Search the California Content Standards

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.

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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:
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. *

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

Standard:
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *

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

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. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]

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 linear and quadratic functions and show intercepts, maxima, and minima. *

Cluster:
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]

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. *

Cluster:
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]

Standard:
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Cluster:
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]

Standard:
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, and y = (1.2)^t/10, and classify them as representing exponential growth or decay.