Common Planner
K–12 Standards

Calculus

Other Iowa Mathematics sets

FunctionsC.F

  • F-LC.

    Limits and Continuity C.F-LC

    1. 1

      Compute limits of functions.C.F-LC.A

      1. 1

        Define limits and explain their significance in calculus.C.F-LC.A.1

      2. 2

        Evaluate limits algebraically, graphically, and numerically.C.F-LC.A.2

    2. 2

      Solve problems involving continuity and determine the continuity of functions.C.F-LC.B

      1. 1

        Use limits to define continuity at a point.C.F-LC.B.1

      2. 2

        Apply the concepts of continuity and the Intermediate Value Theorem. C.F-LC.B.2

  • F-D.

    DerivativesC.F-D

    1. 1

      Use limits to compute derivatives. C.F-D.A

      1. 1

        Estimate derivatives using difference quotients.C.F-D.A.1

      2. 2

        Define the instantaneous rate of change at a point as the limit of average rates of change.C.F-D.A.2

      3. 3

        Identify the derivative of a function using appropriate strategies. For example, rules for sums, differences, products, quotients, and limits of functions.C.F-D.A.3

      4. 4

        Interpret derivatives as instantaneous rates of change.C.F-D.A.4

      5. 5

        Explain the relationship between continuity and differentiability at a point.C.F-D.A.5

      6. 6

        Use limits to define the derivative function.C.F-D.A.6

      7. 7

        Use limits to find derivatives of simple algebraic functions. C.F-D.A.7

    2. 2

      Compute derivatives. C.F-D.B

      1. 1

        Compute derivatives of algebraic, trigonometric, inverse, exponential, and logarithmic functions.C.F-D.B.1

      2. 2

        Apply the rules of differentiation, including the product rule, quotient rule, and chain rule.C.F-D.B.2

      3. 3

        Compute derivatives of general inverse and implicitly defined functions. C.F-D.B.3

      4. 4

        Compute higher-order derivatives. C.F-D.B.4

  • C.

    Apply the concept of the derivative.  C.F-DF.C

    1. 1

      Find the slope of a tangent line at a point.C.F-DF.C.1

    2. 2

      Determine analytically and graphically where a function, or derivative function, is positive or negative, increasing or decreasing, and/or concave up or concave down.C.F-DF.C.2

    3. 3

      Explain the relationships among the behaviors of 𝑓𝑓, 𝑓𝑓′ , 𝑎𝑎𝑎𝑎𝑎𝑎 𝑓𝑓′′; for example, if 𝑓𝑓′′ is positive, then 𝑓𝑓′ is increasing and 𝑓𝑓 is concave up.C.F-DF.C.3

    4. 4

      Analyze and sketch graphs of 𝑓𝑓, 𝑓𝑓′ , 𝑎𝑎𝑎𝑎𝑎𝑎 𝑓𝑓′′.C.F-DF.C.4

    5. 5

      Use the first and second derivative tests to find and classify critical points.C.F-DF.C.5

    6. 6

      Apply the Mean Value Theorem and Extreme Value Theorem. C.F-DF.C.6

    7. 7

      Solve optimization problems involving maxima and minima.C.F-DF.C.7

    8. 8

      Solve related rate problems.C.F-DF.C.8

    9. 9

      Use L’Hospital’s rule to compute limits.C.F-DF.C.9

    10. 10

      Interpret derivatives in real-world contexts, such as motion and growth problems.C.F-DF.C.10

  • F-I .

    IntegralsC.F-I

    1. 1

      Define and interpret integrals.  C.F-I.A

      1. 1

        Use definite integrals to determine net change over an interval. C.F-I.A.1

      2. 2

        Approximate definite integrals using finite Riemann Sums.C.F-I.A.2

      3. 3

        Define the definite integral as a limit of a finite Riemann Sum.C.F-I.A.3

      4. 4

        Interpret definite integrals as net change.C.F-I.A.4

      5. 5

        State the Fundamental Theorem of Calculus and use it to evaluate definite integrals and construct antiderivatives. C.F-I.A.5

    2. 2

      Compute integrals. C.F-I.B

      1. 1

        Compute indefinite and definite integrals of algebraic, trigonometric, exponential, inverse, and logarithmic functions.C.F-I.B.1

      2. 2

        Apply integration techniques, including substitution and integration by parts.C.F-I.B.2

      3. 3

        Determine if an improper integral converges or diverges using limits of definite integrals.C.F-I.B.3

      4. 4

        Transform integrands (using substitution and other techniques) to find antiderivatives using a table of integrals.C.F-I.B.4

    3. 3

      Use integrals to solve problems.C.F-I.C

      1. 1

        Solve problems involving area, volume, and average value of functions.C.F-I.C.1

      2. 2

        Use integrals to find the area between curves and volume of solids of revolution.C.F-I.C.2

      3. 3

        Use integrals to solve problems in physics, economics, and other fields.C.F-I.C.3

  • F-DE.

    Differential EquationsC.F-DE

    1. 1

      Solve and interpret solutions of differential equations.C.F-DE.A

      1. 1

        Explain the concept of a differential equation.C.F-DE.A.1

      2. 2

        Solve first-order differential equations, including linear and exponential growth and decay models. C.F-DE.A.2

      3. 3

        Interpret solutions of differential equations in real-world contexts.C.F-DE.A.3

  • AT.

    Advanced TopicsC.AT

    1. 1

      Apply calculus and related skills to advanced topics. C.F-AT.A

      1. 1

        Explore additional topics such as sequences and series, Taylor polynomials, and polar coordinates (optional depending on course length and student readiness).C.F-AT.A.1

      2. 2

        Apply calculus concepts to interdisciplinary problems and projects.C.F-AT.A.2

      3. 3

        Prepare for further study in mathematics, science, engineering, and related fields. C.F-AT.A.3

Frequently asked questions

What grade levels do these standards cover?
Grade 9, Grade 10, Grade 11, and Grade 12
Where can I read the official document?
Iowa Academic Standards for Mathematics

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