AP Calculus AB Review
Review worksheet
"When you see.." (solutions)
Progress Checks
Unit 1 MCQ & FRQ
PtA (updated 4/12/23)
#1 understanding a limit
#2 identify speed on graph
#3 estimating speed with table
#4 speed is slope
#5 reading limits
#6 definition of limit
#7 limit graphically
#8 limit graphically
#9 definition of limit
#10 solving limits
#11
#12 limit using table (tricky)
#13 limits of piecewise function
#14 basic limit laws
#15 solving limits
#16 manipulating function in limit
#17 solving a limit
#18 limit manipulation with trig
# limits with tables
PtB (updated 4/12/23)
#1 manipulating function in limits
#2 basic limit laws
#3 limit of piecewise function
#4 squeeze theorem
#5 squeeze theorem
#6 squeeze theorem
#7 reading a table
#8 limit of a function in a function
#9 deceptive limit table
#10 piecewise function discontinuous?
#11 jump discontinuity
#12 removable discontinuity
#13 analyzing function with limits
#14 continuity
#15 continuous piecewise function
PtC (updated 4/12/23)
#1 continuity x/x and |x|/x
#2 piecewise function and continuity
#3 intermediate value theorem
#4 continuity from a graph
#5 continuity on closed and open intervals
#6 continuity of a piecewise function
#7 continuity on a piecewise function
#8 limits at asymptotes
#9 limits at asymptotes
#10 reading one sided limits
#11 limits with rational functions
#12 an infinite limit
#13 limits at infinity
#14 intermediate value theorem
#15 intermediate value theorem
U1 FRQ PtA1: Def of a limit and continuity
U1 FRQ PtA2: Limits at infinity, Def of continuity
Unit 2 MCQ & FRQ
PtA (updated 4/12/23)
#1 average rate of change
#2 estimate derivative
#3 differentiability and continuity
#4 differentiable definition
#5 average rate of change
#6 tangent line
#7 average rate of change
#8 tangent line
#9 MVT
#10 derivative of fraction
#11 derivatives w/ calc
#12 differentiability and continuity
#13
#14
#15 power rule
# tangent line
PtB
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
#11
#12
#13
#14
#15
U2 FRQ PtA:
--U2 FRQ PtA by: Mr. Romero
U2 FRQ PtB:
Unit 3 MCQ & FRQ (updated 4/19/23)
#1 chain rule
#2 chain rule
#3 chain rule three times
#4 implicit diff and tangent line slope
#5 implicit differentiation
#6 implicit differentiation w/ table
#7 derivative of inverse function given graph
#8 inverse function
#9 inverse function
#10 derivative of inverse sine
#11 inverse cosine derivative
#12 testing chain rule by proving (arcsine(x))'
#13 when to use product rule
#14 implicit differentiation
#15 when to use quotient rule
#16 fourth derivative of natural log
#17 meaning of f''
#18 implicit w/ chain rule
U3 FRQ PtA: Chain rule and inverse functions
--U3 FRQ PtA by: Mr. Romero
U3 FRQ PtB:
Unit 4 MCQ & FRQ (updated 4/19/23)
#1 Meaning of derivative
#2 Linear approximation
#3 Derivative in context
#4 MVT
#5 Rate graph
#6 Related rates
#7 Particle speed
#8 Meaning of derivative
#9 Related rates
#10 Related rates
#11 Related Rates
#12 Related rates
#13 Related rates
#14 Linear approximation
#15 Linear approximation
#16 Indeterminant
#17 L'Hopital's rule
#18 L'Hopital
U4 FRQ PtA: Related Rates (Click here for Mr. Patey's Reflection)
--U4 FRQ PtA by:Mr. Romero
U4 FRQ PtB:
Unit 5 MCQ & FRQ
PtA (updated 4/19/23)
#1 MVT with calculator
#2 f' below x-axis with calculator
#3 reading f' graph
#4 definition of MVT
#5 definition, of MVT, IVT, and extreme value theorem
#6 definition of extreme value theorem
