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← 2025 HSC Extension 1 paper Question 6

Variation 1 · answer guide

Inverse trigonometric functions — An inverse-cosine graph

Question

Sketch , stating its domain, range and three key points.

  1. Domain , range , decreasing
  2. Domain , range , decreasing
  3. Domain , range , increasing
  4. Domain , range , increasing

This practice question was inspired by Question 6 in the 2025 NSW HSC Mathematics Extension 1 examination, © NESA. It is an original TestMum variation that practises the same mathematical idea, not an official NESA question.

Step by step

  1. Set up the solution: use the restricted domain and range that make the inverse function single-valued. gives .
  2. Simplify the previous line carefully, keeping exact values where possible.The range of is .
  3. Finish the calculation, then check that the result meets the question’s conditions.Evaluate at and join with a decreasing curve.
  4. Match the result to the choices and state the correct option.Therefore option A is correct: Domain , range ; points .

Common mistake: changing so many features that the new example no longer tests the same mathematical idea.

Verification: Applying cosine to each y-value returns at all three key points.

Any mark labels are a TestMum study aid, not an official NESA marking allocation.

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