Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2010 AB1 BC1 analytic exponential total change given rate of change integral of a rate of change to give accumulated change (a) (c) (d) active2010 AB1 BC1 related rates related rates (b)2010 AB1 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (c) 2010 AB1 BC1 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c) 2010 AB2 BC2 tabular general derivative, definition approximate rate of change from graphs and tables of values (a) active2010 AB2 BC2 trapezoidal approximation computation of trapezoidal sum (a)2010 AB2 BC2 definite integral interpretation of definite integrals (b)2010 AB2 BC2 average value average value of a function (b)2010 AB2 BC2 total change given rate of change integral of a rate of change to give accumulated change (c) 2010 AB2 BC2 maximum, minimum absolute extrema (d)2010 AB3 graphical general total change given rate of change integral of a rate of change to give accumulated change (a) (e) neutral2010 AB3 area area of a region (a)2010 AB3 differentiation relationship between the increasing and decreasing behavior of f and the sign of f' (b)2010 AB3 maximum, minimum absolute extrema (c) 2010 AB4 BC4 analytic algebraic area area of a region (a) closed2010 AB4 BC4 integration methods antiderivatives following directly from derivatives of basic funcions (a)2010 AB4 BC4 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)2010 AB4 BC4 volume volume of a solid of revolution (b)2010 AB4 BC4 volume-slicing volume of a solid with known cross section (c) 2010 AB5 graphical general fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a) (b) (c) closed2010 AB5 area area of a region (a)2010 AB5 points of inflection point of inflection (b)2010 AB5 maximum, minimum local extrema (c) 2010 AB5 differentiation derivative of basic functions (c)2010 AB6 analytic algebraic tangents tangent line to a curve at a point (a) closed2010 AB6 tangents local linear approximation (b)2010 AB6 differential equations solving separable differential equations (c)2010 BC3 analytic exponential parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2010 BC3 total change given rate of change integral of a rate of change to give accumulated change (d)2010 BC3 vectors speed (a)2010 BC3 arc length length of a curve given in parametric form (b)2010 BC3 tangents slope of a curve at a point (d)2010 BC3 differentiation interpretation of derivative as a rate of change (c)2010 BC5 analytic algebraic Euler's method Euler's method (a) closed2010 BC5 limits calculating limits using l'Hopital's Rule (b)2010 BC5 differential equations solving separable differential equations (c)2010 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (c)2010 BC5 integration methods antiderivatives by substitution (c)2010 BC6 analytic trigonometric series (a) closed2010 BC6 series manipulation of Taylor series to form new series from known series (a)2010 BC6 maximum, minimum local extrema (b)2010 BC6 series manipulation of Taylor series to form new series from known series (c)2010 BC6 series Taylor polynomial approximation (d)2010 BC6 series alternating series with error bound (d)2010 B AB1 BC1 analytic logarithmic area area of a region (a) active2010 B AB1 BC1 volume volume of a solid of revolution (b)2010 B AB1 BC1 volume-slicing volume of a solid with known cross section (c)2010 B AB2 analytic trigonometric tangents horizontal tangents (a) active2010 B AB2 concavity relationship between the concavity of f and the sign of f'' (b)2010 B AB2 tangents tangent line to a curve at a point (c)2010 B AB2 tangents local linear approximation (d)2010 B AB3 BC3 analytic exponential Riemann sums computation of midpoint Riemann Sum (a) active2010 B AB3 BC3 total change given rate of change integral of a rate of change to give accumulated change (b) (c)2010 B AB3 BC3 related rates related rates (d)2010 B AB3 BC3 differentiation implicit differentiation (d)2010 B AB3 BC3 differentiation chain rule (d)2010 B AB4 BC4 graphical general motion on a line particle motion on a line (a) (b) (c) (d) neutral

Maclaurin series for cos(x)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2010 B AB4 BC4 maximum, minimum absolute extrema (b)2010 B AB4 BC4 derivative, graph of interpretation of derivative in context of velocity, speed, and acceleration (c)2010 B AB4 BC4 total change given rate of change integral of a rate of change to give accumulated change (c) (d)2010 B AB4 BC4 differentiation interpretation of derivative in context of velocity, speed, and acceleration (d)2010 B AB5 analytic algebraic slope fields slope fields (a) closed2010 B AB5 slope fields relationship between slope fields and solution curves for differential equations (b)2010 B AB5 differential equations solving separable differential equations (c)2010 B AB6 analytic trigonometric motion on a line particle motion on a line (a) (b) (c) (d) closed2010 B AB6 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c)2010 B AB6 differentiation derivative of basic functions (a) (c)2010 B AB6 differentiation chain rule (a) (c)2010 B AB6 average value average value of a function (d)2010 B BC2 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2010 B BC2 tangents vertical tangents (a)2010 B BC2 tangents tangent line to a curve at a point (b)2010 B BC2 vectors speed (c)2010 B BC2 vectors acceleration vector (d)2010 B BC5 analytic algebraic differentiation derivative of basic functions (a) closed2010 B BC5 differentiation derivative of a quotient (a)2010 B BC5 maximum, minimum absolute extrema (a)2010 B BC5 area area of a region (b)2010 B BC5 improper integrals improper integrals (b)2010 B BC5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)2010 B BC5 integration methods antiderivatives following directly from derivatives of basic funcions (b)2010 B BC5 limits limits of functions (b)2010 B BC5 limits calculating limits using algebra (b)2010 B BC6 analytic algebraic series Taylor series (a) closed2010 B BC6 interval/convergence interval of convergence of power series (a)2010 B BC6 series manipulation of Taylor series to form new series from known series (b)2009 AB1 BC1 graphical trigonometric motion on a line particle motion on a line (a) (b) (c) (d) neutral2009 AB1 BC1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c) (d) 2009 AB1 BC1 distance distance traveled by a particle along a line (b) (d)2009 AB2 BC2 analytic algebraic total change given rate of change integral of a rate of change to give accumulated change (a) (c) active2009 AB2 BC2 maximum, minimum absolute extrema (b)2009 AB2 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals2009 AB2 BC2 average value average value of a function (d)2009 AB3 verbal algebraic total change given rate of change integral of a rate of change to give accumulated change (a) (b) (c) active2009 AB3 definite integral basic properties of definite integrals (b)2009 AB3 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (d)2009 AB3 fundamental theorem absolute extrema (d)2009 AB4 analytic trigonometric area area of a region (a) closed2009 AB4 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)2009 AB4 integration methods antiderivatives by substitution (b)2009 AB4 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)2009 AB4 volume volume of a solid of revolution (b)2009 AB4 volume-slicing volume of a solid with known cross section (c)2009 AB5 BC5 tabular general derivative, definition approximate rate of change from graphs and tables of values (a) neutral2009 AB5 BC5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)2009 AB5 BC5 Riemann sums computation of left Riemann Sum (c)2009 AB5 BC5 tangents tangent line to a curve at a point (d)2009 AB5 BC5 tangents local linear approximation (d)2009 AB5 BC5 tangents tangent line and concavity (d)2009 AB5 BC5 secant line secant line and concavity (d)2009 AB6 analytic exponential points of inflection point of inflection (a) closed2009 AB6 total change given rate of change integral of a rate of change to give accumulated change (b)2009 AB6 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (c)2009 AB6 maximum, minimum absolute extrema (c)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2009 BC3 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2009 BC3 maximum, minimum absolute extrema (a)2009 BC3 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) 2009 BC3 total change given rate of change integral of a rate of change to give accumulated change (a) (b)2009 BC3 arc length length of a curve given in parametric form (c)2009 BC3 tangents tangent line to a curve at a point (d)2009 BC3 differentiation chain rule (d)2009 BC4 analytic algebraic differential equations solution of a differential equation (a) (c) closed2009 BC4 Euler's method Euler's method (a)2009 BC4 series Taylor polynomial approximation (b)2009 BC6 analytic exponential series manipulation of Taylor series to form new series from known series (a) (b) closed2009 BC6 interval/convergence interval of convergence of power series (c)2009 BC6 limits calculating limits using algebra (c)2009 BC6 points of inflection point of inflection (d)2009 B AB1 analytic trigonometric total change given rate of change integral of a rate of change to give accumulated change (a) active2009 B AB1 related rates related rates (b)2009 B AB1 differentiation chain rule (b)2009 B AB1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c) 2009 B AB1 definite integral interpretation of definite integrals (c) 2009 B AB2 BC2 analytic trigonometric total change given rate of change integral of a rate of change to give accumulated change (a) (d) active2009 B AB2 BC2 differentiation interpretation of derivative as a rate of change (b)2009 B AB2 BC2 maximum, minimum absolute extrema (c)2009 B AB3 BC3 graphical general derivative, definition approximate rate of change from graphs and tables of values (a) neutral2009 B AB3 BC3 differentiability differentiability (a)2009 B AB3 BC3 average rate of change average rate of change (b)2009 B AB3 BC3 Mean value theorem Mean Value Theorem (c)2009 B AB3 BC3 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (d)2009 B AB3 BC3 concavity relationship between the concavity of f and the sign of f'' (d)2009 B AB4 analytic algebraic area area of a region (a) closed2009 B AB4 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)2009 B AB4 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)2009 B AB4 volume-slicing volume of a solid with known cross section (b)2009 B AB4 volume volume of a solid of revolution (c)2009 B AB5 BC5 graphical general derivative, graph of corresponding characteristics of graphs of f and f' (a) (b) (c) (d) closed2009 B AB5 BC5 tangents tangent line to a curve at a point (a)2009 B AB5 BC5 maximum, minimum local extrema (b)2009 B AB5 BC5 concavity relationship between the increasing and decreasing behavior of f and the sign of f' (c)2009 B AB5 BC5 average rate of change average rate of change (d)2009 B AB6 tabular general motion on a line particle motion on a line (a) (b) (c) (d) neutral2009 B AB6 derivative, definition approximate rate of change from graphs and tables of values (a)2009 B AB6 definite integral interpretation of definite integrals (b)2009 B AB6 distance distance traveled by a particle along a line (b)2009 B AB6 total change given rate of change integral of a rate of change to give accumulated change (b) (d)2009 B AB6 trapezoidal approximation computation of trapezoidal sum (b)2009 B AB6 definite integral basic properties of definite integrals (c)2009 B AB6 differentiation interpretation of derivative in context of velocity, speed, and acceleration (c)2009 B BC1 analytic trigonometric area area of a region (a) active2009 B BC1 volume-slicing volume of a solid with known cross section (b)2009 B BC1 arc length length of a curve (c)2009 B BC4 analytic trigonometric polar coordinates polar curves (a) (b) (c) closed2009 B BC4 area area of a region bounded by a polar curve (a)2009 B BC4 differentiation derivative of basic functions (b)2009 B BC4 differentiation derivative of a product (b)2009 B BC4 tangents tangent line to a curve at a point (c)2009 B BC4 differentiation chain rule (c)2009 B BC6 analytic algebraic series function defined by power series (a) (b) (c) (d) closed2009 B BC6 series Taylor series (b)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2009 B BC6 interval/convergence interval of convergence of power series (a)2009 B BC6 limits calculating limits using algebra (a)2009 B BC6 series convergence of series (a)2009 B BC6 interval/convergence convergence of geometric series (b)2009 B BC6 integration methods antiderivatives following directly from derivatives of basic funcions (c)2009 B BC6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)2009 B BC6 series manipulation of Taylor series to form new series from known series (d)2008 AB1 BC1 analytic trigonometric area area of a region (a) (b) active2008 AB1 BC1 algebraic volume-slicing volume of a solid with known cross section (c) (d)2008 AB2 BC2 tabular general derivative, definition approximate rate of change from graphs and tables of values (a) active2008 AB2 BC2 average value average value of a function (b)2008 AB2 BC2 trapezoidal approximation computation of trapezoidal sum (b)2008 AB2 BC2 continuity Intermediate Value Theorem (c)2008 AB2 BC2 Mean value theorem Mean Value Theorem (c)2008 AB2 BC2 analytic exponential total change given rate of change integral of a rate of change to give accumulated change (d)2008 AB3 analytic algebraic related rates related rates (a) active2008 AB3 maximum, minimum absolute extrema (b)2008 AB3 total change given rate of change integral of a rate of change to give accumulated change (c)2008 AB4 BC4 graphical general motion on a line particle motion on a line (a) (b) (c) (d) closed2008 AB4 BC4 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (c) (d)2008 AB4 BC4 maximum, minimum absolute extrema (a)2008 AB4 BC4 total change given rate of change integral of a rate of change to give accumulated change (a)2008 AB4 BC4 definite integral basic properties of definite integrals (a)2008 AB4 BC4 continuity Intermediate Value Theorem (b)2008 AB4 BC4 differentiation relationship between the increasing and decreasing behavior of f and the sign of f' (c) (d)2008 AB5 analytic algebraic slope fields slope fields (a) closed2008 AB5 differential equations solving separable differential equations (b)2008 AB5 limits limits of functions (c)2008 AB6 analytic logarithmic tangents tangent line to a curve at a point (a) closed2008 AB6 maximum, minimum local extrema (b)2008 AB6 points of inflection point of inflection (c)2008 AB6 differentiation derivative of a quotient (c)2008 AB6 limits limits of functions (d)2008 BC3 tabular general series Taylor polynomial approximation (a) (b) active2008 BC3 series Lagrange error bound (c)2008 BC5 analytic algebraic maximum, minimum local extrema (a) closed2008 BC5 differentiation relationship between the increasing and decreasing behavior of f and the sign of f' (b)2008 BC5 differentiation derivative of a product (b)2008 BC5 concavity relationship between the concavity of f and the sign of f'' (b)2008 BC5 integration methods antiderivatives by parts (c)2008 BC6 analytic algebraic slope fields relationship between slope fields and solution curves for differential equations (a) closed2008 BC6 Euler's method Euler's method (b)2008 BC6 differentiation, implicit implicit differentiation (c)2008 BC6 series Taylor polynomial approximation (c)2008 B BC6 differential equations solving logistic differential equations and using them in modeling (d)2008 B AB1 analytic algebraic area area of a region (a) active2008 B AB1 volume volume of a solid of revolution (b)2008 B AB1 volume-slicing volume of a solid with known cross section (c)2008 B AB2 BC2 analytic exponential total change given rate of change integral of a rate of change to give accumulated change (a) (c) active2008 B AB2 BC2 related rates related rates (b)2008 B AB3 BC3 tabular general trapezoidal approximation computation of trapezoidal sum (a) active2008 B AB3 BC3 trigonometric average value average value of a function (b) (d)2008 B AB3 BC3 area area of a region (a) (c)2008 B AB4 analytic algebraic fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a) closed2008 B AB4 trigonometric differentiation chain rule (a)2008 B AB4 tangents tangent line to a curve at a point (b)2008 B AB4 maximum, minimum absolute extrema (c)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2008 B AB5 BC5 graphical general concavity relationship between the increasing and decreasing behavior of f and the sign of f' (a) closed2008 B AB5 BC5 maximum, minimum absolute extrema (b)2008 B AB5 BC5 total change given rate of change integral of a rate of change to give accumulated change (b)2008 B AB5 BC5 average rate of change average rate of change (c) (d)2008 B AB5 BC5 Mean value theorem Mean Value Theorem (d)2008 B AB6 analytic algebraic differentiation, implicit implicit differentiation (a) closed2008 B AB6 tangents tangent line to a curve at a point (b)2008 B AB6 tangents vertical tangents (c)2008 B AB6 tangents horizontal tangents (d)2008 B BC1 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2008 B BC1 trigonometric vectors acceleration vector (a)2008 B BC1 total change given rate of change integral of a rate of change to give accumulated change (b)2008 B BC1 vectors speed (c)2008 B BC1 arc length length of a curve given in parametric form (d)2008 B BC4 analytic algebraic area area of a region (a) closed2008 B BC4 volume volume of a solid of revolution (b)2008 B BC4 arc length length of a curve (c)2008 B BC6 analytic algebraic series manipulation of Taylor series to form new series from known series (a) (c) closed2008 B BC6 series geometric series (a)2008 B BC6 series convergence of series (b)2007 BC6 series alternating series with error bound (d)2007 AB1 BC1 analytic algebraic area area of a region (a) active2007 AB1 BC1 volume volume of a solid of revolution (b)2007 AB1 BC1 volume-slicing volume of a solid with known cross section (c)2007 AB2 BC2 analytic trigonometric total change given rate of change integral of a rate of change to give accumulated change (a) (c) active2007 AB2 BC2 graphical differentiation relationship between the increasing and decreasing behavior of f and the sign of f' (b)2007 AB2 BC2 verbal maximum, minimum absolute extrema (c)2007 AB3 tabular general continuity Intermediate Value Theorem (a) neutral2007 AB3 Mean value theorem Mean Value Theorem (b)2007 AB3 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (c)2007 AB3 differentiation chain rule (b) (c)2007 AB3 differentiation derivative of the inverse of a function (d)2007 AB4 analytic trigonometric maximum, minimum absolute extrema (a) closed2007 AB4 differentiation derivative of a product (a) (b)2007 AB4 differentiation chain rule (a) (b)2007 AB4 differential equations solution of a differential equation (b)2007 AB5 BC5 tabular general tangents local linear approximation (a) closed2007 AB5 BC5 verbal tangents tangent line and concavity (a)2007 AB5 BC5 related rates related rates (b)2007 AB5 BC5 Riemann sums computation of right Riemann Sum (c)2007 AB5 BC5 definite integral interpretation of definite integrals (c)2007 AB6 analytic logarithmic differentiation derivative of basic functions (a) closed2007 AB6 maximum, minimum local extrema (b)2007 AB6 points of inflection point of inflection (c)2007 BC3 analytic trigonometric polar coordinates polar curves (a) (b) (c) active2007 BC3 area area of a region bounded by a polar curve (a)2007 BC3 differentiation interpretation of derivative as a rate of change (b) (c)2007 BC4 analytic logarithmic tangents tangent line to a curve at a point (a) closed2007 BC4 concavity relationship between the concavity of f and the sign of f'' (b)2007 BC4 integration methods antiderivatives by parts (c)2007 BC4 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)2007 BC6 analytic exponential series Maclaurin series for e^x (a) closed2007 BC6 limits limits of functions (b)2007 BC6 series manipulation of series by antidifferentiation (c)2007 B BC6 series alternating series with error bound (d)2007 B AB1 BC1 analytic exponential area area of a region (a) (b) active2007 B AB1 BC1 volume volume of a solid of revolution (c)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2007 B AB2 analytic trigonometric motion on a line particle motion on a line (a) (b) (c) (d) active2007 B AB2 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a)2007 B AB2 distance distance traveled by a particle along a line (b)2007 B AB2 total change given rate of change integral of a rate of change to give accumulated change (c)2007 B AB2 maximum, minimum absolute extrema (d)2007 B AB2 maximum, minimum accumulation function/Fundamental theorem (d)2007 B AB3 BC3 analytic algebraic differentiation interpretation of derivative as a rate of change (a) active2007 B AB3 BC3 verbal average rate of change average rate of change (b)2007 B AB3 BC3 related rates related rates (c)2007 B AB4 BC4 graphical general maximum, minimum local extrema (a) closed2007 B AB4 BC4 concavity relationship between the increasing and decreasing behavior of f and the sign of f' (b) (c)2007 B AB4 BC4 maximum, minimum absolute extrema (d)2007 B AB4 BC4 total change given rate of change integral of a rate of change to give accumulated change (d)2007 B AB5 analytic algebraic slope fields slope fields (a) closed2007 B AB5 differentiation, implicit implicit differentiation (b)2007 B AB5 concavity (b)2007 B AB5 maximum, minimum local extrema (c)2007 B AB5 differential equations solution of a differential equation (d)2007 B AB6 analytic general Mean value theorem Mean Value Theorem (a) (b) closed2007 B AB6 differentiation chain rule (b)2007 B AB6 points of inflection inflection point (c)2007 B AB6 continuity Intermediate Value Theorem (d)2007 B BC2 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2007 B BC2 logarithmic vectors speed (a)2007 B BC2 arc length length of a curve given in parametric form (b)2007 B BC2 total change given rate of change integral of a rate of change to give accumulated change (c)2007 B BC2 tangents tangent line to a curve at a point (d)2007 B BC2 vectors acceleration vector (d)2007 B BC5 analytic algebraic differentiation, implicit implicit differentiation (a) closed2007 B BC5 differential equations solution of a differential equation (b)2007 B BC5 Euler's method Euler's method (c) (d)2007 B BC6 analytic exponential series Maclaurin series for e^x (a) (c)2007 B BC6 series manipulation of series by antidifferentiation (b)2006 BC6 series manipulation of series by differentiation (c)2006 AB1 BC1 analytic logarithmic area area of a region (a) active2006 AB1 BC1 algebraic volume volume of a solid of revolution (b) (c)2006 AB2 BC2 analytic trigonometric total change given rate of change integral of a rate of change to give accumulated change (a) (c) active2006 AB2 BC2 average value average value of a function2006 AB3 graphical general fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a) (c) neutral2006 AB3 maximum, minimum local extrema (b)2006 AB3 periodicity periodic functions (c)2006 AB3 tangents tangent line to a curve at a point (c)2006 AB4 BC4 tabular general average rate of change average rate of change (a) closed2006 AB4 BC4 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c)2006 AB4 BC4 definite integral interpretation of definite integrals (b)2006 AB4 BC4 Riemann sums computation of midpoint Riemann Sum (b)2006 AB4 BC4 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)2006 AB5 analytic algebraic slope fields slope fields (a) closed2006 AB5 differential equations solving separable differential equations (b)2006 AB5 differential equations domain of a function (b)2006 AB6 analytic general differentiation derivative of basic functions (a) (b) closed2006 AB6 differentiation chain rule (a) (b)2006 AB6 differentiation derivative of a product (b)2006 AB6 tangents tangent line to a curve at a point (b)2006 BC3 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (d) (d) active2006 BC3 analytic algebraic vectors acceleration vector (a)2006 BC3 vectors speed (a)

