Mathematics Curriculum
	Calculus
	The purpose of this course (Calculus AB/BC) is to prepare students to take the Advanced Placement examination given each spring, for which placement and/or credit may be awarded at the college level if a qualifying score is obtained. Content of this college-level course is defined by the Advanced Placement Course Description for Calculus AB/BC as stated by the College Board. Teachers should update course content as changes occur in future College Board publications. Content includes concepts and applications of differential and integral calculus. This course carries a weighted grade. As mandated by the College Board, graphing calculators will be required for this course. Computers should also be used where feasible by the student and by the teacher. Any technology that will enhance student learning should be used if available. Instructional activities that engage students in solving application problems of varying complexities are encouraged. Note: Extended refers to topics for Calculus BC	Last Updated: 08/24/12 11:03 AM
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	MTH.CALC
	Standard 1
	DEFINE AND APPLY THE PROPERTIES OF LIMITS
	Benchmark 1.a Define and Apply the Properties of Limits   Indicator 1.a.1 Find the value of a limit from a graph of a function   Indicator 1.a.2 Estimate the value of a limit numerically from a table of values   Indicator 1.a.3 Calculate limits algebraically using various techniques   Indicator 1.a.4 Calculate limits using the limit laws   Indicator 1.a.5 Determine one-sided limits algebraically, graphically, and numerically   Indicator 1.a.6 Determine limits at infinity, infinite limits, and non-existent limits   Indicator 1.a.7 Use l’Hopital’s Rule to find the limit of functions   Indicator 1.a.8 Explore the precise definition of the limit
	MTH.CALC
	Standard 2
	USE LIMITS TO DEFINE AND DETERMINE CONTINUITY
	Benchmark 2.a Use Limits to Define and Determine Continuity   Indicator 2.a.1 Determine continuity from a graph or equation   Indicator 2.a.2 Identify a function's discontinuities and the type of discontinuity   Indicator 2.a.3 Determine whether a function is continuous using the formal definition   Indicator 2.a.4 Apply the Intermediate Value Theorem and the Extreme Value Theorem
	MTH.CALC
	Standard 3
	INVESTIGATE ASYMPTOTIC AND UNBOUNDED BEHAVIOR
	Benchmark 3.a Investigate Asymptotic and Unbounded Behavior   Indicator 3.a.1 Determine equations of asymptotes using limits at infinity   Indicator 3.a.2 Sketch graphs of functions given conditions involving limits   Indicator 3.a.3 Evaluate limits at infinity using the properties of limits   Indicator 3.a.4 Compare relative magnitudes to determine limits of functions
	MTH.CALC
	Standard 4
	INVESTIGATE DERIVATIVES GRAPHICALLY, NUMERICALLY, AND ANALYTICALLY
	Benchmark 4.a Investigate Derivatives Graphically, Numerically, and Analytically   Indicator 4.a.1 Define a tangent to a curve at a point   Indicator 4.a.2 Investigate and compare the slopes of secant lines and tangent lines   Indicator 4.a.3 Estimate derivatives geometrically, numerically, and analytically   Indicator 4.a.4 Define the derivative and use the definition to calculate slopes   Indicator 4.a.5 Determine the differentiability of a function at a point   Indicator 4.a.6 Compare and contrast the concepts of differentiability and continuity   Indicator 4.a.7 Identify where a function fails to be differentiable and the reason
	MTH.CALC
	Standard 5
	INVESTIGATE THE DERIVATIVE AT A POINT
	Benchmark 5.a Investigate the Derivative at a Point   Indicator 5.a.1 Find the slope at a point using the definition of the derivative   Indicator 5.a.2 Use the concept of local linearity to approximate the slope of a curve   Indicator 5.a.3 Define instantaneous rate of change   Indicator 5.a.4 Approximate rates of change from graphs and tables   Indicator 5.a.5 Write equations of lines tangent to a curve at a point
	MTH.CALC
	Standard 6
	ANALYZE THE DERIVATIVE OF A FUNCTION AS ITS OWN FUNCTION
