Search the California Content Standards

Cluster:
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).

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

Standard:
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).

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

Standard:
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. *

Cluster:
Calculate expected values and use them to solve problems.

Standard:
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. *

Cluster:
Calculate expected values and use them to solve problems.

Standard:
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. *

Cluster:
Calculate expected values and use them to solve problems.

Standard:
(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value. For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.*

Cluster:
Calculate expected values and use them to solve problems.

Standard:
(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value. For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households? *

Cluster:
Use probability to evaluate outcomes of decisions.

Standard:
(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. * Find the expected payoff for a game of chance. For example, find the expected winnings from a state lottery ticket or a game at a fast-food restaurant. *

Cluster:
Use probability to evaluate outcomes of decisions.

Standard:
(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. * Evaluate and compare strategies on the basis of expected values. For example, compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident. *

Cluster:
Use probability to evaluate outcomes of decisions.

Standard:
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). *