Search the California Content Standards

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.

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Use coordinates to prove simple geometric theorems algebraically. [Include distance formula; relate to Pythagorean Theorem.]

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Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. *

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Perform arithmetic operations with complex numbers. [i^2 as highest power of i]

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Know there is a complex number i such that i^2 = −1, and every complex number has the form a + bi with a and b real.

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Perform arithmetic operations with complex numbers. [i^2 as highest power of i]

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Use the relation i^2 = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

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Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

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Solve quadratic equations with real coefficients that have complex solutions.

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Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

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(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).

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Use complex numbers in polynomial identities and equations. [Quadratics with real coefficients]

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(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

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

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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. [Include rational, square root and cube root; 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. [Include rational, square root and cube root; emphasize selection of appropriate models.]

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