Common Mistakes

Frequent Errors

1. Average ROC computed as Delta theta / Delta r (3.15.A.4). 2. Assuming r increasing always means distance increases without sign check (3.15.A.1). 3. Ignoring negative r decreasing => distance increases rule (3.15.A.1). 4. Calling any corner an extremum without monotonicity change (3.15.A.3). 5. Confusing closest to origin with smallest theta value. 6. Estimating r far outside the avg-ROC interval without caution (3.15.A.5). 7. Describing "slope" in x-y terms instead of radius vs angle (3.A). 8. Unsupported distance claims without data (3.C).

Why These Happen

Polar rate language is new and overlaps with rectangular slope intuition.

How to Fix Them

• Always: sign of r, then increasing/decreasing, then distance rule.
• Compute ROC with labeled Delta r and Delta theta.
• Point to interval where monotonicity switches for extrema.

Avoidance Scripts

• "Delta r over Delta theta."
• "Distance uses |r| when r is negative."
• "Extremum needs a direction change in r."

Quick Self-Check

• Did I use Delta r / Delta theta?
• Did I apply the correct distance rule for sign/monotonicity?
• Did I support the claim with points or intervals?