relationship between the concavity of f and the sign of f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2006 BC3 tangents vertical tangents (b)2006 BC3 tangents tangent line to a curve at a point (c)2006 BC3 improper integrals improper integrals (d)2006 BC3 limits describing asymptotic behavior in terms of limits at infinity (d)2006 BC3 total change given rate of change integral of a rate of change to give accumulated change (d)2006 BC5 analytic algebraic differentiation implicit differentiation (a) closed2006 BC5 tangents tangent line to a curve at a point (b)2006 BC5 series Taylor polynomial approximation (c)2006 BC5 Euler's method Euler's method (d)2006 BC6 analytic algebraic series function defined by power series (a) (b) closed2006 BC6 interval/convergence interval of convergence of power series (a)2006 B BC6 maximum, minimum local extrema (b)2006 B AB1 BC1 analytic algebraic area area of a region (a) (c) active2006 B AB1 BC1 analytic trigonometric volume volume of a solid of revolution (b)2006 B AB2 analytic trigonometric derivative, graph of corresponding characteristics of graphs of f and f' (a) (b) active2006 B AB2 graphical trigonometric concavity relationship between the increasing and decreasing behavior of f and the sign of f' (a)2006 B AB2 maximum, minimum absolute extrema (b)2006 B AB2 tangents tangent line to a curve at a point (c)2006 B AB2 total change given rate of change integral of a rate of change to give accumulated change (c)2006 B AB3 BC3 graphical algebraic differentiation derivative of basic functions (a) (b) (c) (d) neutral2006 B AB3 BC3 differentiation relationship between the increasing and decreasing behavior of f and the sign of f' (c) (d)2006 B AB4 BC4 graphical algebraic derivative, definition slope of a curve at a point (a) closed2006 B AB4 BC4 analytic algebraic maximum, minimum absolute extrema (b)2006 B AB4 BC4 total change given rate of change integral of a rate of change to give accumulated change (c)2006 B AB4 BC4 average value average value of a function (d)2006 B AB5 analytic trigonometric slope fields slope fields (a) closed2006 B AB5 differential equations solving separable differential equations (b)2006 B AB5 differential equations solving separable differential equations (c)2006 B AB6 tabular general motion on a line particle motion on a line (a) (b) closed2006 B AB6 definite integral interpretation of definite integrals (a) (b)2006 B AB6 trapezoidal approximation computation of trapezoidal sum (a)2006 B AB6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)2006 B AB6 continuity Intermediate Value Theorem (c)2006 B AB6 Mean value theorem Mean Value Theorem (d)2006 B BC2 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2006 B BC2 tangents tangent line to a curve at a point (a)2006 B BC2 vectors acceleration vector (b)2006 B BC2 vectors speed (b)2006 B BC2 arc length length of a curve given in parametric form (c)2006 B BC2 total change given rate of change integral of a rate of change to give accumulated change (d)2006 B BC5 analytic algebraic differential equations solving separable differential equations (a) closed2006 B BC5 differential equations solving logistic differential equations and using them in modeling (b) (c)2006 B BC5 points of inflection point of inflection (c)2006 B BC6 analytic algebraic series Maclaurin series for 1/(1-x) (a)2006 B BC6 series manipulation of series by differentiation (a) closed2006 B BC6 series manipulation of Taylor series to form new series from known series (b)2006 B BC6 series manipulation of series by antidifferentiation (c)2005 BC6 series alternating series with error bound (d)2005 AB1 BC1 analytic trigonometric area area of a region (a) (b) active2005 AB1 BC1 exponential volume volume of a solid of revolution (c)2005 AB2 analytic trigonometric total change given rate of change integral of a rate of change to give accumulated change (a) (b) (d) active2005 AB2 verbal algebraic differentiation interpretation of derivative as a rate of change (c)2005 AB2 maximum, minimum absolute extrema (d)2005 AB3 BC3 tabular general derivative, definition approximate rate of change from graphs and tables of values (a) neutral2005 AB3 BC3 average value average value of a function (b)2005 AB3 BC3 trapezoidal approximation computation of trapezoidal sum (b)2005 AB3 BC3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2005 AB3 BC3 total change given rate of change integral of a rate of change to give accumulated change (c)2005 AB3 BC3 Mean value theorem Mean Value Theorem (d)2005 AB3 BC3 concavity relationship between the increasing and decreasing behavior of f and the sign of f' (d)2005 AB4 tabular general maximum, minimum local extrema (a) (c) closed2005 AB4 curve sketching curve sketching (b)2005 AB4 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (c) (d)2005 AB4 points of inflection point of inflection (d)2005 AB5 BC5 graphical general motion on a line particle motion on a line (a) (b) (c) closed2005 AB5 BC5 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c)2005 AB5 BC5 area area of a region (a)2005 AB5 BC5 total change given rate of change integral of a rate of change to give accumulated change (a)2005 AB5 BC5 differentiability differentiability (b)2005 AB5 BC5 derivative, definition slope of a curve at a point (b)2005 AB5 BC5 differentiation derivative of basic functions (c)2005 AB5 BC5 average rate of change average rate of change (d)2005 AB5 BC5 Mean value theorem Mean Value Theorem (d)2005 AB6 analytic algebraic slope fields slope fields (a) closed2005 AB6 tangents tangent line to a curve at a point (b)2005 AB6 tangents local linear approximation (b)2005 AB6 differential equations solving separable differential equations (c)2005 BC2 analytic trigonometric polar coordinates polar curves (a) (b) (c) (d) active2005 BC2 area area of a region bounded by a polar curve (a)2005 BC2 differentiation interpretation of derivative as a rate of change (c)2005 BC2 maximum, minimum absolute extrema (d)2005 BC4 analytic algebraic slope fields slope fields (a) closed2005 BC4 maximum, minimum local extrema (b)2005 BC4 Euler's method Euler's method (c)2005 BC4 differentiation, implicit implicit differentiation (d)2005 BC4 tangents local linear approximation (d)2005 BC6 analytic general series Taylor polynomial approximation (a) closed2005 BC6 series Taylor series (b)2005 B BC6 interval/convergence interval of convergence of power series (c)2005 B AB1 analytic trigonometric area area of a region (a) active2005 B AB1 exponential volume volume of a solid of revolution (b)2005 B AB1 volume-slicing volume of a solid with known cross section (c)2005 B AB2 BC2 analytic trigonometric total change given rate of change integral of a rate of change to give accumulated change (b) (d) active2005 B AB2 BC2 verbal differentiation interpretation of derivative as a rate of change (a)2005 B AB2 BC2 maximum, minimum absolute extrema (c)2005 B AB3 analytic logarithmic motion on a line particle motion on a line (a) (b) (c) (d) active2005 B AB3 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b)2005 B AB3 total change given rate of change integral of a rate of change to give accumulated change (c)2005 B AB3 average value average value of a function (d)2005 B AB4 BC4 graphical general fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a) (b) (c) (d) closed2005 B AB4 BC4 points of inflection point of inflection (b)2005 B AB5 BC5 analytic algebraic differentiation, implicit implicit differentiation (a) closed2005 B AB5 BC5 tangents tangent line to a curve at a point (b) (c)2005 B AB5 BC5 differentiation chain rule (d)2005 B AB6 analytic algebraic slope fields slope fields (a) closed2005 B AB6 tangents tangent line to a curve at a point (b)2005 B AB6 differential equations solving separable differential equations (c)2005 B BC1 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2005 B BC1 logarithmic vectors acceleration vector (a)2005 B BC1 vectors speed (a) (d)2005 B BC1 total change given rate of change integral of a rate of change to give accumulated change (b)2005 B BC1 tangents tangent line to a curve at a point (c)2005 B BC3 analytic general series Taylor series (a) (c) neutral2005 B BC3 maximum, minimum local extrema (a)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2005 B BC3 series Taylor polynomial approximation (b)2005 B BC3 interval/convergence radius of convergence (c)2005 B BC6 analytic algebraic area area of a region (a) closed2005 B BC6 volume volume of a solid of revolution (b) (c)2004 BC6 improper integrals improper integrals (c)2004 AB1 BC1 analytic trigonometric total change given rate of change integral of a rate of change to give accumulated change (a) active2004 AB1 BC1 verbal differentiation interpretation of derivative as a rate of change (b)2004 AB1 BC1 average value average value of a function (c)2004 AB1 BC1 average rate of change average rate of change (d)2004 AB2 BC2 analytic algebraic area area of a region (a) active2004 AB2 BC2 volume volume of a solid of revolution (b)2004 AB2 BC2 volume-slicing volume of a solid with known cross section (c)2004 AB3 analytic exponential motion on a line particle motion on a line (a) (b) (c) (d) active2004 AB3 trigonometric differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (d)2004 AB3 maximum, minimum absolute extrema (c)2004 AB3 total change given rate of change integral of a rate of change to give accumulated change (d)2004 AB4 BC4 analytic algebraic differentiation, implicit implicit differentiation (a) (c) closed2004 AB4 BC4 differentiation derivative of basic functions (b)2004 AB4 BC4 differentiation derivative of a quotient (c)2004 AB4 BC4 tangents horizontal tangents (b)2004 AB4 BC4 maximum, minimum local extrema (c)2004 AB5 graphical general area area of a region (a) closed2004 AB5 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a)2004 AB5 maximum, minimum local extrema (b)2004 AB5 maximum, minimum absolute extrema (c)2004 AB5 points of inflection point of inflection (d)2004 AB6 analytic algebraic slope fields slope fields (a) (b) closed2004 AB6 differential equations solving separable differential equations (c)2004 BC3 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2004 BC3 total change given rate of change integral of a rate of change to give accumulated change (a)2004 BC3 differentiation derivative of parametric function (b)2004 BC3 vectors velocity vector and speed (c)2004 BC3 vectors acceleration vector (d)2004 BC5 analytic exponential differential equations solving logistic differential equations and using them in modeling (a) (b) closed2004 BC5 differential equations solution of a differential equation (c)2004 BC5 limits limits of functions (a) (d)2004 BC6 analytic trigonometric series Taylor polynomial approximation (a) (d) closed2004 BC6 series Taylor series (b)2004 BC6 series Lagrange error bound (c)2004 B BC6 series manipulation of series by antidifferentiation (d)2004 B AB1 analytic algebraic area area of a region (a) active2004 B AB1 volume volume of a solid of revolution (b) (c)2004 B AB2 analytic trigonometric differentiation interpretation of derivative as a rate of change (a) (b) active2004 B AB2 verbal total change given rate of change integral of a rate of change to give accumulated change (c) (d)2004 B AB2 maximum, minimum absolute extrema (d)2004 B AB3 BC3 tabular general motion on a line particle motion on a line (a) (b) (c) (d) active2004 B AB3 BC3 analytic trigonometric Riemann sums computation of midpoint Riemann Sum (a)2004 B AB3 BC3 mean value theorem Mean Value Theorem (b)2004 B AB3 BC3 differentiation interpretation of derivative in context of velocity, speed, and acceleration (c)2004 B AB3 BC3 average value average value of a function (d)2004 B AB4 BC4 graphical general derivative, graph of corresponding characteristics of graphs of f and f' (a) (b) closed2004 B AB4 BC4 points of inflection point of inflection (a)2004 B AB4 BC4 maximum, minimum absolute extrema (b)2004 B AB4 BC4 differentiation derivative of a product (c)2004 B AB4 BC4 tangents tangent line to a curve at a point (c)2004 B AB5 analytic algebraic slope fields slope fields (a) (b) closed2004 B AB5 differential equations solving separable differential equations (c)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2004 B AB6 BC6 analytic algebraic fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) closed2004 B AB6 BC6 area area of a region (b) (c)2004 B AB6 BC6 maximum, minimum absolute extrema (c)2004 B BC1 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2004 B BC1 exponential vectors speed (a)2004 B BC1 vectors acceleration vector (a)2004 B BC1 differentiation derivative of parametric function (b)2004 B BC1 tangents tangent line to a curve at a point (b)2004 B BC1 arc length length of a curve given in parametric form (c)2004 B BC1 total change given rate of change integral of a rate of change to give accumulated change (d)2004 B BC2 analytic algebraic series Taylor polynomial approximation (a) (b) (c) neutral2004 B BC2 maximum, minimum local extrema (b) (c)2004 B BC2 series Lagrange error bound (d)2004 B BC5 analytic algebraic average value average value of a function (a) (c) (d) closed2004 B BC5 volume volume of a solid of revolution (b)2003 BC5 improper integrals improper integrals (d)2003 AB1 BC1 analytic exponential area area of a region (a) active2003 AB1 BC1 algebraic volume volume of a solid of revolution (b)2003 AB1 BC1 volume-slicing volume of a solid with known cross section (c) 2003 AB2 analytic trigonometric motion on a line particle motion on a line (a) (b) (c) (d) active2003 AB2 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) 2003 AB2 distance distance traveled by a particle along a line (c)2003 AB2 maximum, minimum absolute extrema (d)2003 AB3 tabular general derivative, definition approximate rate of change from graphs and tables of values (a) neutral2003 AB3 graphical differentiation interpretation of second derivative (b)2003 AB3 verbal Riemann sums computation of left Riemann Sum (c)2003 AB3 definite integral interpretation of definite integrals (d)2003 AB4 BC4 graphical general derivative, graph of (a) closed2003 AB4 BC4 points of inflection point of inflection (b)2003 AB4 BC4 tangents tangent line to a curve at a point (c)2003 AB4 BC4 fundamental theorem accumulation function/Fundamental Theorem (d)2003 AB5 BC5 analytic algebraic differentiation derivative of basic functions (a) closed2003 AB5 BC5 verbal differentiation chain rule (a)2003 AB5 BC5 differential equations solving separable differential equations (b)2003 AB5 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (b)2003 AB6 analytic algebraic continuity understanding continuity in terms of limits (a) closed2003 AB6 average value average value of a function (b)2003 AB6 differentiability differentiability (c)2003 AB6 integration methods antiderivatives following directly from derivatives of basic funcions (b)2003 AB6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)2003 BC2 graphical trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2003 BC2 analytic differentiation interpretation of derivative as a rate of change (a) 2003 BC2 differentiation derivative of parametric function (b)2003 BC2 vectors velocity vector and speed (c)2003 BC2 fundamental theorem accumulation function/Fundamental Theorem (d)2003 BC3 analytic algebraic differentiation derivative of basic functions (a) active2003 BC3 trigonometric differentiation chain rule (a)2003 BC3 area area of a region (b)2003 BC3 polar coordinates polar curves (c)2003 BC3 area area of a region bounded by a polar curve (d)2003 BC6 analytic trigonometric series function defined by power series (a) closed2003 BC6 algebraic series alternating series with error bound (b)2003 BC6 series manipulation of Taylor series to form new series from known series (c)2003 BC6 series (c)2003 B BC6 series (c)2003 B AB1 BC1 analytic algebraic differentiation derivative of basic functions (a) neutral2003 B AB1 BC1 tangents tangent line to a curve at a point (a)

