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Skills available for Georgia high school math standards

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MM Mathematical Modeling

  • C.MM.1 Apply mathematics to real-life situations; model real-life phenomena using mathematics.

FGR Functional & Graphical Reasoning

GSR Geometric & Spatial Reasoning

  • Indefinite and Definite Integrals

    • C.GSR.5 Analyze the relationship between the derivative and the integral using the Fundamental Theorem of Calculus.

      • Evaluate and interpret definite integrals.

        • C.GSR.5.1 Use Riemann sums to approximate values of definite integrals.

        • C.GSR.5.2 Interpret a definite integral as a limit of Riemann sums.

        • C.GSR.5.3 Find the exact value of a definite integral using geometric formulas on a coordinate plane.

        • C.GSR.5.4 Demonstrate the use of properties of definite integrals.

        • C.GSR.5.5 Apply the Fundamental Theorem of Calculus as an interpretation of the accumulation in the rate of change of a function as equivalent to the change in the antiderivative over the interval.

      • Find the antiderivative of indefinite integrals.

        • C.GSR.5.6 Apply Fundamental Theorem of Calculus to indefinite integrals to represent the family of antiderivatives.

        • C.GSR.5.7 Apply integration by substitution to definite and indefinite integrals.

PAR Patterning & Algebraic Reasoning

  • Applications of Integrals

    • C.PAR.6 Apply the definite integral and indefinite integral to contextual situations.

      • Apply Integration techniques to solve problems

        • C.PAR.6.1 Find a particular curve in a family of antiderivatives using an initial condition.

        • C.PAR.6.2 Solve separable differential equations and use them to model real-world problems.

        • C.PAR.6.3 Apply definite integrals to find the area between two curves.

        • C.PAR.6.4 Apply definite integrals to find the average value of a function over a closed interval.