Mathematical Methods — Question 9

QCAA 2025, Paper 2 · 1 mark

Q9 · 2025 · Technology-activeSimple familiar1 mark

QUESTION 9

Determine the gradient of the line perpendicular to the tangent to the graph of

y=\ln(4x)

at the point

(0.8,1.163)

(A)

-1.25

(B)

-0.80

(C)

0.80

(D)

1.25

ABCD

WORKED SOLUTION

1 mark

ANSWER

B —

-0.80

Worked solution

y'=1/x

, so at

x=0.8

the tangent gradient is

1.25

. A perpendicular line has gradient

-1/1.25=-0.80

, so option B.

Selects option B.

[1 mark]

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