Final Exam Review (Fall22)(A2)

Final Exam Review (Algebra II)

Multiple Choice

Convert to a rational exponent.

• 4^4/3

• 4^3/4

• 2^4/3

• 2^3/4

Multiple Choice

Convert to a rational exponent.

• 2^3/5

• -2^3/5

• 2^5/3

• 8⁵

Multiple Choice

Simplify the following expression:

• 5

• 25

• 125

• 625

Multiple Select

Rewrite as a radical expression: $$5^{\frac{1}{2}}$$  

• $$\sqrt{5}$$  

• 10

• 25

• $$\sqrt{25}$$  

Multiple Choice

Simplify: $$\left(x^{\frac{1}{2}}\right)^{\frac{3}{5}}$$  

• $$\sqrt[10]{x^3}$$  

• $$\sqrt[3]{x^{10}}$$  

• $$\sqrt[5]{x^3}$$  

• $$\sqrt[5]{x^6}$$  

Multiple Choice

Convert to a radical expression: $$\sqrt[]{x}$$  

• $$x^{\frac{1}{3}}$$  

• $$x^3$$  

• $$x^{\frac{2}{3}}$$  

• $$x^{\frac{1}{2}}$$  

Multiple Select

Convert to a radical expression: $$a^{\frac{3}{4}}$$  

• $$\sqrt[4]{a^3}$$  

• $$\left(\sqrt[4]{a}\right)^3$$  

• $$\sqrt[3]{a^4}$$  

• $$\left(\sqrt[3]{a}\right)^4$$  

Multiple Choice

$$\sqrt{50}$$  

• $$5\sqrt{2}$$  

• $$\sqrt{5}$$   

• $$2\sqrt{5}$$  

• $$25\sqrt{2}$$  

Multiple Choice

$$\sqrt{45}$$  =

• $$3\sqrt{5}$$  

• $$5\sqrt{3}$$  

• $$9\sqrt{5}$$  

• $$5\sqrt{9}$$  

Multiple Choice

$$\sqrt{63}$$  

• $$9\sqrt{7}$$  

• $$6\sqrt{2}$$  

• $$7\sqrt{6}$$  

• $$3\sqrt{7}$$  

Multiple Choice

Simplify

$$\sqrt[]{-25}$$  

• 5

• -5

• 5i

• -5i

Multiple Choice

Simplify

$$\sqrt[]{-24}$$  

• 12i

• $$4i\ \sqrt[]{6}$$  

• $$-2i\ \sqrt[]{6}$$  

• $$2i\ \sqrt[]{6}$$  

Multiple Choice

Simplify √-4

• 2i

• -2i

• 2

• 4i

Multiple Choice

Where is the first error?

• line 2

• line 4

• line 6

• no mistake

Multiple Choice

Where is the first error?

• line 3

• line 5

• line 7

• no mistake

Multiple Choice

Where is the first error?

• line 2
• line 3
• line 6
• no mistake

Multiple Choice

Where is the first error?

• line 2

• line 4

• line 6

• no mistake

Multiple Choice

What value of x makes the equation true?

• -216

• -512

• -125

• -343

Multiple Choice

What value of z makes the equation true?

• 16

• 25

• 9

• 36

Multiple Choice

Determine the solution to the given linear-quadratic function.

• (0, 0)
• (3, 0)
• (2, -3)
• (-3, 2)

Multiple Choice

What are the solutions to the system:
y = x² + 3x - 5
y = x + 3

• (-4, 2) and (-1, 5)

• (-4, -1) and (2, 5)

• (2, -1 and (-4, 5)

• (-4, 1) and (2, -1)

Multiple Choice

Determine the number of solutions to the given linear-quadratic system.

• 0 solutions

• 1 solution

• 2 solutions

• 3 solutions

Multiple Choice

Find the solution.

• (2,3) and (3,4)

• (-3,-15) and (4,-8)

• (-3,10) and (8,4)

• (-8,3) and (-4,10)

Multiple Choice

How many solutions does this system of equations have?

• one solution

• two solutions

• no solution

• infinitely many solutions

Multiple Choice

Solve the system of equations
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Multiple Choice

The axis of symmetry of this parabola is...

• y=4

• y=-4

• x=4

• x=-4

Multiple Choice

If given the equation
y = 3(x + 5)² - 4,
what is the vertex of the parabola?

• (5, -4)

• (-5, -4)

• (-15, -4)

• (15, -4)

Multiple Choice

What direction is the following equation opening?
y=-3x²-7x+8

• Up

• Down

• Left

• Right

Multiple Choice

Find the y-intercept of
f(x) = 2x²-2x + 1

• 2

• -2

• 1

• -1

Multiple Choice

How can you tell the direction of the opening of the graph of a parabola by looking at the equation?

• The vertex tells you the direction of the opening

• The value of "a" tells you the direction of the opening.

• All parabolas open upward

• All parabolas open downward

Multiple Choice

What's the max/min? 

• Minimum: -4

• Minimum: -3

• Maximum: -4 

• Minimum: -3

Multiple Choice

Given the equation for this parabola:
 y=-(x-4)²-3,
does this parabola have a maximum or minimum value?

• Maximum

• Minimum

Multiple Choice

What is the vertex of the quadratic function: y=1/2(x-3)²+8?

• (3,8)

• (-3,-8)

• (-3,8)

• (3,-8)

Multiple Choice

What does the "p" represents?