#7 definition of extreme value theorem
#8 definitions of MVT, IVT, and extreme value theorem
#9 first derivative test
#10 extreme value theorem with e
#11 relative max or min
#12 reading f' graph
PtB (checked 4/19/23)
#1 Point of inflection with calculator
#2 using f'' to find local min (or max)
#3 absolute max
#4 absolute min
#5 non-calculus (abs max)
#6 concavity of f with f' graph
#7 concavity
#8 using f'' for max and min
#9 curve sketching
#10 rate graph
#11 curve sketching with table
#12 definitions of relative extrema and point of inflection
PtC
#1
#2 optimization and finding the hidden function by: Mr. Romero
#3
#4
#5 horizontal tangent
#6
#7
#8
#9
#10
#11
#12
#13
#14
#15
#16
#17
U5 FRQ PtA: Analyzing a function with derivatives (Click here for Mr. Patey's Reflection)
--U5 FRQ PtA by: Mr. Romero
U5 FRQ PtB1
U5 FRQ PtB2
Unit 6 MCQ & FRQ
PtA (updated 4/19/23)
#1 Riemann sum with calculator
#2 midpoint Riemann sum with calculator
#3 relative was with calculator
#4 left hand Riemann sum with table
#5 definition of integral
#6 definition of integral
#7 definition of integral
#8 fundamental theorem of calculus
#9 fundamental theorem of calculus II
#10 fundamental theorem of calculus
#11 fundamental theorem of calculus
#12 integrals and rate graphs
#13 integrals with geometry
#14 Basic laws of integrals
#15 integrals with geometry
PtB (checked 4/19/23)
#1 FTC1 (by: Mr. Romero)
#2 u-sub with table (by: Mr. Romero)
#3 FTC2 (by: Mr. Romero)
#4 FTC2 with graph (by: Mr. Romero)
#5 u-sub given u (by: Mr. Romero)
#6 classic u-sub (by: Mr. Romero)
#7 recognizing antiderivative of arctan (by: Mr. Romero)
#8 recognizing antiderivative of arcsin (by: Mr. Romero)
#9 simplifying the integrand (by: Mr. Romero)
#10 simplifying the integrand (by: Mr. Romero)
#11 classic u-sub (by: Mr. Romero)
#12 classic u-sub (by: Mr. Romero)
U6 FRQ PtA1: Riemann sums and the definition of integrals
--U6 FRQ PtA1 by: Mr. Romero
U6 FRQ PtA2: FTC, Rate graph, extrema, u-sub
--U6 FRQ PtA2 by: Mr. Romero
U6 FRQ PtB:
Unit 7 MCQ & FRQ (updated 4/19/23)
#1 particular solution
#2 decoding word problem
#3 decoding differential word problems
#4 decoding differential word problems
#5 testing solutions to differential equations
#6 testing differential equations solutions
#7 testing solutions for Diff Eq
#8 slope fields
#9 analyzing slope fields
#10 slope fields
#11 general solution
#12 particulate solution two ways
#13 particular solution
#14 particular solution weird variables
#15 hard particular solution
#16 identifying expo models
#17 recognizing expo functions
#18 exponential function word problem
U7 FRQ PtA: differential equations, tangent line approximation
U7 FRQ PtB1:slope field, second derivative, particular solution
U7 FRQ PtB2: sketching a solution, tangent line, particular solution
Unit 8 MCQ & FRQ
PtA (checked 4/19/23)
#1 Average value
#2 Net change
#3 Area between curves
#4 Two areas between two curves
#5 Average value with geometry
#6 Average value and laws of integrals
#7 Position
#8 Displacement and total distance
#9 Total distance
#10 Quantity using definite integral
#11 Definite integral with geo
#12 Vertical area between curves
#13 Integral with respect to y
#14 Area of two regions
#15 Two areas between two curves
PtB
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
#11
#12
#13
#14
#15
#16
#17
#18
U8 FRQ PtA: Given a rate function find displacement, total distance, acceleration etc.
