Mathematical Methods — Question 9

QCAA 2024, Paper 1 · 1 mark

Q9 · 2024 · Technology-freeSimple familiar1 mark

QUESTION 9

At a certain location, the temperature (°C) can be modelled by the function

T=5\sin\left(\frac{\pi}{12}x\right)+23

, where

x

is the number of hours after sunrise. Determine the rate of change of temperature (°C/hour) when

x=4

(A)

\frac{5\pi}{48}

(B)

\frac{5\pi}{24}

(C)

\frac{5\pi\sqrt3}{24}

(D)

\frac{5\pi\sqrt3}{6}

ABCD

WORKED SOLUTION

1 mark

ANSWER

B —

\frac{5\pi}{24}

Worked solution

T'(x)=\frac{5\pi}{12}\cos(\pi x/12)

. At

x=4

\cos(\pi/3)=1/2

, so

T'(4)=\frac{5\pi}{24}

; option B.

Selects option B.

[1 mark]

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