corresponding characteristics of graphs of f and f'

Maclaurin series for sin(x)Maclaurin series for cos(x)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2003 B AB1 BC1 area area of a region (b)2003 B AB1 BC1 volume volume of a solid of revolution (c)2003 B AB2 analytic logarithmic total change given rate of change integral of a rate of change to give accumulated change (a) (c) (d) active2003 B AB2 verbal trigonometric differentiation interpretation of derivative as a rate of change (b)2003 B AB2 maximum, minimum absolute extrema (d)2003 B AB3 BC3 tabular general average value average value of a function (a) neutral2003 B AB3 BC3 verbal Riemann sums computation of midpoint Riemann Sum (b)2003 B AB3 BC3 volume-slicing volume of a solid with known cross section (c)2003 B AB3 BC3 mean value theorem Mean Value Theorem (d)2003 B AB3 BC3 definite integral interpretation of definite integrals (c)2003 B AB4 analytic exponential motion on a line particle motion on a line (a) (b) (c) (d) closed2003 B AB4 derivative, definition interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c) 2003 B AB4 distance distance traveled by a particle along a line (d)2003 B AB4 integration methods antiderivatives following directly from derivatives of basic funcions (d)2003 B AB4 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (d)2003 B AB4 integration methods antiderivatives by substitution (d)2003 B AB5 BC5 graphical general area area of a region (a)2003 B AB5 BC5 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a) closed2003 B AB5 BC5 average rate of change average rate of change (b)2003 B AB5 BC5 mean value theorem Mean Value Theorem (c)2003 B AB5 BC5 points of inflection point of inflection (d)2003 B AB6 analytic algebraic differentiation derivative of basic functions (a) closed2003 B AB6 differentiation chain rule (a)2003 B AB6 differentiation derivative of a product (a)2003 B AB6 differential equations solving separable differential equations (b)2003 B AB6 integration methods antiderivatives following directly from derivatives of basic funcions (b)2003 B BC2 analytic algebraic area area of a region (a) (b) neutral2003 B BC2 trigonometric area area of a region bounded by a polar curve (c)2003 B BC4 analytic exponential parametric equations analysis of planar curve given in parametric form (a) (b (c) (d) closed2003 B BC4 vectors velocity vector and speed (b)2003 B BC4 differentiation derivative of basic functions (b)2003 B BC4 differentiation chain rule (b)2003 B BC4 limits calculating limits using algebra (b)2003 B BC4 tangents vertical tangents (d)2003 B BC4 tangents horizontal tangents (c)2003 B BC6 analytic general series Taylor series (a) closed2003 B BC6 interval/convergence radius of convergence (b)2003 B BC6 series manipulation of Taylor series to form new series from known series (c)2002 BC6 interval/convergence convergence of geometric series (d)2002 AB1 BC1 analytic exponential area area of a region (a) active2002 AB1 BC1 logarithmic volume volume of a solid of revolution (b)2002 AB1 BC1 maximum, minimum absolute extrema (c)2002 AB2 BC2 analytic algebraic total change given rate of change integral of a rate of change to give accumulated change (a) (b) active2002 AB2 BC2 verbal fundamental theorem accumulation function/Fundamental Theorem (c)2002 AB2 BC2 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (c)2002 AB2 BC2 differentiation interpretation of derivative as a rate of change (c)2002 AB2 BC2 definite integral interpretation of definite integrals (c)2002 AB2 BC2 maximum, minimum absolute extrema (d)2002 AB3 analytic trigonometric motion on a line particle motion on a line (a) (b) (c) (d) neutral2002 AB3 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) 2002 AB3 distance distance traveled by a particle along a line (c)2002 AB3 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (d)2002 AB4 BC4 graphical general area area of a region (a) closed2002 AB4 BC4 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a)2002 AB4 BC4 derivative, graph of (b)2002 AB4 BC4 concavity (c)2002 AB4 BC4 derivative, graph of (d)

relationship between the increasing and decreasing behavior of f and the sign of f'relationship between the concavity of f and the sign of f''corresponding characteristics of the graphs of f, f', and f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2002 AB5 verbal algebraic differentiation derivative of basic functions (b) closed2002 AB5 differentiation chain rule (b) (c)2002 AB5 differentiation interpretation of derivative as a rate of change (b) (c)2002 AB6 tabular general total change given rate of change definite integral of a rate of change (a) closed2002 AB6 algebraic integration methods antiderivatives following directly from derivatives of basic funcions (a)2002 AB6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)2002 AB6 tangents tangent line to a curve at a point (b)2002 AB6 tangents local linear approximation (b)2002 AB6 mean value theorem Mean Value Theorem (c)2002 AB6 continuity understanding continuity in terms of limits (d)2002 AB6 differentiation derivative of basic functions (d)2002 BC3 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2002 BC3 tangents slope of a curve at a point (a)2002 BC3 differentiation derivative of parametric function (a)2002 BC3 vectors acceleration vector (b)2002 BC3 maximum, minimum absolute extrema (c)2002 BC3 vectors speed (c) (d)2002 BC3 average value average value of a function (d)2002 BC5 analytic algebraic slope fields relationship between slope fields and solution curves for differential equations (a) closed2002 BC5 Euler's method Euler's method (b)2002 BC5 differential equations solution of a differential equation (c)2002 BC5 maximum, minimum local extrema (d)2002 BC6 analytic algebraic interval/convergence interval of convergence of power series (a) closed2002 BC6 series manipulation of series by differentiation (b)2002 B BC6 series geometric series (c)2002 B AB1 analytic algebraic area area of a region (a) active2002 B AB1 volume volume of a solid of revolution (b)2002 B AB1 volume-slicing volume of a solid with known cross section (c)2002 B AB2 BC2 analytic exponential differentiation interpretation of derivative as a rate of change (a) active2002 B AB2 BC2 verbal maximum, minimum local extrema (b)2002 B AB2 BC2 total change given rate of change integral of a rate of change to give accumulated change (c)2002 B AB2 BC2 tangents tangent line to a curve at a point (d)2002 B AB3 analytic exponential motion on a line particle motion on a line (a) (b) (c) (d) active2002 B AB3 trigonometric differentiation interpretation of derivative in context of velocity, speed, and acceleration (b)2002 B AB3 distance distance traveled by a particle along a line (c)2002 B AB3 definite integral basic properties of definite integrals (d)2002 B AB4 BC4 graphical general area area of a region (a) closed2002 B AB4 BC4 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a)2002 B AB4 BC4 fundamental theorem accumulation function/Fundamental Theorem (b) (c)2002 B AB4 BC4 derivative, graph of (b) 2002 B AB4 BC4 concavity (c)2002 B AB4 BC4 trapezoidal approximation computation of trapezoidal sum (d)2002 B AB5 BC5 analytic algebraic differentiation derivative of basic functions (a) closed2002 B AB5 BC5 maximum, minimum local extrema (a)2002 B AB5 BC5 differential equations solving separable differential equations (b)2002 B AB5 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (b)2002 B AB6 verbal algebraic differentiation derivative of basic functions (b) (c) closed2002 B AB6 trigonometric differentiation chain rule (b) (c)2002 B AB6 related rates related rates (b) (c)2002 B BC1 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2002 B BC1 algebraic maximum, minimum local extrema (c)2002 B BC1 vectors speed (c)2002 B BC1 arc length length of a curve given in parametric form (d)2002 B BC3 analytic algebraic area area of a region (a) active2002 B BC3 volume volume of a solid of revolution (b)2002 B BC3 arc length length of a curve (c)2002 B BC6 analytic logarithmic series manipulation of Taylor series to form new series from known series (a) closed

relationship between the increasing and decreasing behavior of f and the sign of f'relationship between the concavity of f and the sign of f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2002 B BC6 series alternating series test (c)2001 BC6 interval/convergence convergence of p-series (c) (d)2001 AB1 analytic algebraic area area of a region (a) (b) active2001 AB1 trigonometric volume volume of a solid of revolution (c)2001 AB2 BC2 tabular exponential derivative, definition approximate rate of change from graphs and tables of values (a) active2001 AB2 BC2 general average value average value of a function (b) (d)2001 AB2 BC2 trapezoidal approximation computation of trapezoidal sum (b)2001 AB2 BC2 differentiation interpretation of derivative as a rate of change (c)2001 AB3 BC3 graphical general motion on a line particle motion on a line (a) (b) (c) (d) neutral2001 AB3 BC3 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) 2001 AB3 BC3 total change given rate of change integral of a rate of change to give accumulated change (b) (c) (d)2001 AB3 BC3 maximum, minimum absolute extrema (c)2001 AB4 BC4 analytic algebraic tangents horizontal tangents (a) closed2001 AB4 BC4 maximum, minimum local extrema (a)2001 AB4 BC4 differentiation derivative of basic functions (b)2001 AB4 BC4 differentiation derivative of a quotient (b)2001 AB4 BC4 concavity (c)2001 AB4 BC4 concavity tangent line and concavity (d)2001 AB5 analytic algebraic differentiation derivative of basic functions (a) closed2001 AB5 derivative, graph of (a)2001 AB5 concavity (a)2001 AB5 integration methods antiderivatives following directly from derivatives of basic funcions (b)2001 AB5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)2001 AB6 analytic algebraic differentiation derivative of basic functions (a) closed2001 AB6 differentiation, implicit implicit differentiation (a)2001 AB6 differentiation chain rule (a)2001 AB6 differential equations solving separable differential equations (b)2001 AB6 integration methods antiderivatives following directly from derivatives of basic funcions (b)2001 BC1 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active2001 BC1 tangents tangent line to a curve at a point (a)2001 BC1 differentiation derivative of parametric function (a)2001 BC1 vectors speed (b)2001 BC1 arc length length of a curve given in parametric form (c)2001 BC1 total change given rate of change integral of a rate of change to give accumulated change (d)2001 BC5 analytic exponential fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) closed2001 BC5 logarithmic limits properties of limits (a)2001 BC5 Euler's method Euler's method (b)2001 BC5 differential equations solving separable differential equations (c)2001 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (c)2001 BC6 analytic algebraic series function defined by power series (a) (b) (c) (d) closed2001 BC6 interval/convergence interval of convergence of power series (a)2001 BC6 limits calculating limits using algebra (b)2001 BC6 series manipulation of series by antidifferentiation (c)2001 BC6 integration methods antiderivatives following directly from derivatives of basic funcions (c)2001 BC6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)2000 BC6 series geometric series (d)2000 AB1 BC1 analytic exponential area area of a region (a) active2000 AB1 BC1 trigonometric volume volume of a solid of revolution (b)2000 AB1 BC1 volume-slicing volume of a solid with known cross section (c)2000 AB2 BC2 graphical algebraic motion on a line particle motion on a line (a) (b) (c) active2000 AB2 BC2 analytic differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) 2000 AB2 BC2 total change given rate of change integral of a rate of change to give accumulated change (c)2000 AB3 graphical general maximum, minimum local extrema (a) (b) neutral2000 AB3 derivative, graph of (a) (b)2000 AB3 derivative, graph of (c)2000 AB3 maximum, minimum absolute extrema (d)2000 AB3 total change given rate of change integral of a rate of change to give accumulated change (d)

relationship between the concavity of f and the sign of f''

relationship between the increasing and decreasing behavior of f and the sign of f'relationship between the concavity of f and the sign of f''

