Question 1(b) Achieved

A chain-rule power, an oven cooling written in half-powers of t, a trig normal, a tangent to an exponential-plus-quadratic, and a parametric curve where inflection and stationary have to coincide.

The temperature of an oven is C = 60/√t + 5√t + 15, where 0 < t ≤ 12, C is the temperature in °C and t is the time in minutes after the oven has been switched off.

Find the rate of change of the temperature of the oven 4 minutes after the oven was switched off.

The 2025 paper, page 2 ↗ Marking schedule, page 1 ↗

Work it out

Try it on paper first. Stuck? Take one hint at a time.

1. 1 Before differentiating, how can you write each term as a power of t?

   C = 60t^−1/2 + 5t^1/2 + 15

2. 2 Differentiate term by term with the power rule.

   dC/dt = −30t^−3/2 + (5/2)t^−1/2. The constant 15 differentiates to zero.

3. 3 Now put t = 4 in. What are 4^−1/2 and 4^−3/2?

   4^1/2 = 2, so 4^−1/2 = 1/2 and 4^−3/2 = 1/8.
   dC/dt = −30/8 + 5/2 × 1/2 = −3.75 + 1.25 = −2.5

4. 4 What does a negative rate of change mean for the oven?

   The temperature is falling: 2.5 °C each minute at that moment.

What the marker wanted

• Achieved The rate, −2.5, with the derivative shown.

In our words, from NZQA’s 2025 marking schedule.

How did it go?

Got it moves it further out. Review brings it back tomorrow.