3/11/23, 5:33 PM * AP®︎Calculus BC | College Calculus BC | Khan Academy AP®︎/College Calculus BC Math Math AP®︎/College Calculus BC Not feeling ready for this? Check out Get ready for AP® Calculus. Meet an AP®︎teacher who uses AP®︎Calculus in his classroom Bill Scott uses Khan Academy to teach AP®︎Calculus at Phillips Academy in Course challenge Andover, Massachusetts, and he’s part of the teaching team that helped develop Khan Academy’s AP®︎lessons. Phillips Academy was one of the first schools to teach AP®︎nearly This 60 years ago. is the graph of function f . Dashed lines represent asymptotes. y Learn more f 7 6 5 4 3 9,870 / 20,500 (48%) 2 Mastery points 1 -7 -6 -5 -4 -3 -2 1 2 3 4 5 6 7 3:26 x -2 -3Mastery challenge -4 -5Strengthen skills you’ve already practiced in -6just 6 questions. -7 Get started Over which intervals is f continuous? Choose all answers that apply: 2450/3400 Mastery Limits and continuity CORRECT (SELECTED) [−1, 4] INCORRECT About the course Determining Nice work! limits using the squeeze theorem Defining limits and using limit notation Exploring typesanswer. of discontinuities That's the right Keep practicing! Estimating limit values from graphs [−5 −2]Estimating limit values from tables 15 of 30 Defining continuity at a point Confirming continuity over an interval Determining limits using algebraic properties of limits: limit p… Removing discontinuitiesNext question Determining limits using algebraic properties of limits: direct … Connecting infinite limits and vertical asymptotes Determining limits using algebraic manipulation Connecting limits at infinity and horizontal asymptotes Selecting procedures for determining limits Working with the intermediate value theorem Optional videos 1870/2300 Mastery Differentiation: definition and basic derivative rules Defining average and instantaneous rates of change at a point Derivative rules: constant, sum, difference, and constant Defining the derivative of a function and using derivative not… Derivatives of cos(x), sin(x), 𝑒ˣ, and ln(x) Estimating derivatives of a function at a point The product rule Connecting differentiability and continuity: determining whe… The quotient rule https://www.khanacademy.org/math/ap-calculus-bc/test/subject-challenge?modal=1 1/4 3/11/23, 5:33 PM * AP®︎Calculus BC | College Calculus BC | Khan Academy Applying the power rule Finding the derivatives of tangent, cotangent, secant, an Derivative rules: constant, sum, difference, and constant mul… Optional videos AP®︎/College Calculus BC Math Differentiation: composite, implicit, and inverse functions The chain rule: introduction Selecting procedures for calculating derivatives: strategy The chain rule: further practice Selecting procedures for calculating derivatives: multiple Implicit differentiation Calculating higher-order derivatives Differentiating inverse functions Further practice connecting derivatives and limits Differentiating inverse trigonometric functions Optional videos 630/1400 Mastery ContextualCourse applications of differentiation challenge Interpreting the meaning of the derivative in context Solving related rates problems Straight-line motion: connecting position, velocity, and accel… Approximating values of a function using local linearity a This is the graph of function f . Dashed lines represent asymptotes. y Rates of change in other applied contexts (non-motion probl… Using L’Hôpital’s rule for finding limits of indeterminate f Introduction to related rates 7 Optional videos 6 5 4 3 2 1 f -7 -6 -5 -4 -3 -2 1020/1500 Mastery 930/1800 Mastery Applying derivatives to analyze functions x Using the mean value theorem Determining concavity of intervals and finding points of value theorem, global versus local extrema, and criti… -Extreme 2 -3 Determining intervals on which a function is increasing or de… -4 -Using 5 the first derivative test to find relative (local) extrema -6 -Using 7 the candidates test to find absolute (global) extrema Using the second derivative test to find extrema Determining concavity of intervals and finding points of infle… Exploring behaviors of implicit relations 1 2 3 4 5 6 7 Over which intervals is f continuous? Sketching curves of functions and their derivatives Connecting a function, its first derivative, and its second Solving optimization problems Calculator-active practice Choose all answers that apply: 1410/3400 Mastery Integration and accumulation of change [−1, 4] Exploring accumulations of change Approximating areas with Riemann sums Finding antiderivatives and indefinite integrals: basic rul That's the right answer. Keep practicing! Finding antiderivatives and indefinite integrals: basic rul Riemann sums, summation notation, and definite integral not… Integrating using