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Unit 4
· Topic 3
Topic 3: Rates of change and differential equations
Rates of change
3 hours
Use implicit differentiation to determine the gradient of curves whose equations are given in implicit form.
1 interactive
Model and solve related rates problems as instances of the chain rule including situations that involve surface area and volume of cones, pyramids and spheres, with and without technology.
1 interactive
Differential equations
8 hours
Determine general and particular solutions of first-order differential equations of the form dy/dx = f(x), differential equations of the form dy/dx = g(y) and differential equations of the form dy/dx = f(x)g(y) using separation of variables.
Understand and use slope (direction or gradient) fields of a first-order differential equation.
1 interactive
Model and solve problems using provided differential equations, including the logistic equation, Newton’s law of cooling and radioactive decay, with and without technology.
1 interactive