U8 FRQ PtB:
FRQ Review Section
pdf of them grouped by topic: Newton Book
Area and Volume
--NB5 2002 Calc AB FRQ1
Net Change
--NB26 2002 Calc AB FRQ2
Charts with Riemann Sums, MVT, Ave. Rate/Values
--NB41 1999 Calc AB BC FRQ3
Analyzing Graph of f' (writing a function in integral form)
--NB54 2004 Calc AB FRQ4
Slope Fields with differential Equations
Related Rates
--NB70 2002 Calc AB FRQ6 (light house)
--NB71 2002 Calc AB FRQ5 (cone)
Accumulation Functions (writing a function in integral form)
--NB77 1999 Calc AB FRQ5
--NB78 2001 Calc AB FRQ3
--NB80 2002 Calc AB FRQ4
--2009B #2
Implicit Differentiation
--NB93 2001 Calc AB FRQ6
Particle Motion
--NB96 1999 Calc AB FRQ1
Charts of f, f', f''
--NB108 2007 Calc AB FRQ3
Functions/Misc.
--NB115 2003 Calc AB FRQ6
Curve Sketching
--2005 Calc AB FRQ4
2019 FRQs
#1 Rate equations, total amounts, extrema
#2 Trapezoidal sum, total distance, displacement
#3 Rate graph, integration, limits
#4 Cylinder, related rates
#5
#6 Tangent line, chain rule, L'Hopital's, Squeeze
"When you see.." (solutions)
Progress Checks
Unit 1 MCQ & FRQ
PtA (updated 4/12/23)
#1 understanding a limit
#2 identify speed on graph
#3 estimating speed with table
#4 speed is slope
#5 reading limits
#6 definition of limit
#7 limit graphically
#8 limit graphically
#9 definition of limit
#10 solving limits
#11
#12 limit using table (tricky)
#13 limits of piecewise function
#14 basic limit laws
#15 solving limits
#16 manipulating function in limit
#17 solving a limit
#18 limit manipulation with trig
# limits with tables
PtB (updated 4/12/23)
#1 manipulating function in limits
#2 basic limit laws
#3 limit of piecewise function
#4 squeeze theorem
#5 squeeze theorem
#6 squeeze theorem
#7 reading a table
#8 limit of a function in a function
#9 deceptive limit table
#10 piecewise function discontinuous?
#11 jump discontinuity
#12 removable discontinuity
#13 analyzing function with limits
#14 continuity
#15 continuous piecewise function
PtC (updated 4/12/23)
#1 continuity x/x and |x|/x
#2 piecewise function and continuity
#3 intermediate value theorem
#4 continuity from a graph
#5 continuity on closed and open intervals
#6 continuity of a piecewise function
#7 continuity on a piecewise function
#8 limits at asymptotes
#9 limits at asymptotes
#10 reading one sided limits
#11 limits with rational functions
#12 an infinite limit
#13 limits at infinity
#14 intermediate value theorem
#15 intermediate value theorem
U1 FRQ PtA1: Def of a limit and continuity
U1 FRQ PtA2: Limits at infinity, Def of continuity
Unit 2 MCQ & FRQ
PtA (updated 4/12/23)
#1 average rate of change
#2 estimate derivative
#3 differentiability and continuity
#4 differentiable definition
#5 average rate of change
#6 tangent line
#7 average rate of change
#8 tangent line
#9 MVT
#10 derivative of fraction
#11 derivatives w/ calc
#12 differentiability and continuity
#13
#14
#15 power rule
# tangent line
PtB
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
#11
#12
#13
#14
#15
U2 FRQ PtA:
--U2 FRQ PtA by: Mr. Romero
U2 FRQ PtB:
Unit 3 MCQ & FRQ (updated 4/19/23)
#1 chain rule
#2 chain rule
#3 chain rule three times
#4 implicit diff and tangent line slope
