Free Printable Algebra 2 Fall Semester Review

1.

Describe the transformation from $f$ to $g$

$f\left(x\right)=x^2$

g\left(x\right)=4x^2

a)

Vertical stretch

b)

Vertical shrink

c)

Shift left

d)

Shift right

2.

Describe the transformations from $f$ to $g$
$f\left(x\right)=\left|x\right|$

g\left(x\right)=-\frac{2}{3}\left|x+3\right|-3

a)

3 units left, vertical shrink, reflection in the x -axis, and 3 units down

b)

3 units right, vertical shrink, reflection in the x -axis, and 3 units down

c)

3 units right, vertical shrink, reflection in the x -axis, and 3 units up

d)

3 units left, vertical shrink, and 3 units down

3.

Which function is a reflection of $f\left(x\right)$ over the x-axis?

f\left(x\right)=\left|2x-4\right|-7

a)

$g\left(x\right)=-\left|2x+4\right|-7$

b)

$g\left(x\right)=-\left|2x-4\right|-7$

c)

$g\left(x\right)=-\left|2x-4\right|+7$

d)

$g\left(x\right)=\left|2x-4\right|+7$

4.

Solve the equation:

$-6\left|-\frac{5}{7}a+7\right|-1=-13$

a)

$a=7,\ a=-\frac{63}{5}$

b)

$a=-7,a=\frac{63}{5}$

c)

$a=7,\ a=\frac{63}{5}$

d)

$a=-7,\ a=-\frac{63}{5}$

5.

Solve the inequality and graph the solution.
$\left|x-2\right|\ge2$

a)

b)

c)

d)

6.

Use Desmos to find the equation of the line of best fit for the data in the table.

a)

$y=2.57x+64.35$

b)

$y=2.59x+64.35$

c)

$y=2.60x+66$

d)

$y=2.58x+66$

7.

Write the interval in interval notation.

a)

$\left(-\infty,-1\right)$

b)

$\left(-\infty,-1\right]$

c)

$\left(-1,\infty\right)$

d)

$\left[-1,\infty\right]$

8.

Sketch the graph of $\left\{0<x\le5\right\}$

a)

b)

c)

d)

9.

Write the set of numbers in set builder notation.

\left(-\infty,2\right]\cup\left[17,\infty\right)

a)

b)

c)

d)

10.

Graph the system of inequalities:
$3x-2y\ge-6$

6x-2y<2

x+2y\ge-2

a)

b)

c)

d)

11.

Use the Desmos Matrix Calculator to solve the system of equations:

$-4x-4y+z=-70$

7x+5y+7z=21

-2x+6y+4z=-14

a)

$\left(7,8,-10\right)$

b)

$\left(-10,7,8\right)$

c)

$\left(8,7,-10\right)$

d)

No solution

12.

A stadium charges $80 for each seat in section A, $65 for each seat in section B, and $30 for section C. There are two times as many seats in section B as in section A. The revenue from selling all 20,400 seats is $828,000. Write a system to represent the situation.

a)

$a=2\cdot b$
$a+b+c=20,400$
$80a+65b+30c=828,000$

b)

$b=2\cdot c$
$a+b+c=20,400$
$80a+65b+30c=828,000$

c)

$a=2\cdot b$
$a+b+c=20,400$
$30a+65b+80c=828,000$

d)

$b=2\cdot a$
$a+b+c=20,400$
$80a+65b+30c=828,000$

13.

What are the vertex and axis of symmetry of the graph of:

$f\left(x\right)=\left(x-5\right)^2+2$

a)

Vertex: (5, 2)
AoS: x = 5

b)

Vertex: (2, -5)
AoS: x = 2

c)

Vertex: (-5, 2)
AoS: x = -5

d)

Vertex: (-2, -5)
AoS: x = -2

14.

Write an equation of the parabola shown

a)

$x=\frac{1}{12}y^2$

b)

$y=\frac{1}{3}x^2$

c)

$y=\frac{1}{12}x^2$

d)

$x=\frac{1}{3}y^2$

15.

Solve the equation:
$p^2=49$

a)

$p=7$

b)

$p=\pm7$

c)

$p=-7$

d)

No real solution

16.

Solve the equation:

x^2+64=0

a)

$x=8i$

b)

$x=-8i$

c)

$x=\pm8$

d)

$x=\pm8i$

17.

Solve the equation:

x^2+4x+4=17

a)

$x=\pm4i$

b)

$x=-2\pm\sqrt{17}$

c)

$x=19$

d)

$x=2\pm\sqrt{17}$

18.

Solve the equation:
$5x^2+9x=-2$

a)

$x=\frac{9\pm i\sqrt{41}}{10}$

b)

$x=\frac{-9\pm\sqrt{41}}{10}$

c)

$x=\frac{9\pm\sqrt{41}}{10}$

d)

$x=\frac{-9\pm i\sqrt{41}}{10}$

19.

Find the zeros of the function:

g\left(x\right)=x^2+14x+49

a)

$x=7$

b)

$x=-7\ \&\ x=7$

c)

$x=-7$

d)

$x=49$

20.

Distribute and write your answer in standard form:

4i\left(7-6i\right)

a)

$7-2i$

b)

$28-24i$

c)

$-24+28i$

d)

$24+28i$

21.

Multiply using the box method:

$\left(6-9i\right)\left(5-7i\right)$

a)

$93-10i$

b)

$93-87i$

c)

$-33-10i$

d)

$-33-87i$

22.

A boy throws a ball into the air. The equation $h=-16t^2+21t+4$ models the path of the ball, where h is the height (in feet) of the ball t seconds after it is thrown. How long is the ball in the air?

a)

About 0.7 seconds

b)

About -0.2 seconds

c)

About 3.0 seconds

d)

About 1.5 seconds

23.

Graph the inequality:

$y\le-2\left(x-\frac{5}{2}\right)^2-\frac{5}{2}$

a)

b)

c)

d)

24.

Solve the inequality:

$x^2+10x<-21$

a)

$-7<x<-3$

b)

$3<x<7$

c)

$x<3\ or\ x>7$

d)

$x<-7\ or\ x>-3$

25.

Which topic was the most difficult for you this semester?

a)

Transformations

b)

Solving equations & inequalities

c)

Graphing equations & inequalities

d)

Systems of equations & inequalities

e)

Interval and Inequality notation

Algebra 2 Fall Semester Review

Total questions: 25

Worksheet time: 13mins

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