Search the California Content Standards

Cluster:
Interpret the structure of expressions. [Linear, exponential, and quadratic]

Standard:
Use the structure of an expression to identify ways to rewrite it.

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Write expressions in equivalent forms to solve problems. [Quadratic and exponential]

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Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Factor a quadratic expression to reveal the zeros of the function it defines.*

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Write expressions in equivalent forms to solve problems. [Quadratic and exponential]

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Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.*

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Write expressions in equivalent forms to solve problems. [Quadratic and exponential]

Standard:
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.* Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.*

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

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).

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

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Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

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

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Verify experimentally the properties of rotations, reflections, and translations: Lines are taken to lines, and line segments to line segments of the same length.

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

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Verify experimentally the properties of rotations, reflections, and translations: Angles are taken to angles of the same measure.

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

Standard:
Verify experimentally the properties of rotations, reflections, and translations: Parallel lines are taken to parallel lines.