	Benchmark 6.a Analyze the Derivative of a Function as its Own Function   Indicator 6.a.1 Compare corresponding characteristics of the graphs of f, f ' and f "   Indicator 6.a.2 Determine intervals of increasing and decreasing behavior   Indicator 6.a.3 Translate verbal descriptions into equations involving derivatives   Indicator 6.a.4 Apply the Mean Value Theorem and interpret its geometric properties   Indicator 6.a.5 Determine the concavity of functions over intervals   Indicator 6.a.6 Identify points of inflection as places where concavity changes   Indicator 6.a.7 Sketch the graph of f ' given the graph of f   Indicator 6.a.8 Find eqn for derivative fns algebraically using the limit definition   Indicator 6.a.9 Include alternative notations for the derivative
	MTH.CALC
	Standard 7
	APPLY THE DERIVATIVE TO SOLVE PROBLEMS AND TO JUSTIFY SOLUTIONS
	Benchmark 7.a Apply the Derivative to Solve Problems and to Justify Solutions   Indicator 7.a.1 Use first and second derivatives to find monotonicity and concavity   Indicator 7.a.2 Use the first and second derivative tests to determine extrema   Indicator 7.a.3 Solve optimization prob involving abs (global) & rel (local) extrema   Indicator 7.a.4 Find tangent lines, slope, extrema and concavity of implicit functions   Indicator 7.a.5 Model rates of change and solve related rates problems   Indicator 7.a.6 Interpret the derivative as a rate of change in applied contexts   Indicator 7.a.7 Differentiate functions using logarithmic differentiation   Indicator 7.a.8 Analyze curves given in parametric form, polar form, and vector form   Indicator 7.a.9 Test the convergence of improper integrals using l’Hopital’s Rule
	MTH.CALC
	Standard 8
	APPLY RULES TO FIND DERIVATIVES ALGEBRAICALLY
	Benchmark 8.a Apply Rules to Find Derivatives Algebraically   Indicator 8.a.1 Find derivatives of various functions algebraically   Indicator 8.a.2 Find derivatives of sums, products, quotients, inverses and composites   Indicator 8.a.3 Find first and second derivatives of implicitly defined relations   Indicator 8.a.4 Determine higher order derivatives of various functions algebraically   Indicator 8.a.5 Find derivatives of parametric, polar, and vectors algebraically
	MTH.CALC
	Standard 9
	ESTIMATE DEFINITE INTEGRALS USING RIEMANN SUMS AND TRAPEZOIDAL RULE
	Benchmark 9.a Estimate Definite Integrals Using Riemann Sums and Trapezoidal Rule   Indicator 9.a.1 Estimate a definite integral using left, right, and midpoint rules   Indicator 9.a.2 Estimate a definite integral using Trapezoidal rule   Indicator 9.a.3 Determine if a Riemann sum will underestimate or overestimate   Indicator 9.a.4 Evaluate definite integrals geometrically using formulas from Geometry   Indicator 9.a.5 Write the limit of the Riemann sum as a definite integral   Indicator 9.a.6 Write the limit of the Riemann sum as a definite integral & vice versa   Indicator 9.a.7 Evaluate the limit of the Riemann sum algebraically
	MTH.CALC
	Standard 10
	FIND ANTIDERIVATIVES OF BASIC FUNCTIONS
	Benchmark 10.a Find Antiderivatives of Basic Functions   Indicator 10.a.1 Understand and correctly apply the constant of integration   Indicator 10.a.2 Find antiderivatives of basic functions and inverse trig functions   Indicator 10.a.3 Apply the properties of the integrals to evaluate integrals   Indicator 10.a.4 Evaluate integrals using the method of integration by parts   Indicator 10.a.5 Evaluate integrals of rational functions by simple partial fractions   Indicator 10.a.6 Find improper integrals as limits of definite integrals   Indicator 10.a.7 Evaluate integrals using trigonometric substitution
	Benchmark 10.b Use Fundamental Thm of Calc & Substitution to Eval Definite Integrals   Indicator 10.b.1 Compare and contrast the definite and indefinite integrals   Indicator 10.b.2 Evaluate definite integrals of fns using Fundamental Theorem of Calc   Indicator 10.b.3 Evaluate integrals using substitution including change of limits   Indicator 10.b.4 Use a graph of f ' to find values of f using Fundamental Thm of Calc   Indicator 10.b.5 Apply the Fundamental Theorem of Calculus to real-world applications   Indicator 10.b.6 Examine a particular function f, given a graph of its derivative f '
	MTH.CALC
	Standard 11
	EXPLORE DEFINITE INTEGRAL AS AREA USING FUNDAMENTAL THEOREM OF CALC
