College Algebra, Pre-Calculus, & Trigonometry Explained from Udemy

Become a Master of College Algebra, Pre-Calculus, & Trigonometry and Ace your next Algebra/Pre-Calculus/Trigonometry Exam. In this course, you will master all concepts of College-Level Algebra, Pre-Calculus, and Trigonometry, from beginner to advanced, with our step-by-step video tutorials and test your knowledge with over 4500 Practice Test Questions. The concepts you will learn are fundamental to success in higher math classes such as Calculus and Linear Algebra. Note: the Algebra topics covered from Pre-Calculus are also covered in a College Algebra course. Please read the topics below for further details.

The topics of the course include:

Review of Real Numbers
Operations with Polynomials
Factoring Polynomials
Rational Expressions
Rational Exponents
Radical Expressions
Solving Linear Equations/Inequalities
Solving Word Problems with Linear Equations
Complex Numbers
Solving Quadratic Equations (Factoring, Completing the Square, Quadratic Formula)
Solving Word Problems with Quadratic Equations
Solving Quadratic/Rational Inequalities
Solving Radical Equations/Inequalities
Solving Advanced Absolute Value Equations/Inequalities
The Coordinate Plane
Graphing Circles
Distance and Midpoint Formulas
Relations and Functions
Domain and Range
Vertical Line Test
Increasing, Decreasing, Constant Intervals
Graphing Linear Functions
Slope
Forms of a Line
Graphs of Basic Equations (Parent Functions)
Graphing Transformations
Function Operations
The Difference Quotient
Composition of Functions
Solving Linear Systems in Two/Three Variables
Solving Systems of Linear Inequalities in Two Variables
Solving Word Problems with Linear Systems
Curve Fitting, Finding the Equation of a Parabola Given Three Points
Partial Fraction Decomposition
Solving Linear Systems using Gaussian Elimination and Gauss-Jordan Elimination
Matrix Algebra (Adding Matrices, Multiplying Matrices, Solving Matrix Equations)
Finding the Inverse of a Matrix
Solving Linear Systems using the Inverse of a Matrix
Finding the Determinant of a Matrix
Finding the Inverse of a Matrix Using Cofactors
Solving Linear Systems using Cramer's Rule
Applications of determinants: Area of a Triangle, test for collinearity, equation of a line
Determine if functions are one-to-one using the Horizontal line test/algebraic methods
Finding the Inverse of a One-to-One Function
Finding the Inverse of a Domain Restricted Function
Graphing the Inverse of a Function
Graphing Exponential Functions
Solving Exponential Equations with Like Bases
Solving Compound Interest Word Problems
Solving Continuous Compound Interest Word Problems
Graphing Logarithmic Functions
Properties of Logarithms
Expanding Logarithms
Condensing Logarithms
Change of Base Rule for Logarithms
Solving Exponential and Logarithmic Equations
Solving Exponential and Logarithmic Inequalities
Applications of Exponential and Logarithmic Functions
Finding the Vertex Form of a Parabola
How to Graph a Parabola
The Remainder Theorem
Using the Remainder Theorem to test for Zeros of a Polynomial Function
The Factor Theorem
Using the Factor Theorem to factor a polynomial function given one zero
Using the Rational Zeros Theorem to find all possible rational zeros
The Fundamental Theorem of Algebra and the Number of Zeros Theorem
Writing Polynomial Functions Given Zeros and a Point
Conjugate Zeros Theorem
Descartes' Rule of Signs
Intermediate Value Theorem
Boundedness Theorem
Find the upper and lower bounds for zeros of a polynomial function
Solving nonlinear systems of equations
Conic Sections: Parabolas - Focus and Directrix
Conic Sections: Ellipses - Finding the Foci and Graphing
Arithmetic Sequences
Arithmetic Series
Geometric Sequences
Geometric Series
Sets, Subsets, Venn Diagrams
Union of Two or More Sets
Intersection of Two or More Sets
The Binomial Theorem
Counting Theory
Combinations
Permutations
Probability
Angles in Trigonometry
Complementary and Supplementary Angles
Working with Degrees, Minutes, and Seconds
Converting between Decimal Degrees and Degrees, Minutes, and Seconds
