Search the California Content Standards

Cluster:
Visualize relationships between two-dimensional and three-dimensional objects.

Standard:
Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k^2, and k^3, respectively; determine length, area and volume measures using scale factors. CA

Cluster:
Visualize relationships between two-dimensional and three-dimensional objects.

Standard:
Verify experimentally that in a triangle, angles opposite longer sides are larger, sides opposite larger angles are longer, and the sum of any two side lengths is greater than the remaining side length; apply these relationships to solve realworld and mathematical problems. CA

Cluster:
Translate between the geometric description and the equation for a conic section.

Standard:
Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

Cluster:
Translate between the geometric description and the equation for a conic section.

Standard:
Derive the equation of a parabola given a focus and directrix.

Cluster:
Use coordinates to prove simple geometric theorems algebraically.

Standard:
Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). [Include simple circle theorems.]

Cluster:
Use coordinates to prove simple geometric theorems algebraically.

Standard:
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

Cluster:
Interpret functions that arise in applications in terms of the context. [Emphasize selection of appropriate models.]

Standard:
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. *

Cluster:
Interpret functions that arise in applications in terms of the context. [Emphasize selection of appropriate models.]

Standard:
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*

Cluster:
Interpret functions that arise in applications in terms of the context. [Emphasize selection of appropriate models.]

Standard:
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. *

Cluster:
Analyze functions using different representations. [Focus on using key features to guide selection of appropriate type of model function.]

Standard:
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. * Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. *