HUNTERTUTORING
← AP
Get startedBook tutoring

Common Mistakes

Open PDF

Frequent Errors

1. Claiming a function is linear after checking AROC on only one interval. 2. Expecting consecutive quadratic AROCs to form a pattern when $\Delta x$ lengths differ. 3. Confusing "AROC = 0" with "change in AROC = 0." 4. Averaging consecutive AROCs incorrectly instead of listing them in order. 5. Forgetting that linear AROC equals slope $m$ on every interval. 6. Saying quadratic AROCs are constant (they are not; their first differences are). 7. Mixing up which quantity is input when building equal-length intervals from a table. 8. Treating secant slope as an instantaneous rate.

Why These Happen

1.3 adds a second layer (how rates change) on top of 1.2. Students often stop after one AROC. Tables with uneven spacing break the "linear pattern of AROCs" story, so students invent patterns that are not there.

How to Fix Them

  • Always compute AROC on at least two intervals before claiming constant rate.
  • Label interval lengths; only compare the quadratic consecutive-AROC pattern when lengths match.
  • Write two sentences: (1) the AROCs are ___; (2) the AROCs are changing by ___.
  • For linear $f(x)=mx+b$, predict AROC $=m$ before calculating.

Avoidance Scripts

  • "One interval is a value; two or more intervals is a pattern."
  • "Equal $\Delta x$ first, then list consecutive AROCs."
  • "Linear: rates stay put. Quadratic: rates drift by a constant."

Quick Self-Check

  • Did I use equal-length intervals for the quadratic claim?
  • Is my linear conclusion based on more than one interval?
  • Did I distinguish AROC from change-in-AROC?

For your personal study only. Copying, printing, screenshotting, or sharing this material is not permitted and may result in loss of access.

Back to 1.3