Determine if two angles are coterminal angles
Finding angle measures for similar triangles
Finding side lengths for similar triangles
Finding the Trigonometric Function Values of an Angle
Finding the Trigonometric function Values of an Angle Given a Point on the Terminal Side
Finding Trigonometric Function Values Given One Value and the Quadrant
Finding Trigonometric Function Values Based on Pythagorean Identities
Finding Trigonometric Function Values Based on Quotient Identities
Finding Trigonometric Function Values of Acute Angles
Writing Trigonometric Functions in Terms of its Cofunction
Solving Trigonometric Equations Using Cofunction Identities
Reference Angles
Finding Trigonometric Function Values of Non-Acute Angles
Finding Angle Measures with Special Angles
Finding Trigonometric Function Values Using a Calculator
Finding Missing Angle Measures Using Inverse Trigonometric Functions: arcsin, arccos, arctan
Solving Right Triangles
Solving Word Problems with angles of elevation
Solving Word Problems with angles of depression
Radian Measure
Converting Between Radians and Degrees
Finding the Arc Length on a Circle
Finding the Area of a Sector of a Circle
Defining the Six Trigonometric Functions Using the Unit Circle
Solving Trigonometry Word Problems that Involve Linear and Angular Speed
Graphing Sine and Cosine
Graphing Function Transformations of Sine and Cosine
Finding the Amplitude, Period and Phase Shift for Trigonometric Functions
Using the Fundamental Identities to find missing Trigonometric Ratios
Using the Fundamental Identities to rewrite Trigonometric Expressions
Verifying Trigonometric Identities
Sum and Difference Identities for Sine, Cosine, and Tangent
Finding sin(A + B), cos(A + B), and tan(A + B)
Finding sin(A - B), cos(A - B), and tan(A - B)
Finding Trigonometric Function values using Double-Angle Identities
Working with Product-to-Sum and Sum-to-Product Identities
Working with Half-Angle Identities
Evaluating Inverse Trigonometric Functions
Graphing Inverse Trigonometric Functions
Finding the Composition of Inverse Trigonometric Functions
Solving Trigonometric Equations Using Linear Methods
Solving Trigonometric Equations by Factoring
Solving Trigonometric Equations by Squaring/Square Roots
Solving Trigonometric Equations Using Identities
Solving Trigonometric Equations Using the Quadratic Formula
Solving Trigonometric Equations with Half-Angles
Solving Trigonometric Equations with Multiple Angles
Solving Trigonometric Equations Involving Inverse Trigonometric Functions
The Law of Sines (ASA)
The Law of Sines (SAA)
The Area of a Triangle using Sine (SAS)
The Law of Sines Ambiguous case (SSA)
The Law of Cosines (SAS), (SSS)
The Area of a Triangle using Heron's Formula
Finding the Component Form of a Vector
Finding the Magnitude of a Vector
Finding the Direction Angle of a Vector
Finding the Sum (resultant) of Two Vectors
Multiplying a Vector by a Scalar
How to Find the Unit Vector
How to Write a Linear Combination of Unit Vectors
How to Find the Dot Product
How to Find the Angle Between Two Vectors
How to Determine if Two Vectors are Orthogonal
How to Add Two Complex Numbers Graphically
Find the Trigonometric (Polar) Form of a Complex Number
Convert a Complex Number between the Rectangular Form and Polar Form
Multiplying Complex Numbers in Polar Form
Dividing Complex Numbers in Polar Form
Product and Quotient Theorems
De Moivre's Theorem
Powers of Complex Numbers in Polar Form
Roots of Complex Numbers in Polar Form
Solving Equations Using Roots of Complex Numbers
The Polar Coordinate System
Plotting Polar Coordinates on the Polar Grid
Converting Between Polar Coordinates and Rectangular Coordinates
Writing Polar Coordinates in Multiple Forms
Finding the Distance Between Two Polar Points
Converting Linear Equations Between Rectangular and Polar Forms
Graphing Lines on the Polar Coordinate Plane
Converting Circles from Polar to Rectangular Form
Graphing Circles on the Polar Grid
Finding the Inclination of a Line
Finding the Angle Between Two Lines
Finding the Shortest Distance Between a Point and a Line

