggling with, then it’s the style of question you should be doing the most practice on. 

#4: Become familiar with the formula booklet

Know what formulas are in it so that you don’t have to bother memorising them. Also, it can be helpful to have a general idea of where each group of formulae (i.e. trigonometric, logarithmic) is contained within the booklet so that you don’t waste time searching for them during exams. 

Wondering how you measure up compared to your cohort? Give our QCE Cohort Comparison Tool a go to find out!

Also studying QCAA Physics Unit 3? Check out our Guide to Unit 3: Gravity and Electromagnetism here!

Should I drop a subject for my QCE?

Are you looking for some extra help with revising QCAA Maths Methods Unit 3?

We have compiled all of the relevant articles for Term 1 of Year 12 – check them out here!

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Yalindi Binduhewa is an Art of Smart tutor based in Queensland and was part of the very first cohort to go through the ATAR system, so she knows exactly how fun and enjoyable it can be. She is currently studying a Bachelor of Medical Imaging (Honours) at QUT and is loving it. When she’s not doing uni-related stuff or tutoring, she’s hanging out with her friends, rewatching a show for the 100th time, or trying out new crafty projects and discovering that she doesn’t have a talent for everything.

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