Search the California Content Standards

Cluster:
Solve systems of equations. [Linear systems]

Standard:
Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

Cluster:
Solve systems of equations. [Linear systems]

Standard:
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

Cluster:
Construct and compare linear, quadratic, and exponential models and solve problems. [Linear and exponential]

Standard:
Distinguish between situations that can be modeled with linear functions and with exponential functions. * Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. *

Cluster:
Construct and compare linear, quadratic, and exponential models and solve problems. [Linear and exponential]

Standard:
Distinguish between situations that can be modeled with linear functions and with exponential functions. * Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. *

Cluster:
Construct and compare linear, quadratic, and exponential models and solve problems. [Linear and exponential]

Standard:
Distinguish between situations that can be modeled with linear functions and with exponential functions. * Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. *

Cluster:
Construct and compare linear, quadratic, and exponential models and solve problems. [Linear and exponential]

Standard:
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). *

Cluster:
Construct and compare linear, quadratic, and exponential models and solve problems. [Linear and exponential]

Standard:
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. *

Cluster:
Interpret expressions for functions in terms of the situation they model. [Linear and exponential of form f(x) = b^x + k]

Standard:
Interpret the parameters in a linear or exponential function in terms of a context. *

Cluster:
Experiment with transformations in the plane.

Standard:
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

Cluster:
Make geometric constructions. [Formalize and explain processes.]

Standard:
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.