corresponding characteristics of graphs of f and f'corresponding characteristics of the graphs of f, f', and f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator2000 AB4 verbal algebraic total change given rate of change integral of a rate of change to give accumulated change (a) (c) closed2000 AB4 analytic integration methods antiderivatives following directly from derivatives of basic funcions (a)2000 AB4 integration methods antiderivatives by substitution (a)2000 AB4 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)2000 AB4 maximum, minimum absolute extrema (d)2000 AB4 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (d)2000 AB5 BC5 analytic algebraic differentiation, implicit implicit differentiation (a) closed2000 AB5 BC5 differentiation derivative of basic functions (a)2000 AB5 BC5 differentiation chain rule (a)2000 AB5 BC5 tangents tangent line to a curve at a point (b)2000 AB5 BC5 tangents vertical tangents (c)2000 AB6 analytic exponential differential equations solving separable differential equations (a) closed2000 AB6 algebraic integration methods antiderivatives following directly from derivatives of basic funcions (a)2000 AB6 integration methods antiderivatives by substitution (a)2000 AB6 precalculus domain of a function (b)2000 AB6 precalculus range of a function (b)2000 BC3 analytic algebraic series Taylor polynomial approximation (a) active2000 BC3 interval/convergence radius of convergence (b)2000 BC3 series alternating series with error bound (c)2000 BC4 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) closed2000 BC4 vectors acceleration vector (a)2000 BC4 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b)2000 BC4 integration methods antiderivatives following directly from derivatives of basic funcions (b)2000 BC4 differentiation derivative of parametric function (c)2000 BC4 limits describing asymptotic behavior in terms of limits at infinity (d)2000 BC6 analytic algebraic slope fields slope fields (a) closed2000 BC6 slope fields relationship between slope fields and solution curves for differential equations (b)2000 BC6 differential equations solving separable differential equations (c)2000 BC6 integration methods antiderivatives following directly from derivatives of basic funcions (c) 2000 BC6 integration methods antiderivatives by substitution (c)1999 BC6 precalculus range of a function (d)1999 AB1 analytic trigonometric motion on a line particle motion on a line (a) (b) (c) active1999 AB1 differentiation interpretation of derivative in context of velocity, speed, and acceleration1999 AB1 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)1999 AB1 distance distance traveled by a particle along a line (d)1999 AB2 BC2 analytic algebraic area area of a region (a) neutral1999 AB2 BC2 volume volume of a solid of revolution (b) (c)1999 AB3 BC3 tabular general Riemann sums computation of midpoint Riemann Sum (a) active1999 AB3 BC3 algebraic total change given rate of change integral of a rate of change to give accumulated change (a)1999 AB3 BC3 mean value theorem Mean Value Theorem (b)1999 AB3 BC3 average value average value of a function (c)1999 AB3 BC3 definite integral interpretation of definite integrals (c)1999 AB4 analytic exponential tangents tangent line to a curve at a point (a) (c) neutral1999 AB4 points of inflection point of inflection (b)1999 AB4 differentiation derivative of basic functions (d)1999 AB4 differentiation chain rule (d)1999 AB4 maximum, minimum local extrema (d)1999 AB5 BC5 graphical general total change given rate of change definite integral of a rate of change over an interval (a) neutral1999 AB5 BC5 fundamental theorem accumulation function/Fundamental Theorem (b)1999 AB5 BC5 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (c) (d)1999 AB5 BC5 maximum, minimum absolute extrema (c)1999 AB5 BC5 points of inflection point of inflection (d)1999 AB6 analytic algebraic tangents tangent line to a curve at a point (a) neutral1999 AB6 related rates related rates (c) (d)1999 AB6 differentiation interpretation of derivative as a rate of change (d)1999 BC1 analytic logarithmic parametric equations analysis of planar curve given in parametric form (a) (b) (c) active1999 BC1 trigonometric maximum, minimum local extrema (b)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1999 BC1 vectors speed (c)1999 BC1 vectors acceleration vector (d)1999 BC4 analytic general series Taylor polynomial approximation (a) neutral1999 BC4 series Lagrange error bound (b)1999 BC4 series manipulation of Taylor series to form new series from known series (c)1999 BC4 maximum, minimum local extrema (c)1999 BC6 analytic exponential tangents tangent line to a curve at a point (a) active1999 BC6 tangents local linear approximation (a)1999 BC6 Euler's method Euler's method (b)1998 BC6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)1998 AB1 analytic algebraic area area of a region (a) (b) neutral1998 AB1 volume volume of a solid of revolution (c) (d)1998 AB2 BC2 analytic exponential limits limits of functions (a) neutral1998 AB2 BC2 maximum, minimum absolute extrema (b) (d)1998 AB2 BC2 differentiation derivative of basic functions (b) (d)1998 AB2 BC2 differentiation chain rule (b) (d)1998 AB2 BC2 precalculus range of a function (c)1998 AB3 graphical general motion on a line particle motion on a line (a) (b) (c) (d) neutral1998 AB3 tabular differentiation interpretation of derivative in context of velocity, speed, and acceleration (a)1998 AB3 average rate of change average rate of change (b)1998 AB3 derivative, definition approximate rate of change from graphs and tables of values (c)1998 AB3 Riemann sums computation of midpoint Riemann Sum (d)1998 AB3 distance distance traveled by a particle along a line (d)1998 AB3 definite integral interpretation of definite integrals (d)1998 AB4 analytic algebraic tangents slope of a curve at a point (a) active1998 AB4 tangents tangent line to a curve at a point (b)1998 AB4 differential equations solving separable differential equations (c)1998 AB4 integration methods antiderivatives following directly from derivatives of basic funcions (c)1998 AB5 BC5 analytic trigonometric average value average value of a function (b) active1998 AB5 BC5 total change given rate of change integral of a rate of change to give accumulated change (c)1998 AB6 analytic algebraic differentiation derivative of basic functions (a) neutral1998 AB6 differentiation, implicit implicit differentiation (a)1998 AB6 differentiation chain rule (a)1998 AB6 tangents tangent line to a curve at a point (b) (c)1998 AB6 tangents horizontal tangents (b)1998 BC1 analytic algebraic area area of a region (a) active1998 BC1 volume volume of a solid of revolution (b) (c)1998 BC3 analytic general series Taylor polynomial approximation (a) neutral1998 BC3 series manipulation of Taylor series to form new series from known series (b) (c)1998 BC4 analytic algebraic slope fields slope fields (a) active1998 BC4 Euler's method Euler's method (b)1998 BC4 differential equations solving separable differential equations (c)1998 BC4 integration methods antiderivatives following directly from derivatives of basic funcions (c)1998 BC6 analytic algebraic differential equations solving separable differential equations (a) neutral1998 BC6 integration methods antiderivatives following directly from derivatives of basic funcions (a)1998 BC6 integration methods antiderivatives by substitution (a)1998 BC6 differentiation derivative of basic functions (b)1998 BC6 differentiation chain rule (b)1997 BC6 vectors speed (c)1997 AB1 analytic algebraic motion on a line particle motion on a line (a) (b) (c) neutral1997 AB1 integration methods antiderivatives following directly from derivatives of basic funcions (a)1997 AB1 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a)1997 AB1 average rate of change average rate of change (b)1997 AB1 differentiation interpretation of derivative as a rate of change (b)1997 AB1 distance distance traveled by a particle along a line (c)1997 AB2 analytic trigonometric tangents tangent line to a curve at a point (b) neutral1997 AB2 differentiation derivative of basic functions (b)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1997 AB2 mean value theorem Mean Value Theorem (c)1997 AB2 volume volume of a solid of revolution (d)1997 AB3 analytic algebraic area area of a region (b) (c) neutral1997 AB3 fundamental theorem accumulation function/Fundamental Theorem (d)1997 AB4 analytic algebraic differentiation derivative of basic functions (a) neutral1997 AB4 maximum, minimum local extrema (a)1997 AB4 curve sketching analysis of curves (b)1997 AB4 average value average value of a function (c)1997 AB5 BC5 graphical general total change given rate of change definite integral of a rate of change over an interval (a) neutral1997 AB5 BC5 fundamental theorem accumulation function/Fundamental Theorem (b) (c) (d)1997 AB5 BC5 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (b) (c) (d)1997 AB5 BC5 maximum, minimum local extrema (b) (c) (d)1997 AB5 BC5 tangents tangent line to a curve at a point (c)1997 AB5 BC5 points of inflection point of inflection (d)1997 AB6 BC6 analytic algebraic differential equations solving separable differential equations (a) neutral1997 AB6 BC6 exponential integration methods antiderivatives following directly from derivatives of basic funcions (a)1997 AB6 BC6 integration methods antiderivatives by substitution (a)1997 AB6 BC6 limits limits of functions (b)1997 BC1 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active1997 BC1 differentiation derivative of parametric function (d)1997 BC1 vectors velocity vector (d)1997 BC1 arc length length of a curve given in parametric form (e)1997 BC2 analytic algebraic series Taylor polynomial approximation (a) (b) (c) (d) neutral1997 BC2 series manipulation of Taylor series to form new series from known series (b) (c)1997 BC3 analytic logarithmic area area of a region (a) active1997 BC3 trigonometric arc length length of a curve (b)1997 BC3 volume-slicing volume of a solid with known cross section (c)1997 BC4 analytic algebraic tangents tangent line to a curve at a point (b) neutral1997 BC4 area area of a region (c)1997 BC4 fundamental theorem accumulation function/Fundamental Theorem (c)1997 BC4 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (c)1996 BC4 differentiation interpretation of derivative as a rate of change (c)1996 AB1 graphical general derivative, graph of (a) (b) (c) (d) neutral1996 AB1 maximum, minimum local extrema (a) (b)1996 AB1 concavity (c)1996 AB2 analytic algebraic area area of a region (a) (b) neutral1996 AB2 volume-slicing volume of a solid with known cross section (c)1996 AB3 BC3 analytic exponential average value average value of a function (b) active1996 AB3 BC3 trapezoidal approximation computation of trapezoidal sum (c)1996 AB3 BC3 total change given rate of change integral of a rate of change to give accumulated change (d)1996 AB3 BC3 definite integral interpretation of definite integrals (d)1996 AB4 BC4 analytic trigonometric tangents tangent line to a curve at a point (b) active1996 AB4 BC4 maximum, minimum local extrema (c)1996 AB4 BC4 points of inflection point of inflection (d)1996 AB5 analytic algebraic volume-slicing volume of a solid with known cross section (a) neutral1996 AB5 related rates related rates (c)1996 AB6 analytic algebraic tangents tangent line to a curve at a point (a) (b) neutral1996 AB6 tangents local linear approximation (c)1996 AB6 maximum, minimum absolute extrema (c)1996 BC1 analytic exponential volume volume of a solid of revolution (a) neutral1996 BC1 limits limits of functions (a)1996 BC1 maximum, minimum absolute extrema (b)1996 BC1 differentiation derivative of basic functions (b)1996 BC1 differentiation chain rule (b)1996 BC1 points of inflection point of inflection (b)1996 BC2 analytic algebraic series Taylor series (a) (b) (c) neutral1996 BC2 interval/convergence interval of convergence of power series (b)

corresponding characteristics of the graphs of f, f', and f''

relationship between the concavity of f and the sign of f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1996 BC2 series manipulation of Taylor series to form new series from known series (c)1996 BC2 series (d)1996 BC5 analytic algebraic volume-slicing volume of a solid with known cross section (a) neutral1996 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (a)1996 BC5 related rates related rates (a)1996 BC5 work work (b)1996 BC6 analytic algebraic vectors velocity vector and speed (c) active1996 BC6 trigonometric related rates related rates (c)1996 BC6 differentiation derivative of basic functions (c)1995 BC6 differentiation chain rule (c)1995 AB1 analytic algebraic precalculus domain of a function (a) active1995 AB1 precalculus horizontal asymptote (c)1995 AB1 precalculus range of a function (d)1995 AB1 differentiation derivative of basic functions (d)1995 AB1 differentiation chain rule (d)1995 AB1 derivative, graph of (d)1995 AB2 analytic trigonometric motion on a line particle motion on a line (a) (b) (c) (d) neutral1995 AB2 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c) (d)1995 AB2 differentiation derivative of basic functions (b)1995 AB2 integration methods antiderivatives by parts (c)1995 AB2 integration methods antiderivatives following directly from derivatives of basic funcions (c)1995 AB3 analytic algebraic differentiation derivative of basic functions (a) active1995 AB3 differentiation chain rule (a)1995 AB3 tangents tangent line to a curve at a point (b)1995 AB3 tangents local linear approximation (c)1995 AB4 BC2 analytic exponential area area of a region (b) active1995 AB4 BC2 algebraic volume volume of a solid of revolution (c)1995 AB5 BC3 verbal algebraic related rates related rates (b) (c) neutral1995 AB5 BC3 differentiation derivative of basic functions (b) (c)1995 AB5 BC3 differentiation chain rule (b) (c)1995 AB6 graphical general total change given rate of change definite integral of a rate of change over an interval (a) neutral1995 AB6 fundamental theorem accumulation function/Fundamental Theorem (b) (c) (d)1995 AB6 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a) (b) (c) (d)1995 AB6 concavity (c)1995 AB6 maximum, minimum absolute extrema (d)1995 BC1 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d) active1995 BC1 vectors velocity vector (a)1995 BC1 arc length length of a curve given in parametric form (b)1995 BC4 analytic general series Taylor polynomial approximation (a) (b) (c) neutral1995 BC4 series manipulation of Taylor series to form new series from known series (c)1995 BC5 analytic trigonometric differentiation derivative of basic functions (b) (c) active1995 BC5 differentiation chain rule (c)1995 BC5 points of inflection point of inflection (b) (c)1995 BC6 graphical general precalculus domain of a function (a) neutral1995 BC6 fundamental theorem accumulation function/Fundamental Theorem (b)1995 BC6 differentiation chain rule (b)1995 BC6 maximum, minimum local extrema (c)1994 BC6 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a) (b) (c)1994 AB1 analytic algebraic tangents tangent line to a curve at a point (a)1994 AB1 maximum, minimum absolute extrema (b)1994 AB1 differentiation derivative of basic functions (a) (c)1994 AB1 points of inflection point of inflection (c)1994 AB2 BC1 analytic exponential area area of a region (a)1994 AB2 BC1 algebraic integration methods antiderivatives following directly from derivatives of basic funcions (a)1994 AB2 BC1 integration methods antiderivatives by substitution (b) 1994 AB2 BC1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1994 AB2 BC1 volume volume of a solid of revolution (b) (c)

Maclaurin series for e^x

relationship between the increasing and decreasing behavior of f and the sign of f'

relationship between the concavity of f and the sign of f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1994 AB3 analytic algebraic differentiation derivative of basic functions (a)1994 AB3 differentiation, implicit implicit differentiation (a)1994 AB3 differentiation chain rule (a)1994 AB3 differentiation derivative of a product (a)1994 AB3 tangents tangent line to a curve at a point (b)1994 AB3 tangents vertical tangents (c)1994 AB4 analytic logarithmic motion on a line particle motion on a line (a) (b) (c) (d)1994 AB4 differentiation derivative of a product (a)1994 AB4 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c)1994 AB4 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (d)1994 AB5 BC2 verbal algebraic related rates related rates (a) (b)1994 AB5 BC2 differentiation derivative of basic functions (a) (b)1994 AB5 BC2 differentiation chain rule (a) (b)1994 AB6 analytic trigonometric trapezoidal approximation computation of trapezoidal sum (a)1994 AB6 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (b)1994 AB6 derivative, graph of (b)1994 AB6 average rate of change average rate of change (c)1994 BC3 analytic trigonometric parametric equations vector function (a) (b)1994 BC3 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a)1994 BC3 integration methods antiderivatives following directly from derivatives of basic funcions (b)1994 BC3 vectors speed (b)1994 BC4 analytic algebraic tangents tangent line to a curve at a point (a)1994 BC4 differentiation derivative of basic functions (b)1994 BC4 maximum, minimum absolute extrema (b)1994 BC5 analytic exponential series Taylor series (a) (b) (c)1994 BC5 interval/convergence interval of convergence of power series (b)1994 BC5 series alternating series with error bound (c)1994 BC6 analytic general integration methods antiderivatives following directly from derivatives of basic funcions (a)1994 BC6 differential equations solving separable differential equations (b)1994 BC6 integration methods antiderivatives following directly from derivatives of basic funcions (b)1993 BC6 integration methods antiderivatives by substitution (b)1993 AB1 analytic algebraic differentiation derivative of basic functions (a)1993 AB1 derivative, graph of (a)1993 AB1 concavity (b)1993 AB1 maximum, minimum local extrema (c)1993 AB2 analytic exponential motion on a line particle motion on a line (a) (b) (c)1993 AB2 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b)1993 AB2 differentiation derivative of basic functions (a)1993 AB2 differentiation chain rule (a)1993 AB2 differentiation derivative of a product (a)1993 AB2 distance distance traveled by a particle along a line (c)1993 AB3 BC1 analytic algebraic mean value theorem Mean Value Theorem (a)1993 AB3 BC1 differentiation derivative of basic functions (a)1993 AB3 BC1 differentiation chain rule (a)1993 AB3 BC1 tangents tangent line to a curve at a point (a)1993 AB3 BC1 area area of a region (b)1993 AB3 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (b) (c)1993 AB3 BC1 integration methods antiderivatives by substitution (b)1993 AB3 BC1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b) (c)1993 AB3 BC1 volume volume of a solid of revolution (c)1993 AB4 BC3 analytic logarithmic maximum, minimum absolute extrema (a)1993 AB4 BC3 trigonometric points of inflection point of inflection (b)1993 AB4 BC3 differentiation derivative of basic functions (a) (b)1993 AB4 BC3 differentiation chain rule (a) (b)1993 AB5 graphical algebraic anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b)1993 AB5 derivative, graph of (c)1993 AB6 verbal exponential differential equations solving separable differential equations and using them in modeling (a)

relationship between the increasing and decreasing behavior of f and the sign of f'

relationship between the increasing and decreasing behavior of f and the sign of f'relationship between the concavity of f and the sign of f''

corresponding characteristics of graphs of f and f'

