Common Mistakes

Frequent Errors

1. Treating y = f(x) instead of position (x(t), y(t)) (4.2.A.1). 2. Finding vertical extrema from x(t) or horizontal from y(t) (4.2.A.2). 3. Using zeros of y(t) for y-intercepts instead of x(t) (4.2.A.3). 4. Using zeros of x(t) for x-intercepts instead of y(t) (4.2.A.3). 5. Forgetting to evaluate the other coordinate at intercept t. 6. Checking extrema only at integer t when max/min is between integers. 7. Omitting endpoint t-values on a closed domain. 8. Stating intercept as t instead of (x, y) point.

Why These Happen

Students reuse single-variable intercept/extrema habits without separating x and y components.

How to Fix Them

• Horizontal questions --> analyze x(t) only.
• Vertical questions --> analyze y(t) only.
• y-intercept --> solve x(t)=0; x-intercept --> solve y(t)=0.
• Always return a coordinate pair for intercepts.

Avoidance Scripts

• "Which component controls left/right? x(t)."
• "Which zero gives a y-intercept? x(t)=0."
• "Extrema on a closed interval: check endpoints too."

Quick Self-Check

• Did I analyze the correct component for the question?
• Did I solve the correct equation for intercepts?
• Did I give (x, y) points, not just t?