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Showing 161 - 170 of 204 Standards

Standard Identifier: Calculus.4.4

Grade Range: 9–12
Discipline: Calculus

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

Standard Identifier: Calculus.5.0

Grade Range: 9–12
Discipline: Calculus

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

Standard Identifier: Calculus.6.0

Grade Range: 9–12
Discipline: Calculus

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 Identifier: Calculus.7.0

Grade Range: 9–12
Discipline: Calculus

Standard:
Students compute derivatives of higher orders.

Standard Identifier: Calculus.8.0

Grade Range: 9–12
Discipline: Calculus

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

Standard Identifier: Calculus.9.0

Grade Range: 9–12
Discipline: Calculus

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.

Standard Identifier: F-BF.1.b

Grade Range: 9–12
Domain: Building Functions
Discipline: Math III
Conceptual Category: Functions

Cluster:
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. *

Standard Identifier: F-BF.3

Grade Range: 9–12
Domain: Building Functions
Discipline: Math III
Conceptual Category: Functions

Cluster:
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.

Standard Identifier: F-BF.4.a

Grade Range: 9–12
Domain: Building Functions
Discipline: Math III
Conceptual Category: Functions

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.

Standard Identifier: F-IF.4

Grade Range: 9–12
Domain: Interpreting Functions
Discipline: Math III
Conceptual Category: Functions

Cluster:
Interpret functions that arise in applications in terms of the context. [Include rational, square root and cube root; emphasize selection of appropriate models.]

Standard:
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. *

Showing 161 - 170 of 204 Standards


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