	Benchmark 11.a Explore Definite Integral as an Area Using The Fundamental Thm of Calc   Indicator 11.a.1 Apply properties of definite integrals from multiple representations   Indicator 11.a.2 For each x of an accumulation function F, find f(x) or f '(x)   Indicator 11.a.3 Examine an accumulation function F, given a graph of its derivative f   Indicator 11.a.4 Find the derivatives of expressions containing integrals
	MTH.CALC
	Standard 12
	SOLVE SEPARABLE DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS
	Benchmark 12.a Solve Separable Differential Equations and their Applications   Indicator 12.a.1 Create a slope field from a differential equation   Indicator 12.a.2 Match a set of differential equations with corresponding slope fields   Indicator 12.a.3 Define, identify, and verify solutions of differential equations   Indicator 12.a.4 Solve separable differential equations   Indicator 12.a.5 Solve real-world motion problems using differential equations   Indicator 12.a.6 Solve growth and decay problems using differential equations   Indicator 12.a.7 Solve logistic differential equations and use them in modeling   Indicator 12.a.8 Solve differential eqn using Euler’s method given various step sizes
	MTH.CALC
	Standard 13
	USE INTEGRATION TECHNIQUES TO SOLVE REAL-WORLD PROBLEMS
	Benchmark 13.a Use Integration Techniques To Solve Real-World Problems   Indicator 13.a.1 Determine the area of a region defined by two or more functions   Indicator 13.a.2 Find the volume of a solid with a known cross-section   Indicator 13.a.3 Find the volume of a solid of revolution by the disk or washer method   Indicator 13.a.4 Find the average value of a function over a given interval   Indicator 13.a.5 Find the displacement and distance traveled by a particle along a line   Indicator 13.a.6 Find the arc length of curves   Indicator 13.a.7 Find the equation of the tangent line on a parametric curve   Indicator 13.a.8 Find the position, speed, velocity, and acceleration of a particle   Indicator 13.a.9 Find the area of a region and slope of a graph defined by polar curves
	MTH.CALC
	Standard 14
	DEFINE A SEQUENCE AND A SERIES AND TEST FOR CONVERGENCE
	Benchmark 14.a Define a Sequence and a Series and Test for Convergence   Indicator 14.a.1 Determine whether a sequence converges and find the limit   Indicator 14.a.2 Test a series for divergence using the Nth Term test for Divergence   Indicator 14.a.3 Determine the partial sum of a series   Indicator 14.a.4 Determine whether a geometric series converges and if so, find its sum   Indicator 14.a.5 Determine whether a series converges using the integral test   Indicator 14.a.6 Determine whether a p-series converges including the harmonic series   Indicator 14.a.7 Test the convergence of an alternating series and find the error bound   Indicator 14.a.8 Determine the convergence of a series using comparison tests   Indicator 14.a.9 Determine absolute or conditional convergence of a series   Indicator 14.a.10 Determine convergence by applying the root and ratio tests
	MTH.CALC
	Standard 15
	DEFINE, RESTATE, AND APPLY TAYLOR SERIES
	Benchmark 15.a Define, Restate, And Apply Taylor Series   Indicator 15.a.1 Determine Taylor polynomial approximations   Indicator 15.a.2 Find Maclaurin series and the general Taylor series   Indicator 15.a.3 Determine a Maclaurin series for certain functions   Indicator 15.a.4 Use shortcuts to create a new series from known series   Indicator 15.a.5 Determine the radius and interval of convergence for a power series   Indicator 15.a.6 Determine the Lagrange error bound of a Taylor polynomial

Essential - Standard, benchmark, or indicator from the VDOE Standards of Learning document. In the absence of VDOE standards for a given course, content subject to testing such as AP and IB can be labeled Essential.
Expected - Standard, benchmark, or indicator added by the FCPS Program of Studies to provide a context, a bridge, or an enhancement to the Essential SBIs.
Extended - Standard, benchmark, or indicator added by the FCPS Program of Studies generally used to differentiate instruction for advanced learners (Honors/GT)