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CRLS Department AB & BC Curriculum Map/Pacing Guide page 1 of 9

Understanding Goals/ # of Blocks Resources/Assessments Essential Questions AB BC Students will be able to... book other 120 100 Unit 1: Limits and 15 9 Totals Always Include 2 blocks for Review & Test chapter 2 District Google Documents site Continuity

• find the of a numerically, What is a limit? 4 2 2.1,2.2 2.1#37,57,71; 2.2#55 graphically, and analytically

• determine when a function is continuous 2 1 2.3 2.3 #11,20,23,47-50 What does it mean for a function to (formally) be continuous? • determine where and what types of IVT, monk riddle (Zeitz "Art & Craft of Problem 2.3 discontinuities a function has if any Solving")

2 2 • determine the end behavior of a function 2.3 How do you find the of a line to a curve? • find the instantaneous rate of change of a 2.4 #8 function and connect it with the slope of the 2.4 http://calculus.scotthighskyhawks.com/calcab tangent line

• use epsilon- definition to show a limit A3 page 2.1 #77 IMSA Limits6.pdf What is the definition of a limit? 5 2 exists or does not exist in linear situations 569 Limits7.pdf, Foerster Exploration 6

CRLS Mathematics Department AB & BC Calculus Curriculum Map/Pacing Guide page 2 of 9 Understanding Goals/ # of Blocks Resources/Assessments Essential Questions AB BC Students will be able to... book other

Unit 2: 30 22 Totals Always Include 2 blocks for Review & Test District Google Documents site • explain the meaning of the of a What is the derivative of a function? 3 1 3.1 function

2 1 • find the value of the derivative at a point 3.1 cancel factors, binomial expansion, f(x+h) notation What does it mean for a function to be differentiable? 1 • visually graph the derivative of a function 3.1 simplifying expressions • find when a function is differentiable 3.2 • find what types of discontinuities the derivative 4 1 3.2 implicit diff. requires solving literal equations of a functions has if any • find the derivative of a function using: the sum, composites f(g(x)), inverses, transcendental product, quotient, and chain rules, and functions, radical & exponential simplification, unit How do you find the derivative of a 15 11 3.3-3.9 circle, trig identities, IMSA trig(kx).pdf, Chain function? polynomial, implicit, trigonometric, exponential Rule Investigation with Mathematica FIRST and logarithmic differentiation. CLASS ImplicitDifferentiation.pdf

1 • find the derivative of a parametric function 3.6,10.1 IMSA Parametric1.pdf

How does the derivative illuminate 4 1 • use derivative to model particle motion 3.4,10.1 motion?

1 • calculate derivatives of vector motion 10.2 IMSA

How do you find the derivative in 2 • calculate derivatives in polar coordinates 10.3 IMSA polar1.pdf non-euclidean coordinate systems?

CRLS Mathematics Department AB & BC Calculus Curriculum Map/Pacing Guide page 3 of 9 Understanding Goals/ # of Blocks Resources/Assessments Essential Questions AB BC Students will be able to... book other

Applications of Unit 3: 24 15 Totals Always Include 2 blocks for Review & Test District Google Documents site Derivatives

How do you find limits when function 1 • apply L'Hopital's Rule 8.2 IMSA LimitsAgain.pdf is indeterminate? How do you analyze the behavior of 1 1 • apply the 4.2 Calculus in Motion a function? • analyze the behavior of a function using its first 5 4 4.2 two derivatives How is the tangent line useful? • find the critical points of a function 4.2 • find when a function is increasing or decreasing 4.1 How can you approximate the value • find the inflection points of a function 4.3 of a function? • find when a function is concave up or concave 4.3 down How are the rates of change of • optimize the value of a variable given 4 2 4.4 Calculus in Motion variables related? constraint equations • use the tangent line to approximate function 3 1 4.5 values How can you apply complete graph analysis to analyze the motion of an • apply Newton’s Method 4.5 Calculus in Motion object? What are dx and dy? 1 1 • use differentials to approximate function values 4.5 • find the rate of change of a variable using 5 2 4.6 Calculus in Motion • analyze the motion of a particle along a line 3 1 given its position equation

CRLS Mathematics Department AB & BC Calculus Curriculum Map/Pacing Guide page 4 of 9 Understanding Goals/ # of Blocks Resources/Assessments Essential Questions AB BC Students will be able to... book other

Unit 4: Definite 16 10 Totals Always Include 2 blocks for Review & Test District Google Documents site

How can you approximate the area • approximate the area under a curve using the Calculus In Motion; KhanAcademy.org; IMSA 4 1 5.1 under a curve? Rectangle Approximating Methods Approx1.pdf • approximate the area under a curve using The Write Path II Math "But it's not a 5.2 Riemann sums rectangle!" How can you find the exact area • approximate the area under a curve using the 1 5.5 Calculus In Motion; IMSA Approx3.pdf under a curve? 1 • find the anti-derivative of a function 5.4 How do you find the equation of the • use the definite to find the area under a PreCal: area formulas for circle, trapezoid, 5 2 5.2 anti-derivative of a function? curve analytically and geometrically triangle, trig identities • find the average value of a function over a 1 1 5.3,5.5 given What is the connection between the • apply both parts of the Fundamental Theorem area under a function and the anti- 4 2 5.3,5.4 Calculus In Motion; page 289 Exploration 2 of Calculus derivative of the function?

