### legend

- CAHSEE
- STAR(CST) Test
- Example
- Introduction
- Resource
- Linked

# California's Common Core Content Standards

### legend

- CAHSEE
- STAR(CST) Test
- Example
- Introduction
- Resource
- Linked

Calculus

- 1.0Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions. This knowledge includes one-sided limits, infinite limits, and limits at infinity. Students know the definition of convergence and divergence of a function as the domain variable approaches either a number or infinity:
- 2.0Students demonstrate knowledge of both the formal definition and the graphical interpretation of continuity of a function.
- 3.0Students demonstrate an understanding and the application of the intermediate value theorem and the extreme value theorem.
- 4.0Students demonstrate an understanding of the formal definition of the derivative of a function at a point and the notion of differentiability:
- 5.0Students know the chain rule and its proof and applications to the calculation of the derivative of a variety of composite functions.
- 6.0Students find the derivatives of parametrically defined functions and use implicit differentiation in a wide variety of problems in physics, chemistry, economics, and so forth.
- 7.0Students compute derivatives of higher orders.
- 8.0Students know and can apply Rolle's theorem, the mean value theorem, and L'HÃ´pital's rule.
- 9.0Students 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.
- 10.0Students know Newton's method for approximating the zeros of a function.
- 11.0Students use differentiation to solve optimization (maximum-minimum problems) in a variety of pure and applied contexts.
- 12.0Students use differentiation to solve related rate problems in a variety of pure and applied contexts.
- 13.0Students know the definition of the definite integral by using Riemann sums. They use this definition to approximate integrals.
- 14.0Students apply the definition of the integral to model problems in physics, economics, and so forth, obtaining results in terms of integrals.
- 15.0Students demonstrate knowledge and proof of the fundamental theorem of calculus and use it to interpret integrals as antiderivatives.
- 16.0Students use definite integrals in problems involving area, velocity, acceleration, volume of a solid, area of a surface of revolution, length of a curve, and work.
- 17.0Students compute, by hand, the integrals of a wide variety of functions by using techniques of integration, such as substitution, integration by parts, and trigonometric substitution. They can also combine these techniques when appropriate.
- 18.0Students know the definitions and properties of inverse trigonometric functions and the expression of these functions as indefinite integrals.
- 19.0Students compute, by hand, the integrals of rational functions by combining the techniques in standard 17.0 with the algebraic techniques of partial fractions and completing the square.
- 20.0Students compute the integrals of trigonometric functions by using the techniques noted above.
- 21.0Students understand the algorithms involved in Simpson's rule and Newton's method. They use calculators or computers or both to approximate integrals numerically.
- 22.0Students understand improper integrals as limits of definite integrals.
- 23.0Students demonstrate an understanding of the definitions of convergence and divergence of sequences and series of real numbers. By using such tests as the comparison test, ratio test, and alternate series test, they can determine whether a series converges.
- 24.0Students understand and can compute the radius (interval) of the convergence of power series.
- 25.0Students differentiate and integrate the terms of a power series in order to form new series from known ones.
- 26.0Students calculate Taylor polynomials and Taylor series of basic functions, including the remainder term.
- 27.0Students know the techniques of solution of selected elementary differential equations and their applications to a wide variety of situations, including growth-and-decay problems.