2020 HSC Mathematics Extension 1
Question 11(e):
Differential equation
Solve , finding as a function of .
How to recognise this question
Question type: differential equations
- The command and notation point to differential equations.
- The requested response is a worked solution.
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
- Invert: .
- Integrate with respect to : .
- So .
- NESA: 2 marks correct; 1 mark for rewriting as .
Common mistake: choosing a familiar formula before checking that its conditions, signs, interval and units match this question.
The paper records 2 total marks 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
Solve , expressing in terms of .
Question 2
Solve , finding as a function of .
Question 3
Solve with , giving in terms of .