Search the California Content Standards

Cluster:
Understand congruence and similarity using physical models, transparencies, or geometry software.

Standard:
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Cluster:
Understand and apply the Pythagorean Theorem.

Standard:
Explain a proof of the Pythagorean Theorem and its converse.

Cluster:
Understand and apply the Pythagorean Theorem.

Standard:
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Cluster:
Understand and apply the Pythagorean Theorem.

Standard:
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Cluster:
Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Standard:
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Cluster:
Build a function that models a relationship between two quantities. [Quadratic and exponential]

Standard:
Write a function that describes a relationship between two quantities. * Determine an explicit expression, a recursive process, or steps for calculation from a context. *

Cluster:
Build a function that models a relationship between two quantities. [Quadratic and exponential]

Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. *

Cluster:
Build new functions from existing functions. [Quadratic, absolute value]

Standard:
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Cluster:
Build new functions from existing functions. [Quadratic, absolute value]

Standard:
Find inverse functions. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2x^3.

Cluster:
Interpret functions that arise in applications in terms of the context. [Quadratic]

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. *