Mathematical Methods — Question 3

QCAA 2024, Paper 2 · 1 mark

Q3 · 2024 · Technology-activeSimple familiar1 mark

QUESTION 3

The derivative of the function

f(x)

is given by

f'(x)=\sin(2x)

. It is known that

f(\frac{\pi}{2})=4

. Determine

f(x)

(A)

-\cos(2x)+3

(B)

\cos(2x)+5

(C)

-\frac12\cos(2x)+3.5

(D)

\frac12\cos(2x)+4.5

ABCD

WORKED SOLUTION

1 mark

ANSWER

C —

-\frac12\cos(2x)+3.5

Worked solution

Integrating,

f(x)=-\frac12\cos(2x)+C

. Since

f(\pi/2)=4

and

\cos\pi=-1

4=1/2+C

, so

C=3.5

. Hence option C.

Selects option C.

[1 mark]

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