Exam-style question
Try this first
When solving a separable first-order differential equation, what is the correct sequence?.
- A.Separate the variables, integrate both sides, then use any condition to find the constant.
- B.Differentiate both sides twice before separating variables.
- C.Cancel variables without checking for common factors.
- D.State the answer without considering the arbitrary constant.
Model answer
What a good answer should say
- The correct answer is Separate the variables, integrate both sides, then use any condition to find the constant.
- This is the best choice because it names the A-level method being tested and explains the mathematical check needed for this objective.
This answer is tied to the objective: H7 Evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions, where separation of variables may require factorisation involving a common factor..
Explanation
Why this works
Use the explanation to connect the worked answer back to H7 Evaluate the analytical solution of simple first order differential equations with separable variables, including finding particular solutions, where separation of variables may require factorisation involving a common factor..
Separate the variables, integrate both sides, then use any condition to find the constant. is correct.
It is specific to the learning objective, keeps the method visible, and avoids the generic shortcut described by the distractors.
Maths method check
- Topic focus: Pure Mathematics.
- Question style: practice.
- Reasoning demand: application.
- Check the operation, notation, units, and final answer form against the question before moving on.
Common mistake
No common mistake is linked to this question yet.