Free Printable Final Exam Review: Topic 4

1.

Does the table show an inverse variation?

a)

Yes

b)

No

2.

If x varies inversely as the square root of y, and x = 9 when y = 121, find x when y = 81. (Round to the nearest whole number)

a)

7

b)

11

c)

13

d)

17

3.

The current in a simple electrical circuit is inversely proportional to the resistance. If the current is 80 amps when the resistance is 50 ohms, find the current when the resistance is 22 ohms. (Round to the nearest whole number)

a)

190 amps

b)

181 amps

c)

172 amps

d)

163 amps

4.

Is the given table a direct or inverse variation? What is the constant of variation?

a)

Direct. k = 12

b)

Inverse. k = 12

c)

Direct. k = 1/12

d)

Inverse. k = 1/12

5.

Which of the following is NOT a vertical asymptote of the following function?

a)

x = 4

b)

x = -4

c)

x = 2

d)

x = -2

6.

What is the domain for the following function?

a)

All real numbers except 2.

b)

All real number except -2.

c)

All real numbers except 4.

d)

All real numbers.

7.

What is the range for the following function?

a)

All real numbers.

b)

All real numbers except for -2.

c)

All real numbers except for 2.

d)

All real numbers exceptt for 4.

8.

What is the vertical asymptote of the following function?

a)

x = -2

b)

x = 2

c)

y = -3

d)

y = 3

9.

What is the horizontal asymptote of the following function?

a)

x = -2

b)

x = 2

c)

y = -3

d)

y = 3

10.

Select the graph that show the corresponding vertical & horizontal asymptotes to this function

a)

b)

c)

d)

11.

What's the horizontal asymptote of the function?

a)

y = 0

b)

No horizontal asymptote

c)

y = 1

d)

y = 9

12.

What's the vertical asymptote of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

13.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

14.

What is the Vertical Asymptotes?

a)

x= -4

b)

x= -4,5

c)

x= -5,5

d)

x= 4

15.

Factor and cancel out in order to simplify.

a)

9(x+10)

b)

x+10

c)

9

d)

x+9

16.

Solve for x: $\frac{5}{3}-\frac{2}{x}=\frac{8}{x}$

a)

$2$

b)

$\frac{18}{5}$

c)

$\frac{26}{5}$

d)

$6$

17.

Solve: $\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$

a)

$x=-5$

b)

$x=5$

c)

$\frac{5}{\left(x+5\right)\left(x-5\right)}$

d)

No Solution

18.

Solve for x: $\frac{1}{x}=\frac{1}{5x}-\frac{x-1}{5x}$

a)

x = 5

b)

x = -3

c)

x = 3

d)

x = -5

19.

Solve for x: $\frac{5}{x+2}=\frac{1}{x-4}$

a)

x = 5

b)

x = 4

c)

x = 5.5

d)

x = -4

20.

Find the product.
$\frac{4x}{x-1}\times\frac{x^2-1}{3x+3}$

a)

$\frac{4x}{3}$

b)

$\frac{4x^2}{3}$

c)

$\frac{4x^2}{3\left(x+1\right)}$

d)

$\frac{4\left(x+1\right)}{3}$

21.

Simplify.
$\frac{x+3}{4}\times\frac{x+2}{x^2+4x+3}$

a)

$\frac{4\left(x+3\right)}{x+2}$

b)

$\frac{x+2}{4\left(x+1\right)}$

c)

$\frac{x+2}{4\left(x+3\right)}$

d)

$\frac{4\left(x+1\right)}{x+2}$

22.

Simplify.
$\frac{\left(x-5\right)\left(x+8\right)}{x+1}\times\frac{x+1}{\left(x+5\right)\left(x+8\right)}$

a)

1

b)

$\frac{x-8}{x+5}$

c)

$\frac{x-5}{x+5}$

d)

$\frac{x+1}{x+5}$

23.

