CAL.3.1.a: Use the estimation method to find limits of various types of functions, and explain findings

CAL.3.1.b: Define the limit of a function, and use graphical interpretation to illustrate concept

CAL.3.1.c: Calculate limits using limit properties, and outline the steps in doing the calculations

CAL.3.1.d: Find limits using appropriate strategies (e.g., rationalization and cancellation techniques)

CAL.3.1.e: Determine limits at infinity and with relation to vertical and horizontal asymptotes

CAL.3.2.a: Define continuity of a function at a point

CAL.3.2.b: Determine if a function is continuous on an interval, using a graph, and explain reasoning

CAL.3.2.c: Show properties of continuity for various types of functions and combinations of functions, and make a presentation

CAL.3.2.d: Explain the intermediate value theorem, with graphical support

CAL.3.2.e: Show that a function satisfies the intermediate value theorem if it is continuous on a closed interval, in writing and orally

CAL.4.1.a: Define gradient in terms of rate of change, and explain in writing, visually, and orally

CAL.4.1.b: Define the derivative of a function at a point, and explain in writing, visually, and orally

CAL.4.1.c: Find derivatives using the limit definition, and outline the steps

CAL.4.1.d: Find derivatives using addition, product, and quotient rules

CAL.4.1.e: Find the derivatives of polynomial functions, exponential functions, and trigonometric functions using basic differentiation rules

CAL.4.1.f: Find derivatives using implicit differentiation

CAL.4.1.g: Find derivatives of logarithmic functions

CAL.4.1.h: Find derivatives of inverse trigonometric functions

CAL.4.1.i: Find derivatives of higher order (up to 3rd order only)

CAL.4.1.j: Sketch curves using first and/or second derivative tests to show critical and extreme points, concavity, and points where the curve increases and/or decreases, and discuss sketches

CAL.4.2.a: Use related rates equations to solve related rates problems (rates of change of quantities)

CAL.4.2.b: Use the relative extrema theorem to find extrema of any function on a closed interval

CAL.4.2.c: Apply Rolle's theorem and mean value theorem (without proof)

CAL.4.2.d: Apply first and second derivative tests to find the relative minimum and/or maximum

CAL.4.2.e: Use limit and derivative concepts to analyze the graphs of various types of functions

CAL.4.2.f: Use derivatives to solve optimization problems (applied minimum and maximum problems)

CAL.4.2.g: Use Newton's method to approximate the zero(s) of a function

CAL.4.2.h: Interpret and apply derivatives to solve business and economic problems, and participate in a presentation and discussion

CAL.4.3.a: Define the anti-derivative of a function, and explain in writing, visually and orally

CAL.4.3.b: Use appropriate rules and properties to find indefinite integrals of various types of functions (e.g., polynomial, exponential, logarithmic, trigonometric, inverse trigonometric), and discuss

CAL.4.4.a: Integrate composite functions using the substitution method

CAL.4.4.b: Integrate rational algebraic fractions using long division, completing the square, rewriting the numerator, and using a partial fraction

CAL.4.4.c: Integrate the product of functions using integration by parts

CAL.4.4.d: Apply integration to solving real-world and mathematical problems, and explain findings

CAL.4.5.a: Approximate the area of a plane region, and find upper and lower sums for a region

CAL.4.5.b: Explain the concept of definite integral, and explain in writing, visually and orally

CAL.4.5.c: Demonstrate, using the Riemann sum method, how to approximate the total area under a graph

CAL.4.5.d: Evaluate definite integrals of various types of functions using appropriate properties

CAL.4.5.e: Apply the fundamental theorems of calculus (the first fundamental theorem; mean value theorem; the average value of a function on an interval; and the second fundamental theorem)

CAL.4.5.f: Use integration to find the area of a region between two curves or between two intersecting curves

CAL.4.5.g: Use the trapezoidal rule and Simpson's rule to approximate definite integral, and estimate errors involved in the use of Simpson's and trapezoidal rules

CAL.4.5.h: Demonstrate knowledge of the disc method to find the volume of a solid of revolution

CAL.4.5.i: Find the arc length and area of a surface of revolution