2020 HSC Mathematics Extension 1
Question 3:
Inverse trigonometric functions
Which of the following is an anti-derivative of ?
How to recognise this question
Question type: inverse trigonometric functions
- The command and notation point to inverse trigonometric functions.
- The requested response is a multiple choice.
How to handle it: use the restricted domain and range that make the inverse function single-valued.
Watch out: Do not select a formula until its domain, interval, sign and units match the question.
Step-by-step answer
- Rewrite .
- Use with .
- Then the antiderivative is .
- Differentiate to verify: .
- Answer: 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
Which of the following is an anti-derivative of ?
Question 2
Which of the following is an anti-derivative of ?
Question 3
Which of the following is an anti-derivative of ?