Simplify.
$\frac{n-4}{7n^2-28n}\times\frac{3n}{n-2}$

a)

$\frac{3n^2}{7}$

b)

$\frac{3}{7\left(n-2\right)}$

c)

$\frac{3}{n-2}$

d)

$\frac{3n}{n-4}$

24.

Simplify.

$\frac{12a^2b^8}{24a^4b^2}$

a)

$2a^2b^6$

b)

$\frac{1}{2a^2b^6}$

c)

$\frac{b^6}{2a^2}$

d)

$\frac{2b^6}{a^2}$

25.

Simplify.
$\frac{7}{4x^3}\times\frac{10x}{2x}$

a)

$\frac{3x}{10}$

b)

$\frac{35}{4x^3}$

c)

$\frac{5}{4}$

d)

$7$

26.

Simplify.
$\frac{x^3-9x}{x^2+10x+21}\times\frac{x^2+7x}{x^2+5x-24}$

a)

$\frac{2x}{x+8}$

b)

$\frac{x^2}{x+8}$

c)

$\frac{x}{x+4}$

d)

$\frac{x^2\left(x-9\right)}{x+8}$

27.

Simplify.

$\frac{6}{k-4}\div\frac{k+6}{k^2+2k-24}$

a)

$\frac{9}{k-4}$

b)

$\frac{k+7}{8}$

c)

$6$

d)

$k-3$

28.

Simplify.

$\frac{2x^2}{x^2-1}\times\frac{x-1}{x}$

a)

$\frac{2x}{x-1}$

b)

$2$

c)

$\frac{2}{x}$

d)

$\frac{2x}{x+1}$

29.

Simplify.

$\frac{x+9}{x^2-81}$

a)

$\frac{x-9}{x+9}$

b)

$\frac{1}{x-9}$

c)

$x+9$

d)

$\frac{1}{x+9}$

30.

Simplify,

$\frac{r^2+3r+2}{r+2}\times\frac{r-9}{r+1}$

a)

$\frac{r-7}{3}$

b)

$r-9$

c)

$\frac{r+10}{\left(r-7\right)\left(r-5\right)}$

d)

$5$

31.

Simplify and state the excluded values. $\frac{4}{49x^2+49x}\times\frac{56x+56}{4}$

a)

$9x;\ x\ne0$

b)

$\frac{4}{3};\ x\ne0,\ -1$

c)

$\frac{8}{7x};\ x\ne0,\ -1$

d)

$6;\ x\ne-1$

32.

Simplify.

$\frac{x+8}{6x+60}\div\frac{x^2-64}{x^2+2x-80}$

a)

$\frac{1}{6}$

b)

$\frac{x+10}{6x+60}$

c)

$\frac{x+8}{6x+60}$

d)

$\frac{\left(x+10\right)\left(x+8\right)}{6x+60}$

33.

What are the excluded values of the rational expression? $\frac{6a^2}{15a+10}\div\frac{5}{15a+10}$

a)

$0$

b)

$-\frac{2}{3}$

c)

$\frac{2}{3}$

d)

$0,\ \frac{2}{3}$

34.

Simplify

$\frac{x^2+10x+21}{x^2-9}\div\frac{x+3}{x-3}$

a)

$\frac{\left(x+7\right)\left(x+3\right)}{x-3}$

b)

$\left(x+7\right)\left(x+3\right)$

c)

$\frac{x+3}{x-7}$

d)

$\frac{x+7}{x+3}$

35.

Simplify the expression.

a)

b)

c)

d)

36.

Simplify the expression.

a)

b)

c)

d)

37.

Simplify the expression.

a)

$\frac{2}{3n+12}$

b)

$\frac{4}{3n+12}$

c)

$\frac{5}{2n+8}$

d)

$\frac{3}{2n+8}$

38.

Simplify the expression.

a)

b)

c)

d)

39.

Simplify the expression.

a)

b)

c)

d)

40.

Simplify the expression.

a)

$\frac{4m+3}{3\left(6+m\right)}$

b)

$\frac{5m^2+25m+3}{3m+15}$

c)

$\frac{5m^2+23m+3}{3\left(m+5\right)}$

d)

$\frac{m+1}{6+m}$

41.

