Algebra 2 Semester Exam Review (Spring 2025)

Algebra 2:
Semester Exam Review,
Spring 2025

By Chanoy Gandolfi

Solving, Factoring, Analyzing, and Graphing

Equations and Functions

Add,
Subtract,
Multiply,
Divide with polynomials

Operations

Chapter 4:
Polynomial Functions

Multiple Choice

Find the sum of difference.

(3x² + 4x − 1) + (−2x² − 3x + 2)

• x² + x + 1

• 5x² - x + 1

• 5x² - x + 3

• 5x² + x + 3

Multiple Choice

Find the sum of difference.

(3x³ − 2x² + 4x − 8) − (5x³ + 12x² − 3x − 4)

• -2x³ - 10x² + 7x - 12

• 7x³ - 10x² + 7x - 4

• -2x³ - 14x² + 7x - 4

• 2x³ - 14x² + x - 4

Multiple Select

Find the product.

(5x² − 4x + 6)(−2x + 3.5)

• 10x³ + 25.5x² + 26x +9.5

• −10x³ + 25.5x² − 26x + 21

• 10x³ + 25.5x² − 26x + 9.5

• −10x³ − 25.5x² − 26x + 21

Multiple Choice

Factor the polynomial completely.

x² + 6x − 16

• (x + 2)(x + 8)

• (x + 2)(x - 8)

• (x - 2)(x + 8)

• (x - 4)(x + 4)

Multiple Choice

Factor the polynomial completely.

x² + 6x + 5

• (x + 1)(x + 5)

• (x + 2)(x + 3)

• (x - 1)(x + 5)

• (x - 1)(x + 6)

Fill in the Blank

What is the degree of the function below?

f(x) = x⁴ + 3x³ − x² − 8x + 2

Fill in the Blank

What is the degree of the function below?

f(x) = −2x³ − 3x² − 1

Operations and composite

Functions

Properties and solving

Radicals

Chapter 5: Rational Exponents and Radical Functions

Fill in the Blank

Evaluate the expression.

$$64^{\frac{1}{6}}$$

Fill in the Blank

Evaluate the expression.

$$25^{\frac{3}{2}}$$

Fill in the Blank

Evaluate the expression.

$$8^{-\frac{2}{3}}$$

/

Fill in the Blank

Find the real solution(s) of the equation.

$$x^{3\ }=\ 125$$

Fill in the Blank

Find the real solution(s) of the equation.

$$x^{6\ }+36=\ 100$$

Fill in the Blank

Find the real solution(s) of the equation.

$$\frac{1}{3}x^{4\ }=\ 27$$

Multiple Choice

Pick the equivalent expression.

$$\left(\sqrt[3]{5}\right)^4$$

• 5 ^-1/4

• 5 ^4/3

• -5 ^1/4

• 5 ^3/4

Multiple Choice

Pick the equivalent expression.

$$\left(\sqrt[4]{5}\right)^3$$

• 5 ^-1/4

• 5 ^4/3

• -5 ^1/4

• 5 ^3/4

Multiple Choice

Pick the equivalent expression.

$$\frac{1}{\sqrt[4]{5}}$$

• 5 ^-1/4

• 5 ^4/3

• -5 ^1/4

• 5 ^3/4

Multiple Choice

Pick the equivalent expression.

$$-\sqrt[4]{5}$$

• 5 ^-1/4

• 5 ^4/3

• -5 ^1/4

• 5 ^3/4

Multiple Choice

Find f(g(x)) using the functions below.

f(x) = x² + 7, g(x) = 2x + 5

• (2x+5)² + 7

• 4x² + 20x + 7

• 4x² + 20x + 32

• 4x² + 10x + 25

Multiple Choice

Find g(f(x)) using the functions below.

f(x) = x² + 7, g(x) = 2x + 5

• 2x² + 19

• 2x² + 12

• 2x³ + 19

• 2x³ + 12

Multiple Choice

Find (f + g)(x) using the functions below.

f(x) = x² + 7, g(x) = 2x + 5

• x² + 2x + 12

• 3x² + 12

• x² + 9x + 5

• 3x² + 2x + 12

Multiple Choice

Find (f - g)(x) using the functions below.

f(x) = x² + 7, g(x) = 2x + 5

• x² + 2x + 12

• x² - 2x + 2

• x² - 5x - 5

• x² - 2x + 12

Multiple Choice

Find (fg)(x) using the functions below.

f(x) = x² + 7, g(x) = 2x + 5

• 7x² + 7x + 35

• 3x² + 9x + 35

• 3x³ + 5x² + 7x + 35

• 2x³ + 5x² + 14x + 35

Fill in the Blank

Find ( $$\frac{f}{g}$$ )(x) using the functions below.

f(x) = x² - 4, g(x) = x + 2

-

Multiple Choice

Determine if the function is invertible or non-invertible.

• invertible

• non-invertible

• can not determine

Multiple Choice

Determine if the function is invertible or non-invertible.

• invertible

• non-invertible

• can not determine

Multiple Choice

Determine if the function is invertible or non-invertible.

• invertible

• non-invertible

• can not determine

Multiple Choice

Determine if the function is invertible or non-invertible.

• invertible

• non-invertible

• can not determine