Algebra I

In this course, students will significantly broaden their understanding of equations and inequalities. This includes delving into one-variable equations and inequalities with unknown coefficients, two-variable linear equations and inequalities, and systems of equations and inequalities. Students will acquire the skills necessary to apply this knowledge in modeling a variety of real-world situations.

Students will deepen their comprehension of units of measurement. They will learn to approach units from an algebraic perspective and master the art of using unit manipulations to solve problems.

This course sees the introduction of functions into the student's mathematical journey. Here, they will explore fundamental concepts such as domain, range, roots, extrema, end behavior, and inverse functions. Armed with this knowledge, students will delve into the study of specific function types - including exponential, absolute value, and piecewise functions - establishing a solid foundation for analyzing more advanced functions in subsequent courses.

Students will learn to perform arithmetic operations with rational and radical expressions and solve simple rational and radical equations.

For the first time, students will encounter polynomials. They will become proficient in terminology associated with one-variable polynomials and master fundamental polynomial operations such as addition, subtraction, multiplication, and factoring.

Students will master solving, graphing, and interpreting quadratic equations and functions. They will become adept at using various techniques for analyzing quadratics, including factoring, completing the square, and applying the quadratic formula. Real-world applications, including vertical motion and profit function analysis, are tackled within these units.

In the final unit, students will explore the world of sequences. They will dive deeply into arithmetic and geometric sequences and learn to identify, model, and apply sequences in various situations.

• Master linear equations, including cases with one or multiple unknown coefficients, and apply their skills to real-world problems involving consecutive integers, speed, distance, time, work, and mixtures.
• Become proficient in solving linear inequalities. They will apply interval notation to describe solutions, find unions and intersections of intervals, solve systems of inequalities, graph solutions to inequalities, and model situations using inequalities.
• Develop proficiency in two-variable linear equations, including point-slope form, standard form, and master procedures for determining properties of straight lines. They will also describe how parallel and perpendicular lines in the coordinate plane are related.
• Gain mastery in solving two-variable systems of linear equations using substitution and elimination. This includes cases with fractional and decimal coefficients, systems with no solutions, and many solutions. Students will relate solutions to the intersection of two lines and apply their understanding to modeling situations. Furthermore, students will begin to develop an understanding of systems of nonlinear equations.
• Solve simple square root, cube root, and higher-root equations and identify cases with no real solutions.
• Gain a deeper understanding of units and their applications, including unit conversions using algebraic techniques and working with direct and inverse variation.
• Explore radical and rational expressions, and develop the ability to manipulate and solve equations involving these concepts.
• Begin their journey into functions. Students will also be introduced to key concepts such as various representations of functions, the vertical line test, domain, range, global extrema, end-behavior, increasing and decreasing functions, function arithmetic (including function composition), and inverse functions.
• Master the rules of absolute value, solving simple absolute value equations and inequalities, and plotting and analyzing absolute value functions.
• Develop a strong foundation in exponential equations and functions, including manipulating expressions, solving equations, graphing exponential functions, and exponential growth and decay applications.
• Become proficient in working with polynomials, including simplifying, adding, subtracting, multiplying, and factoring polynomials.
• Solve quadratic equations using various methods, including applying the zero product rule, completing the square and the quadratic formula.
• Graph and analyze quadratic functions, calculate the axis of symmetry using various methods and find intersections of lines and quadratic functions.
• Model real-world situations using quadratic functions, including vertical motion, revenue, cost, and profit functions.
• Understand formal sequence notation, recursive, arithmetic, geometric sequences, and applications.