Mathematical Methods — Question 10

QCAA 2025, Paper 2 · 1 mark

Q10 · 2025 · Technology-activeSimple familiar1 mark

QUESTION 10

The outside air temperature,

T

(°C), on a particular day at a certain location is modelled by the function

T=25-7\cos\left(\frac{\pi t}{12}\right),\qquad0\le t\le24,

where

t

is the time (hours) since 6:00 am. The rate of change of temperature at 11:30 am is

(A)

1.833

(B)

1.817

(C)

0.334

(D)

0.239

ABCD

WORKED SOLUTION

1 mark

ANSWER

B —

1.817

Worked solution

At 11:30 am,

t=5.5

. Since

T'(t)=\frac{7\pi}{12}\sin(\pi t/12)

T'(5.5)\approx1.817

, so option B.

Selects option B.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.