Calculus (Iowa Core)

Limits and Continuity (F-LC)

• C.F-LC.A.1 Define a limit and explain why limits matter in calculus.
• C.F-LC.A.2 Find limits using algebra, graphs and tables of values.
• C.F-LC.B.1 Define continuity at a point using limits.
• C.F-LC.B.2 Use continuity and the Intermediate Value Theorem.

Derivatives (F-D)

• C.F-D.A.1 Estimate derivatives with difference quotients.
• C.F-D.A.2 Define the instantaneous rate of change as a limit of average rates of change.
• C.F-D.A.3 Find derivatives using suitable strategies such as sum, product and quotient rules.
• C.F-D.A.4 Read a derivative as an instantaneous rate of change.
• C.F-D.A.5 Explain how continuity and differentiability at a point are related.
• C.F-D.A.6 Define the derivative function through limits.
• C.F-D.A.7 Find derivatives of simple algebraic functions from the limit definition. (being checked)
• C.F-D.B.1 Differentiate algebraic, trig, inverse, exponential and log functions.
• C.F-D.B.2 Use the product, quotient and chain rules.
• C.F-D.B.3 Differentiate inverse functions and implicitly defined functions.
• C.F-D.B.4 Find second and higher derivatives.
• C.F-D.C.1 Find the slope of the tangent line at a point.
• C.F-D.C.2 Decide from formulas and graphs where f or f′ is positive, increasing or concave up, and the reverse.
• C.F-D.C.3 Explain how the behaviors of f, f′ and f″ relate to one another.
• C.F-D.C.4 Analyze and sketch the graphs of f, f′ and f″.
• C.F-D.C.5 Locate and classify critical points with the first and second derivative tests.
• C.F-D.C.6 Use the Mean Value and Extreme Value Theorems.
• C.F-D.C.7 Solve optimization problems about maximum and minimum values.
• C.F-D.C.8 Solve related-rates problems.
• C.F-D.C.9 Evaluate limits with L'Hospital's rule.
• C.F-D.C.10 Interpret derivatives in context, such as motion and growth.

Integrals (F-I)

• C.F-I.A.1 Find net change over an interval with definite integrals.
• C.F-I.A.2 Approximate definite integrals with finite Riemann sums.
• C.F-I.A.3 Define the definite integral as the limit of Riemann sums.
• C.F-I.A.4 Read a definite integral as net change.
• C.F-I.A.5 State the Fundamental Theorem of Calculus and apply it to evaluate integrals and construct antiderivatives.
• C.F-I.B.1 Integrate algebraic, trig, exponential, inverse and log functions.
• C.F-I.B.2 Integrate by substitution and by parts.
• C.F-I.B.3 Decide whether improper integrals converge using limits.
• C.F-I.B.4 Rewrite integrands to find antiderivatives with a table of integrals.
• C.F-I.C.1 Solve problems on area, volume and the average value of a function.
• C.F-I.C.2 Find areas between curves and volumes of solids of revolution.
• C.F-I.C.3 Apply integrals in physics, economics and other fields.

Differential Equations (F-DE)

• C.F-DE.A.1 Explain what a differential equation is.
• C.F-DE.A.2 Solve first-order differential equations, including growth and decay models.
• C.F-DE.A.3 Interpret solutions of differential equations in context.

Additional Topics (F-AT)

• C.F-AT.A.1 Optionally explore series, Taylor polynomials and polar coordinates as time allows.
• C.F-AT.A.2 Apply calculus to cross-subject problems and projects.
• C.F-AT.A.3 Build readiness for further study in math, science and engineering.