Free Printable Revision 2.0 SM015

1.

What are the asymptotes?

a)

x=-1 y = -3

b)

x=1 y = -3

c)

x=-1 y =3

d)

x=1, y=3

2.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

3.

(x²+11x+24)/(x²+4x-32)

a)

A.(x+7)/(x+4)

b)

B.3/4

c)

C.(x+3)/(x+4)

d)

D.(x+3)/(x-4)

4.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

5.

What is the X-Intercept?

a)

(0,0)

b)

(4,0)

c)

(0,4)

d)

(-5,0)

6.

What is the Vertical Asymptotes?

a)

x= -5

b)

x= 5

c)

x= 6

d)

x= -6

7.

Simplify:
√-108

a)

3i√6

b)

3i√20

c)

6i√3

d)

20i√3

8.

a)

A.

b)

B.

c)

C.

d)

D.

9.

What does i² equal?

a)

-1

b)

√-1

c)

1

d)

-√1

10.

a)

A

b)

B

c)

C

d)

D

11.

When the numerator is greater than or equal to the denominator is called____

a)

proper fraction

b)

improper fraction

c)

mixed number

d)

all of the above

12.

Select the improper fractions

a)

2/5

b)

5/2

c)

15/12

d)

12/15

13.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

14.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

15.

Solve.
|2t + ⅔| < 4

a)

-5/3 < t < 7/3

b)

t > 7/3 or t < -5/3

c)

-7/3 < t < 5/3

d)

t > 5/3 or t < -7/3

16.

The derivative, $f'\left(x\right)$ of

f\left(x\right)=2\cot\left(4x\right)

is

a)

$-2\ \operatorname{cosec}^2\left(4x\right)$

b)

$2\ \operatorname{cosec}^2\left(4x\right)$

c)

$-8\ \operatorname{cosec}^2\left(4x\right)$

d)

$8\ \operatorname{cosec}^2\left(4x\right)$

17.

Given $f\left(x\right)=\cos^2\left(4x\right)$ . The derivative, $f'\left(x\right)$

is

a)

$2\cos\left(4x\right)\sin\left(4x\right)$

b)

$8\cos\left(4x\right)\sin\left(4x\right)$

c)

$-8\cos\left(4x\right)\sin\left(4x\right)$

d)

$-2\cos\left(4x\right)\sin\left(4x\right)$

18.

Given $f\left(x\right)=\tan^3\left(4x^2\right)$ . The derivative, $f'\left(x\right)$

a)

$3\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

b)

$12\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

c)

$24\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

d)

$24x\tan^2\left(4x^2\right)\sec^2\left(4x^2\right)$

19.

$\frac{\text{d}}{\text{d}y}\left(\frac{x}{\cos x}\right)^2$ ,

a)

$\frac{2x\left(\cos x+x\sin x\right)}{\cos^3x}$

b)

$\frac{2x\left(\cos x-x\sin x\right)}{\cos^3x}$

c)

$\frac{2x\left(\cos^2x+x\sin x\right)}{\cos^4x}$

d)

$\frac{2x\left(\cos^2x-x\sin x\right)}{\cos^4x}$

e)

$-\frac{2x\left(\cos x+x\sin x\right)}{\cos^3x}$

20.

Find the derivative of

y=e^{\tan x}

a)

$e^{\tan x}$

b)

$e^{\tan x}\left(\sec^2x\right)$

c)

$e^{\tan x}\left(-\sec^2x\right)$

d)

$e^{\tan x}\left(\cot\ x\right)$

21.

$\frac{\text{d}}{\text{d}y}\left(\tan\left(\frac{x^3}{2}+\frac{\pi}{6}\right)\right)$

a)

$\frac{3}{2}x^2\sec^2\left(\frac{x^3}{2}+\frac{\pi}{6}\right)$

b)

$\frac{3}{2}x^2\sec\left(\frac{x^3}{2}+\frac{\pi}{6}\right)$

c)

$2x^2\sec^2\left(\frac{x^3}{2}+\frac{\pi}{6}\right)$

d)

$2x^2\sec\left(\frac{x^3}{2}+\frac{\pi}{6}\right)$

e)

$x^2\sec^2\left(\frac{x^3}{2}+\frac{\pi}{6}\right)$

22.

