Five Calculus Mistakes ECAT Students Repeat

Under time pressure, ECAT calculus punishes rushed setup far more than it rewards flashy shortcuts. The same handful of mistakes show up in mock after mock.

1. Confusing the chain and product rules

When two operations stack, students reach for the wrong rule on autopilot. Slow down for two seconds and name the structure before you differentiate.

2. Mishandling limits at discontinuities

A limit is not simply the value you plug in. Check the behavior from both sides before committing to an answer.

3. Integrating without checking bounds

• Always re-read the limits of integration before evaluating.
• Sketch the region for area and volume problems.
• Verify units and sign on the final line.

After every wrong question, write one sentence on why the trap worked. Repeat that type the next day until it feels boring.

4. Dropping constants of integration

In multi-step problems, a lost constant compounds into a wrong final answer. Carry it explicitly.

5. Skipping the sanity check

Ten seconds estimating whether an answer is even plausible catches more errors than any single technique.