Integrated Math I

In this course, students broaden their understanding of equations and inequalities, delivering into one-variable equations with unknown coefficients, two-variable linear equations and inequalities, systems of equations, and nonlinear equations. They will learn how to apply their knowledge to model a variety of situations. Students will also deepen their understanding of units and discover how to think of them algebraically and use them to solve problems.

This course marks the beginning of students' journey into the world of functions. They will explore key concepts such as domain, range, roots, extrema, and end-behavior. Furthermore, they will apply this newfound knowledge to study specific function types, namely exponential, absolute value, and piecewise functions, creating a solid foundation for analyzing more advanced functions in future courses.

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.

Building upon their prior understanding of sequences, students will learn to work with formal sequence notation, delve into recursive sequences, and master arithmetic sequences.

This course also introduces various critical geometric concepts. Students will become adept at performing geometric transformations in the coordinate plane and will be able to describe their functional representations. In addition, they will study essential geometric principles, such as the Pythagorean theorem, special right triangles, circles, and the distance formula.

Lastly, students will learn the fundamentals of linear correlation, emphasizing the important distinction between correlation and causation.

By the end of this comprehensive course, students will have significantly enhanced their mathematical skills and knowledge, equipping them for more advanced studies in mathematics.

• 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 of systems 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.
• 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.
• Understand formal sequence notation, recursive and arithmetic sequences, and applications.
• Perform geometric transformations in the coordinate plane, such as translations, rotations, reflections, and composite transformations, and describe and work with their functional representations.
• Gain an in-depth understanding of fundamental geometric concepts such as triangle congruence, the Pythagorean theorem, special right triangles, the area and circumference of a circle, and the distance formula in two dimensions.
• Plot data on a scatter plot, describe the (linear) correlation between two data sets, approximate a trend line and interpret the coefficients. Distinguish between correlation and causation.