• Mathematics Extension 1
• Year 12

# Applications of Calculus to the Physical World

approx. 22 hrs

8 topics

41 concepts

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

Available in
NSW

### Overview

This program covers the curriculum for Applications of Calculus to the Physical World in Year 12 Mathematics Extension 1, as determined by the NSW Mathematics syllabus.  We help students study rates of change of a particle in motion and its application to problems of exponential growth and decay. In addition, we work with students to translate between practical problems and their mathematical model in areas, including simple harmonic motion and projectile motion.

### Topics & Concepts We Cover

This learning program is made up of the following 8 topics, broken down into 41 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

• #### Related Rates of Change 2 concepts

1. Related rates of change requiring one use of the chain rule

2. Related rates of change requiring two uses of the chain rule

• #### 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

• #### Simple Harmonic Motion 5 concepts

1. Form a trigonometric equation of motion to model simple harmonic motion

2. Solving tides problems using techniques from simple harmonic motion

3. Use the equation of simple harmonic motion to find unknown quantities

4. Transform unfamiliar equations into the standard form for simple harmonic motion

5. Main features of the equation of simple harmonic motion

• #### Projectile Motion 8 concepts

1. Find the angle of inclination at any given time

2. Derive the time equations of projectile motion from the second-order differential equations of motion

3. Calculate expressions for displacement, velocity and acceleration of projectile motion in terms of time

4. Find the range of the projectile on the horizontal plane

5. Use the Cartesian equation of projectile motion to find unknown quantities

6. Find the highest point of the path of a projectile

7. Find the instantaneous velocity at any given time

8. Derive the Cartesian equation of projectile 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

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