Algebra 2 Final Exam Review

Algebra 2 Final Exam Review

Here are the topics we covered this year that will be included on your final exam!!

Unit 1: Tools for Algebra

-Basic Equation Solving

-Sets of Numbers

-Properties of Algebra

-Literal Equations

-Inequalities

Multiple Choice

What property does the following equation show?

-8 + 8 = 0

• Additive Inverse

• Additive Identity

• Commutative Add

• Addition Property of Zero

Multiple Choice

What is the set of numbers that includes fractions?

• Whole numbers

• Integers

• Rational Numbers

• Natural Numbers

Multiple Choice

Solve for f:

f - 4 = 6f + 26

• f = -5

• f = 5

• f = 6

• f = -6

Multiple Choice

Solve for x:   $$ax+c=R$$  

• $$ax=R+c$$  

• $$ax=R-c$$  

• $$x=a\left(R-c\right)$$  

• $$x=\frac{R-c}{a}$$  

Multiple Choice

Solve: -4x + 14 ≤ 54

• x ≥ - 10

• x ≤ -10

• x ≥ 10

• x ≤ 10

Unit 2: Functions

-Function Notation

-Finding Domain and Range from a Graph.

-The Vertical Line Test.

-Families of Functions.

-Transformation of Functions.

Multiple Choice

Which graph represents

y = |x + 3| − 4 ?

• Graph A

• Graph B

• Graph C

• Graph D

Multiple Choice

Which is the parent function of the graph?

• f(x) = log x

• f(x) = x³

• f(x) = 1 ∕ x

• f(x) = ∛x

Multiple Choice

What is the DOMAIN?

• [0, ∞)

• (-∞, 0)

• All real numbers

• {0, 1, 2, 3, 4,...}

Multiple Choice

• Function

• Not a Function

Multiple Choice

Evaluate f(x)=-2x+13 for f(10)

• -7

• 1

• -8

• 7

Unit 3: Linear Systems

-Finding Slope.

-Graphing Lines.

-Solving Systems of Equations.

-Solving Systems of Linear Inequalities.

Multiple Choice

Find the slope of the line.

• 1/2

• -1/2

• 2

• -2

Multiple Choice

What is the equation of the line?

• y = -3/4x + 3

• y = 4/5x + 3

• y = -4/5x + 3

• y = -4/5x

Multiple Choice

Solve the system of equations by elimination.

-x + y = -13

-8x - 4y = -8

• (5, 8)

• (5, -8)

• (-5, -18)

• (-5, 8)

Unit 4: Quadratic Functions

-Factoring.

-Solve using factoring.

-Solve using Square Roots.

-The Quadratic Formula.

-The Discriminant.

Multiple Choice

Factor:
x² - 5x - 14

• (x - 2)(x + 3)

• (x - 2)(x + 7)

• (x + 2)(x - 7)

• (x - 2)(x - 3)

Multiple Choice

What is the discriminant of -2x² − x − 1 = 0

• 76

• -7

• 9

• none of these

Multiple Choice

Solve for x:
8x² + 24 = 0

• x = ± i √ (3)

• x = ± 3i

• x = ± √(3)

• x = ± 2

Unit 5: Polynomial Functions.

-Exponent Properties.

-Classifying Polynomials.

-Polynomial Operations.

-Synthetic Division.

Multiple Choice

Classify the polynomial by its degree.

$$8x-4$$  

• CONSTANT

• LINEAR

• QUADRATIC

• CUBIC

• QUARTIC

Multiple Choice

2x³ + 5x² + 9 ÷ x + 3

• 2x² - x + 3

• 2x³ - x² + 3x

• 2x² + 11x + 33 + 108/x+3

• 2x² - 5x + 12

Multiple Choice

Simplify the exponents:

(x⁴ y³ z)⁵(4zx⁸)²

• 16x³⁶y¹⁵z⁷

• 8x³⁶y¹⁵z⁷

• 16x³⁶y⁸z⁶

• 16x¹⁹y⁸z⁷

Unit 6: Exponential and Logarithmic Functions

-Evaluating Logarithms.

-Properties of Logarithms.

-Change of Base Formula.

-Solving Exponential and Logarithmic Equations.

Multiple Choice

Condense $$\log_35+\log_34$$  

• $$\log_39$$  

• $$\log_320$$  

• $$\log_69$$  

• $$\log_620$$  

Multiple Choice

log(x+6) = 1

• 4

• 4.222

• -5

• -9.550

Multiple Choice

Solve: 7^-x = 49

• 1

• -1

• 2

• -2

Multiple Choice

Evaluate the following logarithm:

log₃27

• 3

• 2

• -3

• ¹/₃

Unit 7: Complex Numbers

-Simplifying Powers of i.

-Operations with Complex Numbers.

-Using the Quadratic Formula with Complex Numbers.

Multiple Choice

Simplify:  i¹²¹

• i

• -i

• 1

• -1

Multiple Choice

Multiply:

(4 – 3i)(7 + 2i)

• A. 22 - 13i

• B. 28 - 19i

• C. 34 - 13i

• D. -34 - 29i

Unit 8: Radical & Rational Functions

-Simplifying Square Roots.

-Operations on Radical Expressions.

-Solving Radical Equations.

-Operations on Rational Expressions.

-Solving Rational Equations.

Multiple Choice

Simplify:

• A

• B

• C

• D

Multiple Choice

Simplify:  $$\frac{3x}{10x^2}+\frac{7}{5x^2}$$  

• $$\frac{2}{3x^3}$$  

• $$\frac{3x+7}{10x^2}$$  

• $$\frac{1}{x^2}$$  

• $$\frac{3x+14}{10x^2}$$  

Multiple Choice

2√5 + 4√5 =

• 6√10

• 8√10

• 8√5

• 6√5

Multiple Choice

$$\frac{\left(x+9\right)\left(x+8\right)}{8}\cdot\frac{\left(x-1\right)}{\left(x+8\right)\left(x-1\right)}$$  

• $$\frac{\left(x+9\right)}{8}$$   

• $$\frac{\left(x-1\right)}{8}$$  

• $$\frac{1}{8}$$  

•   $$\frac{\left(x+9\right)\left(x+8\right)}{8}$$  

Multiple Choice

• A

• B

• C

• D

Multiple Choice

Simplify:  $$\frac{3x}{10x^2}+\frac{7}{5x^2}$$  

• $$\frac{2}{3x^3}$$  

• $$\frac{3x+7}{10x^2}$$  

• $$\frac{1}{x^2}$$  

• $$\frac{3x+14}{10x^2}$$  

Multiple Choice

(x²+11x+24)/(x²+4x-32)

• A.(x+7)/(x+4)

• B.3/4

• C.(x+3)/(x+4)

• D.(x+3)/(x-4)