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Common Mistakes

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Frequent Errors

1. Saying "moving up" when x(t) increases (confusing x with y) (4.3.A.1). 2. Reversing right/left or up/down sign rules (4.3.A.1). 3. Assuming constant direction for all t on a curve (4.3.A.2). 4. Treating different parametrizations as different curves always (4.3.A.3). 5. Computing secant slope as Delta t / Delta x (4.3.A.4). 6. Dividing by zero when average ROC of x is 0 (4.3.A.4). 7. Using position at one t as direction for whole interval. 8. Unsupported direction claims without table evidence (3.C).

Why These Happen

Students merge x/y direction language or reuse single-variable slope habits.

How to Fix Them

  • Two columns: Delta x --> right/left; Delta y --> up/down.
  • Always write [t1, t2] before rates.
  • Quote table values when justifying (3.C).

Avoidance Scripts

  • "x controls left/right; y controls up/down."
  • "Average rate first, ratio second."
  • "Same curve can, different t-order can."

Quick Self-Check

  • Did I separate horizontal and vertical direction?
  • Did I check avg ROC x before forming slope ratio?
  • Did I support the conclusion with numbers?

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