Search the California Content Standards

Cluster:
Define trigonometric ratios and solve problems involving right triangles.

Standard:
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. *

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Define trigonometric ratios and solve problems involving right triangles.

Standard:
Derive and use the trigonometric ratios for special right triangles (30°, 60°, 90°and 45°, 45°, 90°). CA

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Apply trigonometry to general triangles.

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(+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

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Build a function that models a relationship between two quantities. [Include all types of functions studied.]

Standard:
Write a function that describes a relationship between two quantities. * Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. *

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Build new functions from existing functions. [Include simple radical, rational, and exponential functions; emphasize common effect of each transformation across function types.]

Standard:
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.

Cluster:
Build new functions from existing functions. [Include simple radical, rational, and exponential functions; emphasize common effect of each transformation across function types.]

Standard:
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 or f(x) = (x + 1)/(x − 1) for x ≠ 1.

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Understand and evaluate random processes underlying statistical experiments.

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Understand statistics as a process for making inferences about population parameters based on a random sample from that population. *

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Understand and evaluate random processes underlying statistical experiments.

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Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? *

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Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

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Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. *

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Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Standard:
Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. *