- Mathematics Advanced
- 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.
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.
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.
This learning program is made up of the following 5 topics, broken down into 26 concepts.
Integrating the expression for the rate to obtain an expression for quantity
Using the definite integral to find net change
Finding the rate of change of a quantity expressed as a function of time
Use the equation for natural growth and decay to find unknown quantities
The first-order differential equation for natural growth and decay
Verify the explicit solution of the first-order differential equation using differentiation
Use given information to produce a model for natural growth and decay
The first-order differential equation for modified natural growth and decay with a finite non-zero quantity limit
Use given information to produce a model for modified natural growth and decay
Use the equation for modified natural growth and decay to find unknown quantities
Verify the explicit solution of the first-order differential equation for modified natural growth and decay using differentiation
Finding when a particle changes direction
Finding the velocity-time equation using integration
Describing the behaviour of a particle by analysing the equations of motion
Finding the acceleration-time equation using differentiation
Solve motion problems involving the velocity-time equation
Solve motion problems involving the acceleration-time equations
Average velocity and average speed using the displacement-time equation
Using the definite integral to find net changes in displacement
Finding the displacement-time equation using integration
Displacement-time equation
Finding the velocity-time equation using differentiation
Solve problems requiring techniques of rectillinear motion
Convert a velocity-displacement equation to an acceleration-displacement equation
Convert a velocity-displacement equation to a displacement-time equation
Convert an acceleration-displacement equation to a velocity-displacement equation
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