BC-only material. Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions. Prerequisites (Topics 4.2, 8.2, 9.3, 9.4 and 9.5) are on the Calculus BC roadmap.
Understanding
- I can explain the difference between velocity (a vector) and speed (a number), and between displacement (a vector) and distance (a number). (Guide: “The motion toolkit”)
- I can explain why total distance is never less than the length of the displacement. (Guide: “Integrals: displacement, position and distance”; Practice Q6(d))
- I can explain why a particle is at rest only when both velocity components are zero at the same time. (Guide: “Derivatives: velocity, speed and direction”; Practice Q5(d))
Skills
- I can find the velocity vector, acceleration vector and speed from a position function. (Guide: Worked example 1; Practice Q1, Q2, Q5(a)–(b))
- I can use a sign table for x′ and y′ to describe the direction of motion on each interval. (Guide: Worked example 1; Practice Q3, Q5(c))
- I can find a position at a later time by adding the integral of velocity to the starting position. (Guide: Worked example 2; Practice Q6(a))
- I can find the displacement vector and its length over a time interval. (Practice Q4, Q6(d), Q7(d))
- I can find total distance travelled as the integral of speed, exactly when possible and with a calculator otherwise. (Guide: “An exact example”, Worked example 2; Practice Q4, Q6(c), Q7(c))
- I can find the greatest value of a coordinate using where its rate changes sign and the endpoint values. (Practice Q7(a))
Reasoning
- I can decide whether the speed is increasing or decreasing at a given time and justify it with the sign of x′x″ + y′y″ or the derivative of speed. (Guide: “Is the speed increasing or decreasing?”; Practice Q5(b), Q7(b))
- I can choose between a derivative and an integral for each part of a motion problem. (Guide: “Choosing the right tool”; Practice Q7)
- I can give answers with correct units and avoid the common traps (adding components, forgetting the starting position, degree mode). (Guide: Common misconceptions)
All ticked? Move on to Topic 9.7, Defining Polar Coordinates and Differentiating in Polar Form, or return to the Calculus BC roadmap.