Free Printable Algebra 2: chapter 9 test

1.

Simplify and state the restrictions on the values of x in this expression $\frac{x^2\ +7x\ +12}{x^2\ -\ 9}$

a)

(x+4)/(x-3); x not equal to 3

b)

(x-4)/(x+3) ;x not equal 3 or -3

c)

(x+4)/(x-3); x not equal 3 or -3

2.

Write a function that models this variation: $x\ =\ \frac{1}{3},\ y\ =\ \frac{1}{5},\ and\ r\ =\ 3\ when\ z\ =\ \frac{1}{2},\$
z varies directly with x and inversely with the product of r^2 and y.

a)

$\frac{27x}{r^2y}$

b)

$\frac{2.7x}{ry}$

c)

$\frac{2.7x}{r^2y}$

3.

$y\ =\ \frac{2x^2}{x^2-4x}$ For questions 3 - 6, identify any holes, horizontal or vertical asymptotes. Hint: VA: Vertical Asymptotes, HA: Horizontal Asymptotes

a)

VA: x = 4, HA: y = 2, hole at x = 0

b)

VA: x = 2, HA: y = 4, hole at x = 0

c)

VA: x = 0, HA: y = 2, hole at x = 2

4.

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

a)

VA: x = 2, HA: y = -3, hole at x = 0

b)

VA: x = -2, HA: y = -3

c)

VA: x = 2, HA: y = 3

5.

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

a)

HA: y = -3

b)

hole at x = -3

c)

VA: x = -3

6.

$\frac{x^2\ +\ 5}{x\ -\ 5}$

a)

Hole at x = 5

b)

VA: x = 5

c)

HA: x = 5

7.

Find the least common multiple of this pair: 5(x+3)(x+1) and 2(x+1)(x-3)

a)

10(x+3)(x+1)(x-6)

b)

10(x+3)(x+1)(x-3)

c)

20(x+3)(x-3)(x+1)

8.

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

a)

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

b)

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

c)

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

9.

Simplify:

\frac{3-\frac{3}{4}}{\frac{1}{2}-\frac{1}{4}}

a)

not possible

b)

3

c)

9

10.

$\frac{1}{x}+\frac{1}{3}\ =\ \frac{6}{x^2}$ Solve the equation

a)

6 or 3

b)

6 or -3

c)

-6 or 3

11.

$\frac{1}{x}+\frac{x}{x+2}=1$ Solve:

a)

2

b)

-1

c)

1

12.

Use this information for 12-14

Suppose you select a number at random from the set {90,91,92,...,99}. Event A is selecting a multiple of 3 and Event B is selecting a multiple of 4.

Are these two events mutually exclusive?

a)

Yes

b)

No

13.

What is P(A or B)

a)

0.1

b)

0.5

c)

0.2

14.

P(A and B)

a)

0.5

b)

0.1

c)

0.2

15.

James can seal a driveway in 4 hours. Working together, he and Louis can seal it in 2.3 hours. How long would it take Louis to seal it alone?

a)

5.4 hours

b)

4.5 hours

c)

6.5 hours

16.

Simplify: $\frac{x+2}{\left(x-3\right)\left(x+1\right)}+\frac{\left(x-1\right)\left(x+2\right)}{x-3}$

a)

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

b)

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

c)

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

17.

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

a)

$-\frac{\left(x+1\right)\left(2x^2-9x+5\right)}{\left(x-2\right)\left(3x-1\right)\left(x+3\right)}$

b)

Answer option 2

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

c)

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

18.

What is the restriction after simplifying: $\frac{\left(4x^2-2x\right)}{x^2+5x+4}\div\frac{2x}{x^2+2x+1}$

a)

x $\ne$ 4, -1, or 0

b)

x $\ne$ -4, -1 or 0

c)

x $\ne$ -5, -4 or -1

19.

Write an equation for the translation of xy = 4 that has the given asymptotes: x = 0, y = 3

a)

$y\ =\ \frac{4}{x\ }-3$

b)

$y\ =\ \frac{x}{4}+3$

c)

$y\ =\ \frac{4}{x\ }+3$

20.

Write an equation for the translation of xy = 4 that has the given asymptotes: x = -3, y = -4

a)

$y\ =\ \frac{4}{x+3}-4$

b)

$y=\frac{4}{x-3}-4$

c)

$y=\frac{4}{x+3}+4$

Algebra 2: chapter 9 test

Total questions: 20

Worksheet time: 35mins

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