Work through the list without notes. 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 adding (width × height) over thin strips approximates the area under a curve. (Guide: “The problem”)
- I can explain why a left sum is too small and a right sum too big for an increasing function, using a picture. (Guide: Figure 1; Practice Q3)
- I can explain why a trapezoidal sum is too big and a midpoint sum too small for a concave-up function. (Guide: Figure 2 and “Over or under?”; Practice Q3, Q5(c))
- I can say when a table does not give enough information to decide over or under. (Guide: “Two cautions”; Worked example 2)
Skills
- I can find left and right sums from a table with equal widths. (Guide: Worked example 1; Practice Q1)
- I can read heights from a graph only at points where the value is certain, and use facts stated in words. (Guide: Worked example 3; Practice Q3, Q5)
- I can use the correct width for each term when the subintervals are unequal. (Guide: Worked example 2; Practice Q2, Q6(a))
- I can find a midpoint sum from a formula, and from a table when the midpoints are given. (Guide: Worked example 1(d); Practice Q4, Q5(a))
- I can find a trapezoidal sum directly and check it with T = (L + R)/2. (Guide: “A useful link”; Practice Q2, Q5(b), Q6(b))
- I can write a sum in full before giving its value when technology does the arithmetic. (Guide: “Using technology”; Practice Q7(d))
Reasoning
- I can justify over or under in a sentence that names the property of f and links it to the sum. (Guide: “How to justify on paper”; Practice Q5(c), Q6(c))
- I can interpret a Riemann sum in context with units. (Guide: Worked example 2(a); Practice Q5(d))
- I can use Rₙ − Lₙ to decide how many subintervals give a required accuracy. (Practice Q7)
All ticked? Move on to Topic 6.3, Riemann Sums, Summation Notation, and Definite Integral Notation, or return to the Calculus AB roadmap or the Calculus BC roadmap.