Search the California Content Standards

Cluster:
Prove and apply trigonometric identities.

Standard:
Prove the Pythagorean identity sin^2(θ ) + cos^2(θ ) = 1 and use it to find sin(θ ), cos(θ ), or tan(θ ) given sin(θ ), cos(θ ), or tan(θ ) and the quadrant of the angle.

Cluster:
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]

Standard:
Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

Cluster:
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]

Standard:
Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

Cluster:
Prove geometric theorems. [Focus on validity of underlying reasoning while using variety of ways of writing proofs.]

Standard:
Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

Cluster:
Understand and evaluate random processes underlying statistical experiments.

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

Cluster:
Understand and evaluate random processes underlying statistical experiments.

Standard:
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? *

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

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

Cluster:
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. *

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

Standard:
Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. *

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

Standard:
Evaluate reports based on data. *