Search the California Content Standards

Standard:
Students derive derivative formulas and use them to find the derivatives of algebraic, trigonometric, inversetrigonometric, exponential, and logarithmic functions.

Standard:
Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite functions.

Standard:
Students find the derivatives of parametrically defined functions and use implicit differentiation in a wide variety of problems in physics, chemistry, economics, and so forth.

Standard:
Students compute derivatives of higher orders.

Standard:
Students know and can apply Rolle’s Theorem, the mean value theorem, and L’Hôpital’s rule.

Standard:
Students use differentiation to sketch, by hand, graphs of functions. They can identify maxima, minima, inflection points, and intervals in which the function is increasing and decreasing.

Cluster:
Understand independence and conditional probability and use them to interpret data.

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.

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.

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. *

Cluster:
Understand independence and conditional probability and use them to interpret data.

Standard:
Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. *