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 why the area under a constant-rate graph equals the change in the quantity, using rate × time. (Guide: “Starting simple”; Revision notes self-check 1)
- I can explain why the area under any rate graph gives the accumulated change over an interval. (Guide: “Rates that change smoothly”)
- I can explain why an area below the axis counts as a decrease. (Guide: “The sign of an accumulated change”; Practice Q3)
- I can tell apart the height of a rate graph, an area under it and the amount of the quantity. (Guide: Worked example 3; Practice Q4)
Skills
- I can state the units of an area under a rate graph as rate units × input units. (Guide: units table; Practice Q1)
- I can split a region into rectangles, triangles, trapezoids and parts of circles to find its area. (Guide: Worked examples 1 and 2; Practice Q2, Q5, Q7(a))
- I can find a net change as area above minus area below, and a total change (such as distance) as area above plus area below. (Guide: Worked example 2; Practice Q6, Q7(b))
- I can find the amount at the end of an interval from a starting amount and the accumulated change. (Guide: Worked example 1(d); Practice Q3, Q5(c), Q6(d))
Reasoning
- I can write an interpretation that names what accumulated, the interval, the size and direction, and the units. (Guide: Worked example 3; Practice Q5(b), Q6(d))
- I can explain where a quantity is greatest from where its rate changes sign. (Guide: Worked example 1 check; Practice Q5(d), Q7(d))
- I can set up an equation using areas to find when an accumulated change reaches a given value. (Practice Q7(c))
All ticked? Move on to Topic 6.2, Approximating Areas with Riemann Sums, or return to the Calculus AB roadmap or the Calculus BC roadmap.