Free Printable Reviewer for Final Exam

1.

Perform the indicated operation and simplify as much as possible.

$\frac{x^2+5x+4}{x^2+4x+3}\times\frac{5x^2+15x}{x+4}$

a)

$x$

b)

$3x$

c)

$5x$

d)

$7x$

2.

$\frac{x^2-4}{x^2+4x+4}\times\frac{7}{x-2}$

a)

$\frac{7}{x-2}$

b)

$\frac{7}{x+4}$

c)

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

d)

$\frac{7}{x+2}$

3.

$\frac{4x^2-12x}{5x+10}\times\frac{x+2}{x}\div\frac{x-3}{1}$

a)

$\frac{4}{5}$

b)

$\frac{4x}{5x}$

c)

$\frac{\left(x+2\right)}{5x}$

d)

$\frac{x}{5\left(x+2\right)}$

4.

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

a)

$\frac{x-4}{2}$

b)

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

c)

$2\left(x+1\right)\left(x-4\right)$

d)

$\frac{1}{2}$

5.

$\frac{2x^3+8x}{x+1}\div\frac{x}{2x^2-2}$

a)

$4\left(x^2+4\right)$

b)

$4\left(x^2+4\right)\left(x-1\right)$

c)

$2\left(x+1\right)$

d)

$2x\left(x^2+4\right)$

6.

$\frac{3x-1}{x^2+2x-15}-\frac{2}{x+5}$

a)

$\frac{x-3}{x^2-2x-15}$

b)

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

c)

$\frac{x+5}{x-3}$

d)

$\frac{1}{x-3}$

7.

$\frac{-4}{2+\frac{-4}{2+\frac{-4}{2+\frac{-4}{2+\frac{-4}{2+...}}}}}$

a)

$x^2+2x+4$

b)

$x^2-2x+4$

c)

$x^2+2x-4$

d)

$-x^2+2x-4$

8.

$\frac{2}{x+7}+\frac{1}{x-7}$

a)

$\frac{3x-21}{\left(x+7\right)\left(x-7\right)}$

b)

$\frac{x+21}{\left(x+7\right)\left(x-7\right)}$

c)

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

d)

$\frac{x-21}{\left(x+7\right)\left(x-7\right)}$

9.

$\frac{2}{x-6}-\frac{x-9}{x^2-3x-18}$

a)

$\frac{x+15}{\left(x+3\right)\left(x+6\right)}$

b)

$\frac{x+15}{\left(x+3\right)\left(x-6\right)}$

c)

$\frac{x-15}{\left(x+3\right)\left(x-6\right)}$

d)

$\frac{3x+15}{\left(x+3\right)\left(x-6\right)}$

10.

Write the full name of your Maths Teacher, including middle name.

(a)

11.

Simplify the given rational expressions and state the excluded values:

$\frac{4x}{8x^3+16x^2}$

a)

$\frac{1}{2\left(x^2+2x\right)}$ Excluded values: 0, -2

b)

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

Excluded values: 0, 2

c)

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

Excluded values: 2, -2

d)

$\frac{1}{8x\left(x^2+2x\right)}$

Excluded values: -2, 0

12.

Simplify the expression: $\frac{x^2+4x-60}{x^2+2x-3}\times\frac{x^2+5x+6}{x^2+12x+20}$

a)

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

b)

$\frac{x-6}{x-1}$

c)

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

d)

$\frac{x+10}{x-1}$

13.

Perform the indicated operation and reduce the answer to the lowest term.

$3x^2y\ \times\ \frac{2y}{xy^2}.$

a)

$\frac{6}{xy}$

b)

$5x$

c)

$6x$

d)

$\frac{6y}{x}$

14.

Simplify: $\frac{7x^2+3x-4}{x+8}\div\left(7x-4\right).$

a)

$\frac{x-8}{x-1}$

b)

$\frac{x+1}{x-8}$

c)

$\frac{x-8}{x+1}$

d)

$\frac{x+1}{x+8}$

15.

Perform the indicated operation and simplify:

$2xy\ \div\frac{2x^2}{y}$

a)

$\frac{x}{y}$

b)

$\frac{y^2}{x}$

c)

$\frac{x^2}{y}$

d)

$\frac{y^2}{x^2}$

16.

Divide the following expression:

$\frac{c-1}{c^2-c-30}\div\frac{c-5}{c^2-11c+30}$

a)

$\frac{c+4}{c+7}$

b)

$\frac{c-1}{c+5}$

c)

$\frac{c+2}{c-3}$

d)

$\frac{c-5}{c-1}$

17.

Divide using synthetic division:

$\frac{7x^2-23x+6}{x-3}.$

a)

$7x-2$

b)

$x^2+5x-2$

c)

$7x^2-2$

d)

$x^2+7x+2$

Reviewer for Final Exam

Total questions: 17

Worksheet time: 42mins

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