2021 HSC Mathematics Extension 1
Question 4:
Differential equation
Consider the differential equation .
Which of the following equations best represents this relationship between and ?
How to recognise this question
Question type: differential equations
- The command and notation point to differential equations.
- The requested response is a multiple choice.
How to handle it: separate or integrate the differential equation, include the constant, then use the initial condition.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Separate variables: (for ).
- Integrate: , so with .
- Option B halves only the term; C and D do not arise from separation of this DE.
- Answer: A. (NESA multiple-choice key: A.)
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 1 total mark for this group. Where the official marking guide provides useful partial-credit criteria, those criteria are stated in the steps above.
Try your hand at it again by answering these questions
Question 1
Which equation best represents solutions of (for )?
Question 2
Which equation best represents solutions of ?
Question 3
The family of curves satisfying is best written as