Free Printable 2nd Semester Review 2022

1.

Simplify $\frac{2x-3}{x^2-8x+12}-\frac{x-1}{x^2-8x+12}$ as much as possible.

a)

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

b)

$\frac{x-4}{x^2-8x+12}$

c)

$\frac{x}{x+12}$

d)

$\frac{1}{x^2-8x+12}$

2.

Add and simplify. $\frac{3x}{x^2+x-6}+\frac{x-2}{x^2+x-6}$

a)

$\frac{4x-2}{x^2+x-6};\ x\ne-3,\ 2$

b)

$\frac{4x-2}{x^2+x-6};\ x\ne3,\ -2$

c)

$\frac{2x}{x^2+x-6};\ x\ne-3,\ 2$

d)

$\frac{2x}{x^2+x-6};\ x\ne3,\ -2$

3.

Simplify the radical expression. $\frac{x^2-x-12}{x^2+5x+6}$

a)

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

b)

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

c)

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

d)

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

4.

Solve for x. $\frac{x}{3}=\frac{x+2}{6}$

a)

6

b)

-2

c)

2

d)

-6

5.

Solve for x. $\frac{x}{10}=\frac{x-5}{8}$

a)

-10

b)

25

c)

-25

d)

10

6.

Determine the restriction(s) for the following. $\frac{x^2-8x-9}{x^2-1}$

a)

$x\ne\pm1$

b)

$x\ne\pm9$

c)

$x\ne8$

d)

$x\ne-1$

7.

In the equations shown, x represents a real number. What is the solution to this equation? $\sqrt[]{3x-5}=8$

a)

$x=16$

b)

$x=64$

c)

$x=23$

d)

$x=-23$

8.

Solve for x. $\sqrt[]{2x-3}-5=-2$

a)

x=4

b)

x=6

c)

x=-6

d)

x=-4

9.

What are the best first two(2) steps in solving he equation below for x?

$\sqrt[]{x+5}-4=6$

a)

Add 4 to both sides of the equation, and then square both sides.

b)

Subtract 4 from both sides of the equation, and then square both sides.

c)

Square both sides of the equation, and then add 4 to both sides.

d)

Square both sides of the equation, and then subtract 4 to both sides.

10.

What are the best first two(2) steps in solving the equation below for x?

$\sqrt[]{6x-11}=15$

a)

Add 11 to both sides of the equation, and then take the square root of both sides.

b)

Take the square root of both sides of the equation, and then add 11 to both sides.

c)

Add 11 to both sides of the equation, and then square both sides.

d)

Square both sides of the equation, and then add 11 to both sides.

11.

Rewrite in exponential form: $\sqrt[]{\left(5b\right)^3}$

a)

$\left(5b\right)^{\frac{2}{3}}$

b)

$\left(5b\right)^{\frac{3}{2}}$

c)

$5b^{\frac{3}{2}}$

d)

$5b^{\frac{2}{3}}$

12.

Rewrite in exponential form $\left(\sqrt[]{x}\right)^3$

a)

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

b)

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

c)

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

d)

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

13.

Simplify $\sqrt[]{45y^7}$

a)

$3y\sqrt[]{5y}$

b)

$3y^3\sqrt[]{5y}$

c)

$3y^2\sqrt[]{5}$

d)

$9y^2\sqrt[]{5}$

14.

Simplify $3\sqrt[]{16x^5y^7}$

a)

$6x^2y^2\sqrt[]{2xy}$

b)

$6x^2y^3\sqrt[]{2xy}$

c)

$12x^2y^3\sqrt[]{2xy}$

d)

$12x^2y^2\sqrt[]{2xy}$

15.

Simplify $\sqrt[3]{16x^5}$

a)

$2x\sqrt[3]{2x^2}$

b)

$3x^2\sqrt[3]{2x}$

c)

$8x^2\sqrt[3]{2x}$

d)

$2x^2\sqrt[3]{2x^2}$

16.

Solve the equation. Check to determine if extraneous solutions exist.

$\sqrt[]{7x+35}=x+5$

a)

The equation has no real solutions (both are extraneous)

b)

The equations has two solutions; $x=-5$ or $x=2$ .

c)

The solution to the equation is $x=-5$ and $x=2\$ is an extraneous solution.

d)

The solution to the equation is $x=2$ , and $x=-5$ is an extraneous solution.

17.

Solve the equation. Check to determine if extraneous solutions exist.

$\sqrt[]{x+2}=x-4$

a)

The equation has two solutions; 2 and 7

b)

The solutions to the equation is 2, and 7 is an extraneous solution.

c)

The solutions to the equation is 7, and 2 is an extraneous solution.

d)

The equation has no real solutions (both are extraneous)

18.

Multiply, then simplify.

$\sqrt[]{5}\left(2\sqrt[]{5}-\sqrt[]{45}\right)$

a)

$5$

b)

$-35$

c)

$35$

d)

$-5$

19.

Multiply, then simplify

$\sqrt[]{7}\left(5\sqrt[]{7}-\sqrt[]{28}\right)$

a)

14

b)

0

c)

21

d)

28

20.

The population of bears in a national forest is changing according to the function

$N\left(t\right)=900\left(.95\right)^t$ where t is the time in years and N(t) is the number of bears. Which statement explains how the bear population is changining?

a)

The population is decreasing by 5% per year.

b)

The population is increasing by 95% per year.

c)

The population is decreasing by 95% per year.

d)

The population is increasing by 5% per year.

21.

The population of deer in a national forest is changing according tot he function, $N\left(t\right)=875\left(1.05\right)^t$ where t is the time in years and N(t) is the number of deer. Which statement explains how the deer population is changing?

a)

The population is decreasing by 5% per year.

b)

The population is increasing by 105% per year.

c)

The population is decreasing by 105% per year.

d)

The population is increasing by 5% per year.

22.

Rewrite using the properties of logarithms.

$\log\left(\frac{w^2}{x^3}\right)$

a)

$\log\ 2w-3\log x$

b)

$2\log w-3\log x$

c)

$2\log w-\log3x$

d)

$\log2w-\log3x$

23.

Evaluate $\sum_{x=2}^{11}\left(5x-2\right)$

a)

53

b)

503

c)

305

d)

8

24.

Expand $\sum_{k=3}^6\left(2k-1\right)$

a)

4, 6, 8, 10

b)

4, 6, 8

c)

5, 7, 9, 11

d)

5, 7, 9

25.

How many outfits are possible with 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes?

a)

15

b)

40

c)

10

d)

80

26.

How many 5-digit (numerical) passwords are possible for the school email system? (repetition is allowed)

a)

11,424,400

b)

10,967,424

c)

9000

d)

100,000

27.

A multiple choice test consists of 10 questions, each permitting a choice of 3 options. In how many ways may a student fill in the answers if they answer each question?

a)

30

b)

59,049

c)

120

d)

720

2nd Semester Review 2022

Total questions: 27

Worksheet time: 27mins

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