Quiz about Algebra Competency Assessment

Question 1

Simplify the following expression: $$\left(2x^2-3x+4\right)-\left(x^2+2x-5\right)$$ .

Include a step by step explanation of how you arrived at your solution.

Accepted Answer

$$x^2-5x+9$$

Answer

$$x^2-x-1$$

Answer

$$3x^2+x-1$$

Answer

$$x^2-x+9$$

Question 2

Select all the expressions that are equivalent to $$x^2-6x+9$$

Accepted Answer

$$\left(x-3\right)^2$$

Accepted Answer

$$x\left(x-6\right)+9$$

Accepted Answer

$$x^{2\ }-\ 3x-3x+9$$

Answer

$$\left(x-9\right)^2$$

Question 3

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

Accepted Answer

$$x=3,\ x=-\frac{1}{2}$$

Answer

$$x=2,\ x=1$$

Answer

$$x=4.\ x=-1$$

Answer

$$x=\frac{5}{2},\ x=-\frac{3}{2}$$

Question 4

Solve the inequality and choose all possible solutions.

$$\frac{2x-1}{x+3}>0$$

Accepted Answer

-6

Accepted Answer

3/4

Accepted Answer

-7/2

Answer

-3

Answer

0

Question 5

Solve the logarithmic equation:

$$\log_2\left(x\right)\ +\ \log_2\left(x-2\right)\ =\ 3$$

Accepted Answer

$$x=4$$

Answer

$$x=2$$

Answer

$$x=6$$

Answer

$$x=-2$$

Question 6

Solve: $$3\left(x-4\right)\ =\ 2x+5$$

Cynthia's Solution:

3x - 4 = 2x + 5

3x - 2x = 5 + 4

x = 9

What mistake did Cynthia make when solving the equation?

Accepted Answer

Distributed incorrectly on the left side

Answer

Combined like terms incorrectly after distributing

Answer

Incorrectly isolated the variable x.

Answer

Mistakenly added 4 instead of subtracting 4

Question 7

Simplify.

$$\frac{20x^3}{5x+10}$$

Accepted Answer

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

Answer

$$\frac{4x^3}{x+10}$$

Answer

$$\frac{2x^3}{5x+10}$$

Answer

$$\frac{2x^3}{x+5}$$

Question 8

A student was given the equation $$3\left(x^2+4\right)-2\left(5x^2+1\right)$$ and simplified it to equal $$13x^2-14$$ . See their work below. Which of the following is the first step with an error?

Step 1: $$3\left(x^2+4\right)-2\left(5x^2+1\right)$$ simplified to $$3x^{2\ }+12\ -\ 2\left(5x^{2\ }+1\right)$$

Step 2: $$3x^2+12-2\left(5x^2+1\right)\ $$ simplified $$3x^2+12-10x^2-2$$

Step 3: $$3x^2+12-10x^2-2$$ simplified to $$3x^2+10x^2-12-2$$

Step 4: $$3x^2+10x^2-12-2$$ simplified to $$13x^{2\ }-14$$

Accepted Answer

Step 3

Answer

Step 1

Answer

Step 2

Answer

Step 4

Algebra Competency Assessment

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