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1993 AB6 limits calculating limits using algebra (c)1993 AB6 integration methods antiderivatives following directly from derivatives of basic funcions (a)1993 AB6 integration methods antiderivatives by substitution (a)1993 BC2 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b)1993 BC2 vectors velocity vector (a)1993 BC2 vectors speed (a)1993 BC2 differentiation derivative of basic functions (a)1993 BC2 arc length length of a curve given in parametric form (b)1993 BC2 integration methods antiderivatives following directly from derivatives of basic funcions (b)1993 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1993 BC2 differentiation derivative of parametric function (c)1993 BC4 analytic trigonometric polar coordinates polar curves (a) (b) (c)1993 BC4 area area of a region bounded by a polar curve (b)1993 BC4 integration methods antiderivatives by substitution (b)1993 BC4 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1993 BC4 differentiation derivative of basic functions (c)1993 BC4 differentiation chain rule (c)1993 BC5 analytic exponential differentiation derivative of basic functions (a) (c)1993 BC5 differentiation chain rule (a)1993 BC5 series Taylor series (a)1993 BC5 series manipulation of Taylor series to form new series from known series (b) (c)1993 BC5 differentiation derivative of a quotient (c)1993 BC6 analytic general derivative, definition derivative defined as the limit of the difference quotient (b)1993 BC6 differential equations solving separable differential equations (c)1992 BC6 integration methods antiderivatives following directly from derivatives of basic funcions (c)1992 AB1 analytic algebraic derivative, graph of (a)1992 AB1 differentiation derivative of basic functions (a) (b)1992 AB1 concavity (b)1992 AB1 tangents horizontal tangents (c)1992 AB2 analytic algebraic motion on a line particle motion on a line (a) (b) (c)1992 AB2 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (c)1992 AB2 distance distance traveled by a particle along a line (b)1992 AB2 maximum, minimum absolute extrema (a)1992 AB2 average value average value of a function (c)1992 AB2 differentiation derivative of basic functions (a)1992 AB2 differentiation derivative of a product (a)1992 AB2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b) (c)1992 AB3 analytic logarithmic precalculus domain of a function (a)1992 AB3 precalculus odd and even functions (b)1992 AB3 maximum, minimum local extrema (c)1992 AB3 differentiation derivative of basic functions (c)1992 AB3 differentiation chain rule (c)1992 AB3 precalculus range of a function (d)1992 AB4 BC1 analytic trigonometric differentiation derivative of basic functions (a) (c)1992 AB4 BC1 differentiation, implicit implicit differentiation (a) (c)1992 AB4 BC1 differentiation chain rule (a) (c)1992 AB4 BC1 tangents vertical tangents (b)1992 AB5 BC2 analytic exponential tangents tangent line to a curve at a point (a)1992 AB5 BC2 area area of a region (b)1992 AB5 BC2 integration methods antiderivatives following directly from derivatives of basic funcions (b)1992 AB5 BC2 integration methods antiderivatives by substitution (b)1992 AB5 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1992 AB5 BC2 volume volume of a solid of revolution (c)1992 AB6 verbal algebraic differential equations solving separable differential equations (a)1992 AB6 integration methods antiderivatives following directly from derivatives of basic funcions (a)1992 AB6 related rates related rates (a) (b)1992 AB6 differentiation derivative of basic functions (a)

relationship between the increasing and decreasing behavior of f and the sign of f'

relationship between the concavity of f and the sign of f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1992 AB6 differentiation chain rule (a)1992 BC3 analytic exponential parametric equations analysis of planar curve given in parametric form (a) (b) (c)1992 BC3 trigonometric arc length length of a curve given in parametric form (c)1992 BC3 vectors speed (b)1992 BC3 differentiation derivative of basic functions (a)1992 BC3 differentiation chain rule (a)1992 BC3 differentiation derivative of a product (a)1992 BC3 integration methods antiderivatives following directly from derivatives of basic funcions (c)1992 BC3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)1992 BC4 analytic algebraic continuity continuity (a)1992 BC4 differentiability differentiability (a)1992 BC4 derivative, graph of (b)1992 BC4 points of inflection point of inflection (c)1992 BC5 verbal algebraic related rates related rates (a) (b)1992 BC5 work work (c)1992 BC5 differentiation derivative of basic functions (b)1992 BC5 differentiation chain rule (b)1992 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (c)1992 BC5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)1992 BC6 analytic logarithmic series series (a) (b) (c)1991 BC6 interval/convergence interval of convergence of power series (a) (b) (c)1991 AB1 analytic algebraic anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) (b)1991 AB1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1991 AB1 average value average value of a function (c)1991 AB1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)1991 AB2 analytic trigonometric area area of a region (a)1991 AB2 algebraic volume volume of a solid of revolution (b) (c)1991 AB2 integration methods antiderivatives following directly from derivatives of basic funcions (a)1991 AB2 integration methods antiderivatives by substitution (a)1991 AB2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1991 AB3 analytic trigonometric tangents tangent line to a curve at a point (a)1991 AB3 differentiation derivative of basic functions (a) 1991 AB3 differentiation chain rule (a)1991 AB3 tangents local linear approximation (b)1991 AB3 precalculus inverse function (c)1991 AB4 analytic algebraic precalculus zeroes of a function (a)1991 AB4 differentiation derivative of basic functions (b)1991 AB4 differentiation derivative of a quotient (b)1991 AB4 precalculus range of a function (d)1991 AB5 verbal general maximum, minimum absolute extrema (a)1991 AB5 points of inflection point of inflection (b)1991 AB5 derivative, graph of (c)1991 AB6 verbal algebraic differentiation derivative of basic functions (a) (c)1991 AB6 differentiation chain rule (a) (c)1991 AB6 related rates related rates (a) (b) (c)1991 BC1 analytic algebraic motion on a line particle motion on a line (a) (b) (c) (d)1991 BC1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (b)1991 BC1 maximum, minimum absolute extrema (c)1991 BC1 distance distance traveled by a particle along a line (d)1991 BC1 differentiation derivative of basic functions (c)1991 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (a)1991 BC1 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a)1991 BC2 analytic exponential differentiation derivative of basic functions (a) (c)1991 BC2 differentiation chain rule (a) (c)1991 BC2 differentiation derivative of a product (a) (c)1991 BC2 precalculus range of a function (b)1991 BC2 derivative, graph of (c)

relationship between the increasing and decreasing behavior of f and the sign of f'

corresponding characteristics of the graphs of f, f', and f''

corresponding characteristics of the graphs of f, f', and f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1991 BC3 analytic trigonometric area area of a region (a)1991 BC3 volume volume of a solid of revolution (b)1991 BC3 volume-slicing volume of a solid with known cross section (c) 1991 BC3 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b) (c)1991 BC3 integration methods antiderivatives by substitution (b) (c)1991 BC3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b) (c)1991 BC4 analytic algebraic fundamental theorem accumulation function/Fundamental Theorem (a)1991 BC4 differentiation chain rule (a)1991 BC4 precalculus domain of a function (b)1991 BC4 limits calculating limits (c)1991 BC4 definite integral basic properties of definite integrals (c)1991 BC4 arc length length of a curve (d)1991 BC4 integration methods antiderivatives following directly from derivatives of basic funcions (d)1991 BC4 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (d)1991 BC5 analytic algebraic series geometric series (a)1991 BC5 series manipulation of series by differentiation (b)1991 BC5 interval/convergence interval of convergence of power series (c)1991 BC6 analytic exponential differentiation derivative of basic functions (a)1991 BC6 maximum, minimum absolute extrema (a)1991 BC6 differential equations solving separable differential equations (b)1991 BC6 integration methods antiderivatives by partial fractions (b)1991 BC6 integration methods antiderivatives by substitution (b)1990 BC6 integration methods antiderivatives following directly from derivatives of basic funcions (b)1990 AB1 analytic algebraic motion on a line particle motion on a line (a) (b) (c)1990 AB1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (b)1990 AB1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1990 AB1 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) (b)1990 AB1 distance distance traveled by a particle along a line (c)1990 AB1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)1990 AB2 analytic logarithmic precalculus domain of a function (a)1990 AB2 differentiation derivative of basic functions (b)1990 AB2 differentiation chain rule (b)1990 AB2 differentiation derivative of a quotient (b)1990 AB2 precalculus inverse function (c)1990 AB3 analytic exponential area area of a region (a)1990 AB3 algebraic volume volume of a solid of revolution (b) (c)1990 AB3 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1990 AB3 integration methods antiderivatives by substitution (a) (b)1990 AB3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1990 AB4 verbal algebraic related rates related rates (a) (b) (c)1990 AB4 differentiation derivative of basic functions (a) (b)1990 AB4 differentiation chain rule (a) (b)1990 AB5 analytic trigonometric precalculus zeroes of a function (a)1990 AB5 derivative, graph of (b)1990 AB5 maximum, minimum absolute extrema (c)1990 AB6 analytic algebraic precalculus even functions (a)1990 AB6 limits calculating limits using algebra (a)1990 AB6 differentiation derivative of basic functions (a)1990 AB6 differentiation chain rule (a)1990 AB6 tangents vertical asymptotes (b)1990 AB6 precalculus horizontal asymptote (b)1990 BC1 analytic algebraic motion on a line particle motion on a line (a) (b) (c)1990 BC1 differentiation derivative of basic functions (a)1990 BC1 differentiation chain rule (a)1990 BC1 differentiation derivative of a product (a)1990 BC1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (c)1990 BC2 analytic exponential volume volume of a solid of revolution (a) (b)

relationship between the increasing and decreasing behavior of f and the sign of f'

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1990 BC2 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1990 BC2 integration methods antiderivatives by substitution (a) (b)1990 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1990 BC3 analytic algebraic tangents tangent line to a curve at a point (a)1990 BC3 maximum, minimum absolute extrema (b)1990 BC3 maximum, minimum optimization (b)1990 BC4 analytic trigonometric polar coordinates polar curves (a) (b)1990 BC4 area area of a region bounded by a polar curve (b)1990 BC4 integration methods antiderivatives following directly from derivatives of basic funcions (b)1990 BC4 integration methods antiderivatives by substitution (b)1990 BC4 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1990 BC5 analytic algebraic series Taylor series (a) (b) (c)1990 BC5 logarithmic series manipulation of Taylor series to form new series from known series (b)1990 BC5 series alternating series with error bound (c)1990 BC6 analytic general definite integral basic properties of definite integrals (a)1990 BC6 average value average value of a function (b)1990 BC6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1989 BC6 integration methods antiderivatives by substitution (c)1989 AB1 analytic algebraic precalculus zeroes of a function (a)1989 AB1 tangents tangent line to a curve at a point (b)1989 AB1 mean value theorem Mean Value Theorem (c)1989 AB1 differentiation derivative of basic functions (b)1989 AB2 analytic algebraic area area of a region (a)1989 AB2 volume volume of a solid of revolution (b) (c)1989 AB2 integration methods antiderivatives following directly from derivatives of basic funcions (a)1989 AB2 integration methods antiderivatives by substitution (a)1989 AB2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1989 AB3 analytic trigonometric motion on a line particle motion on a line (a) (b) (c)1989 AB3 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1989 AB3 integration methods antiderivatives by substitution (a) (b)1989 AB3 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) (b)1989 AB3 differentiation interpretation of derivative in context of velocity, speed, and acceleration (c)1989 AB4 analytic algebraic precalculus domain of a function (a)1989 AB4 tangents vertical asymptotes (b)1989 AB4 precalculus horizontal asymptote (c)1989 AB4 differentiation derivative of basic functions (d)1989 AB4 differentiation derivative of a quotient (d)1989 AB5 graphical general tangents horizontal tangents (a)1989 AB5 maximum, minimum local extrema (b)1989 AB5 concavity (c)1989 AB5 derivative, graph of (c)1989 AB6 verbal exponential differential equations solving separable differential equations (a)1989 AB6 integration methods antiderivatives following directly from derivatives of basic funcions (a)1989 AB6 differentiation interpretation of derivative as a rate of change (b)1989 BC1 analytic algebraic anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a)1989 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1989 BC1 tangents tangent line to a curve at a point (a)1989 BC1 average value average value of a function (b)1989 BC1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1989 BC2 analytic algebraic area area of a region (a)1989 BC2 volume volume of a solid of revolution (b)1989 BC2 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1989 BC2 integration methods antiderivatives by substitution (b)1989 BC2 integration methods antiderivatives by partial fractions (a) (b)1989 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1989 BC3 analytic exponential maximum, minimum absolute extrema (a)1989 BC3 trigonometric differentiation derivative of basic functions (a) (c)

relationship between the concavity of f and the sign of f''corresponding characteristics of the graphs of f, f', and f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1989 BC3 differentiation derivative of a product (a) (c)1989 BC3 derivative, graph of (b)1989 BC3 points of inflection point of inflection (c)1989 BC4 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c)1989 BC4 differentiation derivative of parametric function (a)1989 BC4 tangents tangent line to a curve at a point (b)1989 BC4 tangents vertical tangents (c)1989 BC4 tangents horizontal tangents (c)1989 BC4 differentiation derivative of basic functions (a)1989 BC5 analytic exponential motion on a line particle motion on a line (a) (b) (c)1989 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (a)1989 BC5 integration methods antiderivatives by substitution (a)1989 BC5 differential equations first order linear differntial equations (a)1989 BC5 differentiation interpretation of derivative in context of velocity, speed, and acceleration (c)1988 BC6 analytic general derivative, definition definition of derivative (c)1988 AB1 analytic algebraic precalculus domain of a function (a)1988 AB1 precalculus symmetry of the graph of a function (b)1988 AB1 differentiation derivative of basic functions (c)1988 AB1 differentiation chain rule (c)1988 AB1 normals slope of normal line (d)1988 AB2 analytic trigonometric motion on a line particle motion on a line (a) (b) (c)1988 AB2 differentiation derivative of basic functions (a)1988 AB2 differentiation chain rule (a)1988 AB2 differentiation interpretation of derivative in context of velocity, speed, and acceleration (b)1988 AB2 integration methods antiderivatives following directly from derivatives of basic funcions (c)1988 AB2 integration methods antiderivatives by substitution (c)1988 AB2 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)1988 AB3 analytic algebraic volume volume of a solid of revolution (a) (b)1988 AB3 integration methods antiderivatives following directly from derivatives of basic funcions (a)1988 AB3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1988 AB4 analytic exponential precalculus horizontal asymptote (a)1988 AB4 maximum, minimum local extrema (b)1988 AB4 differentiation derivative of basic functions (b) (c)1988 AB4 differentiation chain rule (b) (c)1988 AB4 differentiation derivative of a product (b) (c)1988 AB4 concavity (c)1988 AB4 derivative, graph of (d)1988 AB5 analytic algebraic area area of a region (a)1988 AB5 average value average value of a function (c)1988 AB5 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b) (c)1988 AB5 integration methods antiderivatives by substitution (a) (b)1988 AB5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b) (c)1988 AB6 analytic algebraic differentiation derivative of basic functions1988 AB6 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions1988 AB6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals1988 AB6 integration methods antiderivatives following directly from derivatives of basic funcions1988 BC1 analytic exponential derivative, graph of (a)1988 BC1 points of inflection point of inflection (b)1988 BC1 maximum, minimum absolute extrema (c)1988 BC1 differentiation derivative of a product (a) (b)1988 BC1 differentiation derivative of basic functions (a) (b)1988 BC2 analytic algebraic area area of a region (a)1988 BC2 volume volume of a solid of revolution (b)1988 BC2 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1988 BC2 integration methods antiderivatives by substitution (a)1988 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1988 BC3 verbal algebraic differentiation derivative of basic functions (a) (b) (c)

relationship between the increasing and decreasing behavior of f and the sign of f'

relationship between the concavity of f and the sign of f''corresponding characteristics of the graphs of f, f', and f''

relationship between the increasing and decreasing behavior of f and the sign of f'

