Search the California Content Standards

Cluster:
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]

Standard:
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = (1.01)^12t, and y = (1.2)^t/10, and classify them as representing exponential growth or decay.

Cluster:
Analyze functions using different representations. [Linear, exponential, quadratic, absolute value, step, piecewise-defined]

Standard:
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Cluster:
Extend the properties of exponents to rational exponents.

Standard:
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.

Cluster:
Extend the properties of exponents to rational exponents.

Standard:
Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Cluster:
Use properties of rational and irrational numbers.

Standard:
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). *

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). *

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. *

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. *

Cluster:
Understand independence and conditional probability and use them to interpret data. [Link to data from simulations or experiments.]

Standard:
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. *