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 explain what a related rates problem asks: one rate found from other known rates at the same instant. (Guide: “From technique to problem solving”)
- I can decide which lengths in a situation are constants and which are variables, and label a diagram that way. (Guide: Figure 1; Practice Q6(a))
- I can explain why a related rate usually changes from moment to moment, using the shape of the container or the geometry. (Guide: Worked example 2(b); Practice Q4, Q7(c))
Skills
- I can use Pythagoras to link distances and find a missing side at the instant before substituting. (Guide: Worked example 1(a); Practice Q1, Q6)
- I can use tan θ to find the rate of change of an angle, including the sec²θ factor. (Guide: Worked example 1(b); Practice Q3)
- I can use similar triangles to remove a variable whose rate is unknown, in a cone, a trough or a shadow problem. (Guide: Worked example 2; Practice Q2, Q5, Q7)
- I can combine an inflow and an outflow into a net rate of change of volume. (Practice Q7(b))
- I can give each rate with correct units and the correct sign for an increasing or decreasing quantity. (Guide: “A six-step method”; Practice Q6(b))
Reasoning
- I can write a full interpretation: which quantity, direction, size with units, and the instant. (Guide: “Interpreting the answer”; Practice Q6(c))
- I can tell the rate of change of a length apart from the speed of a moving point, such as a shadow’s length versus its tip. (Practice Q5(d))
- I can judge whether an answer is reasonable, and say when a model stops being realistic. (Guide: Worked example 1 check; Practice Q6(d))
All ticked? Move on to Topic 4.6, Approximating Values of a Function Using Local Linearity and Linearization, or return to the Calculus AB roadmap or the Calculus BC roadmap.