Search the California Content Standards

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

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

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

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

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

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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.

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

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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.

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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.