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 what one segment of a slope field represents, and why it is a piece of a tangent line and not the solution itself. (Guide: “What a slope field shows”)
- I can explain why a slope field can be drawn without solving the differential equation. (Guide: “What a slope field shows”; Revision notes)
- I can say what identical columns, identical rows and horizontal segments tell me about dy/dx. (Guide: “Patterns that let you read a field quickly”; Practice Q2)
Skills
- I can find the slope of the segment at a given point, substituting x and y in the right places. (Guide: Worked example 1; Practice Q1)
- I can sketch a slope field at a given grid of points from a table, with short, centred segments and consistent steepness. (Guide: “How to sketch a slope field by hand”; Practice Q5(a))
- I can sketch a slope field for an equation written with other variables, such as dH/dt, and label the axes correctly. (Practice Q6(a))
- I can find every line or curve where the segments are horizontal by solving dy/dx = 0. (Guide: “Patterns”; Practice Q4, Q5(c))
Reasoning
- I can match an equation to a slope field by checking structure, then zero slopes, then the sign at a test point. (Guide: Worked example 2; Practice Q3)
- I can use the signs of factors to say where segments rise and where they fall. (Guide: Worked example 1 “Check by signs”; Practice Q5(d), Q7)
- I can interpret horizontal and steep segments in a real context, with units. (Practice Q6(c), Q6(d))
- I can trace a rough solution curve through a point by following the segments. (Guide: “A first look at solution curves”)
All ticked? Move on to Topic 7.4, Reasoning Using Slope Fields, or return to the Calculus AB roadmap or the Calculus BC roadmap.