Algebra 1

Whether you are currently studying Algebra 1, are looking to get ahead and learn part or all of Algebra 1, or are in Algebra 2 or beyond and are struggling with your fundamentals, this course is a perfect match for you!  The course includes topics covered in Algebra 1 curricula in schools all across the globe.  Get ready for an engaging, comprehensive, and motivating journey towards mastering Algebra 1!

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Chapter 1: Algebraic Expressions and Operations with Real Numbers

This chapter is a comprehensive tour through the basic operations of real numbers and the foundations of algebraic expressions. You will begin with learning about variables and how to translate to and from words and algebraic expressions. From there, a healthy dose of the order of operations (PEMDAS) and plugging numbers into expressions involving variables is your next stop. You will then rock square roots of perfect squares and classify and study the properties of real numbers. Then comes the core part of the chapter where you will review all forms of adding, subtracting, multiplying, and dividing integers, decimals, and fractions. The distributive property and combining like terms are then explored before rounding out the chapter with a brief reintroduction into equations and a review of graphing on the coordinate plane.  Let’s start this Algebra party off right!!

Chapter 2: Solving Equations – From One-Step to Multi-Step

This chapter explores how to solve equations and why the solution processes make sense in great depth. You will first learn how to solve one-step equations involving all four operations and all types of real numbers – integers, fractions, and decimals. With this solid foundation you will then master solving two-step and multi-step equations, all the while translating and crushing word problems involving these equation types. The chapter rounds out with a thorough exploration of solving equations with variables on both sides of the equal sign and a world tour of solving literal equations (equations involving many different variables!). Time to rock these fundamentals of Algebra!!

Chapter 3: Ratios, Proportions, & Percents

This chapter begins with a journey through ratios and rates and includes the all-important technique of converting units using dimensional analysis. You will then rocket into solving proportions and setting up proportions to solve word problems involving scale factors and similar figures. From here it will be time to master how to find the part, whole, and percent in various percentage problems. These concepts are taught both by setting up & solving equations or proportions – both are excellent solution methods. The chapter concludes with the study of calculating simple interest and percent of change, markups, and discounts. Now that you have read the description, let’s get rolling!

Chapter 4: Solving Inequalities

This chapter starts with a review of what inequalities are and how to graph them on number lines before taking you through how to solve one-step inequalities with all four operations, including learning when to (and why to) switch the direction of the inequality signs. From here you will learn how to solve two-step and multi-step inequalities by treating them like they are in their are equations. Then, it is off to a very cool and deep study of compound inequalities and interval notation! The chapter comes to completion with your mastery of absolute value equations and inequalities. Word problems, as always, will be taught throughout the lessons. Let’s go be greater than these inequalities!!!

Chapter 5: Introduction to Graphs and Functions

This chapter gets under way with a lesson on how to graph and interpret real-world data. From there you will study patterns and sequences (including a study of arithmetic sequences). Then, it is off to understanding functions and function rules, which will contain the all-important lesson on domain, range, and the vertical line test! You will master how to create tables of data, function rules, and graphs given real-world word problems – super important! After interpreting and sketching graphs that describe real-world events or “stories”, you will conclude the chapter with understanding the difference between linear and non-linear functions. Ready? Set? Go start learning the foundations of functions!!!!

Chapter 6: Linear Functions and Graphing Lines

This chapter is one of the core branches of Algebra 1. Your journey through lines begins with a super thorough tour of rate of change and slope along with direct variation. From there you will learn the three forms of a linear function: slope-intercept form, point-slope form, and standard form. In your explorations of these three forms, you will learn to graph, construct, and use these linear functions in various scenarios. You will then rock horizontal and vertical lines followed by mastering the ins and outs of parallel and perpendicular lines. The chapter finishes off with a study of scatterplots and the all-important graphing of absolute value functions to understand how graphs are shifted in all directions. Let’s start up this linear awesomeness!!!

Chapter 7: Systems of Linear Equations and Linear Inequalities

This chapter kicks off with learning what systems of linear equations are and how they can be represented and solved by graphing. You will then shuttle over to learning the two core methods for solving systems of linear equations: substitution and elimination. From here you will learn how to translate word problems into systems of linear equations in order to solve the word problems. The last several sections of the chapter will have you learning how to graph linear inequalities and systems of inequalities before finishing up with a lesson on linear inequality word problems. Go see just how great you can be at systems!!