$\frac{\text{d}}{\text{d}y}\left(\sqrt{3\sin x+4\cos x}\right)$

a)

$\frac{3\cos x-4\sin x}{2\sqrt{3\sin x+4\cos x}}$

b)

$\frac{3\cos x+4\sin x}{2\sqrt{3\sin x+4\cos x}}$

c)

$\frac{3}{2}\left(3\cos x-4\sin x\right)\sqrt{\left(3\sin x+4\cos x\right)^3}$

d)

$\frac{3}{2}\left(3\cos x+4\sin x\right)\sqrt{\left(3\sin x+4\cos x\right)^3}$

e)

$-\frac{3\cos x-4\sin x}{2\sqrt{3\sin x+4\cos x}}$

23.

A closed rectangular shipping box with square base is to be made from 120 square inches of cardboard. What dimensions should the box be for maximum volume?

Choose the constraint and optimization equations that represent the problem.

a)

$x^2=120$ and $V=x^3$

b)

$2x+y=120$ and $V=xy$

c)

$x^2y=120$ and $V=2x^2+4xy$

d)

$2x^2+4xy=120$ and $V=x^2y$

24.

A rectangle is bounded by the x-axis and the parabola $y=12-x^2$ . What length and width should the rectangle have so that its area is a maximum?

Given the constraint equation above and the optimization equation $A=2xy$ , choose the DERIVATIVE of the merged (combined) equation.

a)

$A'=2xy$

b)

$A'=\ \ 24-6x^2$

c)

$A'=2x\left(12-x^2\right)$

d)

$A'=12-2x$

25.

Which equation would be used to find the volume of the open box? Don't forget to write down the letter of your answer before clicking!

a)

$\ \ M.\ \ \ V=\ \left(50\right)\left(20\right)\left(x\right)$

b)

$E.\ \ \ \ V=\ \left(50-2x\right)\left(20-2x\right)\left(x\right)$

c)

$P.\ \ \ V=\ \left(50-x\right)\left(20-x\right)\ x$

26.

If a function has a second derivative that is negative, what does that tell you?

a)

The function is increasing.

b)

The function is decreasing.

c)

The function has a local minimum.

d)

The function has a local maximum.

27.

The slope of a function is described by its ____________.

a)

First derivative

b)

Second derivative

c)

Third derivative

d)

Expression

28.

Given that $f\left(x\right)=x^4-2x^3+1$ . Find the nature of the stationary points.

a)

$\left(0,1\right)$ is a point of inflection

b)

$\left(0,1\right)\$ is a relative maximum point

c)

$\left(\frac{3}{2},-\frac{11}{16}\right)$ is a relative minimum point

d)

$\left(\frac{3}{2},-\frac{11}{16}\right)$ is a relative maximum point

29.

A conical tank with radius 2m and height 3m is completely filled with water. Water is leaking from the vertex of the tank a rate of $0.1m^3$ per minute. At the instant when the height of water is 1m, calculate the rate of change of the water level.

a)

$\frac{3}{20\pi}$ m/min

b)

$-\frac{3}{20\pi}$ m/min

c)

$-\frac{9}{40\pi}$ m/min

d)

$\frac{9}{40\pi}$ m/min

30.

A cylindrical steel container of volume $250\pi\ m^3$ is to be constructed by using the same material for the top, bottom and lateral side. Find the dimensions of the container that will minimise the amount of material used.

a)

A is minimum when r=10m and h=20m.

b)

A is minimum when r=5m and h=10m.

c)

A is minimum when r=5m and h=20m.

d)

A is minimum when r=10m and h=10m.

Revision 2.0 SM015

Total questions: 30

Worksheet time: 5hrs 0mins

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