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1988 BC3 differentiation chain rule (a) (b) (c)1988 BC3 related rates related rates (a) (b) (c)1988 BC4 analytic logarithmic interval/convergence interval of convergence of power series1988 BC5 analytic trigonometric volume-slicing volume of a solid with known cross section (b)1988 BC5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1988 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (b)1988 BC5 integration methods antiderivatives by substitution (b)1988 BC6 analytic general average value average value of a function (a)1988 BC6 fundamental theorem accumulation function/Fundamental Theorem (b)1988 BC6 differentiation derivative of a product (b)1988 BC6 differentiation derivative of basic functions (b)1988 BC6 differential equations solving separable differential equations (c)1988 BC6 integration methods antiderivatives following directly from derivatives of basic funcions (c)1987 BC6 integration methods antiderivatives by substitution (c)1987 AB1 analytic algebraic motion on a line particle motion on a line (a) (b) (c) (d)1987 AB1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (b)1987 AB1 distance distance traveled by a particle along a line (d)1987 AB1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (c)1987 AB1 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) (c)1987 AB2 analytic trigonometric precalculus domain of a function (a) (c)1987 AB2 differentiation derivative of basic functions (b)1987 AB2 differentiation chain rule (b)1987 AB2 tangents tangent line to a curve at a point (d)1987 AB3 analytic algebraic volume volume of a solid of revolution (a)1987 AB3 integration methods antiderivatives following directly from derivatives of basic funcions (a)1987 AB3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1987 AB4 analytic logarithmic maximum, minimum local extrema (a)1987 AB4 points of inflection point of inflection (b)1987 AB4 maximum, minimum absolute extrema (c)1987 AB4 differentiation derivative of basic functions (a) (b)1987 AB4 differentiation chain rule (a)1987 AB4 differentiation derivative of a quotient (b)1987 AB5 verbal algebraic related rates related rates (a) (b) (c)1987 AB5 differentiation derivative of basic functions (b) (c)1987 AB5 differentiation chain rule (b) (c)1987 AB6 analytic general area area of a region (a)1987 AB6 derivative, graph of (b) (c)1987 AB6 differentiation derivative of basic functions (b) (c)1987 AB6 differentiation chain rule (b) (c)1987 BC1 analytic exponential differential equations solving separable differential equations (a)1987 BC1 exponential growth exponential growth (a) (b) (c)1987 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (a)1987 BC2 analytic algebraic differentiation, implicit implicit differentiation (a)1987 BC2 differentiation derivative of basic functions (a)1987 BC2 differentiation chain rule (a)1987 BC2 tangents tangent line to a curve at a point (b)1987 BC2 maximum, minimum absolute extrema (c)1987 BC3 analytic logarithmic area area of a region (a)1987 BC3 volume volume of a solid of revolution (b) (c)1987 BC3 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1987 BC3 integration methods antiderivatives by parts (a) (b)1987 BC3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1987 BC4 analytic algebraic series geometric series (a)1987 BC4 series Taylor series (a) (b) (c)1987 BC4 interval/convergence interval of convergence of power series (b)1987 BC4 integration methods partial fractions (c)1987 BC4 series manipulation of Taylor series to form new series from known series (c)

relationship between the increasing and decreasing behavior of f and the sign of f'

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1987 BC5 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d)1987 BC5 vectors velocity vector and speed (a)1987 BC5 differentiation interpretation of derivative in context of velocity, speed, and acceleration (b)1987 BC6 analytic general fundamental theorem accumulation function/Fundamental Theorem (a) (c)1986 BC6 differentiation derivative of basic functions (b)1986 AB1 analytic algebraic precalculus zeroes of a function (a)1986 AB1 tangents tangent line to a curve at a point (b)1986 AB1 points of inflection point of inflection (c)1986 AB1 differentiation derivative of basic functions (b) (c)1986 AB2 analytic algebraic precalculus symmetry of the graph of a function (a)1986 AB2 tangents vertical asymptotes (b)1986 AB2 precalculus horizontal asymptote (b)1986 AB2 derivative, graph of (c)1986 AB2 derivative, graph of (d)1986 AB2 differentiation derivative of basic functions (c)1986 AB2 differentiation derivative of a quotient (c)1986 AB3 BC1 analytic algebraic motion on a line particle motion on a line (a) (b) (c)1986 AB3 BC1 logarithmic integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1986 AB3 BC1 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) (b)1986 AB3 BC1 integration methods antiderivatives by parts (b)1986 AB3 BC1 maximum, minimum absolute extrema (c)1986 AB4 analytic algebraic continuity understanding continuity in terms of limits (a) (b)1986 AB4 differentiability differentiability (c)1986 AB4 differentiation derivative of basic functions (c)1986 AB5 BC2 analytic exponential maximum, minimum absolute extrema (b)1986 AB5 BC2 average value average value of a function (c)1986 AB5 BC2 differentiation derivative of basic functions (b)1986 AB5 BC2 differentiation derivative of a product (b)1986 AB5 BC2 differentiation chain rule (b)1986 AB5 BC2 integration methods antiderivatives following directly from derivatives of basic funcions (c)1986 AB5 BC2 integration methods antiderivatives by substitution (c)1986 AB5 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)1986 AB6 BC3 analytic trigonometric area area of a region (a)1986 AB6 BC3 volume volume of a solid of revolution (b)1986 AB6 BC3 integration methods antiderivatives following directly from derivatives of basic funcions (a)1986 AB6 BC3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1986 BC4 analytic trigonometric differential equations first order linear differntial equations (a) (b)1986 BC4 integration methods antiderivatives following directly from derivatives of basic funcions (a)1986 BC4 differentiation derivative of basic functions (b)1986 BC5 analytic algebraic series Taylor series (a) (b) (c)1986 BC5 series manipulation of Taylor series to form new series from known series (b) (c)1986 BC6 analytic algebraic derivative, definition definition of derivative (b)1986 BC6 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)1985 BC6 integration methods antiderivatives following directly from derivatives of basic funcions (c)1985 AB1 analytic algebraic precalculus domain of a function (a)1985 AB1 tangents vertical asymptotes (b)1985 AB1 precalculus horizontal asymptote (b)1985 AB1 differentiation derivative of basic functions (c)1985 AB1 differentiation derivative of a quotient (c)1985 AB1 tangents tangent line to a curve at a point (d)1985 AB2 BC1 analytic trigonometric motion on a line particle motion on a line (a) (b) (c) (d)1985 AB2 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1985 AB2 BC1 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) (b)1985 AB2 BC1 differentiation interpretation of derivative as a rate of change (c)1985 AB2 BC1 distance distance traveled by a particle along a line (d)1985 AB3 analytic exponential area area of a region (a)1985 AB3 volume volume of a solid of revolution (b) (c)

relationship between the increasing and decreasing behavior of f and the sign of f'corresponding characteristics of graphs of f and f'

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1985 AB3 integration methods antiderivatives following directly from derivatives of basic funcions (a)1985 AB3 integration methods antiderivatives by substitution (a)1985 AB3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1985 AB4 BC3 analytic trigonometric average value average value of a function (a) (b)1985 AB4 BC3 algebraic integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1985 AB4 BC3 integration methods antiderivatives by substitution (b)1985 AB4 BC3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1985 AB5 BC2 verbal algebraic related rates related rates (a) (b)1985 AB5 BC2 differentiation derivative of basic functions (a) (b)1985 AB5 BC2 differentiation chain rule (a) (b)1985 AB6 graphical general maximum, minimum local extrema (a)1985 AB6 concavity (b)1985 AB6 derivative, graph of (c)1985 BC4 analytic logarithmic differential equations solving separable differential equations (a) (b)1985 BC4 algebraic integration methods antiderivatives by substitution (a)1985 BC4 integration methods antiderivatives following directly from derivatives of basic funcions (a)1985 BC4 precalculus domain of a function (c)1985 BC5 analytic logarithmic area area of a region (a)1985 BC5 improper integrals improper integrals (a) (b)1985 BC5 volume volume of a solid of revolution (b)1985 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1985 BC5 integration methods antiderivatives by substitution (a) (b)1985 BC5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1985 BC5 limits calculating limits using algebra (a) (b)1985 BC6 analytic general maximum, minimum local extrema (b)1985 BC6 concavity (c)1985 BC6 derivative, graph of (d)1985 BC6 differentiation derivative of basic functions (b)1985 BC6 differentiation chain rule (b)1984 BC6 differentiation derivative of a product (b)1984 AB1 analytic algebraic motion on a line particle motion on a line (a) (b) (c)1984 AB1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (c)1984 AB1 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) (c)1984 AB1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (b)1984 AB2 analytic trigonometric precalculus odd and even functions (a)1984 AB2 differentiation derivative of basic functions (b)1984 AB2 differentiation derivative of a quotient (b)1984 AB2 tangents tangent line to a curve at a point (c)1984 AB3 BC1 analytic exponential area area of a region (a)1984 AB3 BC1 volume volume of a solid of revolution (b)1984 AB3 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1984 AB3 BC1 integration methods antiderivatives by parts (b)1984 AB3 BC1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1984 AB4 BC3 tabular general maximum, minimum absolute extrema (a)1984 AB4 BC3 points of inflection point of inflection (b)1984 AB4 BC3 derivative, graph of (c)1984 AB5 verbal algebraic related rates related rates (a) (b) (c)1984 AB5 differentiation derivative of basic functions (a) (b)1984 AB5 differentiation chain rule (a) (b) (c)1984 BC2 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c)1984 BC2 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a)1984 BC2 differentiation derivative of parametric function (b) (c)1984 BC2 differentiation derivative of basic functions (a) (b) (c)1984 BC2 differentiation chain rule (b) (c)1984 BC4 analytic algebraic series function defined by power series (a) (b) (c)1984 BC4 interval/convergence radius of convergence (a)1984 BC4 series alternating series with error bound (c)

relationship between the concavity of f and the sign of f''corresponding characteristics of graphs of f and f'

relationship between the concavity of f and the sign of f''corresponding characteristics of the graphs of f, f', and f''

corresponding characteristics of the graphs of f, f', and f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1984 BC5 analytic trigonometric polar coordinates polar curves (a) (b)1984 BC5 area area of a region bounded by a polar curve (b)1984 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (b)1984 BC5 integration methods antiderivatives by substitution (b)1983 BC5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1983 AB1 analytic logarithmic precalculus domain of a function (a)1983 AB1 precalculus zeroes of a function (b)1983 AB1 tangents tangent line to a curve at a point (c)1983 AB2 analytic algebraic motion on a line particle motion on a line (a) (b) (c)1983 AB2 differentiation interpretation of derivative in context of velocity, speed, and acceleration (b)1983 AB2 distance distance traveled by a particle along a line (c)1983 AB2 differentiation derivative of basic functions (a)1983 AB3 BC1 analytic trigonometric differentiation derivative of basic functions (a) (c)1983 AB3 BC1 differentiation chain rule (a)1983 AB3 BC1 maximum, minimum local extrema (b)1983 AB3 BC1 points of inflection point of inflection (c)1983 AB4 analytic algebraic area area of a region (a)1983 AB4 volume volume of a solid of revolution (b) (c)1983 AB4 integration methods antiderivatives following directly from derivatives of basic funcions (a)1983 AB4 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1983 AB5 BC3 verbal algebraic integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1983 AB5 BC3 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a)1983 AB5 BC3 distance distance traveled by a particle along a line (b)1983 BC2 analytic algebraic arc length length of a curve (a)1983 BC2 surface area area of a surface of revolution (b)1983 BC3 analytic exponential differential equations solving differential equations (integrating factor) (a)1983 BC3 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b)1983 BC5 analytic algebraic series function defined by power series (a) (b) (c)1983 BC5 interval/convergence interval of convergence of power series (b)1982 BC5 series manipulation of series by differentiation (c)1982 AB1 analytic algebraic motion on a line particle motion on a line (a) (b) (c)1982 AB1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) 1982 AB1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1982 AB1 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) (b)1982 AB2 analytic algebraic limits calculating limits using algebra (a)1982 AB2 precalculus zeroes of a function (b)1982 AB2 tangents vertical asymptotes (c)1982 AB2 precalculus horizontal asymptote (c)1982 AB2 precalculus symmetry of the graph of a function (d)1982 AB2 curve sketching curve sketching (e)1982 AB3 BC1 analytic trigonometric area area of a region (a)1982 AB3 BC1 volume volume of a solid of revolution (b)1982 AB3 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1982 AB3 BC1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1982 AB4 verbal algebraic related rates related rates (a) (b)1982 AB4 differentiation derivative of basic functions (a) (b)1982 AB4 differentiation chain rule (a) (b)1982 AB5 BC2 analytic exponential maximum, minimum absolute extrema (a)1982 AB5 BC2 points of inflection point of inflection (b)1982 AB5 BC2 differentiation derivative of basic functions (a) (b)1982 AB5 BC2 differentiation chain rule (a) (b)1982 AB5 BC2 differentiation derivative of a product (a) (b)1982 AB6 BC3 verbal algebraic maximum, minimum absolute extrema1982 AB6 BC3 differentiation derivative of basic functions1982 AB6 BC3 differentiation chain rule1982 AB6 BC3 maximum, minimum extreme value problems1982 AB7 analytic general differentiation derivative of basic functions (a)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1982 AB7 differentiation chain rule (a)1982 AB7 tangents tangent line to a curve at a point (c)1982 BC4 analytic exponential differential equations second order differential equation1982 BC4 motion on a line particle motion on a line (a) (b) (c)1982 BC4 differentiation interpretation of derivative in context of velocity, speed, and acceleration (c)1982 BC5 analytic logarithmic series Taylor series (a) (b) (c)1982 BC5 interval/convergence interval of convergence of power series (b)1982 BC5 series alternating series with error bound (c)1982 BC5 series manipulation of Taylor series to form new series from known series (d)1982 BC6 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d)1982 BC6 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b) (c) (d)1982 BC6 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) 1982 BC6 average rate of change average rate of change (c)1982 BC6 differentiation derivative of parametric function (d)1982 BC6 differentiation interpretation of derivative as a rate of change (d)1982 BC7 analytic trigonometric differentiability differentiability (a)1982 BC7 derivative, definition definition of derivative (a)1982 BC7 differentiation derivative of basic functions (b)1982 BC7 differentiation chain rule (b)1981 BC7 continuity continuity (c)1981 AB1 analytic algebraic precalculus zeroes of a function (a)1981 AB1 tangents tangent line to a curve at a point (b)1981 AB2 analytic algebraic area area of a region (a)1981 AB2 volume volume of a solid of revolution (b)1981 AB2 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1981 AB2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1981 AB3 BC1 analytic algebraic derivative, graph of (a)1981 AB3 BC1 concavity (d)1981 AB3 BC1 curve sketching curve sketching (e)1981 AB3 BC1 differentiation derivative of basic functions (a) (d)1981 AB3 BC1 maximum, minimum local extrema (b) (c)1981 AB4 analytic exponential precalculus odd and even functions (a)1981 AB4 precalculus domain of a function (b)1981 AB4 precalculus range of a function (c)1981 AB4 differentiation derivative of basic functions (d)1981 AB4 differentiation chain rule (d)1981 AB5 BC2 analytic algebraic continuity understanding continuity in terms of limits (a)1981 AB5 BC2 differentiability differentiability (b) (c)1981 AB5 BC2 derivative, definition definition of derivative (b) (c)1981 AB6 BC4 analytic trigonometric motion on a line particle motion on a line (a) (b) (c) (d)1981 AB6 BC4 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c) (d)1981 AB6 BC4 differentiation derivative of basic functions (a) (b)1981 AB6 BC4 differentiation chain rule (a) (b)1981 AB7 analytic general average value average value of a function (a)1981 AB7 definite integral basic properties of definite integrals (b)1981 AB7 integration methods antiderivatives following directly from derivatives of basic funcions (c)1981 AB7 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)1981 BC3 analytic algebraic series power series (a) (b) (c)1981 BC3 interval/convergence convergence of geometric series (a) (b) 1981 BC3 interval/convergence interval of convergence of power series (b)1981 BC5 analytic exponential differential equations second order differential equation (a)1981 BC5 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b) (c)1981 BC6 verbal algebraic volume-slicing volume of a solid with known cross section (a)1981 BC6 related rates related rates (b)1981 BC6 differentiation chain rule (b)1981 BC7 analytic general differentiation derivative of basic functions (a)1981 BC7 differentiation chain rule (a)