CRLS Mathematics Department AB & BC Calculus Curriculum Map/Pacing Guide page 5 of 9 Understanding Goals/ # of Blocks Resources/Assessments Essential Questions AB BC Students will be able to... book other

Differential Unit 5: 17 13 Totals Always Include 2 blocks for Review & Test District Google Documents site Equations

How do you find the equation of a • find the integral of a function using the 6 4 6.2,6.3 function given its derivative? substitution method and 3 1 • solve a separable differential equation 6.2 APCentral Module on Differential Equations P.Mili's handout, Calculus In Motion, How will graphing the slope of APCentral SlopeField pdf by Nancy Stephenson, TI-84 Slope, Euler's Method GSP a function help you analyze the 2 1 graph a slope field • (FIRST CLASS), function? http://staff.imsa.edu/~dover/Site/Semester_Tw o.html, http://worrydream.com/KillMath 1 • apply Euler’s Method 6.1 Exer 41-48, AP FRQ How do find integral of rational 1 • apply Method of Partial Fractions 6.5 function? What types of real-life situations are • find the model for an exponential growth or modeled using exponents and 4 3 6.4 decay problem, Newton's Law of Cooling logarithms? 1 • find the model for a logistic growth problem 6.5 Calculus in Motion, AP FRQ

CRLS Mathematics Department AB & BC Calculus Curriculum Map/Pacing Guide page 6 of 9 Understanding Goals/ # of Blocks Resources/Assessments Essential Questions AB BC Students will be able to... book other Applications of Unit 6: 18 12 Totals Always Include 2 blocks for Review & Test District Google Documents site Definite Integrals

How do you find the change of a • use the definite integral to discuss the net 5 1 7.1 Calculus in Motion, AP FRQ variable given its rate? change of a variable given its rate How do you find the area between 5 1 • find the area between curves 7.2 Calculus in Motion, AP FRQ curves? How do you find area between polar Nate Burchell's PolarFunctionsGSP 2 • find area with sector-shaped differentials 10.3 functions? (FIRSTCLASS) • find the volume of a solid with known cross- How do you find the volume of an Calculus in Motion, AP FRQ, Bundt cake, 6 4 sections and a solid of revolution using the 7.3 object? orange/pear, rice crispy treat models washer and shell methods How do you find the length of a • find the length of a rectangular curve and a 2 7.4 Calculus in Motion, AP FRQ curve parametric curve • find the work equation for various different 2 7.5 Exer.#1-11 page 425 physics-type problems

CRLS Mathematics Department AB & BC Calculus Curriculum Map/Pacing Guide page 7 of 9 Understanding Goals/ # of Blocks Resources/Assessments Essential Questions AB BC Students will be able to... book other

Unit 7: Improper Integrals, Rates of 6 Totals Always Include 2 blocks for Review & Test District Google Documents site Growth

What is a ?What is 1 • apply limits to understand infinite 8.1 GeometricSeries.pdf (IMSA) convergence? What functions grow faster than • compare the relative rates of growth of 1 8.2 others? functions How do you find the area under the • express an as a limit, curve when you are working with 2 8.3 ImproperIntegrals (FIRSTCLASS) evaluate the limit ?

CRLS Mathematics Department AB & BC Calculus Curriculum Map/Pacing Guide page 8 of 9 Understanding Goals/ # of Blocks Resources/Assessments Essential Questions AB BC Students will be able to... book other

Unit 8: Convergence, 13 Totals Always Include 2 blocks for Review & Test District Google Documents site Infinite

How do you find the sum of an • find the sum and partial sum of an infinite 1 9.1 APCentral Visual Proofs of Calculus infinite ? geometric series 1 • find the of a function 9.1 Calculus In Motion • find the Taylor and Maclaurin series for a How can you rewrite functions as 3 function around different values of x and the 9.2,9.3 Calculus In Motion equivalent infinite polynomials? Lagrange Error Does an infinite series have a finite • test for the convergence of a function using the 3 9.3 Lagrange Pdf sum? various testing methods

What can predict convergence • find the radius and interval of convergence for a Convergence Test Summary, numerous IMSA 3 9.4,9.5 without actually summing the series? power series pdfs

http://staff.imsa.edu/~dover/Site/Semester_Thr ee_files/TaylorReview.pdf

CRLS Mathematics Department AB & BC Calculus Curriculum Map/Pacing Guide page 9 of 9

Resource List: http://staff.imsa.edu/~dover/Site/Calculus.html Calculus in Motion Foerster, Calculus Explorations http://calculus.scotthighskyhawks.com/calcab Firstclass calculus desk APCentral teacher resources khanacademy.org burchellmath.blogspot.com TI programs Online applets Wolfram Alpha The Write Path II Math Amsco AP prep Calculus: Graphical, Numerical, Algebraic textbook Mathematica