AI-A.REI Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning.
AI-A.REI.1a Explain each step when solving a linear or quadratic equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
AI-A.REI.4 Solve quadratic equations in one variable.
AI-A.REI.4.a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Understand that the quadratic formula is a derivative of this process.
AI-A.REI.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
Understand the concept of a function and use function notation.
AI-F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
AI-S.ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, sample standard deviation) of two or more different data sets.
Summarize, represent, and interpret data on two categorical and quantitative variables.
AI-S.ID.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
AI-S.ID.6 Represent bivariate data on a scatter plot, and describe how the variables' values are related.
AI-S.ID.6.a Fit a function to real-world data; use functions fitted to data to solve problems in the context of the data.