Chapter 8: Exponent Rules & Exponential Functions

This chapter takes you on a math excursion through all the rules of exponents and provides an introduction into exponential functions. You will begin with the rules for multiplying powers with the same bases and raising a power to a power. From there, you will master how to divide powers with the same bases. Then it is off to zero and negative exponents before rocking multiple practice exercises involving several rules in each problem – awesome practice found there! You will master simplifying operations involving scientific notation. The chapter finishes with a flurry of learning about exponential growth and decay, graphing exponential functions, calculating compound interest, and last, but not least, geometric sequences. Yeah…it is a pretty sweet chapter!!! Now go get math-ing!!!

Chapter 9: Polynomials

Welcome to a major bridge between Algebra 1 and Algebra 2! This chapter begins with an introduction to what monomials and polynomials are and how to name them. You will then learn to add and subtract polynomials like a pro. From there you will master how to multiply polynomials, starting with the product of a monomial and a polynomial before rocking the FOIL method to multiply two binomials. A nice lesson on polynomial word problems follows and then it is off to factoring out greatest common factors (GCFs). The chapter ends with the all-important lessons on factoring polynomials employing the “reverse FOIL”, “guess and check”, and factoring by grouping techniques. Awe yeah!!! This chapter is pure math awesomeness!!!

Chapter 10: Graphing and Solving Quadratic Equations

This chapter dives right into how to graph parabolas represented by various types of quadratic equations and tours through the key parts of parabolas and what they look like graphically. From here you will learn how to solve quadratic equations graphically by understanding x-intercepts. Then you are off to the land of solving quadratic equations using the square root and factoring techniques – so massively crucial for your math future! Word problems are interspersed throughout. You will then learn to complete the square of a polynomial before learning how to solve any quadratic equation using the quadratic formula. The chapter comes to a soft landing when you master the discriminant to determine how many solutions a quadratic equation will have. Dig into this fantastically logical journey!

Chapter 11: Introduction to Rational Expressions

This chapter sets you up beautifully for a deep study of Rational Expressions in Algebra 2 and beyond! Please make sure you can rock multiplying and factoring polynomials in Algebra 1 Chapter 9 before crushing this chapter. Your path begins with learning what rational expressions are and how to simplify them. The connections to basic fraction operations are made throughout. You will then become a titan at multiplying and dividing rational expressions before closing out the chapter in style by learning to add and subtract rational expressions. It may be a short party in this chapter, but it is a fun and worthwhile one!! Let’s go!

Chapter 12: Radicals and An Introduction to Trigonometry

This lively chapter begins with a lesson on simplifying square roots of whole numbers that are not perfect squares. From there you will handle how to simplify square roots involving variables raised to powers before learning to multiply radicals. Next stop involves mastering dividing square roots, which includes rationalizing the denominator. Then it is off to adding, subtracting, and using the distributive property with square roots. The next portion of the chapter takes you on a tour of the Pythagorean Theorem and Special Right Triangles.  The chapter finishes with gusto as you learn about Trigonometry and how to apply it to real-world word problems. This is a truly powerful chapter full of exciting stuff connecting you to future courses of math studies! Time to rock it!

Chapter 13: Data Analysis: Techniques and Calculations

This chapter visits many ways you can represent real-world data with mathematics. The tour of knowledge begins with a thorough lesson on Mean, Median, Mode, Range, and Outliers. From there you will master how to construct and analyze Box-and-Whisker Plots before making Frequency Tables and Line Plots. You will learn how to make and interpret Histograms and then accomplish the same goals with Stem-and-Leaf Plots. Your learning excursion through Data Analysis rounds out nicely with the study of how to make Bar and Line Graphs. Jump into some very cool data analysis techniques!!

Chapter 14: Probability, Combinations, and Permutations

This chapter is a deep dive introduction into a serious study of probability and counting the number of ways things in this world can happen! Your rad road starts with an introduction to theoretical probability. From there you will learn about the counting principle and why it works (so very cool!!!). A short hop from here you will learn about compound events – A.K.A. independent and dependent events. Your studies continue with permutations, combinations, and a new math operation – factorials!! The chapter ends with explorations into experimental probability and using probability to make predictions. The world around us is full of seemingly countless possibilities and chances…learn how to calculate some of these scenarios!