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Exam Strategy

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Readiness Check

  • Compute AROC and recognize when it is constant across intervals (linear).
  • For equal-length intervals on a quadratic, list consecutive AROCs and find the common difference.
  • State that linear AROCs change at rate 0; quadratic AROCs change at a constant rate.
  • Connect AROC to secant slope.

Before the Exam

1. Drill: same linear $f$, three different intervals, same AROC. 2. Drill: quadratic table with $\Delta x$ constant; compute 3+ consecutive AROCs; find common difference. 3. Practice "change in the average rates of change" wording from the CED. 4. Contrast a linear table vs quadratic table side by side.

During Multiple Choice

  • Check whether intervals are equal length before claiming the quadratic pattern.
  • Constant AROC across unequal lengths strongly suggests linear.
  • Consecutive AROCs in arithmetic progression (equal steps) suggests quadratic (among common models).

During Free Response

1. Show AROC computations for each requested interval. 2. Compare rates explicitly (equal? common difference?). 3. Conclude function-type behavior with CED language: constant AROC vs AROCs changing at a constant rate. 4. Mention secant slope when the stem asks for geometric meaning.

Common Traps

  • Comparing AROCs over intervals of different lengths and expecting a clean linear pattern for a quadratic.
  • Saying "rate of change is zero" when they mean "the AROCs are not changing."
  • Using only one interval and claiming linearity.

60-Second Checklist

  • Equal-length intervals when needed?
  • Multiple AROCs shown?
  • Linear vs quadratic conclusion justified?
  • Secant language if asked?

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