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← 2020 HSC Extension 1 paper Question 10

Variation 1 · answer guide

Rates of change — Flipped first sign

Question

Suppose , , with . Then

  1. decreasing and decreasing
  2. increasing and increasing
  3. decreasing and increasing
  4. increasing and decreasing

This practice question was inspired by Question 10 in the 2020 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: write the geometric constraint, differentiate every changing quantity with respect to time, then substitute..
  2. Simplify the previous line carefully, keeping exact values where possible., so decreases.
  3. Finish the calculation, then check that the result meets the question’s conditions., so decreases.
  4. Match the result to the choices and state the correct option.Therefore option A is correct.

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

Verification: Positive preserves the sign from to .

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

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