relationship between the increasing and decreasing behavior of f and the sign of f'relationship between the concavity of f and the sign of f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1981 BC7 mean value theorem Mean Value Theorem (b)1980 BC7 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)1980 AB1 analytic algebraic area area of a region (a)1980 AB1 volume volume of a solid of revolution (b)1980 AB1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1980 AB1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1980 AB2 analytic algebraic differentiation chain rule (a) (b)1980 AB2 maximum, minimum extreme value problems (a)1980 AB2 related rates related rates (b)1980 AB3 analytic exponential precalculus domain of a function (a) (b) (c)1980 AB3 logarithmic precalculus function composition (a) (b)1980 AB3 precalculus inverse function (c)1980 AB4 BC1 analytic exponential motion on a line particle motion on a line (a) (b) (c) 1980 AB4 BC1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c) 1980 AB4 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (a) (c)1980 AB4 BC1 integration methods antiderivatives by substitution (a) (c)1980 AB4 BC1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1980 AB5 BC2 analytic trigonometric precalculus zeroes of a function (a)1980 AB5 BC2 maximum, minimum local extrema (b)1980 AB5 BC2 derivative, graph of (c)1980 AB5 BC2 derivative, graph of (d)1980 AB5 BC2 differentiation derivative of basic functions (b)1980 AB5 BC2 differentiation chain rule (b)1980 AB5 BC2 curve sketching curve sketching (d)1980 AB6 BC4 analytic algebraic differentiation, implicit implicit differentiation (a)1980 AB6 BC4 differentiation derivative of basic functions (a)1980 AB6 BC4 differentiation chain rule (a)1980 AB6 BC4 tangents tangent line to a curve at a point (b)1980 AB7 analytic algebraic continuity understanding continuity in terms of limits (a) (c)1980 AB7 differentiability differentiability (b)1980 AB7 differentiation derivative of basic functions (b) (c)1980 BC3 analytic algebraic series series (a) (b) (c)1980 BC3 interval/convergence convergence of p-series (c)1980 BC3 interval/convergence convergence of series (a) (c)1980 BC5 analytic algebraic differential equations solving separable differential equations (a) (b)1980 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1980 BC5 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)1980 BC6 analytic exponential area area of a region (a)1980 BC6 improper integrals improper integrals (a)1980 BC6 volume volume of a solid of revolution (b)1980 BC6 volume-slicing volume of a solid with known cross section (c)1980 BC6 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b) (c)1980 BC6 integration methods antiderivatives by substitution (a) (b) (c)1980 BC6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b) (c)1980 BC6 limits calculating limits using algebra (a)1980 BC7 graphical general derivative, graph of (a) (b) (c) (d) (e)1980 BC7 maximum, minimum local extrema (a) 1980 BC7 maximum, minimum absolute extrema (b)1980 BC7 concavity (c)1980 BC7 points of inflection point of inflection (d)1979 BC7 curve sketching curve sketching (e)1979 AB1 analytic algebraic precalculus zeroes of a function (a)1979 AB1 normals normal line to a curve at a point (b)1979 AB1 differentiation derivative of basic functions (b)1979 AB2 analytic exponential differentiation derivative of basic functions (a)1979 AB2 differentiation chain rule (a)1979 AB2 differentiation derivative of a product (a)

relationship between the increasing and decreasing behavior of f and the sign of f'corresponding characteristics of the graphs of f, f', and f''

corresponding characteristics of the graphs of f, f', and f''

relationship between the concavity of f and the sign of f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1979 AB2 derivative, graph of (a)1979 AB2 maximum, minimum absolute extrema (b)1979 AB3 BC3 verbal algebraic differentiation derivative of basic functions1979 AB3 BC3 maximum, minimum absolute extrema1979 AB3 BC3 maximum, minimum extreme value problems1979 AB4 BC1 analytic trigonometric motion on a line particle motion on a line (a) (b) (c) (d)1979 AB4 BC1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c) (d)1979 AB4 BC1 differentiation derivative of basic functions (a) (b) 1979 AB4 BC1 differentiation chain rule (a) (b)1979 AB4 BC1 maximum, minimum absolute extrema (d)1979 AB5 BC5 analytic logarithmic area area of a region (a)1979 AB5 BC5 volume volume of a solid of revolution (b)1979 AB5 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1979 AB5 BC5 integration methods antiderivatives by substitution (a)1979 AB5 BC5 integration methods antiderivatives by parts (b)1979 AB5 BC5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1979 AB6 analytic algebraic differentiability differentiability (b)1979 AB6 graphical derivative, definition definition of derivative (b)1979 AB6 continuity understanding continuity in terms of limits (d)1979 AB6 curve sketching curve sketching with absolute values (a) (c)1979 AB7 analytic algebraic differentiation derivative of basic functions (a)1979 AB7 integration methods antiderivatives following directly from derivatives of basic funcions (a)1979 AB7 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1979 AB7 average value average value of a function (a)1979 AB7 points of inflection point of inflection (a)1979 AB7 mean value theorem Mean Value Theorem (b)1979 BC2 analytic exponential differential equations second order differential equation (a) (b) (c)1979 BC2 differentiation derivative of basic functions (a) 1979 BC4 analytic algebraic series Taylor series (a) (b) (c)1979 BC4 interval/convergence interval of convergence of power series (b)1979 BC4 series alternating series with error bound (c)1979 BC6 analytic exponential parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d)1979 BC6 differentiation derivative of basic functions (a)1979 BC6 differentiation chain rule (a)1979 BC6 differentiation derivative of parametric function (a)1979 BC6 limits calculating limits using algebra (b)1979 BC6 vectors velocity vector (a) (d)1979 BC7 analytic general derivative, definition definition of derivative (a)1978 BC7 mean value theorem Mean Value Theorem (c)1978 AB1 analytic algebraic precalculus zeroes of a function (a)1978 AB1 tangents tangent line to a curve at a point (b)1978 AB1 differentiation derivative of basic functions (b)1978 AB2 analytic logarithmic precalculus function composition (a)1978 AB2 differentiation derivative of basic functions (b) (c)1978 AB2 differentiation chain rule (b) (c)1978 AB2 curve sketching curve sketching (d)1978 AB3 analytic algebraic continuity continuity (a)1978 AB3 limits calculating limits using algebra (b)1978 AB3 tangents vertical asymptotes (c)1978 AB3 precalculus horizontal asymptote (c)1978 AB4 analytic trigonometric motion on a line particle motion on a line (a) (b) (c)1978 AB4 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c)1978 AB4 integration methods antiderivatives following directly from derivatives of basic funcions (b) (c)1978 AB4 average value average value of a function (c)1978 AB4 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)1978 AB4 integration methods antiderivatives by substitution (a) (c)1978 AB5 BC1 analytic algebraic differentiation, implicit implicit differentiation (a) (c)

relationship between the increasing and decreasing behavior of f and the sign of f'

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1978 AB5 BC1 differentiation derivative of basic functions (a) (c)1978 AB5 BC1 differentiation chain rule (a) (c)1978 AB5 BC1 tangents vertical tangents (b)1978 AB5 BC1 differentiation derivative of a product (a) 1978 AB5 BC1 differentiation derivative of a quotient (c)1978 AB6 BC3 analytic exponential maximum, minimum absolute extrema (a)1978 AB6 BC3 maximum, minimum extreme value problems (a)1978 AB6 BC3 differentiation derivative of basic functions (a)1978 AB6 BC3 differentiation chain rule (a)1978 AB6 BC3 volume volume of a solid of revolution (b)1978 AB6 BC3 integration methods antiderivatives following directly from derivatives of basic funcions (b)1978 AB6 BC3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1978 AB6 BC3 integration methods antiderivatives by substitution (b)1978 AB6 BC3 limits calculating limits using algebra (c)1978 AB7 BC6 analytic general differentiation derivative of basic functions (a) (c)1978 AB7 BC6 differentiation chain rule (a) (c)1978 AB7 BC6 maximum, minimum local extrema (b)1978 AB7 BC6 points of inflection point of inflection (c)1978 BC2 analytic algebraic derivative, graph of (a)1978 BC2 concavity (b)1978 BC2 curve sketching curve sketching (c)1978 BC2 continuity understanding continuity in terms of limits (d)1978 BC4 analytic trigonometric differential equations solving differential equations (integrating factor) (a)1978 BC4 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b)1978 BC5 analytic logarithmic series function defined by power series (a) (b)1978 BC5 interval/convergence interval of convergence of power series (b)1978 BC7 analytic exponential parametric equations analysis of planar curve given in parametric form (a) (b) (c)1978 BC7 differentiation derivative of parametric function1978 BC7 vectors velocity vector (a) (b) (c)1978 BC7 arc length length of a curve given in parametric form (b)1978 BC7 integration methods antiderivatives following directly from derivatives of basic funcions (b)1978 BC7 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1978 BC7 integration methods antiderivatives by substitution (b)1977 BC7 surface area area of a surface of revolution (c)1977 AB1 analytic logarithmic precalculus domain of a function (a)1977 AB1 trigonometric precalculus range of a function (b)1977 AB1 precalculus zeroes of a function (c)1977 AB1 differentiation derivative of basic functions (d)1977 AB1 differentiation chain rule (d)1977 AB2 analytic algebraic derivative, graph of (a)1977 AB2 maximum, minimum local extrema (b)1977 AB2 differentiation derivative of basic functions (a) (c)1977 AB2 differentiation chain rule (a) (c)1977 AB2 concavity (c)1977 AB2 differentiation derivative of a product (c)1977 AB2 curve sketching curve sketching (d)1977 AB3 analytic exponential area area of a region (a)1977 AB3 volume volume of a solid of revolution (b)1977 AB3 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1977 AB3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1977 AB3 integration methods antiderivatives by substitution (a)1977 AB4 BC2 tabular general differentiation derivative of a sum (a)1977 AB4 BC2 differentiation derivative of a product (b)1977 AB4 BC2 differentiation derivative of a quotient (c)1977 AB4 BC2 differentiation chain rule (d)1977 AB4 BC2 differentiation derivative of the inverse of a function (e)1977 AB5 BC3 analytic algebraic motion on a line particle motion on a line (a) (b) (c)

relationship between the increasing and decreasing behavior of f and the sign of f'relationship between the concavity of f and the sign of f''

relationship between the increasing and decreasing behavior of f and the sign of f'

relationship between the concavity of f and the sign of f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1977 AB5 BC3 differentiation interpretation of derivative in context of velocity, speed, and acceleration (b)1977 AB5 BC3 integration methods antiderivatives following directly from derivatives of basic funcions (a)1977 AB5 BC3 integration methods antiderivatives by parts (c)1977 AB5 BC3 maximum, minimum absolute extrema (b)1977 AB5 BC3 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)1977 AB6 verbal algebraic related rates related rates (a) (b)1977 AB6 differentiation derivative of basic functions (a) (b)1977 AB6 differentiation chain rule (a) (b)1977 AB6 differentiation derivative of a product (a)1977 AB7 BC6 analytic trigonometric differentiation derivative of basic functions (a) (b)1977 AB7 BC6 differentiation chain rule (a) 1977 AB7 BC6 continuity understanding continuity in terms of limits (c)1977 AB7 BC6 differentiability differentiability (d)1977 AB7 BC6 derivative, definition definition of derivative (d)1977 BC1 analytic algebraic precalculus zeroes of a function (a)1977 BC1 precalculus symmetry of the graph of a function (a)1977 BC1 maximum, minimum local extrema (a)1977 BC1 differentiation derivative of basic functions (a)1977 BC1 differentiation derivative of a quotient (a)1977 BC1 limits calculating limits using algebra (a)1977 BC1 curve sketching curve sketching (a)1977 BC1 area area of a region (b)1977 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (b)1977 BC1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1977 BC1 integration methods antiderivatives by substitution (b)1977 BC4 analytic exponential differential equations second order differential equation (a) (b)1977 BC4 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b)1977 BC5 analytic trigonometric interval/convergence convergence of series (a)1977 BC5 definite integral definition of a definite integral as the limit of a Riemann sum (b)1977 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (b)1977 BC5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1977 BC5 integration methods antiderivatives by substitution (b)1977 BC7 analytic algebraic fundamental theorem accumulation function/Fundamental Theorem (a) (b) (c) (d)1977 BC7 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (b)1977 BC7 definite integral basic properties of definite integrals (c)1976 BC7 integration methods antiderivatives by substitution (d)1976 AB1 analytic algebraic precalculus domain of a function (a)1976 AB1 precalculus range of a function (a)1976 AB1 differentiation derivative of basic functions (b)1976 AB1 differentiation chain rule (b)1976 AB1 tangents tangent line to a curve at a point (c)1976 AB2 analytic algebraic precalculus zeroes of a function (a)1976 AB2 continuity understanding continuity in terms of limits (b)1976 AB2 precalculus even functions (c)1976 AB3 BC2 analytic algebraic area area of a region (a)1976 AB3 BC2 volume volume of a solid of revolution (b)1976 AB3 BC2 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1976 AB3 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1976 AB3 BC2 integration methods antiderivatives by substitution (b)1976 AB4 analytic algebraic related rates related rates (a)1976 AB4 differentiation derivative of basic functions (a) (b)1976 AB4 differentiation chain rule (a) (b)1976 AB5 BC3 analytic exponential maximum, minimum local extrema (a)1976 AB5 BC3 trigonometric differentiation derivative of basic functions (a)1976 AB5 BC3 differentiation chain rule (a)1976 AB5 BC3 curve sketching curve sketching (b)1976 AB5 BC3 precalculus axis of symmetry of the graph of a function (c)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1976 AB6 analytic algebraic fundamental theorem accumulation function/Fundamental Theorem (a) (b)1976 AB6 fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem (a) (b)1976 AB7 BC6 analytic algebraic limits calculating limits using algebra (a) (b)1976 AB7 BC6 trigonometric derivative, definition definition of derivative (c)1976 BC1 analytic algebraic motion on a line particle motion on a line (a) (b) (c)1976 BC1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c)1976 BC1 maximum, minimum absolute extrema (c)1976 BC4 analytic exponential integration methods antiderivatives by parts (a) (b)1976 BC4 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1976 BC5 analytic exponential differential equations second order differential equation (a) (b)1976 BC5 trigonometric anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)1976 BC7 analytic trigonometric series manipulation of Taylor series to form new series from known series (a)1976 BC7 series (a)1976 BC7 interval/convergence interval of convergence of power series (b)1975 BC7 series alternating series with error bound (c)1975 AB1 analytic logarithmic precalculus domain of a function (b)1975 AB1 precalculus symmetry of the graph of a function (a)1975 AB1 precalculus zeroes of a function (c)1975 AB1 precalculus inverse function (d)1975 AB2 analytic algebraic motion on a line particle motion on a line (a) (b) (c) (d)1975 AB2 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c) (d)1975 AB2 differentiation derivative of basic functions (a)1975 AB2 distance distance traveled by a particle along a line (d)1975 AB3 analytic algebraic precalculus range of a function (a)1975 AB3 continuity continuity (b)1975 AB3 continuity understanding continuity in terms of limits (c)1975 AB3 integration methods antiderivatives following directly from derivatives of basic funcions (d)1975 AB3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (d)1975 AB4 BC1 analytic trigonometric maximum, minimum local extrema (a)1975 AB4 BC1 differentiation derivative of basic functions (a) (b)1975 AB4 BC1 points of inflection point of inflection (b)1975 AB4 BC1 curve sketching curve sketching (c)1975 AB5 analytic algebraic differentiation derivative of basic functions (a)1975 AB5 tangents tangent line to a curve at a point (b)1975 AB6 BC2 analytic algebraic area area of a region (a)1975 AB6 BC2 volume volume of a solid of revolution (b) (c)1975 AB7 BC5 analytic exponential derivative, definition definition of derivative (b) (c)1975 BC3 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c)1975 BC3 differentiation derivative of parametric function (a) 1975 BC3 vectors velocity vector (a)1975 BC3 differentiation interpretation of derivative in context of velocity, speed, and acceleration (b)1975 BC3 limits calculating limits using algebra (c)1975 BC4 analytic algebraic series series (a) (b)1975 BC4 interval/convergence convergence of series (a) 1975 BC4 interval/convergence interval of convergence of power series (c)1975 BC6 analytic exponential limits calculating limits using l'Hopital's Rule (a)1975 BC6 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b)1975 BC6 limits calculating limits using l'Hopital's Rule (c)1975 BC7 analytic logarithmic differentiation derivative of basic functions (a) (b)1975 BC7 tangents tangent line to a curve at a point (a)1974 BC7 maximum, minimum absolute extrema (b)1974 AB1 BC1 analytic trigonometric curve sketching curve sketching (a)1974 AB1 BC1 algebraic precalculus function composition (b)1974 AB1 BC1 precalculus domain of a function (c)1974 AB1 BC1 precalculus range of a function (c)1974 AB1 BC1 tangents tangent line to a curve at a point (d)1974 AB2 analytic algebraic precalculus symmetry of the graph of a function (a)

