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PreCalculus: First Semester Test (Midterm) and Study Guide

This 125 question study guide and 60 question first semester test (all multiple choice) was created for a Pre-Calculus class. Topics covered are as follows:

• Graphs of basic parent functions

• Transformations of functions

• Writing and Graphing Functions using Transformations

• Domain and Range

• Symmetry of Graphs

• Even and Odd Functions

• Continuity of Functions; Types of Discontinuity

• Operations with Functions

• Compositions of Functions

• Piecewise Functions

• Graph and Characteristics of Polynomial Functions

• Predicting End Behavior of a Polynomial Function

• Factored Form of a Polynomial Functions

• Linear Factors and Zeros

• Multiplicity and the Effect on the Graph

• The Remainder Theorem

• The Factor Theorem

• The Rational Zero Theorem

• Descartes' Rule of Signs

• Solving Polynomial Equations (rational, irrrational, and complex solutions)

• Writing the Complete Factorization of a Polynomial Functions

• Writing a Polynomial Function given its zeros

• Graphs and Characteristics of Rational Functions

• Graphs and Characteristics of Exponential Functions

• Graphs and Characteristics of Logarithmic Functions

• Properties of Logarithms

• Expanding and Condensing Logarithms

• Solving Logarithmic Equations

• Solving Exponential Equations

• Exponential Growth and Decay Applications

• Compound Interest and Continuous Compound Interest

• Degrees and Radians

• Degree-Minute-Second Form and Decimal-Degree-Form

• Arc Length

• Area of Sectors

• Finding the Exact Value of the Six Trigonometric Functions for an angle in standard position.

• The Unit Circle

• Graphs and Characteristics of Trigonometric Functions

• Inverse Trigonometric Functions

• Compositions of Trigonometric Functions

• Fundamental Identities: Reciprocal, Quotient, Pythagorean

• Cofunction Identities

• Even-Odd Identities

• Sum and Difference of Angles Identities

• Double-Angle and Half-Angle Identities

• Product-to-Sum Identities

• Sum-to-Product Identities

• Simplifying Trigonometric Expressions

• Solving Trigonometric Equations

• Law of Sines

• Law of Cosines

**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):**

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

**Unit 2 – Functions and Their Graphs**

**Unit 3 – Polynomial and Rational Functions**

**Unit 4 – Exponential and Logarithmic Functions**

**Unit 5 – Trigonometric Functions**

**Unit 6 – Trigonometric Identities and Equations**

**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.

Total Pages

53 pages

Answer Key

Included

Teaching Duration

N/A

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