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← 2020 HSC Extension 1 paper Question 10

Variation 2 · answer guide

Rates of change — Negative link from P to Q

Question

Suppose , , with . Then

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

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.As in the original, .
  2. Simplify the previous line carefully, keeping exact values where possible.Now .
  3. Finish the calculation, then check that the result meets the question’s conditions.So increases and 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: The minus sign before flips the sign of .

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

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