Building upon the content learned in middle school, students will strengthen their ability to solve equations and inequalities in one variable. Students will analyze and explain the process of solving an equation by using the Properties of Equality and solving an inequality using the Properties of Inequality. Students develop fluency by writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. Students will also expand their knowledge to solving and graphing absolute value equations and inequalities, as well as solving and graphing compound inequalities.

To prepare for later chapters about functions and the various graphing forms, equations with more than one variable are introduced. Students will see common formulas such as area and volume and learn to manipulate these literal equations so that solving for a missing measurement can be made easier.

Real world scenarios are included to show the applicability of these skills. The general concept of proportionality is explored in depth to further student understanding of ratios and proportions, including unit rates. These are then solved using the Properties of Equality and the Cross Products Property. Unit conversions and dimensional analysis are taught both with conversion factors within measurement systems and between measurement systems; common topics include weight, volume, rate, and speed. Students will also enhance their rounding skills to learn about making smart choices when working with a variety of mathematical topics. Students will be able to make informed decisions about appropriate levels of accuracy and correctly use significant figures — also known as significant digits.

In previous courses, students have learned the basics of graphing points and figures within the coordinate plane. In this chapter, students will expand their knowledge to include graphing lines and functions. At first, linear equations will be graphed using a table of values. Tables of values allow students the opportunity to explore the relationship between points, equations, and eventually functions.

As an introduction to graphing linear equations, students will learn about rate of change, constant rate of change, direct variation, and proportional relationships as prerequisite knowledge to finding the slope and y-intercept of a line. Once the foundational knowledge is understood, graphing and equation writing skills are strengthened by teaching students about how and when to use the various graphing forms of linear equations. Students will explore slope-intercept form, point-slope form, and the standard form. Students will also learn what it means for two lines to be parallel or perpendicular, and how to find this out by looking at or manipulating the various graphing forms.

After students have a firm grasp of graphing lines, their graphing knowledge will be expanded upon to include linear inequalities, absolute value equations, and absolute value inequalities. Students will learn about the difference between strict and nonstrict inequalities and whether to shade above or below the boundary line.

In this chapter, students will learn to apply the skills they have learned about relations and equations to functions. Relations will be displayed using tables, mapping diagrams, equations, and graphs. The Vertical Line Test will be introduced as a method of reliably determining whether or not a relation is a function. Students will learn how to use function notation to write and evaluate function rules, think about ordered pairs on the coordinate plane as inputs and outputs, classify variables as independent or dependent, and build upon their foundational knowledge of domain and range. Real world scenarios are included to emphasize the applicability of these skills to everyday life.

Functions operations will be seen. By the end of this chapter, students will be able to add, subtract, multiply, and divide functions and determine the new domain and range for the transformed function. Additionally, students will learn to compose functions; the composition of functions will be further applied to the concept of inverse functions so that students can see how inverse functions undo each other.

Students will explore several examples of functions including linear functions and absolute value functions. Students will also explore the various forms of transformations including translations, reflections, stretches, and shrinks. They will be able to interpret functions given graphically, numerically, and verbally as well as translate between these representations and understand the limitations of each type.

Finally, students will learn about arithmetic sequences. Common differences are found and used to write explicit and recursive rules for these sequences and to describe patterns. Students will also be able to find a missing term or the $n$th term of a sequence. Arithmetic sequences can be graphed in a coordinate plane and then written as a linear function.

This chapter builds upon students' prior experiences with data, providing students with more formal means of assessing how a model fits data. Various ways of representing and interpreting data in graphical displays such as dot plots, histograms, stacked histograms, and box plots — also known as box and whisker plots — will be investigated. Using these data visualizations, students will be able to analyze measures of center and measures of spread. Mean, mean absolute deviation, and standard deviation are taught as methods of comparisons between different data sets. Students are taught to accurately determine if an extreme value is mathematically an outlier and how these values can affect the measures of spread and center. It will also be shown when it is appropriate to consider removing an extreme value from a data set, perhaps when the value is caused by a data recording error.

In addition to quantitative data, the topic of categorical data is discussed. Categorical data is explored through two-way tables and two-way frequency tables as well as joint and marginal frequency tables. Students learn to find the probability of categorical events in terms of conditional frequencies, joint frequencies, marginal frequencies, conditional relative frequencies, and joint and marginal relative frequencies.

Students use linear regression techniques to describe approximate linear relationships between quantities in bivariate data sets. They use graphical representations, usually scatter plots, and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at correlation, correlation coefficients, and residuals to analyze the goodness of fit of trend lines and lines of best fit. These lines of fit are then used to make predictions about future behavior.

The purpose of this chapter is to teach the fundamentals of systems of equations and inequalities, focusing primarily on linear equations and linear inequalities. Students will learn what a system of equations is and the significance of a point of intersection. Solutions to systems of equations are found graphically and algebraically through both the Elimination Method and the Substitution Method.

Students will learn what it means when there are no solutions, the system is inconsistent, and when there are infinitely many solutions, the system is dependent, as opposed to when there is exactly one solution, the system is consistent and independent. Students will be taught to identify these special system types when seen on coordinate planes as parallel or coincidental lines and by comparing equations. They will also learn to interpret the result when an algebraic solving method has concluded with either a contradiction or an identity.

For systems of inequalities, students will review what they previously learned about boundary lines and directional shading and learn to apply these skills to situations where there is more than one linear inequality on one coordinate plane. It is shown how to interpret the overlapping region as the solution set of the system.

Finally, students will expand their knowledge to include new function types: piecewise functions, step functions, and greatest integer or floor functions. After they have a firm grasp of piecewise functions, students will be shown how to draw absolute value functions and inequalities as piecewise functions, each side of the vertex being treated as its own piece.