substitution The fundamental theorem of calculus and accumulation func… Integrating functions using long division and completing Interpreting the behavior of accumulation functions involvin… Using integration by parts Applying properties of definite integrals Integrating using linear partial fractions The fundamental theorem of calculus and definite integrals Evaluating improper integrals Finding antiderivatives and indefinite integrals: basic rules an… Optional videos [−5 −2] 15 of 30 Nice work! Differential equations 550/1300 Mastery Modeling situations with differential equations Approximating solutions using Euler’s method Verifying solutions for differential equations Finding general solutions using separation of variables Sketching slope fields Finding particular solutions using initial conditions and s Reasoning using slope fields Exponential models with differential equations Logistic models with differential equations https://www.khanacademy.org/math/ap-calculus-bc/test/subject-challenge?modal=1 2/4 3/11/23, 5:33 PM * AP®︎Calculus BC | College Calculus BC | Khan Academy AP®︎/College Calculus BC Math 500/2000 Mastery Applications of integration Finding the average value of a function on an interval Volumes with cross sections: triangles and semicircles Connecting position, velocity, and acceleration functions usi… Volume with disc method: revolving around x- or y-axis Using accumulation functions and definite integrals in applie… Volume with disc method: revolving around other axes Finding the area between curves expressed as functions of x Volume with washer method: revolving around x- or y-ax Finding the area between curves expressed as functions of y Volume with washer method: revolving around other axe Finding the area between curves that intersect at more than … The arc length of a smooth, planar curve and distance tr Volumes with cross sections: squares and rectangles Calculator-active practice Course challenge Parametric equations, polar coordinates, and vector-valued functions This is the graphDefining of function f . Dashedparametric lines represent and differentiating equations asymptotes. -7 -6 -5 -4 -3 -2 Defining polar coordinates and differentiating in polar fo Finding arc lengths of curves given by parametric equations Finding the area of a polar region or the area bounded b 7 Defining and differentiating vector-valued functions 6 5 4 3 2 1 1 2 3 4 5 6 7 -2 convergent and divergent infinite series -Defining 3 -Working 4 with geometric series -5 -The 6 nth-term test for divergence -7 Determining absolute or conditional convergence Alternating series error bound Finding Taylor polynomial approximations of functions Lagrange error bound Radius and interval of convergence of power series Ratio test for convergence [−1, 4] Finding Taylor or Maclaurin series for a function Representing functions as power series Optional videos Nice work! AP Calculus BC solved exams [−5 −2]AP Calculus BC 2017 Differential equations 0/2000 Mastery Harmonic series and p-series Alternating Choose all answers that apply: series test for convergence Integration and accumulation of change Calculator-active practice Integral test for convergence Comparison tests for convergence functions Finding the area of the region bounded by two polar cur Infinite sequences and x series Over which intervals is f continuous? 15 of 30 Solving motion problems using parametric and vector-va Second derivatives of parametric equations y f 510/1400 Mastery That's the right answer. Keep practicing! Mastery unavaila AP Calculus BC 2008 AP Calculus BC 2015 AP Calculus BC 2011 AP®︎Calculus BC Standards mappings Mastery unavaila See how our content aligns with AP®︎Calculus BC standards Applications of integration Parametric equations, polar coordinates, and vector-valued functions Course challenge Test your knowledge of the skills in this course. Have a test coming up? The Course challenge can help you understand what C h ll https://www.khanacademy.org/math/ap-calculus-bc/test/subject-challenge?modal=1 3/4 3/11/23, 5:33 PM * AP®︎Calculus BC | College Calculus BC | Khan Academy Course challenge Test your knowledge of Math the skills in this course. you need to review. AP®︎/College Calculus BC Start Course challenge Community questions AP® is a registered trademark of the College Board, which has not reviewed this resource. Course challenge This is the graph of function f . Dashed lines represent asymptotes. y 7 6 5 4 3 2 1 f -7 -6 -5 -4 -3 -2 -2 -3 -4 -5 -6 -7 1 2 3 4 5 6 7 x Over which intervals is f continuous? Choose all answers that apply: [−1, 4] Nice work! That's the right answer. Keep practicing! [−5 −2] 15 of 30 https://www.khanacademy.org/math/ap-calculus-bc/test/subject-challenge?modal=1 4/4