What's inside

Syllabus

In this section, students will review basic concepts from pre-algebra and algebra 1. These concepts are important to understand in order to succeed in precalculus, calculus, and higher level math.

Welcome to the Course :)

In this lesson, we will review how to classify real numbers as natural numbers, whole numbers, integers, rational numbers, or irrational numbers. We will also review the basics of inequality relationships between two numbers using a number line.

Study Notes for Classifying Real Numbers.

Practice test for classifying real numbers.

(Optional) Practice Test Step-by-Step Solutions

This quiz will test your knowledge of how to classify real numbers.

(Optional) Quiz Step-by-Step Solutions

In this lesson, we will review the concept of an exponent. We will look at how to use exponents to write the repeated multiplication of the same number. We will explore how to work with exponents that have a negative base. Lastly, we will review the rules used to simplify an expression with more than one operation. This procedure is known formally as the order of operations.

Study Notes for Exponents and the Order of Operations.

Practice test for exponents and the order of operations.

In this lesson, we review the product and power rules for exponents.

This quiz will test your knowledge of exponents and the order of operations.

In this lesson, we will review ratios, rates, and proportions.

Study Notes for Ratios, Rates, and Proportions.

Practice test for ratios, rates, and proportions.

Practice test for the product and power rules for exponents.

This quiz will test your knowledge of ratios and proportions.

In this lesson, we will review some basic properties of real numbers. These include:

the commutative properties
the associative properties
the inverse properties
the identity properties
the distributive property

Study Notes for the Properties of Real Numbers.

Practice test for properties of real numbers

This quiz will test your knowledge of the properties of real numbers.

This quiz will test your ability to work with the product and power rules for exponents.

This quiz will test your understanding of how to classify numbers, the order of operations, ratios, rates, proportions and properties of real numbers.

In this lesson, we will review the concept of inequality relationships.

Study Notes for Inequalities, the Number Line, and Interval Notation.

Practice test for inequalities, the number line, and interval notation.

This quiz will test your knowledge of inequalities, the number line, and interval notation.

In this lesson, we will review the basic definition of a polynomial. We will learn how to identify a monomial, binomial, and trinomial. We will also learn how to find the degree of a term and the degree of a polynomial.

In this lesson, we will review the concept of absolute value.

Practice test for absolute value and the distance between two points.

This quiz will test your ability to multiply polynomials.

This quiz will test your knowledge of absolute value and the distance between two points on a number line.

This quiz will test your knowledge of inequalities and absolute value.

In this section, students will review basic concepts from algebra 1. We will review how to perform operations with polynomials (adding, subtracting, multiplying, and dividing).

Practice test for what is a polynomial.

In this lesson, we will learn how to factor a four-term polynomial using the grouping method.

This quiz will test your understanding of the definition of a polynomial.

In this lesson, we will learn how to find frequently occurring polynomial products using special products formulas.

In this lesson, we will learn how to add and subtract polynomials.

Practice test for adding and subtracting polynomials.

In this lesson, we learn how to divide polynomials using synthetic division.

This quiz will test your ability to add and subtract polynomials.

In this lesson, we will learn how to multiply polynomials. We will cover how to multiply a monomial by a polynomial. We will also learn how to find the product of two binomials using FOIL. Lastly, we will learn how to multiply more complex polynomials together.

Practice test for multiplying polynomials.

This quiz will test your ability to find commonly occuring binomial products, more often called "special products".

In this lesson, we will learn how to identify the GCF or greatest common factor for a group of monomial terms. We will then learn how to factor out the GCF from a polynomial.

In this lesson, we will learn how to divide polynomials.

This quiz will test your ability to divide polynomials using long division.

This quiz will test your ability to divide polynomials using synthetic division.

This quiz will test your knowledge of how to perform operations with polynomials.

This quiz will test your ability to find and factor out the GCF (Greatest Common Factor) from a polynomial.

This quiz will test your ability to factor a four-term polynomial using grouping.

In this lesson, we will learn how to factor trinomials with a leading coefficient of 1 into the product of two binomials.

This quiz will test your ability to factor a trinomial when the leading coefficient is 1.

In this lesson, we will learn how to factor trinomials when the leading coefficient is not 1, using the AC Method (factoring by grouping).

This quiz will test your ability to factor trinomials using the AC Method.

In this lesson, we will learn how to factor trinomials when the leading coefficient is not 1, using the reverse FOIL method.

This quiz will test your ability to factor trinomials using reverse FOIL.

In this lesson, we will learn how to factor commonly occuring polynomials using special factoring formulas.

This quiz will test your ability to factor commonly occuring polynomials using special factoring formulas.

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in College Algebra, Pre-Calculus, & Trigonometry Explained with these activities:

Review Properties of Real Numbers

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Solidify your understanding of the fundamental properties of real numbers before diving into more complex algebraic manipulations.

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Review definitions of commutative, associative, and distributive properties.
Work through practice problems applying each property.
Identify examples of each property in algebraic expressions.

Review 'Precalculus Mathematics in a Nutshell' by George F. Simmons

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Get a concise overview of precalculus topics to reinforce your understanding of key concepts.

View Precalculus Mathematics in a Nutshell: Geometry... on Amazon

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Read through chapters on algebra and trigonometry.
Focus on key definitions and formulas.
Work through selected examples.

