Free Printable Algebra Competency Assessment

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.

a)

$x^2-x-1$

b)

$x^2-5x+9$

c)

$3x^2+x-1$

d)

$x^2-x+9$

2.

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

a)

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

b)

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

c)

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

d)

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

3.

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

a)

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

b)

$x=2,\ x=1$

c)

$x=4.\ x=-1$

d)

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

4.

Solve the inequality and choose all possible solutions.

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

a)

-6

b)

-3

c)

0

d)

3/4

e)

-7/2

5.

Which of the following is not a function? Why?

A. $\left\{\left(2,1\right),\left(3,1\right),\left(4,1\right)\right\}$

B. $\left\{\left(1.2\right),\left(2,3\right),\ \left(3.4\right),\ \left(1,\ 5\right)\right\}$

C. $y=2x+1$

D. $x^3+4$

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6.

Given $f\left(x\right)\ =\ 3x-2$ , find the inverse function.

Explain your steps for solving for x in terms of y, and then write $f^{-1}\left(x\right)$ .

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7.

Solve the logarithmic equation:

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

a)

$x=2$

b)

$x=4$

c)

$x=6$

d)

$x=-2$

8.

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?

a)

Distributed incorrectly on the left side

b)

Combined like terms incorrectly after distributing

c)

Incorrectly isolated the variable x.

d)

Mistakenly added 4 instead of subtracting 4

9.

"A plant grows 3 cm per day." A student models it as : $h\left(t\right)\ =\ 3^t$

What misunderstanding does the student demonstrate? How would you guide them to correct the model?

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10.

Given: $f\left(x\right)\ =\ x^2$ , student writes the transformation $g\left(x\right)\ =\ \left(x-2\right)^2+3$ as a reflection over the y-axis, then translated 2 units left and 3 up.

What errors are present in the student’s interpretation of the transformation? Provide the corrected interpretation.

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11.

Simplify.

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

a)

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

b)

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

c)

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

d)

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

12.

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 $13x^{2\ }-14$

a)

Step 1

b)

Step 2

c)

Step 3

d)

Step 4

Algebra Competency Assessment

Total questions: 12

Worksheet time: 20mins

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