Search the California Content Standards

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Understand and apply the Pythagorean Theorem.

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

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Understand and apply the Pythagorean Theorem.

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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.

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

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Create equations that describe numbers or relationships.

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Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA *

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Create equations that describe numbers or relationships.

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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. *

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Create equations that describe numbers or relationships.

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Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. * [Include formulas involving quadratic terms.]

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Apply geometric concepts in modeling situations.

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Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). *

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Apply geometric concepts in modeling situations.

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Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). *

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Apply geometric concepts in modeling situations.

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Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). *

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Extend the properties of exponents to rational exponents.

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Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^1/3 to be the cube root of 5 because we want (5^1/3)^3 = 5(^1/3)^3 to hold, so (5^1/3)^3 must equal 5.