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AP Calculus AB (Calculus 1) Handwritten Notes
These notes cover all AP Calc AB (Calc 1) topics with examples and explanations. They are mostly taken from the Princeton Review and summarized to give the main topics needed.
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AP CALCULUS ABCalculus 1
, Table of Contents
Limits and Continuity……………………………………………………………………………………………………………………………………………………………4
When Does a Limit DNE……………………………………………………………………………………………………………………………………………………….5
Limit Flowchart…………………………………………………………………………………………………………………………………………………………….………..6
Squeeze Theorem…………………………………………………………………………………………………………………………………………………………………..7
Continuity…………………………………………………………………………………………………………………………………………………………….…………………….7
Infinity Wars………………………………………………………………………………………………………………………………………………………….………………..8
Vertical and Horizontal Asymptote………………………………………………………………………………………………………………………..….8
Intermediate Value Theorem…………………………………………………………………………………………………………………………………………..9
Derivatives………………………………………………………………………………………………………………………………………………………………………………10
Connecting f and f’.................……………………………………………………………………………………………………………………………………....11
Relative Minimum/Maximum…………………………………………………………………………………………………………………………………………11
When Does a Derivative DNE……………………………………………………………………………………………………………………………….………..11
Derivative Application Review……………………………………………….…………………………………………………………………………………….12
Basic Derivative Rules……………………………………………………………………………………………………………………………………………………..12
Basic Derivative Rules……………………………………………………………………………………………………………………………………………………..13
Derivative Examples…………………………………………………………………………………………………………………………………………………………..13
Chain Rule……………………………………………………………………………………………………………………………………………………………………………….14
Inverse Trig Rules…………………………………………………………………………………………………………………………………………………………………14
FRQ Practice………………………………………………………………………………………………………………………………………………………………………….15
FRQ Practice………………………………………………………………………………………………………………………………………………………………………….16
FRQ Practice………………………………………………………………………………………………………………………………………………………………………….17
Rectangular Motion………………………………………………………………………………….……………………………………………………………………….18
Position-Time Graph………………………………………………………………………………………………………….……………………………………………..18
Velocity-Time Graph…………………………………………………………………………………………………………………………………………………………19
Limits of Trig Functions……………………………………………………………………………………………………………………………………………………20
Properties of Limits as x→ infinity……………………………………………………………………………………………………………………………..21
,Graphical Derivatives..…………………………………………………………………………………………………………………………………………………….22
Mean Value Theorom………………………………………………………………………………………………………………………………………………………..23
Minima and Maxima………………………………………………………………………………………………………………………….……………………………..24
Extreme Value Theorem………………………………………..………………………………………………………………………………………………………24
Local Linear Approximation……………………………………………………………………………………………………………………………….……….25
L’Hospitals Rules………………………………………………………………………………………………………………………………………………………………….26
Implicit Differentiation……………………….……..…………………………………………………………………………………………………………………..27
Related Rates……………………………………………………………………………………………………………………………………………………………..…………28
Graphs of f, f’, f’’.....………………………………………………….…………………………………………………………………………………..................29
The Integral……………………………………………………….……………………………………………………………………………………………………….………….30
Integral Rules…………………………………………………………………………………………………………………………………………….………………………….31
Evaluation Therom………………………………………………………………………………………………………………………………………….………………….31
Net Change Theorem………………………………………………………………………………………………………………………………………………………….31
The Fundamental Theorem of Calculus…………………………………………………………………………………………………………………..32
U-Substitution……………………………………………………………………………………………………………………………………………………………………….33
Left and Right Riemann Sums……………………………………………………………………………………………………………….…………………….34
Trapezoid Approximation…………………………………………………………………………………………………………………….…………………………35
Mean Value Theorom For Integrals…………………………………………………………………………………………………………………………..35
Rate In/Out……………………………………………………………………………………………………………………………………………………………………………..36
Over/Under Estimates for Sums…………………………………………………………………………………………………………………………………36
Slope Feilds…………………………………………………………………………………………………………………………………………………….……………………..37
Separation of Variables…………………………………………………………………………………………………………………………………………………..38
The volume of Disks with Example…………………………………………………………………………………………………………………………….39
The volume of Washers with Example…………………………………………………………………………………………………………………….40
The Volume of Cylindrical Shells with Example………………………………………………………………………….…………..………..41
The volume of Cross Sections……………………………………………………………….……………………………………………………………………..42
Area Between Two Curves………………………………………………………………………………………………………………………………..…………..43
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