Integrated Math I

Students broaden their understanding of equations and inequalities by solving one-variable equations with unknown coefficients, two-variable linear equations and inequalities, systems of equations, and nonlinear expressions and equations. They will expand their understanding of units to incorporate algebraic methods and study direct and inverse variation.

This course marks the beginning of students' exploration of 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 exponential, absolute value, and piecewise functions, creating a solid foundation for analyzing more advanced functions in future courses.

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

This course introduces various critical geometric concepts. Students will become adept at performing single and multi-step geometric transformations in the coordinate plane and describing their functional representations. They will also study essential geometric principles, such as the Pythagorean theorem, special right triangles, circles, and the distance formula.

Students will learn how to apply their knowledge to model various contextual situations at multiple points throughout the course.

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.

Equations & Inequalities

• Solving linear equations and inequalities containing unknown coefficients.
• Using linear equations to model and solve real-world multi-step problems involving speed, distance, time, work, and mixtures.
• Solving compound inequalities and systems of inequalities, graphing their solutions, and modeling situations in context.
• Interval notation, including unbounded intervals and computing unions and intersections of intervals.
• Solving simple polynomial equations using the nth root method.

Two-Variable Equations & Inequalities

• Constructing equations of lines in point-slope and standard form and determining properties of lines given in these forms.
• Solving two-variable systems of linear equations using substitution and elimination, including cases with fractional and decimal coefficients.
• Determining when systems of equations have one, none, or infinitely many solutions and correctly applying consistency and dependency terminology.
• Using two-variable systems to model and solve contextual problems.

Units

• Performing unit conversions using algebraic techniques, including two-step conversions and converting between area units.
• Determining units associated with variables in formulas, including rates of change, and working with standard and non-standard units.
• Understanding and applying the concepts of direct and inverse variation, including modeling and solving real-world and mathematical problems.

Radicals & Rationals

• Manipulating and simplifying radical expressions using the rules of radicals.
• Simplifying simple rational expressions by factoring.
• Solving simple rational equations using various techniques.

Functions

• Interpreting and evaluating functions represented using algebraic notation, mapping diagrams, tables, and graphs.
• Determining whether a given relation is a function, including applying the vertical line test.
• The concepts of domain, range, root, global extrema, and end behavior of functions, and describing these properties for simple functions.
• Identifying the intervals where a function is increasing or decreasing, including the distinction between strict and non-strict increase or decrease.

Absolute Value

• Applying the rules of absolute value.
• Solving absolute value equations and inequalities, including cases with extraneous solutions.
• Plotting graphs of shifted, stretched, and reflected absolute value functions.
• Finding the range and roots of an absolute value function.

Exponents

• Simplifying algebraic expressions using the rules of exponents.
• Solving exponential equations with integer and fractional solutions.
• Constructing expressions and functions that model exponential growth and decay situations given in context.
• Comparing exponential and linear growth and decay.
• Graphing elementary growth and decay functions.

Polynomials

• Defining polynomials, the degree of a polynomial, monomials, binomials, and trinomials.
• Simplifying, adding, subtracting, and multiplying polynomials.
• Calculating a binomial expansion using Pascal's triangle.
• Factoring quadratic polynomials using greatest common factors, perfect squares, difference of squares, and grouping.

Geometry

• Applying translations, reflections, dilations, stretches, and composite transformations to two-dimensional figures.
• Using functions to represent transformations in the coordinate plane and using them to find the image of an object.
• Applying the Pythagorean Theorem.
• Understanding the special right triangles and using them to calculate areas.
• Solving problems relating to medians and centroids of triangles.
• Partitioning line segments.
• Solving problems related to squares inscribed in circles and vice-versa.
• Calculating areas and circumferences of circles and solving related problems.
• Finding perimeters and areas of circular sectors.
• Applying the distance formula in two dimensions.
• Working with parallel and perpendicular lines in the coordinate plane.