Work through the list without notes. Use a calculator only where a statement mentions one. 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 region with a gap between itself and the axis produces ring-shaped cross sections. (Guide: “From discs to washers”; Practice Q6(a))
- I can explain why the area of a washer is π(R² − r²) and not π(R − r)². (Guide: Figure 1 and “The trap”; Practice Q4, Q7(c))
- I can describe the disc method as the washer method with r = 0. (Guide: “When does a washer become a disc?”)
Skills
- I can find R and r as distances from the axis, using a test point to decide which boundary is farther away. (Guide: “Finding R and r”; Practice Q1, Q5(b))
- I can write and evaluate a washer integral around the x-axis in terms of x. (Guide: Worked example 1; Practice Q1, Q7(a))
- I can rewrite curves as x in terms of y and write a washer integral around the y-axis with y-limits. (Guide: Worked example 2; Practice Q2, Q5, Q7(b))
- I can use a calculator to find intersection values, store them and evaluate a washer integral. (Guide: Worked example 3; Practice Q3, Q6(b))
- I can write a complete integral, with π, brackets, limits and dx or dy, before evaluating. (Guide: “The method, step by step”)
Reasoning
- I can round only the final answer to three decimal places and explain how early rounding changes it. (Guide: “Rounding on calculator questions”; Practice Q3, Q6(d))
- I can check a washer volume against a simpler shape, such as a cylinder or cone. (Guide: Worked example 1 check; Practice Q5(d))
- I can spot a negative or unreasonably small volume and trace it to a swapped or wrongly squared radius. (Practice Q1, Q4)
All ticked? Move on to Topic 8.12, Volume with Washer Method: Revolving Around Other Axes, or return to the Calculus AB roadmap or the Calculus BC roadmap.