Work through the list without notes. Use a calculator only where a statement says so. 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 why ∫ (a to b) v(t) dt equals x(b) − x(a), using the Fundamental Theorem. (Guide: “Displacement: the integral of velocity”)
- I can explain why an integral of velocity needs a starting position before it gives a position. (Guide: Figure 1; Practice Q2)
- I can explain the difference between displacement and total distance, and say when they are equal. (Guide: “Total distance: the integral of speed”; Practice Q4)
- I can give the units of ∫ v dt and ∫ a dt from the units of v, a and t. (Guide: “Units” in “Displacement: the integral of velocity”)
Calculation
- I can find v(b) from v(a) and a(t), and x(b) from x(a) and v(t). (Guide: Worked example 1; Practice Q2, Q3)
- I can find total distance by hand, splitting at the times where v changes sign. (Guide: Worked example 1(c); Practice Q1, Q7(d))
- I can read positions, displacement and distance from a velocity graph using signed areas. (Guide: Worked example 2; Practice Q5)
- I can use a graphing calculator to find a position, a total distance with ∫ |v|, and the zeros of v, to three decimal places. (Guide: Worked example 3; Practice Q6)
- I can find average velocity and average speed over an interval. (Guide: Worked examples 1 and 2; Practice Q5(d))
Reasoning
- I can find the leftmost or rightmost position by comparing positions at the end points and at direction changes. (Guide: Worked examples 2(c) and 3(c); Practice Q5(c), Q6(d))
- I can justify a direction change by a sign change in v, not by a = 0 or v = 0 alone. (Practice Q6(a))
- I can compare two moving objects by writing each position as a starting value plus an integral. (Practice Q7)
All ticked? Move on to Topic 8.3, Using Accumulation Functions and Definite Integrals in Applied Contexts, or return to the Calculus AB roadmap or the Calculus BC roadmap.