• Distance from the vertex to the focus

• Distance from the vertex to the directrix

• The vertex of the parabola

• Distance from the focus to the directrix

Multiple Choice

The focus is always inside the parabola.

• true

• false

Multiple Choice

Given the graph, what is the equation of the parabola?

• $$x=\frac{1}{12}(y-4)^2-2$$

• $$x=-\frac{1}{12}(y-4)^2+2$$

• $$x=-\frac{1}{12}(y+4)^2+2$$

• $$x=\frac{1}{12}(y+4)^2+2$$

Multiple Choice

Given the graph, what is the equation of the parabola?

• $$x=\frac{1}{12}(y-4)^2-2$$

• $$x=-\frac{1}{12}(y-4)^2+2$$

• $$x=-\frac{1}{12}(y+4)^2+2$$

• $$x=\frac{1}{12}(y+4)^2+2$$

Multiple Choice

Which direction does this parabola open?

• Up

• Down

• Left

• Right

Multiple Choice

(3 + 2i) + (4 - 5i)

• 7 + 7i

• 1 - 3i

• 1 - 7i

• 7 - 3i

Multiple Choice

(4 - 2i) - (3 + 6i)

• 7 - 4i

• 1 + 4i

• 1 - 8i

• 7 - 8i

Multiple Choice

What does i² equal?

• -1

• √-1

• 1

• -√1

Multiple Choice

Simplify:
i⁷

• i

• -i

• 1

• -1

Multiple Choice

Solve
3x² - 5 = -446

• ±√-147

• 7i√3

• ±7i√3

• -7√3

Multiple Choice

i⁶⁶

• 1

• i

• -1

• -i

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Solve $$x^2+49=0$$  

• $$-7$$  

• $$7$$  

• $$7i$$  

• $$\pm7i$$  

Multiple Choice

(3 - 3i)(5 - 7i)

• -6 - 36i

• $$21i^2-36i+15$$  

• 36 + 6i

• -6 + 36i

Multiple Choice

The expression (2 + 3i)² is equal to

• -5

• -5 + 12i

• 13

• 13 + 12i

Multiple Choice

Simplify $$\frac{5}{-1-9i}$$  

• $$\frac{-2+18i}{41}$$  

• $$\frac{-5+45i}{82}$$  

• $$\frac{-5+45i}{86}$$  

• $$\frac{-2+9i}{17}$$  

Multiple Choice

Find all the solutions for x when

x² + 9x - 36 = 0

• A.

  (x + 12)(x - 3)

• B.

  x = 12 and x = -3

• C.

  x = -12 and x = 3

• D.

  (x - 9)(x - 4)

Multiple Choice

Solve by factoring: $$3x^2\ +\ 2x\ -\ 1\ =\ 0$$  

• A. x = 1 and x = 1/3

• B. x = 1 and x = 3

• C. x = -1 and 1/3

• D. x = 1 and -1

Multiple Choice

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution

Multiple Choice

Solve using the quadratic formula...

9x² = 4 + 7x

• No solution

Multiple Choice

• x = 2

• x = 4

• x = 7

• x = 9

Multiple Choice

• x = 5

• x = 10

• x = -9

• x = -5

Multiple Choice

Rewrite in exponential form:

log₃(9)=2.

• 3⁹=2

• 3²=9

• x²=9

• 3^x=2

Multiple Choice

Rewrite in logarithmic form:

6² = 36

• log₆ 2 = 36

• log₆ 36 = 2

• ln 36 = 2

• 6³⁶ = 2

Multiple Choice

Rewrite in logarithmic form:

5³ = 125

• log ₅ 125 = 3

• log ₃ 125 = 5

• log ₅ 3 =125

• log₁₂₅ 3 = 5

Multiple Choice

Rewrite in exponential form:

log₂ 0.25 = -2

• -2² = 0.25

• -2^0.25 = 2

• 2^-2 = 0.25

• No correct answer

Multiple Choice

log ₃ 9 =

• 1/2

• 2

• 1/3

• 3

Multiple Choice

log ₂₅ 5 =

• 1/2

• 2

• 1/5

• 5

Multiple Choice

When talking about exponential functions.

If the number in parenthesis is less, than 1, my graph will:

• go up

• go down

Multiple Choice

In the equation y = 150(1.2)^x , what does 150 represent?

• the ending amount

• the starting amount

• the growth

Multiple Choice

In the equation y = 120(1.4)^x , what does 1.4 represent?

• the answer

• the start

• the growth

Multiple Choice

let y = money made. Let x = months. How much money will you make in 8 months if you start with $1000, and it grows 1.15 each month?

• y = 1.15(1000)⁸ = $3059.02

• y = 1,000(1.15)⁸ = $2000

• y = 1,000(1.15)⁸ = $3059.02

• y = 1,000(1.15)⁸ = $6059.02

Multiple Choice

Solve

• x=3

• x=4

• x=5

• x=6

Multiple Choice

Solve

• 2

• 3

• 4

• 5

Multiple Choice

In which of the following does x = 3?

• 2^x-2=8

• 5^x-2=25^3x

• 2^x+3=4^x

• 4x+6=9

Multiple Choice

Solve the following exponential equation.

• -15

• -3

• 7/4

• -8

Multiple Choice

Solve the exponential equation

• 5

• 5/4

• 4/5

• 4