• Year 12

# Applications of Calculus to the Physical World

approx. 14 hrs

5 topics

26 concepts

Gain proficiency in the Applications of Calculus to the Physical World for success in the HSC and further university study.

Available in
NSW

### Overview

This program covers the components of  Applications of Calculus to the Physical World in Year 12 Mathematics Advanced, as specified in the NSW Mathematics syllabus.  We help students understand rates of change of a particle in motion and its application to problems of exponential growth and decay.

### Topics & Concepts We Cover

This learning program is made up of the following 5 topics, broken down into 26 concepts.

• #### Rates of Change 3 concepts

1. Integrating the expression for the rate to obtain an expression for quantity

2. Using the definite integral to find net change

3. Finding the rate of change of a quantity expressed as a function of time

• #### Exponential Growth and Decay 4 concepts

1. The first-order differential equation for natural growth and decay

2. Verify the explicit solution of the first-order differential equation using differentiation

3. Use the equation for natural growth and decay to find unknown quantities

4. Use given information to produce a model for natural growth and decay

• #### Modified Growth and Decay 4 concepts

1. The first-order differential equation for modified natural growth and decay with a finite non-zero quantity limit

2. Use the equation for modified natural growth and decay to find unknown quantities

3. Use given information to produce a model for modified natural growth and decay

4. Verify the explicit solution of the first-order differential equation for modified natural growth and decay using differentiation

• #### Motion 11 concepts

1. Finding the velocity-time equation using integration

2. Describing the behaviour of a particle by analysing the equations of motion

3. Finding when a particle changes direction

4. Solve motion problems involving the acceleration-time equations

5. Finding the acceleration-time equation using differentiation

6. Solve motion problems involving the velocity-time equation

7. Displacement-time equation

8. Finding the displacement-time equation using integration

9. Average velocity and average speed using the displacement-time equation

10. Using the definite integral to find net changes in displacement

11. Finding the velocity-time equation using differentiation

• #### Rectilinear Motion 4 concepts

1. Convert an acceleration-displacement equation to a velocity-displacement equation

2. Convert a velocity-displacement equation to a displacement-time equation

3. Convert a velocity-displacement equation to an acceleration-displacement equation

4. Solve problems requiring techniques of rectillinear motion

### 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 Applications of Calculus to the Physical World

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

We'll be in contact to match you with one of our top tutors and book your first session

Starting at

\$49(inc. GST)

per session

Fully flexible

PAYG and bundle plans

Use anytime