Free Printable Module 8 Assessment

1.

$\frac{x^2+8x+7}{2x^2+14x}\cdot\frac{x-10}{10x+10}$

a)

$4\left(x+5\right)$

b)

$x+7$

c)

$\frac{x-10}{20x}$

d)

$\frac{x+6}{x+7}$

2.

$\frac{2a^2-6a}{2a^2-16a}\div\frac{a-3}{8a-56}$

a)

$\frac{\left(a-10\right)\left(a+9\right)}{4a^2}$

b)

$\frac{8\left(a-7\right)}{a-8}$

c)

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

d)

$\frac{6\left(a-5\right)}{a+4}$

3.

$\frac{3}{3xy}+\frac{2y}{6x}$

Find the least common denominator of the expression.

(a)

4.

$\frac{3a}{12b^2}-\frac{a-4b}{12b^2}$

a)

$\frac{\left(2a+4b\right)}{12b^2}$

b)

$\frac{\left(a-b\right)}{6b^2}$

c)

$\frac{\left(2a-4b\right)}{12b^2}$

d)

$\frac{\left(a+2b\right)}{6b^2}$

5.

$\frac{3}{n-4}+\frac{3}{5n-6}$

a)

$\frac{9}{\left(n-4\right)\left(5n-6\right)}$

b)

$\frac{18n-30}{\left(5n-6\right)\left(n-4\right)}$

c)

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

d)

$\frac{12}{\left(n-4\right)\left(5n-6\right)}$

6.

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

(a)

7.

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

a)

6

b)

$\frac{17}{5}$

c)

$\frac{19}{2}$

d)

-6

8.

Lucy and Quinn have started a car washing business. Lucy can wash a car in 3 hours and Quinn can wash a car in 2 hours. How long will it take both of them to wash a car together? (Hint: set your problem up as a rational equation.)

a)

$\frac{3}{2}hours$

b)

I don't know. It's too cold to wash cars! *DON'T PICK THIS!!*

c)

$\frac{8}{5}hours$

d)

$\frac{6}{5}hours$

9.

$\frac{x^2+11x+24}{x^2+4x-32}$

Simplify the expression.

a)

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

b)

$\frac{\left(x+7\right)}{\left(x+4\right)}$

c)

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

d)

$\frac{\left(x+7\right)}{\left(x-4\right)}$

10.

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

a)

x=10

b)

No Solution

c)

x=2

d)

x=-10

11.

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

(a)

12.

$\frac{r^2-5r-36}{3r+10}\cdot\frac{r-7}{r^2-16r+63}$
Multiply the rational expression

a)

$r+10$

b)

$\frac{r+4}{3r+10}$

c)

$\frac{r-8}{\left(r-2\right)\left(r+6\right)}$

d)

$\frac{\left(r+7\right)\left(r+4\right)}{r+5}$

13.

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

Divide the rational expression

(a)

14.

$\frac{4a}{4ab^2}-\frac{2a-3b}{4}$
Simplify the expression

a)

$\frac{4a-2a^2b^2-3ab^3}{4ab^2}$

b)

$\frac{4-2ab^2+3b^3}{4ab^2}$

c)

$\frac{4a-8a^2b^2+12ab^3}{4ab^2}$

d)

$\frac{4-2ab^2-3b^3}{4ab^2}$

15.

$\frac{2}{2n-5}+\frac{6n}{n+2}$

Simplify the expression

a)

$\frac{12n^2-28n+4}{\left(2n-5\right)\left(n+2\right)}$

b)

$\frac{12n^2+28n+4}{\left(2n-5\right)\left(n+2\right)}$

c)

$\frac{12n^2+2n-3}{\left(2n-5\right)\left(n+2\right)}$

d)

$\frac{8n}{\left(3n+3\right)}$

16.

Easy points: What are your plans over winter break? Do you have any fun traditions?

4 lines

Module 8 Assessment

Total questions: 16

Worksheet time: 13mins

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