The tool below drills the method and its traps from your own notes.
WeSolve+ reads the whole document and writes the questions for you
Upload your PDF, photograph your notebook, or point the camera. WeSolve+ writes questions from that material, explains why each answer is right, reads the chapter back to you as a podcast, and remembers every item you missed until you own it.
The tool below is a small browser-only tool and it is not WeSolve+: paste a few lines and text rules turn them into cards on the spot. The real app, the one that uses AI, is behind the link above.
Unit 7 equations, from your own notes
This is a browser-only tool, and that is all it isIt splits the text you paste by rule, and nothing else. WeSolve+ is a different thing entirely: it reads your whole PDF with AI, writes the reasoning behind every question, speaks the chapter back to you, and remembers what you missed so it can return it. Try the real app now, free!
What you paste is what gets carded. Fixed rules split the text and nothing outside it is known, which makes the paste itself the real decision.
A slope field is the equation drawn, so read it before solving
Each dash shows the slope the equation assigns at that point, and matching questions are process of elimination: where is the slope zero, where positive, does it depend on x alone, y alone, or both. Check one row and one column and most wrong fields disqualify themselves. A solution curve simply follows the dashes it is born onto.
Verification is substitution, and no question in the unit costs less
To verify a proposed solution, differentiate it and substitute both the derivative and the function into the equation; equality of the two sides is the whole argument. Nothing needs solving. Students burn minutes solving anyway, which is why this question type exists: it rewards knowing what would count as evidence rather than reflexively computing.
Separation of variables is one method with a fixed ritual
Move every y next to dy and every x next to dx, integrate both sides, and write the constant the moment integration happens. Separation then finishes by solving for y where the algebra allows. The rubric awards the separation, the antiderivatives, the constant and the condition as separate points, so each step written plainly is money.
The constant is graded, and its timing is the trap
Plus C enters at integration, one constant absorbed to one side, and the initial condition pins it before any exponentiation. Exponentiating first turns addition into a multiplied constant, which is legal only when handled honestly. The reliable order: integrate, add C, apply the condition, then rearrange. Most unit 7 penalties are this paragraph ignored under time.
Exponential models are the unit's applied face
When a rate is proportional to the amount, dy dt equals k y, the solution family is exponential, y equals the initial amount times e to the k t. Population, decay and temperature difference prompts hand you the sentence in words and expect the translation, then a solved k from one data point. The phrase proportional to is the trigger.
What to photograph for Differential Equations
Your worked separations and field sketches. Related: Unit 5, photo to quiz and pricing.
Sources used on this page
- College Board, AP Calculus AB
- Differential equation
- Slope field
- Separation of variables
- Exponential growth
- Active recall
- Spaced repetition
- Testing effect
- Forgetting curve
- Generation effect
- Judgment of learning
- Metacognition
- Desirable difficulty
- Distributed practice
- Formative assessment
- Flashcard
- Cloze test
- Multiple choice
- Test (assessment)
- Educational assessment
- Advanced Placement
- Curriculum
- Study skills
- Study guide
- Note-taking
- Overlearning
- Instructional scaffolding
- Item analysis
- Mastery learning
| Step | What it looks like | Where the point dies |
|---|---|---|
| Separate | y terms with dy, x terms with dx | A term left on the wrong side |
| Integrate | Both sides, antiderivatives shown | Skipping straight to the answer |
| Constant | Plus C at integration time | C appearing after exponentiation |
| Condition | Initial point pins C | Solving for C before integrating |
| Solve for y | Exponentiate honestly | Sign and absolute value dropped |
| Domain | The piece through the condition | Reporting the whole formula's domain |
What does AP Calculus AB Unit 7 cover?
Differential equations: slope fields, verifying solutions, separation of variables and exponential growth and decay models.
How do I match a slope field to an equation?
Interrogate the dashes: where slope is zero, where positive, and whether it changes along rows, columns or both. Eliminate fields that contradict.
When does the constant of integration appear?
The moment you integrate, absorbed to one side. Applying the initial condition then pins it, before any exponentiation.
What does proportional growth mean?
The rate equals a constant times the amount, dy dt equals k y, and the solutions are exponentials through the initial value.
How do I verify a proposed solution without solving?
Differentiate it and substitute into the equation. If both sides agree, the verification is complete; no solving is required.
Can I build questions from my own Unit 7 notes?
Yes. Photograph the pages or upload the PDF and the questions stay inside this unit rather than sampling the whole course.
Last updated: 2026-08-15