- Gavin Walton
- August 17, 2024

Welcome to the one and only guide for passing your study.com Math 105: Precalculus Algebra exam! So if you are preparing for this course, you will be set for a mathematical ride where the outcome would prepare you on how to approach different higher mathematics courses plus real-life problems. This course is intended to study mathematical modeling deeply, derivatives, and solutions of different equations and inequalities with symbols and graphs. From the purely mathematical lover to the student merely enduring, there’s something interesting in this class.

Think of study.com Math 105: Precalculus Algebra as your tool kit for how you want to read and perceive mathematics. You will be able to write and solve equations that describe the situations you meet in everyday life, compare the values of functions, and even take a glimpse at the derivatives. It concerns going beyond simple analytics and learning a systematic way to think that will be valuable in every future assignment. Therefore, sit tight, put on your seat belt, and let me help you to defeat the precalculus algebra and the world with it!

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## A Sneak Peek into Math 105📖

Embarking on study.com Math 105: Precalculus Algebra tells you that you are going to study a range of mathematical ideas that will help pave the way for other math classes. This class comprises numerous subjects each of which is central to achieving mastery in precalculus algebra.

Starting with Mathematical Modeling, here are some of the courses you are going to learn. This entails the use of symbols on a pattern, which best represents an occurrence in the real world. The topics include how to write and assess expressions associated with geometric figures, learn about linear models, also use systems of linear equations to get the breakeven points and market equilibrium. These are not just theoretical ideas; they are the strategies that are used in different decision-making processes in different areas including commerce and engineering.

Then, Linear Equations & Inequalities present the next topic in the course. By the end of the combined course, you will be able to recognize and plot linear equations, comprehend the concepts of slope and intercepts, as well as solve systems of equations. This segment is elementary because linear equations are encountered throughout mathematics, as well as in other spheres of human life and education.

Further on, Quadratic Functions and Rational Expressions & Functions are included in what is to be covered. These sections are important for the proctored final exam, specifically the Speaking Section. Quadratic equations will be factored in, the process of completing the square will be viewed, and solving quadratic inequalities will also be developed. For rational functions, you will learn operations on rational expressions, their graphs, and asymptotes.

The content of the book is divided into chapters and each chapter progresses from the previous one, hence a clear understanding of precalculus algebra. It is pertinent to spend time doing problems since this is an excellent way of revising and grasping the concepts in the book. self-paced will enable you to take more time on sections that you need to practice as you prepare for the final exam of the course.

### How to Study Weekly for Math 105📝

Are you ready to ace your study.com Math 105: Precalculus Algebra? Below is a suggested plan of study for a week to ensure that you do not lag behind and are well-prepared for the final exam. The reader of this guide will be guided towards successful abstractions that lay a strong base and use regular exercises for creating different concepts

**Week 1: Introduction & Mathematical Modeling**

**Lessons to Cover:**Introduction to algebraic expressions and linear models.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Practice writing and solving algebraic expressions.
**External Resource:**Khan Academy – Algebra Basics

**Week 2: Linear Equations & Inequalities**

**Lessons to Cover:**Linear equations, slope-intercept form, and graphing inequalities.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Solve practice problems on graphing linear equations.
**External Resource:**PatrickJMT – Linear Equations

**Week 3: Quadratic Functions**

**Lessons to Cover:**Factoring quadratics, quadratic formula, and graphing parabolas.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Practice solving quadratic equations using different methods.
**External Resource:**Professor Leonard – Quadratics

**Week 4: Rational Expressions & Functions**

**Lessons to Cover:**Multiplying, dividing, adding, and subtracting rational expressions.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Practice simplifying rational expressions and solving rational equations.
**External Resource:**Mathispower4u – Rational Expressions

**Week 5: Polynomial Functions**

**Lessons to Cover:**Adding, subtracting, and multiplying polynomials; polynomial long division.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Practice polynomial operations and solve practice problems.
**External Resource:**Khan Academy – Polynomial Operations

**Week 6: Geometry Basics**

**Lessons to Cover:**Area and circumference of a circle, distance formula, and midpoint formula.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Solve problems involving geometric figures and formulas.
**External Resource:**Math Antics – Geometry

**Week 7: Functions Overview**

**Lessons to Cover:**Domain and range, power and radical functions, points of discontinuity.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Practice identifying domain and range and graphing functions.
**External Resource:**PatrickJMT – Functions

**Week 8: Function Operations**

**Lessons to Cover:**Adding, subtracting, multiplying, and dividing functions; inverse functions.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Practice performing operations on functions and finding inverses.
**External Resource:**Khan Academy – Function Operations

**Week 9: Graph Symmetry**

**Lessons to Cover:**Symmetry in graphs, even and odd functions.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Practice identifying symmetry and classifying functions as even or odd.
**External Resource:**Mathispower4u – Graph Symmetry

**Week 10: Exponential and Logarithmic Functions**

**Lessons to Cover:**Exponential growth and decay, properties of logarithms, graphing logarithmic functions.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Practice solving exponential and logarithmic equations.
**External Resource:**Khan Academy – Exponential & Logarithmic Functions

**Week 11: Essentials of Trigonometry**

**Lessons to Cover:**Trigonometric functions, identities, and equations.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Practice solving trigonometric equations and proving identities.
**External Resource:**Khan Academy – Trigonometry

**Week 12: Introduction to the Derivative**

**Lessons to Cover:**Rate of change, formal definition of the derivative, graphing derivatives.**Activities:**- Watch video lessons and take notes.
- Complete quizzes for each lesson.
- Practice calculating and graphing derivatives.
**External Resource:**Paul’s Online Math Notes – Derivatives

This, of course, will help you prepare well for the final exam, and if you stick to the study plan above, you’ll definitely be ready for the test. Repetition is important, do not rush through the material and if there is a hard topic that was discussed just go over it again and do not be shy to use an extra resource.

