HS.C

Calculus(+)

HS.C.1(+)Understand limits. (MP.2, MP.3)HS.C.10(+)Communicate an understanding of continuity using precise mathematical symbols and language. (MP.2, MP.6)HS.C.11(+)Define derivatives. (MP.5, MP.8)HS.C.12(+)Use average rate of change to estimate the derivative from a table of values or a graph. (MP.2, MP.8)HS.C.13(+)Understand the derivative as a function. (MP.2, MP.5)HS.C.14(+)Apply the definition of derivative to find derivative values and derivative functions. (MP.2, MP.3)HS.C.15(+)Explain why differentiability implies continuity yet continuity does not imply differentiability. (MP.3, MP.6)HS.C.16(+)Understand and apply the Mean Value Theorem, including numerical, graphical and algebraic representations. (MP.2, MP.5)HS.C.17(+)Understand the relationship between the concavity of a function and the sign of the second derivative. (MP.2, MP.3)HS.C.18(++)Understand Rolle’s Theorem as a special case of the Mean Value Theorem. (MP.2, MP.3)HS.C.19(+)Efficiently find derivatives of functions with and without technology. (MP.2, MP.5)HS.C.2(+)Demonstrate an understanding of limits by estimating and finding the limit of a function at a point graphically, numerically and algebraically. (MP.5, MP.8)HS.C.20(+)Understand and use derivative rules for sums, differences, products and quotients of two functions and calculate the derivative of a composite function using the chain rule. (MP.2, MP.3)HS.C.21(+)Use implicit differentiation to find a derivative in an equation of two variables. (MP.1, MP.2)HS.C.22(+)Use implicit differentiation to find the derivative of the inverse of a function. (MP.2, MP.3)HS.C.23(+)Understand the relationship between the increasing and decreasing behavior of a function and the sign of the first derivative of the function. (MP.1, MP.2)HS.C.24(+)Use the first derivative to analyze curves and identify relative extrema. (MP.2, MP.3)HS.C.25(+)Understand the relationship of concavity to the second derivative. (MP.2, MP.5)HS.C.26(+)Use the second derivative to find points of inflection. (MP.2, MP.3)HS.C.27(+)Use the second derivative to analytically locate intervals on which a function is concave up, concave down or neither. (MP.2, MP.3)HS.C.28(+)Describe how graphical characteristics of a given function, the first derivative of that function and the second derivative of that function interrelate. (MP.2, MP.5)HS.C.29(+)Use derivatives to express rate of change in a variety of contexts. (MP.2, MP.4)HS.C.3(+)Apply properties and theorems of limits, including limits of indeterminate forms. (MP.2, MP.3)HS.C.30(+)Use derivatives to solve a variety of problems including related rates, optimization, tangent line approximations and growth and decay models. (MP.1, MP.4)HS.C.31(+)Use differentiation to solve problems involving velocity, speed and acceleration. (MP.1, MP.2)HS.C.32(+)Understand and apply differential equations. (MP.1, MP.4)HS.C.33(+)Understand the definite integral of a function over an interval. Interpret a definite integral as a limit of Riemann Sums and as net accumulation of change. (MP.2, MP.5)HS.C.34(+)Write a Riemann sum that represents the definition of a definite integral. (MP.2, MP.3)HS.C.35(+)Calculate the values of Riemann Sums over equal subdivisions to approximate definite integrals of functions represented graphically and numerically (using tables). Use left-hand sums, right-hand sums, midpoint sums and trapezoidal sums. (MP.2, MP.3)HS.C.36(+)Recognize differentiation and integration as inverse operations. (MP.2, MP.8)HS.C.37(+)Understand how the Fundamental Theorem of Calculus connects differentiation and integration and use it to evaluate definite and indefinite integrals and to represent particular antiderivatives. (MP.2, MP.3)HS.C.38(+)Perform analytical and graphical analysis of functions using the Fundamental Theorem of Calculus. (MP.2, MP.5)HS.C.39(+)Understand and use the definite integral of a function over an interval and understand its use as a mathematical tool. (MP.1, MP.2)HS.C.4(+)Communicate understanding of limits using precise mathematical symbols and language. (MP.3, MP.6)HS.C.40(+)Find antiderivatives of a variety of basic functions including power, exponential, logarithmic and trigonometric and apply basic properties of definite integrals. (MP.2, MP.7)HS.C.41(+)Use substitution techniques and change of limits of integration to find antiderivatives. (MP.2, MP.3)HS.C.42(+)Find particular antiderivatives given initial conditions. (MP.1, MP.2)HS.C.43(+)Model, solve and interpret applications of antiderivatives including finding area, velocity, acceleration and volume of a solid. (MP.1, MP.4)HS.C.44(+)Apply integration to solve problems including particle motion and exponential growth and decay. (MP.1, MP.4)HS.C.45(+)Describe the application of integration to a variety of problems using precise mathematical language and notation. (MP.4, MP.6)HS.C.5(+)Describe asymptotic behavior (analytically and graphically) in terms of infinite limits and limits at infinity. (MP.2, MP.5)HS.C.6(+)Discuss the end behavior of functions; identify representative functions for each type of end behavior using precise mathematical symbols and language. (MP.2, MP.6)HS.C.7(+)Understand and use the limit definition of continuity to determine whether a given function is continuous at a specific point. (MP.2, MP.3)HS.C.8(+)Define and identify different types of discontinuity—removable (hole) or non-removable (jump, asymptote)—in terms of limits. (MP.3, MP.6)HS.C.9(+)Understand and apply continuous function theorems. (MP.2, MP.3)
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