Introduction to integration — Question 167

Original QCE Vault practice · 1 mark

Q167 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 167

A curve has gradient

\dfrac{dy}{dx}=4-3x^2

and passes through

(1,5)

. Determine its

y

-intercept.

(A)

-2

(B)

1

(C)

2

(D)

5

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

Integrating gives

y=4x-x^3+C

. Using

(1,5)

gives

5=4-1+C

, so

C=2

. Therefore the

y

-intercept is

2

Selects the correct option.

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.