Algebra II Mid-Term Review

Algebra II Mid-Term Review

Algebra II Mid-Term 2020

Review questions

Multiple Choice

Divide:

(4x² - 24x + 35) / (2x - 5)

• 2x - 7

• 2x - 12

• 2x + 12

• 2x + 7

Multiple Choice

Which equation matches the graph?

• y=(x-2)²+3

• y=(x-2)²-3

• y=(x+2)²+3

• y=(x+2)²-3

Multiple Choice

Which of the following is the graph of  $y=\left(x-2\right)^3-4$  

Multiple Choice

Factor:

x² - 10x + 24

• (x - 6)(x - 4)

• (x + 6)(x + 4)

• (x - 12)(x + 2)

• (x - 8)(x - 3)

Multiple Choice

Factor:

x² - 10x + 24

• (x - 6)(x - 4)

• (x + 6)(x + 4)

• (x - 12)(x + 2)

• (x - 8)(x - 3)

Multiple Choice

Factor:

x² + 11x + 24

• (x + 6)(x + 4)

• (x + 12)(x + 2)

• (x - 8)(x - 3)

• (x + 8)(x + 3)

Multiple Choice

Solve by factoring.

x² + 15x + 44 = 0

• {-8, 2}

• {-7, 5}

• {-11, -4}

• {-11}

Multiple Choice

The expression

 $\frac{4x^2+5x+10}{2x+3}$  is equivalent to 

•  $2x^2+3x-7+\frac{31}{2x+3}$  

•  $2x^2-3x+7-\frac{11}{2x+3}$  

Multiple Choice

Which factorization is incorrect?

• $4k^2-49=\left(2k+7\right)\left(2k-7\right)$

• $m^3+3m^2-4m+12\ =\ \left(m-2\right)^2\left(m+3\right)$

Multiple Choice

Determine which expression is equivalent to

 $\left(2x^3-5x^2-4x\ -\ 25\right)\div\left(x-4\right)$  

•  $2x^2+3x+8+\frac{7}{x-4}$  

•  $2x^2+3x+8$  

Multiple Choice

Which is the solution to

 $\left|2x-6\right|+4=14$  ?

•  $x=8,\ -6$  

•  $x=-2,\ 8$  

•  $x=-6,\ 12$  

•  $x=10,\ -4$  

Multiple Choice

A polynomial function of degree four is given by

 $f\left(x\right)=4x^4-8x^3-5x^2+18x\ -\ 9.\ \$  Which of the following represents the complete linear factorization of the function? **Hint-multiply your answer choice

•  $f\left(x\right)=\left(2x+3\right)\left(2x-3\right)\left(x-1\right)^2$  

•  $f\left(x\right)=\left(2x-3\right)\left(x-1\right)^2$  

Determining the inverse remember...

• Rewrite function using y

• Interchange the x and y variables

• Solve for y

Multiple Choice

Which function is the inverse of

 $f\left(x\right)=x^2+6$  ?

•  $x^2+6$  

•  $\sqrt{x}+6$  

•  $\sqrt{x}-6$  

•  $\sqrt{x-6}$  

Multiple Choice

What is the solution set for the following equation?

 $3\left|1-\frac{1}{4}x\right|=9$  

•  $\left\{-\frac{1}{2},\ \frac{1}{2}\right\}$  

•  $\left\{-\frac{1}{2},\ 1\right\}$  

•  $\left\{-8,\ 16\right\}$  

•  $\left\{-8,\ -16\right\}$  

Multiple Choice

Paula is planning on installing a pool in his backyard. The pool has the following dimensions:

 $l=x$  and  $w=2x\ +4$  .  The backyard has dimensions:   $l=7x$   and  $w=3x+5$  . Which of the following polynomials could be used to repreent the area of the backyard that would remain after the pool is installed?

•  $11x^2+25x$  

•  $17x^2+33x$  

•  $19x^2+31x$  

•  $21x^2+35x$  

Multiple Choice

The graph of a quadratic function is shown. Determine the equation of the quadratic function

• $y=\left(x+3\right)^2+2$

• $y\ =\ \left(x-3\right)^2-2$

• $y=\left(x+3\right)^2-2$

• $y=\left(x+3\right)^2$

Multiple Choice

 $g\left(x\right)=-\sqrt{x-c}$  

Which two transformations can be used to obtain the graph of  $g\left(x\right)$  from the graph of  $f\left(x\right)=\sqrt{x}$  if  $c>0$  ?

• A translation to the right c units followed by a reflection across the x-axis

• A translation to the left c units followed by a reflection across the x-axis

• A translation to the right c units followed by a reflection across the y-axis

• A translation to the left c units followed by a reflection across the y-axis