Review 'Algebra and Trigonometry' by Michael Sullivan

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Supplement your learning with a widely-used textbook that provides comprehensive coverage of algebra and trigonometry.

View Algebra & Trigonometry Enhanced with Graphing... on Amazon

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Read relevant chapters corresponding to course topics.
Work through example problems in the book.
Complete practice exercises at the end of each chapter.

Four other activities

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Show all seven activities

Practice Factoring Polynomials

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Reinforce your factoring skills through repetitive practice to improve speed and accuracy.

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Solve a variety of factoring problems.
Check your answers against solutions.
Identify areas where you struggle.
Repeat with more challenging problems.

Tutor a Student in Algebra

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Solidify your understanding by explaining algebraic concepts to someone else.

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Identify a student who needs help.
Review the material they are struggling with.
Explain the concepts in your own words.
Work through practice problems together.

Develop a Function Graphing Tool

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Apply your knowledge of functions and graphing transformations by creating a tool that visualizes different types of functions.

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Choose a programming language or graphing software.
Implement basic function plotting capabilities.
Add features for transformations and analysis.
Test the tool with various functions.

Create a Trigonometry Cheat Sheet

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Synthesize your knowledge of trigonometric identities and formulas into a concise and useful reference guide.

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Compile all trigonometric identities.
Organize identities by category.
Design a visually appealing cheat sheet.
Share with peers for feedback.

Career center

Learners who complete College Algebra, Pre-Calculus, & Trigonometry Explained will develop knowledge and skills that may be useful to these careers:

Actuary

Actuaries analyze and manage risk, often in the insurance and finance industries. They use mathematical and statistical models to assess the likelihood and potential financial impact of future events. This career path requires a strong foundation in mathematics, and this course helps students master important areas. The skills gained from this course can be directly applied to building and interpreting models which might be used to predict future events. The course's numerous practice questions can improve a student's ability to solve complex problems which is useful in this field.

See salaries and explore the career path for Actuary

Data Scientist

A data scientist analyzes and interprets complex data to identify trends and insights that can help organizations make better decisions. This role involves a strong understanding of mathematical concepts, and this course helps build a foundation in algebra, precalculus, and trigonometry. By mastering these fundamentals, a prospective data scientist is better equipped to understand the mathematical underpinnings of statistical models and algorithms. The problem-solving skills developed through the 4500 practice test questions in the course are also beneficial. The course's coverage of topics like functions, equations, and inequalities helps with the mathematical modeling required in this data-driven role.

See salaries and explore the career path for Data Scientist

Teacher

Teachers educate students in a variety of subjects. This option is specifically for teachers of mathematics at the high school or secondary level. This course helps teachers master algebra, precalculus, and trigonometry and prepare them to clearly and accurately explain these concepts to students. The course's comprehensive coverage and numerous practice test questions can build confidence. In addition, the course helps a teacher prepare lesson plans and assessments which will help their students succeed.

See salaries and explore the career path for Teacher

Financial Analyst

A financial analyst evaluates financial data, provides investment recommendations, and helps organizations make sound financial decisions. This field requires strong quantitative skills, and this course helps develop proficiency in various mathematical areas. The ability to solve equations, work with functions, and understand mathematical models is crucial for tasks such as financial forecasting and risk assessment. A financial analyst will benefit from the numerous practice test questions in the course, which help reinforce understanding and build confidence in problem-solving. Knowledge of the properties of real numbers, combined with skills in solving equations and inequalities, helps with the analytical thinking required for this role.

See salaries and explore the career path for Financial Analyst

Game Developer

Game developers create video games for computers, consoles, and mobile devices. This field increasingly involves mathematical concepts, especially in areas like physics simulations, artificial intelligence, and graphics rendering. This course helps a future game developer to build a foundation in essential mathematical areas. Game developers use mathematical concepts to create realistic and engaging game experiences. Expertise in areas like transformations and trigonometry can be used when designing game mechanics and environments. The course's comprehensive coverage and numerous practice test questions can reinforce mathematical understanding, thus preparing candidates for the challenges of game development.

See salaries and explore the career path for Game Developer

Software Engineer

A software engineer designs, develops, and tests software applications. While computer science is not all math, a solid understanding of mathematical principles helps with algorithm design, problem-solving, and optimization. This course helps a future software engineer to build a foundation in essential mathematical areas. Software engineers often use mathematical concepts to solve complex problems. Expertise in areas like functions, equations, and inequalities comes in handy when designing efficient and stable applications. The course's comprehensive coverage and numerous practice test questions reinforce mathematical understanding, thus preparing candidates for the challenges of software engineering.