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### Supplement Your Math 105 Learning with Free Resources📂

Below is a list of the best and actually free resources on the Internet that will make it easy to understand the intricate concepts in study.com Math 105: Precalculus Algebra, and perform great on the final exam.

**Khan Academy**

**Algebra Basics:**Khan Academy – Algebra Basics**Polynomial Operations:**Khan Academy – Polynomial Operations**Function Operations:**Khan Academy – Function Operations**Trigonometry:**Khan Academy – Trigonometry**Exponential & Logarithmic Functions:**Khan Academy – Exponential & Logarithmic Functions

**YouTube Channels and Playlists**

**PatrickJMT:**For clear and concise explanations on various math topics.**Mathispower4u:**A great resource for step-by-step tutorials on numerous algebra and precalculus topics.**Professor Leonard:**Excellent in-depth lectures that cover a wide range of math topics.

These resources are perfect for supplementing your study.com materials, providing different perspectives, explanations, and plenty of practice problems. Make sure to take advantage of them!

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### Focus Topics for Success in Math 105🔑

Explaining the major terms used in study.com Math: Precalculus Algebra is helpful in understanding the subject, especially in the final exam in Math 105. Below are four big subjects that are clearly described with examples and the possibilities to compare to enhance your knowledge.

**Quadratic Functions**

Quadratic functions are a cornerstone of this course. They are typically written in the form y=ax2+bx+cy = ax^2 + bx + cy=ax2+bx+c. Understanding how to factor these functions, use the quadratic formula, and complete the square is essential.

**Rational Expressions**

Rational expressions involve fractions where the numerator and/or the denominator are polynomials. You need to know how to perform operations on these expressions and solve rational equations.

**Exponential and Logarithmic Functions**

Exponential and logarithmic functions are vital for modeling growth and decay processes.

**Trigonometric Functions**

Trigonometric functions relate angles to side lengths in right triangles. Understanding their properties and identities is crucial.

These key concepts are not only heavily featured in the course but are also critical for solving complex problems efficiently. Mastering these areas will give you a significant advantage on the final exam.

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### Top Questions about Math 105 Answered❓

While going through study.com Math 105: Precalculus Algebra, you may have these few questions. Here are some frequently asked questions that might help clear up any confusion:

**Q: What should I do to make preparation for the proctored final exam efficient?**

A: If you want to follow a good week-by-week study schedule, you can use the following guidelines: Each day should be devoted to understanding a particular concept and the Migliorini Chapter Recaps can be used for self-testing. Take the quizzes at the end of each lesson, make use of the additional external resources, and revisit the topics that were covered frequently.

**Q: Is it allowed to use a calculator while taking proctored exams?**

A: Yes, the use of a non-graphing, scientific calculator will be allowed. Study.com will similarly allow the use of the Desmos scientific calculator during the exam. Nevertheless, any computer, calculator especially graphing calculators, and any other programs are prohibited.

**Q: What should I do if I find some topic to be a bit difficult for me to understand?**

A: If you are having a problem comprehending a certain topic, go back to the video lessons and jot down notes in detail. The Use of external resources mentioned above, for other explanations and the practice problems mentioned above. Of course, do not forget to contact study.com for further support.

**Q: To what extent are the quizzes in this course essential?**

A: It is common knowledge that quizzes are very important as they contribute to a large percentage of the final grade (points 100 out of 300). They assist in re-stating and checking up on what has been understood and being practiced. Here, one gets to attempt each quiz three times and the best score will be considered.

**Q: What will I do if I fail the final exam in the initial attempt?**

A: In case you are not satisfied with the score you got on the proctored final exam, you have to wait for 3 days to take the test again. You can take this exam twice, after which you can no longer try to improve your score. For this reason, ensure you use the study guide and take your time when seeking the exam.

**Q: Are there any specific strategies for solving quadratic equations?**

A: Yes, there are several strategies including factoring, using the quadratic formula, and completing the square. Practice each method to understand their applications and choose the most suitable one depending on the equation.

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### Math 105: Wrap-Up📄

In Math 105: Precalculus Algebra, it will be evident that this course provides you with a core foundation for progression mathematically and solving real-life applications. Through a particular schedule, using resources from the Internet, and studying the main topics of a course, you are to be ready for the more severe proctored final exam.

Remember, consistency is key. Always solve exercises, go through the information that is difficult to understand, and do not shy away from asking a tutor for more assistance. This makes it easy for you not only to learn but to also apply this knowledge as seen from the video lessons, quizzes, and even the proctored exam offered.

Come to this course with confidence and open mind as each topic connects to the next to provide the overall picture of precalculus algebra. Good luck, and enjoy your mathematical journey!