Work through the list without notes or a calculator. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. This topic is shared by Calculus AB and Calculus BC.
Understanding
- I can say what a differential equation is and give an example that links a function, its input and its derivative. (Guide: “The big idea”)
- I can explain why the solution of a differential equation is a function, not a number. (Guide: “The big idea”)
- I can tell a first-order equation from a second-order one. (Guide: “The big idea”; Practice Q7(c))
- I can explain, using a graph, how a rate that depends on the quantity changes the steepness of the curve. (Guide: Figure 1)
Skills
- I can translate “proportional to”, “inversely proportional to”, “jointly proportional to” and “the difference between” into symbols. (Guide: “From words to symbols”; Practice Q1, Q2, Q5)
- I can build a “rate in minus rate out” model. (Guide: Worked example 2; Practice Q6)
- I can choose the sign of the rate from the wording and say which sign k has. (Guide: “Getting the sign right”; Practice Q2, Q7(a))
- I can find k from one given rate, and give its units. (Guide: Worked example 1; Practice Q3, Q5(b), Q7(b))
- I can use a differential equation to find the rate at a new value and interpret it with units. (Guide: Worked examples 1 and 2; Practice Q3, Q6(c))
Reasoning
- I can put a given differential equation into words. (Guide: Worked example 3; Practice Q4)
- I can find the value of the quantity at which the rate is zero, and say what that means in context. (Guide: Worked example 2; Practice Q6(d))
- I can explain in context why a rate is large or small at a given value. (Practice Q5(c), Q7(d))
All ticked? Move on to Topic 7.2, Verifying Solutions for Differential Equations, or return to the Calculus AB roadmap or the Calculus BC roadmap.