In this chapter, students will begin by expanding their knowledge of exponents from previous courses to include rational number exponents. Students will explore the relationship between rational exponents and radicals; the denominator of a rational exponent being the index of a root and the numerator being the power to which the radicand is raised. The Properties of Exponents — the Product of Powers Property, Quotient of Powers Property, Power of a Product Property, Power of a Quotient Property, and Power of a Power Property — are used to simplify both radicals and roots as well as translate between the two forms.

Once exponents are understood, exponential functions — both equations and inequalities — are introduced. Students will be able to graph exponential functions by interpreting the coefficient $a$ and the base $b.$ They will also be able to identify key features of graphs such as domain, range, and end behavior. After the basics of graphing are grasped, transformations of the parent function, such as reflections, translations, and stretches and shrinks, will be investigated. This chapter will continue on to inform students about methods for solving exponential equations and inequalities. The methods discussed in this course are graphing both sides of the equation or inequality to find the point(s) of intersection and rewriting the expressions to have the same exponential base on both sides.

Exponential functions are discussed in real-world scenarios and applications. The values of $a$ and $b$ tell us if a function is an example of exponential growth or exponential decay and the functions can be used to calculate compound interest or devaluation. Students will learn to determine if a situation would be better described by a linear or exponential model by interpreting the given information such as rate of change.

The final lesson analyzes geometric sequences as a type of exponential relationship. Students are taught how the rate of change is the common ratio of a geometric sequence and the $y\text{-}$intercept is the first term, also known as the initial value. Geometric sequences can be described by explicit rules and recursive rules, both of which can be used to find any missing terms.

The first half of this chapter focuses on how the Properties of Real Numbers and Properties of Exponents are applied to polynomials and polynomial operations. First, students will learn how to know if an algebraic expression is a monomial, polynomial, or neither. Then students will learn how to identify characteristics of monomials and polynomials — the terms and the parts of each term such as the coefficients, or leading coefficient for the first term, and degree. Once the various aspects of polynomials are understood, students will learn how to combine like terms when adding and subtracting these expressions; the Closure Property of Polynomial Addition and Subtraction is discussed in this process.

Students will learn about polynomial multiplication and how it relates to the Distributive Property. Multiple methods, such as the table method and FOIL, are taught to help students remember to multiply all of the terms in the polynomials. Special products of polynomials are also explored. These special products include that the square of a binomial is a perfect square trinomial, that the multiplication of conjugate binomials results in a difference of squares, and the special pattern for the cube of a binomial.

In the later lessons, students will take what they've learned about polynomial multiplication and apply it in reverse to factor quadratic trinomial expressions. Students will factor by identifying greatest common factors, by analyzing the coefficients of trinomials to find factor pairs that will result in the known product, and by recognizing special polynomial products.

By the time students are studying this chapter, they should have a firm grasp on functions and their graphs as well as factoring quadratic trinomials. The introductory lesson will discuss the key characteristics and features of quadratic functions such as the minimum or maximum value, the vertex and direction of opening of the parabola, the $x\text{-}$intercepts and how they relate to the factors of a quadratic trinomial, the $y\text{-}$intercept and its relationship to the constant of the trinomial, and the axis of symmetry. After students understand the characteristics of quadratic functions, they will learn how to draw these functions from the vertex form, factored form, and standard form of quadratic functions. Conversely, they will be able to write the function in each of these forms given a graph or given a different form.

Continuing through the chapter, students will learn to solve quadratic equations in a variety of methods. In addition to analyzing the graph of an equation to find its roots, quadratic equations can be solved by taking square roots, by factoring and using the Zero Product Property, by completing the square, and by using the Quadratic Formula. Students will also learn how to determine when, and what it means if, an equation has one, two, or no solutions. They will be able to do this by either looking at the direction of opening in relation to the vertex or by using the discriminant of the Quadratic Formula.

To ensure that students do not struggle with any of the solving methods, an additional lesson is included to review and expand upon the more difficult aspects of working with square roots. The Properties of Square Roots are reviewed, rationalizing a denominator is introduced, irrational conjugates are taught, and many examples are given.

The goal of this chapter is to show students the practical applications of quadratic functions. Throughout the lessons, students will learn how to interpret the vertex, maximum or minimum value, periods of increasing and decreasing, $x\text{-}$ and $y\text{-}$intercepts, domain and range, and end behavior of a quadratic function in situations such as the optimization of area, the valuation of a classic car, and the flight path of a football.

Additional topics covered in this chapter are inverses of quadratic functions, transformations of quadratic functions, and systems of equations involving quadratic equations. Students will investigate square root functions as the inverse functions of quadratic functions. Students will see the relationship between square root functions and quadratic functions in the coordinate; as a reflection over the line $y=x.$ The Vertical Line Test and the Horizontal Line Test are discussed as methods to know if a function is invertible and how restricting a domain can fix any invertibility. Transformations of quadratic functions include reflections, translations, and stretches and shrinks. Students will learn how these transformations affect both the graphs of the functions as well as the equations of the functions. Knowledge of solving systems of equations learned in previous chapters and courses will be expanded upon to involve linear-quadratic systems, quadratic-quadratic systems, and systems involving circles.

Finally, differences between linear, quadratic, and exponential functions will be observed. These functions can be compared by their exponents, rate of change, and function graphs; linear models have a common difference or constant rate of change, exponential models have a common ratio, and quadratic models have a constant second difference. Real world examples of each type of function are seen and students are taught to make logical decisions when choosing which type of function best fits a given scenario.