QCE Mathematical Methods Practice Questions & Past Papers

Q239 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 239

A lantern display has brightness

B(t)=120e^{-0.3t}

, where

t

is measured in minutes. Which expression gives

B^{\prime}(t)

(A)

-36e^{-0.3t}

(B)

120e^{-0.3t}-0.3

(C)

36e^{-0.3t}

(D)

-120e^{-0.3t}

ABCD

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Q240 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 240

The graph represents

y=\ln(x-2)+1

. Which pair states its domain and vertical asymptote?

Graph of y=ln(x-2)+1, to the right of a dashed vertical asymptote x=2.

(A)

x\geq2

;

y=1

(B)

x>2

;

x=2

(C)

x>0

;

x=0

(D)

x<2

;

x=2

ABCD

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Q241 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 241

For

f(x)=x^2\sin x

, the derivative is

(A)

2x\sin x-x^2\cos x

(B)

2x\sin x+x^2\cos x

(C)

2x\cos x

(D)

x^2\cos x

ABCD

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Q242 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 242

y=\cos(3x-1)

, then

\dfrac{dy}{dx}

(A)

-\sin(3x-1)

(B)

3\sin(3x-1)

(C)

-3\sin(3x-1)

(D)

3\cos(3x-1)

ABCD

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Q243 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 243

The graph shows

f^{\prime}(x)=(x+2)(x-1)

. At which value of

x

does

f

have a local maximum?

Upward-opening graph of f prime(x)=(x+2)(x-1), crossing the horizontal axis at -2 and 1.

(A)

-\dfrac12

(B)

2

(C)

-2

(D)

1

ABCD

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Q244 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 244

For

f(x)=x^3-6x^2+9x+4

, the point of inflection is

(A)

(1,8)

(B)

(3,4)

(C)

(2,2)

(D)

(2,6)

ABCD

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Q245 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 245

Which is an antiderivative of

6\cos(2x)

(A)

3\sin(2x)

(B)

6\sin(2x)

(C)

12\sin(2x)

(D)

-3\sin(2x)

ABCD

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Q246 · Practice questionTechnology-freeSimple familiar1 mark

QUESTION 246

A moving tile has velocity

v(t)=4t-6

and position

s(0)=5

. Which expression gives its position?

(A)

s(t)=2t^2-6t

(B)

s(t)=4t^2-6t+5

(C)

s(t)=4t-1

(D)

s(t)=2t^2-6t+5

ABCD

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