Common Mistakes
Calculus BC · AP · Differential Equations
Focus
Finding General Solutions Using Separation of Variables
This topic is assessed on the AP Exam.
Frequent mistakes
### 1. +C before initial condition
What it looks/sounds like: Initial condition is applied before finding +C.
Why it happens: Particular solution is jumped to incorrectly.
How to fix: Find general solution +C, then substitute the initial point.
### 2. Slope field inconsistency
What it looks/sounds like: Solution curve crosses segments with wrong slope sign.
Why it happens: Sketch is not checked against dy/dx.
How to fix: Follow slope segments locally from the initial point.
### 3. Correct work, wrong question
What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.
Why it happens: Attention locks onto the first operation instead of the final ask.
How to fix: Underline the final question; after solving, verify the boxed answer matches it.
### 4. Notation and justification gaps
What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.
Why it happens: Notation is treated as decoration rather than part of the score.
How to fix: Add one justification phrase per major step (definition, theorem, or rule).
How to avoid them
1. Verify separability before separating variables. 2. Substitute back to check a proposed solution. 3. Interpret parameters in growth/logistic models.
Quick self-check
- [ ] Can solve a separable DE with IC
- [ ] Can read a slope field
- [ ] Can verify a solution by substitution