Maclaurin series for sin(x)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1974 AB2 maximum, minimum local extrema (a)1974 AB2 differentiation derivative of basic functions (a)1974 AB3 analytic algebraic tangents tangent line to a curve at a point (a)1974 AB3 differentiation derivative of basic functions (a)1974 AB4 BC2 analytic algebraic integration methods antiderivatives following directly from derivatives of basic funcions1974 AB4 BC2 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions1974 AB5 BC4 analytic exponential maximum, minimum absolute extrema (a) (b)1974 AB5 BC4 differentiation derivative of basic functions (a) (b)1974 AB5 BC4 differentiation derivative of a quotient (a)1974 AB5 BC4 differentiation chain rule (a) (b)1974 AB6 analytic trigonometric area area of a region (b)1974 AB6 integration methods antiderivatives following directly from derivatives of basic funcions (b)1974 AB6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1974 AB7 verbal exponential related rates related rates (a) (b) (c)1974 AB7 differential equations solving separable differential equations (a) 1974 AB7 integration methods antiderivatives following directly from derivatives of basic funcions (a)1974 AB7 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b)1974 BC3 analytic logarithmic volume volume of a solid of revolution1974 BC3 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1974 BC3 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1974 BC3 integration methods antiderivatives by parts (a) (b)1974 BC5 analytic trigonometric parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d)1974 BC5 differentiation derivative of parametric function (a) 1974 BC5 tangents tangent line to a curve at a point (b) (c)1974 BC5 arc length length of a curve given in parametric form (d)1974 BC6 analytic exponential differential equations second order differential equation (a)1974 BC6 trigonometric anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b)1974 BC6 limits calculating limits using algebra (c)1973 BC7 analytic exponential mean value theorem Mean Value Theorem (a)1973 AB1 analytic algebraic precalculus zeroes of a function (b)1973 AB1 precalculus range of a function (c)1973 AB1 maximum, minimum absolute extrema (c)1973 AB1 differentiation derivative of basic functions (c)1973 AB2 analytic algebraic motion on a line particle motion on a line (a) (b) (c)1973 AB2 integration methods antiderivatives following directly from derivatives of basic funcions (a) (c)1973 AB2 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) (c)1973 AB3 analytic algebraic differentiation, implicit implicit differentiation (a)1973 AB3 differentiation derivative of basic functions (a)1973 AB3 differentiation chain rule (a)1973 AB3 differentiation derivative of a product (a)1973 AB3 tangents tangent line to a curve at a point (b)1973 AB4 BC2 analytic algebraic area area of a region (b) 1973 AB4 BC2 volume volume of a solid of revolution (c)1973 AB4 BC2 integration methods antiderivatives following directly from derivatives of basic funcions (b) (c)1973 AB4 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b) (c)1973 AB5 BC3 analytic exponential maximum, minimum absolute extrema (a) (b)1973 AB5 BC3 differentiation derivative of basic functions (a)1973 AB5 BC3 differentiation chain rule (a)1973 AB6 verbal algebraic maximum, minimum absolute extrema1973 AB6 maximum, minimum extreme value problems1973 AB6 differentiation derivative of basic functions1973 AB7 analytic trigonometric area area of a region (a)1973 AB7 integration methods antiderivatives following directly from derivatives of basic funcions (a)1973 AB7 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1973 AB7 related rates related rates (c)1973 AB7 differentiation derivative of basic functions (c)1973 AB7 differentiation chain rule (c)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1973 BC4 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c) (d)1973 BC4 related rates related rates (b) (c) (d)1973 BC4 differentiation derivative of basic functions (b) (c) 1973 BC4 differentiation chain rule (b) (c) 1973 BC5 analytic exponential differential equations second order differential equation (a)1973 BC5 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b)1973 BC6 analytic algebraic interval/convergence convergence of series (a) (b) (c)1972 BC7 analytic trigonometric integration methods antiderivatives by substitution (a) (b)1972 AB1 analytic algebraic precalculus zeroes of a function (a)1972 AB1 tangents tangent line to a curve at a point (b)1972 AB1 precalculus symmetry of the graph of a function (c)1972 AB2 BC1 analytic algebraic motion on a line particle motion on a line (a) (b) (c) (d)1972 AB2 BC1 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c) (d)1972 AB2 BC1 differentiation derivative of basic functions (a)1972 AB2 BC1 differentiation derivative of a product (a)1972 AB2 BC1 maximum, minimum absolute extrema (d)1972 AB3 BC2 analytic trigonometric area area of a region (a)1972 AB3 BC2 integration methods antiderivatives following directly from derivatives of basic funcions (a)1972 AB3 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1972 AB3 BC2 tangents tangent line to a curve at a point (b)1972 AB4 BC3 verbal algebraic maximum, minimum absolute extrema (b)1972 AB4 BC3 maximum, minimum extreme value problems (a) (b)1972 AB4 BC3 differentiation derivative of basic functions (b)1972 AB4 BC3 differentiation chain rule (b)1972 AB5 analytic trigonometric differentiation derivative of basic functions (a)1972 AB5 exponential differentiation chain rule (a)1972 AB5 differentiation derivative of a product (a)1972 AB5 related rates related rates (b)1972 AB6 analytic algebraic volume volume of a solid of revolution (a) (b)1972 AB6 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1972 AB6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1972 AB7 analytic general derivative, definition definition of derivative (b) (c)1972 AB7 integration methods antiderivatives following directly from derivatives of basic funcions (c)1972 AB7 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)1972 BC4 analytic algebraic series series (a) (b)1972 BC4 interval/convergence convergence of series (a) 1972 BC4 interval/convergence interval of convergence of power series (b)1972 BC5 analytic exponential differential equations second order differential equation (a)1972 BC5 differentiation derivative of basic functions (b)1972 BC5 differentiation derivative of a product (b)1972 BC6 analytic logarithmic continuity continuity (a)1972 BC6 precalculus symmetry of the graph of a function (b)1972 BC6 maximum, minimum local extrema (c) (d)1972 BC6 differentiation derivative of basic functions (d)1972 BC6 differentiation derivative of a quotient (d)1972 BC7 analytic algebraic parametric equations analysis of planar curve given in parametric form (a) (b) (c)1972 BC7 differentiation derivative of basic functions (a) 1972 BC7 arc length length of a curve given in parametric form (a)1972 BC7 volume volume of a solid of revolution (b)1971 BC7 surface area area of a surface of revolution (c)1971 AB1 analytic logarithmic precalculus function composition (a) (c)1971 AB1 precalculus domain of a function (a) (c)1971 AB1 precalculus range of a function (b) (d)1971 AB1 differentiation derivative of basic functions (e)1971 AB1 differentiation chain rule (e)1971 AB2 analytic algebraic area area of a region (a) 1971 AB2 integration methods antiderivatives following directly from derivatives of basic funcions (a)

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1971 AB2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) 1971 AB2 differentiation interpretation of derivative as a rate of change (c)1971 AB2 related rates related rates (c)1971 AB2 differentiation derivative of basic functions (c)1971 AB2 differentiation chain rule (c)1971 AB3 analytic trigonometric precalculus zeroes of a function (a)1971 AB3 maximum, minimum local extrema (b)1971 AB3 differentiation derivative of basic functions (b) (c)1971 AB3 differentiation chain rule (b) (c)1971 AB3 concavity (c)1971 AB4 BC1 analytic algebraic maximum, minimum absolute extrema1971 AB4 BC1 maximum, minimum extreme value problems1971 AB4 BC1 differentiation derivative of basic functions1971 AB5 analytic algebraic volume volume of a solid of revolution (a) (b)1971 AB5 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1971 AB5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1971 AB6 analytic algebraic motion on a line particle motion on a line (a) (b) (c) (d)1971 AB6 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a)1971 AB6 differentiation derivative of basic functions (a)1971 AB6 differentiation derivative of a quotient (a)1971 AB6 integration methods antiderivatives following directly from derivatives of basic funcions (b)1971 AB6 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (b)1971 AB6 limits calculating limits using algebra (c)1971 AB6 continuity continuity (d)1971 AB7 BC3 analytic algebraic precalculus symmetry of the graph of a function (a)1971 AB7 BC3 derivative, graph of (b)1971 AB7 BC3 differentiation derivative of basic functions (b)1971 AB7 BC3 differentiation chain rule (b)1971 AB7 BC3 differentiation derivative of a product (b)1971 AB7 BC3 curve sketching curve sketching (c)1971 BC2 analytic algebraic volume volume of a solid of revolution (a) (b)1971 BC2 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1971 BC2 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1971 BC4 analytic trigonometric series Taylor series (a)1971 BC4 interval/convergence interval of convergence of power series (b)1971 BC4 series Taylor polynomial approximation (c)1971 BC4 series alternating series with error bound (d)1971 BC5 analytic exponential integration methods antiderivatives by parts1971 BC5 integration methods antiderivatives following directly from derivatives of basic funcions1971 BC5 improper integrals improper integrals1971 BC5 limits evaluating limits1971 BC6 analytic logarithmic fundamental theorem analysis of a function defined by a definite integral using the Fundamental Theorem1971 BC6 differentiation derivative of basic functions1971 BC6 integration methods antiderivatives following directly from derivatives of basic funcions1971 BC6 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions1971 BC7 analytic general limits definition of limit at infinity (a) (b) (c)1970 BC7 precalculus asymptotes (c)1970 AB1 BC1 analytic algebraic normals normal line to a curve at a point (a)1970 AB1 BC1 differentiation derivative of basic functions (a)1970 AB1 BC1 area area of a region (b)1970 AB1 BC1 integration methods antiderivatives following directly from derivatives of basic funcions (b)1970 AB1 BC1 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1970 AB2 graphical general curve sketching curve sketching (a) (b) (c) (d) (e)1970 AB2 precalculus symmetry of the graph of a function (a) (b) (c)1970 AB2 precalculus horizontal translation of the graph of a function (e)1970 AB2 precalculus horizontal dilation of the graph of a function (d)1970 AB3 BC2 analytic algebraic tangents horizontal tangents (a)

relationship between the concavity of f and the sign of f''

relationship between the increasing and decreasing behavior of f and the sign of f'

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1970 AB3 BC2 tangents vertical tangents (b)1970 AB3 BC2 differentiation derivative of basic functions (a) (d)1970 AB3 BC2 maximum, minimum absolute extrema (c)1970 AB3 BC2 concavity (d)1970 AB3 BC2 curve sketching curve sketching (e)1970 AB4 verbal algebraic related rates related rates1970 AB4 differentiation derivative of basic functions1970 AB4 differentiation chain rule1970 AB5 analytic trigonometric motion on a line particle motion on a line (a) (b) (c)1970 AB5 exponential differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c)1970 AB5 differentiation derivative of basic functions (a) (c)1970 AB5 differentiation chain rule (a) (c)1970 AB6 BC5 analytic exponential volume volume of a solid of revolution (b)1970 AB6 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (b)1970 AB6 BC5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (b)1970 AB6 BC5 maximum, minimum absolute extrema (c)1970 AB6 BC5 differentiation derivative of basic functions (c)1970 AB6 BC5 differentiation derivative of a quotient (c)1970 AB7 analytic trigonometric definite integral basic properties of definite integrals1970 AB7 integration methods antiderivatives following directly from derivatives of basic funcions1970 AB7 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals1970 BC3 analytic trigonometric motion on a line particle motion on a line (a) (b) (c)1970 BC3 exponential differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) 1970 BC3 differentiation derivative of basic functions (a)1970 BC3 differentiation chain rule (a)1970 BC3 precalculus zeroes of a function (c)1970 BC4 analytic algebraic differential equations second order differential equation (a) (b) (c)1970 BC4 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (c)1970 BC6 analytic trigonometric integration methods antiderivatives following directly from derivatives of basic funcions (a)1970 BC6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a)1970 BC6 integration methods antiderivatives by substitution (a)1970 BC6 interval/convergence convergence of series (b)1970 BC7 analytic trigonometric continuity understanding continuity in terms of limits (a)1969 BC7 derivative, definition definition of derivative (b)1969 AB1 analytic algebraic precalculus even functions (a)1969 AB1 trigonometric precalculus inverse function (b)1969 AB1 exponential precalculus periodic functions (c)1969 AB1 continuity continuity (d)1969 AB2 analytic algebraic motion on a line particle motion on a line (a) (b) (c) (d)1969 AB2 differentiation interpretation of derivative in context of velocity, speed, and acceleration (a) (b) (c) (d)1969 AB2 differentiation derivative of basic functions (a)1969 AB3 BC3 analytic logarithmic maximum, minimum absolute extrema (a)1969 AB3 BC3 differentiation derivative of basic functions (a) (b)1969 AB3 BC3 concavity (b)1969 AB3 BC3 curve sketching curve sketching (c)1969 AB3 BC3 average value average value of a function (d)1969 AB4 BC4 analytic exponential maximum, minimum absolute extrema (a) (b)1969 AB4 BC4 differentiation derivative of basic functions (a) (b)1969 AB4 BC4 differentiation chain rule (a) (b)1969 AB5 analytic algebraic area area of a region (a) 1969 AB5 volume volume of a solid of revolution (b)1969 AB5 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1969 AB5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1969 AB6 verbal algebraic area area of a region (c)1969 AB6 trigonometric integration methods antiderivatives following directly from derivatives of basic funcions (c)1969 AB6 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)1969 AB6 integration methods antiderivatives by substitution (c)

relationship between the concavity of f and the sign of f''

relationship between the concavity of f and the sign of f''

Year Number Function Presentation Function Type General Topics Course Description Topics Part Calculator1969 AB7 analytic exponential curve sketching curve sketching (a)1969 AB7 tangents tangent line to a curve at a point (b)1969 AB7 differentiation derivative of basic functions (b)1969 AB7 differentiation chain rule (b)1969 AB7 limits calculating limits using algebra (c)1969 BC1 analytic trigonometric curve sketching curve sketching (a)1969 BC1 area area of a region (b)1969 BC1 volume volume of a solid of revolution (b)1969 BC1 arc length length of a curve (b)1969 BC1 differentiation derivative of basic functions (b)1969 BC1 differentiation chain rule (b)1969 BC5 analytic exponential area area of a region (a)1969 BC5 integration methods antiderivatives following directly from derivatives of basic funcions (a) (b)1969 BC5 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (a) (b)1969 BC5 integration methods antiderivatives by substitution (a) (b)1969 BC5 improper integrals improper integrals (a) (b)1969 BC5 volume volume of a solid of revolution (b)1969 BC6 analytic algebraic differential equations second order differential equation (a) (b)1969 BC6 anti-differentiation (initial conditions) finding specific antiderivatives using initial conditions (a) (b)1969 BC7 analytic algebraic integration methods antiderivatives following directly from derivatives of basic funcions (a)1969 BC7 Riemann sums numerical approximations to definite integrals (a) (c)1969 BC7 interval/convergence convergence of series (b)1969 BC7 fundamental theorem use of the Fundamental Theorem to evaluate definite integrals (c)

BC7 improper integrals improper integrals (c)