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Algebra 2: First Semester Test (Midterm) and Study Guide

This 94 question study guide and 60 question first semester test (all multiple choice) was created for a high school Algebra 2 class. Objectives covered are as follows:

-Simplify radicals containing variables (higher indexes included)

-Add, subtract, multiply, and divide radicals

-Rationalizing the denominator (with monomial or binomial divisors)

-Converting from radical notation to exponential notation and vica versa

-Simplifying expressions with rational exponents

-Simplify radical expressions containing negative radicands and write as a complex number.

-Simplify powers of i

-Add, subtract, multiply, and divide complex numbers (includes rationalizing)

-Arrange the following sets of numbers in a hierarchy: complex, pure imaginary, real, rational, irrational, integers, whole, and natural

-Name all sets to which a value belongs

-Identifying properties

-Factor polynomials: including greatest common factor, difference of squares, sum of cubes, difference of cubes, trinomials, and four terms

-Divide polynomials using long or synthetic division

-Solve absolute value equations

-Solve absolute value inequalities

-Calculate the discriminant of a quadratic equation to determine the number and type of roots

-Solve quadratic equations using the most appropriate method

-Solve polynomial equations by factoring

-Define a polynomial equation in factored/standard form given its zeros

-Identify the multiplicity of zeros and describe the effect of those zeros on the graph

-Solve radical equations

-Recognize the shape of the following parent functions: linear, absolute value, quadratic, cubic, square root, cube root

-Given the graph of a function, identify the parent function

-Given the graph or equation of a function, identify the transformations that took place

-Given the transformations from a parent function, write the equation of the function

-Identify the domain, range, zeros, end behavior, increasing intervals, and decreasing intervals of a function

-Graphing absolute value inequalities

-Systems of equations applications

-Quadratic equations applications

-Determine the equation for the line/curve of best fit using linear, quadratic, cubic, or quartic regression.

-Make predictions using the equation for the line/curve of best fit.

-Evaluate functions

-Operations with functions

-Compositions of functions

-Write the inverse of a function

-Graph the inverse of a function as a reflection across the line y = x

-Use compositions to verify two functions are inverses

**Suggestions:**

1) Assign sections of the study guide over the course of a couple weeks.

2) Consider allowing students to omit any 10 questions should you worry that the test length is too long.

**NEW!** An **editable version** of the test is now included so you can easily make multiple versions or customize to fit your needs! PowerPoint and Equation Editor (usually built in to PowerPoint) are required to edit this file. If your Equation Editor is incompatible with mine, simply delete my equation and insert your own.

**This resource is included in the following bundle(s):**

Algebra 2 Curriculum

**This study guide and test work perfect in conjunction with the following units:**

Unit 1 – Equations and Inequalities

Unit 2 – Linear Functions and Systems

Unit 3 – Parent Functions and Transformations

Unit 4 – Solving Quadratics and Complex Numbers

Unit 5 – Polynomial Functions

Unit 6 – Radical Functions

**LICENSING TERMS: **This purchase includes a license for ** one teacher only **for personal use in their classroom. Licenses are **non-transferable**, meaning they can not be passed from one teacher to another. No part of this resource is to be shared with colleagues or used by an entire grade level, school, or district without purchasing the proper number of licenses. If you are a coach, principal, or district interested in transferable licenses to accommodate yearly staff changes, please contact me for a quote at allthingsalgebra@gmail.com.

**COPYRIGHT TERMS:** This resource may not be uploaded to the internet in any form, including classroom/personal websites or network drives, unless the site is password protected and can only be accessed by students.

This 94 question study guide and 60 question first semester test (all multiple choice) was created for a high school Algebra 2 class. Objectives covered are as follows:

-Simplify radicals containing variables (higher indexes included)

-Add, subtract, multiply, and divide radicals

-Rationalizing the denominator (with monomial or binomial divisors)

-Converting from radical notation to exponential notation and vica versa

-Simplifying expressions with rational exponents

-Simplify radical expressions containing negative radicands and write as a complex number.

-Simplify powers of i

-Add, subtract, multiply, and divide complex numbers (includes rationalizing)

-Arrange the following sets of numbers in a hierarchy: complex, pure imaginary, real, rational, irrational, integers, whole, and natural

-Name all sets to which a value belongs

-Identifying properties

-Factor polynomials: including greatest common factor, difference of squares, sum of cubes, difference of cubes, trinomials, and four terms

-Divide polynomials using long or synthetic division

-Solve absolute value equations

-Solve absolute value inequalities

-Calculate the discriminant of a quadratic equation to determine the number and type of roots

-Solve quadratic equations using the most appropriate method

-Solve polynomial equations by factoring

-Define a polynomial equation in factored/standard form given its zeros

-Identify the multiplicity of zeros and describe the effect of those zeros on the graph

-Solve radical equations

-Recognize the shape of the following parent functions: linear, absolute value, quadratic, cubic, square root, cube root

-Given the graph of a function, identify the parent function

-Given the graph or equation of a function, identify the transformations that took place

-Given the transformations from a parent function, write the equation of the function

-Identify the domain, range, zeros, end behavior, increasing intervals, and decreasing intervals of a function

-Graphing absolute value inequalities

-Systems of equations applications

-Quadratic equations applications

-Determine the equation for the line/curve of best fit using linear, quadratic, cubic, or quartic regression.

-Make predictions using the equation for the line/curve of best fit.

-Evaluate functions

-Operations with functions

-Compositions of functions

-Write the inverse of a function

-Graph the inverse of a function as a reflection across the line y = x

-Use compositions to verify two functions are inverses

1) Assign sections of the study guide over the course of a couple weeks.

2) Consider allowing students to omit any 10 questions should you worry that the test length is too long.

Algebra 2 Curriculum

Unit 1 – Equations and Inequalities

Unit 2 – Linear Functions and Systems

Unit 3 – Parent Functions and Transformations

Unit 4 – Solving Quadratics and Complex Numbers

Unit 5 – Polynomial Functions

Unit 6 – Radical Functions

Total Pages

50 pages

Answer Key

Included

Teaching Duration

N/A

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