2023 HSC Mathematics Extension 1
Question 1:
Rates of change
The temperature C of an object at time seconds is modelled using Newton's Law of Cooling,
What is the initial temperature of the object?
How to recognise this question
Question type: rates motion
- The command and notation point to rates motion.
- The requested response is a multiple choice.
How to handle it: write the geometric constraint, differentiate every changing quantity with respect to time, then substitute.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Initial temperature means : substitute into the model.
- .
- Ambient temperature is the limiting value as ; the excess is the initial temperature above ambient, so .
- Option A is the decay constant; B is only the excess; C is ambient only.
- Answer: D. (NESA multiple-choice key: D.)
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
If , what is the initial temperature of the object?
Question 2
For , the temperature the object approaches as is
Question 3
For , find .