See salaries and explore the career path for Software Engineer

Statistician

Statisticians collect, analyze, and interpret data to solve problems in various fields. The role requires a strong mathematical background. This course may help in developing foundational skills in algebra, precalculus, and trigonometry. The course covers topics like functions, equations, and data analysis techniques. It can be useful for understanding statistical concepts and methodologies. With the understanding of concepts covered in this course, statisticians can interpret and draw conclusions from data. The course's approach and practice questions might reinforce mathematical understanding, thus preparing candidates for the challenges of advanced statistical work.

See salaries and explore the career path for Statistician

Operations Research Analyst

Operations research analysts use advanced analytical techniques to help organizations solve problems and make better decisions. This field requires strong quantitative skills, and this course may help in building a foundation in important mathematical areas. An operations research analyst uses these skills to optimize processes, improve efficiency, and reduce costs. The course covers topics like functions, equations, and optimization techniques, which are directly relevant to operations research. The approach and practice questions in the course may help with the analytical thinking required for this role.

See salaries and explore the career path for Operations Research Analyst

Aerospace Engineer

Aerospace engineers design, develop, and test aircraft, spacecraft, and missiles. This field demands a strong understanding of mathematics, and this course can help in building a foundation in important mathematical areas. An aerospace engineer uses these skills to analyze and design complex aerospace systems. The course covers algebra, precalculus, and trigonometry, which are used when modeling flight dynamics and solving engineering problems. The course's comprehensive coverage and practice test questions help reinforce mathematical understanding, this preparing candidates for the challenges of aerospace engineering.

See salaries and explore the career path for Aerospace Engineer

Mechanical Engineer

Mechanical engineers research, design, develop, manufacture, and test mechanical devices and systems. This field requires a robust understanding of mathematics, and this course helps build a foundation in key mathematical areas. A mechanical engineer uses these skills to analyze and design mechanical systems and components. The course's coverage of algebra and trigonometry can be used when modeling physical systems and solving engineering problems. The course's numerous practice test questions help reinforce mathematical understanding, thus preparing candidates for the challenges of mechanical engineering.

See salaries and explore the career path for Mechanical Engineer

Civil Engineer

Civil engineers design, construct, and maintain infrastructure projects such as roads, bridges, and buildings. These professionals need a solid foundation in mathematics, and this course helps students master fundamental mathematical concepts. They use mathematical principles to ensure the safety and stability of structures. The course's coverage of trigonometry helps with surveying and structural analysis. The practice test questions help to reinforce understanding and build problem-solving skills, which are essential for a civil engineer.

See salaries and explore the career path for Civil Engineer

Economist

Economists study the production and distribution of resources, goods, and services by collecting and analyzing data, researching trends, and evaluating economic issues. The role often requires an advanced degree. Quantitative skills are essential for economic modeling and analysis, and a course like this may help in building a foundation in key mathematical fields. Topics like functions, equations, and data analysis can be useful for understanding economic theories and models. The course's approach and practice questions may strengthen mathematical ability, thus preparing candidates for the challenges of economic research and analysis.

See salaries and explore the career path for Economist

Market Research Analyst

Market research analysts study market conditions to examine potential sales of a product or service. They help companies understand what products people want, who will buy them, and at what price. Quantitative skills are essential for analyzing market data, and this course may help in building a foundation in mathematical areas. Topics like functions, equations, and data analysis can be useful for examining market trends and predicting consumer behavior. The course's comprehensive coverage and practice test questions may reinforce analytical skills, thus preparing candidates for the challenges of market analysis.

See salaries and explore the career path for Market Research Analyst

Researcher

Researchers conduct investigations to gain knowledge, often requiring advanced degrees. The specific area can vary widely, but many research roles require the ability to analyze data and solve complex problems. This course may help in developing foundational skills in areas such as algebra and precalculus since the topics range from fundamental to advanced. The work in this course may be beneficial in building a foundation for the mathematical and logical reasoning skills needed to design experiments, interpret results, and draw conclusions. The course's numerous practice test questions reinforce mathematical ability.

See salaries and explore the career path for Researcher

Technical Writer

Technical writers create documentation and instructions for technical products and services. Although not heavily mathematical, a tech writer will inevitably face situations where mathematical literacy is needed. This course helps writers communicate technical information accurately and effectively. Skills in algebra, precalculus, and trigonometry can be useful for understanding and explaining technical concepts. A technical writer can use this training to create clear and concise documentation for a variety of audiences. The skills taught in the course may enhance a technical writer's understanding and improve the clarity of their writing.

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College Algebra, Pre-Calculus, & Trigonometry Explained

What's inside

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