Simplify the expression.

a)

b)

c)

d)

42.

Simplify the expression.

a)

b)

c)

d)

43.

Simplify the expression.

a)

b)

c)

d)

44.

Find the least common denominator of the expression

a)

$\frac{3+y^2}{3xy}$

b)

6x

c)

3xy

d)

6xy

45.

Simplify the expression

a)

$\frac{6x}{20xy}$

b)

$\frac{3}{10y}$

c)

$\frac{6x+1}{20xy}$

d)

$\frac{3}{20xy}$

46.

Simplify the expression

a)

$\frac{n}{2m}$

b)

$\frac{n}{3m}$

c)

$\frac{m^2+4n^2}{12m}$

d)

$\frac{n}{4m}$

47.

Simplify the expression

a)

$\frac{2a+4b}{12b^2}$

b)

$\frac{2a-4b}{12b^2}$

c)

$\frac{a-b}{6b^2}$

d)

$\frac{a+2b}{6b^2}$

48.

Simplify the expression

a)

$\frac{30ab^3+8a}{10b^3}$

b)

$\frac{4a+15ab^3}{5b^3}$

c)

$\frac{10a}{7b^3}$

d)

$\frac{10a}{5b^3+2}$

49.

Simplify the expression

a)

\frac{6x}{20xy}

b)

$\frac{3}{10y}$

c)

$\frac{6x+1}{20xy}$

d)

$\frac{3}{20xy}$

50.

Solve for r.

$1-\frac{1}{r-2}=\frac{2}{r-2}$

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

51.

Solve for x.

$\frac{x^2-3x-10}{x^2-8x+15}=3$

a)

1/3

b)

-5.5

c)

5.5

d)

2.5

52.

Solve for x.

$\frac{x^2-36}{x^2+5x-6}=2$

a)

4

b)

2

c)

-2

d)

-4

53.

Solve the equation for x.

$\frac{2}{x+2}+\frac{5}{x-2}=\frac{6}{x^2-4}$

a)

7

b)

6

c)

14

d)

0

54.

Solve for x.

$\frac{1}{x}=\frac{1}{5x}-\frac{x-1}{5x}$

a)

5

b)

-3

c)

3

d)

-5

55.

Solve for x.

$\frac{6x+18}{x^2}+\frac{1}{x}=\frac{3}{x}$

a)

4.5

b)

-4.5

c)

3

d)

-3

56.

Solve the equation for x.

$\frac{3-x}{6}=\frac{6-x}{12}$

a)

6

b)

12

c)

0

d)

3

57.

Solve for x.

$\frac{x+3}{x}-\frac{16}{15}=\frac{x-3}{3x}$

a)

x = 10

b)

x = -30/13

c)

x = 6

d)

no solution

58.

Solve for x.

$\frac{x+2}{8}=\frac{3}{4}$

a)

x = 2

b)

x = 6

c)

x = 4

d)

x = 8

59.

Solve for x.

$\frac{4}{x+2}=\frac{6}{x-2}$

a)

x = 2

b)

No Solution

c)

x = -10

d)

x = 10

60.

Solve for x.

$\frac{9}{3x}=-\frac{6}{2}$

a)

x = -1

b)

x = 1

c)

x = -9

d)

x = 9

61.

Solve for x.

$\frac{12}{x}+\frac{3}{4}=\frac{3}{2}$

a)

8.9

b)

16

c)

9

d)

12

62.

Solve for x.

$2+\frac{1}{x}=4$

a)

2

b)

3/4

c)

4

d)

1/2

63.

Solve for x.

$\frac{3}{5}=\frac{3}{5n}-\frac{1}{5}$

a)

3/5

b)

3/4

c)

1/4

d)

4/5

64.

Solve for n.

$\frac{3}{n}-\frac{3}{2n^2}=\frac{3}{n}$

a)

6

b)

no solution

c)

0

d)

-3

Final Exam Review: Topic 4

Total questions: 64

Worksheet time: 4hrs 51mins

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