2025 HSC Mathematics Extension 1
Question 7:
Differential equation
A slope field is shown in the examination paper. Which of the following could be the differential equation represented by the slope field?
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
- Along each vertical line the field shows the same gradient, so depends only on .
- The gradients are zero at , positive on both sides and symmetric about the y-axis.
- That matches , so option A is correct.
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
Solve given .
Question 2
Solve with .
Question 3
Solve with and .