AP Calculus AB Learning Targets

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Unit 1 – Functions, Graphs, and Limits

Concept Category: Functions & Limits

LT / Learning Target / Recall & Reproduction
DOK 1 / Routine
DOK 2 / Non-Routine
DOK 3
1A / Describe the behavior of a graph (domain, end behavior, intercepts, symmetry, inc/dec, max/min), interpret the meaning of function values for a given context. / Pg. 11 Sketch & identify key characteristics#13-25, #51, 52
Pg. 27 #3-13 / Curve Sketching Defense
1A: pg. 11 #27-30 (analyze) #42, 43, 44
1A: Pg. 27 #24-28
1B: pg. 52, #55-58 #59-62, pg. 58 #37-38, pg. 71 #47, pg. 57 #14-21, #25-33
1C: pg. 71 #49-51, pg. 105 #41-46 / Explain how the formal definition of a limit (epsilon/delta) works. Use the formal definition of a limit to prove that a limit exists (pg. 40 17-24, pg. 51, #1-10,)
Prove the Squeeze Thm & explain the proof (educreations)
Pg. 101 #42
Pg. 108 #109
1B / State and explain the definition of a limit, explain the conditions for the existence of a limit, give a variety of examples including finding limits from a given graph or by making a table, and justify using properties/theorems of limits. (Formal and Informal) / Conceptual:
pg. 52, # 11-24, 31-46, #55-58, pg. 58 #35-36, pg. 71# 45-46
1C / Explain how to manipulate limits of indeterminate form (0/0) in order to determine the value of the limit. Evaluate the limit of a piecewise function or a function with an absolute value term. / Analytical: pg. 51 #11-24, 31-46, pg. 57 #1-13 pg. 105 #47-54
1D / Use trigonometric identities to evaluate limits with trigonometric functions and derive the limits of sin(x)/x and (1-cos(x))/x as x tends to 0. / Pg. 101 #1-20
Pg. 105 #55-62
Zill HO.

Concept Category: Continuity and Asymptotes

LT / Learning Target / Recall & Reproduction
DOK 1 / Routine
DOK 2 / Non-Routine
DOK 3
1E / Explain the meaning of the continuity of a function at a point, and analyze and describe the discontinuities (essential versus removable) of a function on an interval. / Pg. 80 #1-12, #15-22, #45-46
Pg. 91 #25-28, #7-12 / 1E: Pg. 106 #85-88, #97-98
1E: pg. 80 #12-14, #24-28, #41-44, #47-48, #53 pg. 91 #13-16
pg. 106 #90-92, 99-102
1F: pg. 101 #29-36, pg. 274 #35-54, 57-58 / Pg. 82 #55-57
Pg. 92 #54
1F / Explain how to find vertical and horizontal asymptotes of a function and give a variety of examples. Explain the similarities and differences between infinite limits and limits at infinity, give a variety of examples of evaluating each type of limit, and explain how these types of limits are related to continuity. / Pg. 70 #37-44 (find both horizontal & vertical)
Pg. 105 #63-68,
Pg. 274 #11-30, 55-56

Unit 2 – Limits, Derivatives, and Rates of Change

Concept Category: Slope and Rates of Change

LT / Learning Target / Recall & Reproduction
DOK 1 / Routine
DOK 2 / Non-Routine
DOK 3
2A / Explain how a limit is used to define a tangent line to a function at a given point, and write the equations of tangent and normal lines. / 2A: Pg. 116 #1-16 / 2A: pg. 116 #45-50, pg. 162 #29, 30, pg. 204 #33-35
2B:p.g 161 #8-18
2C: pg 243 #42-44 / 2B: pg. 162 #32, 33
2C: pg. 244 #55
2B / Compare and contrast average rate of change on an interval with instantaneous rate of change at a point, and apply to a variety of applications / 2B: Pg. 160 #1-6
2C / Explain how the slopes of tangent lines are used to determine where a function is increasing or decreasing, and give examples. Explain the connection between a function's graph and the graph of its derivatives. / 2C: Pg. 242 #39-41

Concept Category: Concept of the Derivative & Differentiability

LT / Learning Target / Recall & Reproduction
DOK 1 / Routine
DOK 2 / Non-Routine
DOK 3
2D / Use a limit to define the derivative of a function, and use the definition of the derivative to find the derivatives of given functions (both analytically and graphically). / 2D: Pg. 117 #21-44 / 2D: pg. 142 #43-46
2G: pg. 126 #21-26, #27-30 / 2D: pg. 117 #53
2G: pg. 127 #46
2G / Explain the relationship between differentiability and continuity, give examples using piecewise defined functions, and explain cases where f’(x) does not exist / 2G: Pg. 125 #1-20

Concept Category: Applied Derivatives

LT / Learning Target / Recall & Reproduction
DOK 1 / Routine
DOK 2 / Non-Routine
DOK 3
2E / Evaluate higher order derivatives, explain the connection between a function's graph and the graph of its derivatives, and explain their connection to position, velocity, and acceleration. / 2E: Pg. 141 #37-42
2E: Pg. 205 #67 / 2E: pg. 154 #25-26
2F: pg. 154 #33
2H: Given criteria, sketch pg. 254 #45-50
2H: Given sketch: pg. 263 #14-26
2H: Given function: pg. 282 #1-14 & #17-24 / 2E: pg. 207 #104**
2F: pg. 206 #76
2H: pg. 255 #52-55
2F / Use derivatives to model rates of change in a variety of different applied contexts, including rectilinear motion. / 2F: Pg. 152 #1-8
2H / Explain how to use the first derivative of a function to determine where the function is increasing/decreasing, and where the function might have relative extrema. Explain how to use the second derivative to determine concavity and possible inflection points of a function. Use derivatives to sketch, by hand, the graphs of a variety of functions. Identify key information about, f, f', and f" and be able to sketch each from either f or f’ / 2H: Given criteria, sketch pg. 254 #23-30
2H: Given sketch: pg. 262 #7-12
2H: Given function: pg. 254 #1-6, #17-22

Concept Category: Derivative Rules

LT / Learning Target / Recall & Reproduction
DOK 1 / Routine
DOK 2 / Non-Routine
DOK 3
2I / Prove and use the power, sum, and difference rules for derivatives. Prove the product and quotient rule for derivatives, and give a variety of examples using these rules. / See worksheets given in class.
2J / Know the derivatives of sin(x), cos(x), tan(x), cot(x), sec(x), and csc(x), and their corresponding integrals, and use trigonometric identities to help in differentiation.
2K / Know the derivatives and integrals of a^x, e^x, 1/x, and ln(x), and give a variety of examples using a combination of these functions.
4L / Explain how to calculate the derivatives of a variety of composite functions using the chain rule, and give examples.

Updated 11-02-14