Units 6-8 Common Assessment Practice

Which of the following is equivalent to the expression below?

 $8^5\cdot8^{-12}$  

•  $8^{-60}$  

•  $\frac{1}{8^7}$  

•  $-8^7$  

•  $\frac{1}{8^{17}}$  

Which expressions are equivalent to the one below?
Select ALL that apply.

 $\frac{4^{-7}}{4^{-2}}$  

•  $4^{3.5}$  

•  $4^{-9}$  

•  $4^{-5}$  

•  $\frac{1}{4^9}$  

•  $\frac{1}{4^5}$  

Completely simplify the following expression.

 $x^{10}\cdot x^{-10}$  

•  $x^{-20}$  

•  $x^0$  

•  $x^{-100}$  

•  $1$  

What is equivalent to the expression below?

 $25^{\frac{3}{2}}$  
Hint:  This would be a good question to do using DESMOS.

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•  $\sqrt{75}$  

• 6

• 125

Solve: 5√75 + 8√27

Hint: DESMOS!

• 13√3

• 13√102

• 49√3

• 5√75 + 8√27

Select ALL expressions that are equivalent to the one below.

 $3\sqrt{12}\cdot\sqrt{8}$  
Hint: DESMOS!

•  $6\sqrt{3}\cdot2\sqrt{2}$  

•  $12$  

•  $6\sqrt{24}$  

•  $3\sqrt{20}$  

•  $12\sqrt{6}$  

A real estate agent has a client interested in buying two oceanfront pieces of land.  The area of the first plot is modeled by 
 $\ \ \ \ 7.2x^2-0.3x+5.8$  and the area of the second plot is modeled by  $-2.3x^2+6.4x+9.1$ .  Write a polynomial that expresses the total area of both pieces of land.

• $9.5x^2+6.7x+14.9$

• $4.9x^2+6.1x+14.9$

• $4.9x^2-6.7x+3.3$

• $-4.9x^2+6.1x-14.9$

Subtract the polynomials:

 $\left(6b^3+6-b^4\right)-\left(8b^3-6b^4+2\right)$  
HInt:  Distribute (-1) to the second set of parentheses then 
           combine like terms.

•  $4b^4-2b^3+7$  

•  $5b^4-2b^3+4$  

•  $b^4-2b^3+7$  

•  $5b^4-2b^3+7$  

Four students tried to multiply the binomials (3x - 2)(x + 4).

Which student's work is correct?

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Given the polynomial:   $7x^2+9y^3+2y-8$ ,

select the word which best describes the following:

 $7x^2,\ 9y^3,\ 2y,\ 8$  

• Variable(s)

• Term(s)

• Coefficient(s)

• Constant(s)