# BPS District Mathematics Standards Book

## HS Math Courses

### Algebra I

Algebra I is a branch of mathematics that includes the use of variables to express general rules about numbers, number relationships, and operations. This is the first course in the traditional college preparatory sequence. This course will also be beneficial for anyone interested in a technical career.
Note: Standards Identifiers auto-link to popup a detailed description and links to Proficiency Scales with Prioritized Standards Identifiers being highlighted a sky-blue.

## MAT-09.NO (NO) Number and Operations

• MAT-09.NO.01    Explain how the definition of rational exponents follows from extending the properties of integer exponents; rewrite simple expressions involving radicals and rational exponents using the properties of exponents.
• MAT-09.NO.02    Perform basic operations on simple radical expressions to write a simplified equivalent expression.
• MAT-09.NO.03    Choose and interpret the scale and the units in graphs and data displays.
• MAT-09.NO.04    Define appropriate quantities and units for the purpose of descriptive modeling.
• MAT-09.NO.05    Choose a level of accuracy or precision appropriate to limitations on measurement when reporting quantities.

## MAT-09.AR (AR) Algebraic Reasoning

• MAT-09.AR.01    Use the structure of an expression (i.e., quadratic and exponential) to identify ways to rewrite it.
• MAT-09.AR.02    Rearrange formulas to isolate a quantity or variable(s) of interest using the same reasoning as in solving equations.
• MAT-09.AR.03    Create equations and inequalities in one variable and use them to solve problems.
• MAT-09.AR.04    Create linear and exponential equations in two or more variables to represent relationships between quantities.
• MAT-09.AR.05    Justify each step in solving a linear equation that may or may not have a solution.
• MAT-09.AR.06    Solve linear equations and inequalities (to include compound inequalities) in one variable.
• MAT-09.AR.07    Solve a system of linear equations graphically and algebraically.
• MAT-09.AR.08    Graph the solution set to a two-variable system of linear inequalities.
• MAT-09.AR.09    Solve absolute value equations and inequalities in one or two variables.
• MAT-09.AR.10    Solve quadratic equations in one variable by inspection (e.g., for x² = 49) taking square roots, the quadratic formula, and factoring, as appropriate to the initial form of the equation.
• MAT-09.AR.11    Add, subtract, and multiply polynomials.

## MAT-09.AR (F) Function

• MAT-09.AR.F.01    Determine whether a relationship is a function given a table, graph, or words, identifying x as an element of the domain and f(x) as an element in the range.
• MAT-09.AR.F.02    Use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in context.
• MAT-09.AR.F.03    Sketch the key features (to include intercepts, maximums, minimums, and lines of symmetry, where applicable) of linear, exponential, and quadratic functions modeling the relationship between two quantities using tables, graphs, written descriptions, and equations.
• MAT-09.AR.F.04    Relate the domain of a linear, quadratic, or exponential function to its graph and, where applicable, to the quantitative relationship it describes.
• MAT-09.AR.F.05    Calculate and interpret the rate of change of linear, quadratic, or exponential functions (presented algebraically or as a table) over specified intervals. Estimate the rate of change from a graph.
• MAT-09.AR.F.06    Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.
• MAT-09.AR.F.07    Compare key features of two linear, exponential, or quadratic functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
• MAT-09.AR.F.08    Identify situations that can be modeled with linear, quadratic, and exponential functions. Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays.
• MAT-09.AR.F.09    Identify the effect of transformations on the graph of a linear, absolute value, or quadratic function by replacing f(x) with af(x), f(x - h), and f(x) + k, for specific values of a, h, and k (both positive and negative). Find the value of a, h, and k given the graph of the function.
• MAT-09.AR.F.10    Find the inverse of a linear function and describe the relationship between the domain,range, and graph of the function and its inverse in context.
• MAT-09.AR.F.11    Interpret the parameters in a linear,quadratic, or exponential function in context.
• MAT-09.AR.F.12    Identify, using graphs or tables, the solution(s) to linear and exponential functions f(x) = g(x) as x-value(s) that result in equivalenty-values.