AP CALCULUS AB
Calculus 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
,
,
,
Calculus 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
,
,
,