#5 implicit differentiation
#6 implicit differentiation w/ table
#7 derivative of inverse function given graph
#8 inverse function
#9 inverse function
#10 derivative of inverse sine
#11 inverse cosine derivative
#12 testing chain rule by proving (arcsine(x))'
#13 when to use product rule
#14 implicit differentiation
#15 when to use quotient rule
#16 fourth derivative of natural log
#17 meaning of f''
#18 implicit w/ chain rule
U3 FRQ PtA: Chain rule and inverse functions
--U3 FRQ PtA by: Mr. Romero
U3 FRQ PtB:
Unit 4 MCQ & FRQ (updated 4/19/23)
#1 Meaning of derivative
#2 Linear approximation
#3 Derivative in context
#4 MVT
#5 Rate graph
#6 Related rates
#7 Particle speed
#8 Meaning of derivative
#9 Related rates
#10 Related rates
#11 Related Rates
#12 Related rates
#13 Related rates
#14 Linear approximation
#15 Linear approximation
#16 Indeterminant
#17 L'Hopital's rule
#18 L'Hopital
U4 FRQ PtA: Related Rates (Click here for Mr. Patey's Reflection)
--U4 FRQ PtA by:Mr. Romero
U4 FRQ PtB:
Unit 5 MCQ & FRQ
PtA (updated 4/19/23)
#1 MVT with calculator
#2 f' below x-axis with calculator
#3 reading f' graph
#4 definition of MVT
#5 definition, of MVT, IVT, and extreme value theorem
#6 definition of extreme value theorem
#7 definition of extreme value theorem
#8 definitions of MVT, IVT, and extreme value theorem
#9 first derivative test
#10 extreme value theorem with e
#11 relative max or min
#12 reading f' graph
PtB (checked 4/19/23)
#1 Point of inflection with calculator
#2 using f'' to find local min (or max)
#3 absolute max
#4 absolute min
#5 non-calculus (abs max)
#6 concavity of f with f' graph
#7 concavity
#8 using f'' for max and min
#9 curve sketching
#10 rate graph
#11 curve sketching with table
#12 definitions of relative extrema and point of inflection
PtC
#1
#2 optimization and finding the hidden function by: Mr. Romero
#3
#4
#5 horizontal tangent
#6
#7
#8
#9
#10
#11
#12
#13
#14
#15
#16
#17
U5 FRQ PtA: Analyzing a function with derivatives (Click here for Mr. Patey's Reflection)
--U5 FRQ PtA by: Mr. Romero
U5 FRQ PtB1
U5 FRQ PtB2
Unit 6 MCQ & FRQ
PtA (updated 4/19/23)
#1 Riemann sum with calculator
#2 midpoint Riemann sum with calculator
#3 relative was with calculator
#4 left hand Riemann sum with table
#5 definition of integral
#6 definition of integral
#7 definition of integral
#8 fundamental theorem of calculus
#9 fundamental theorem of calculus II
#10 fundamental theorem of calculus
#11 fundamental theorem of calculus
#12 integrals and rate graphs
#13 integrals with geometry
#14 Basic laws of integrals
#15 integrals with geometry
PtB (checked 4/19/23)
#1 FTC1 (by: Mr. Romero)
#2 u-sub with table (by: Mr. Romero)
#3 FTC2 (by: Mr. Romero)
#4 FTC2 with graph (by: Mr. Romero)
#5 u-sub given u (by: Mr. Romero)
#6 classic u-sub (by: Mr. Romero)
#7 recognizing antiderivative of arctan (by: Mr. Romero)
#8 recognizing antiderivative of arcsin (by: Mr. Romero)
#9 simplifying the integrand (by: Mr. Romero)
#10 simplifying the integrand (by: Mr. Romero)
#11 classic u-sub (by: Mr. Romero)
#12 classic u-sub (by: Mr. Romero)
U6 FRQ PtA1: Riemann sums and the definition of integrals
--U6 FRQ PtA1 by: Mr. Romero
U6 FRQ PtA2: FTC, Rate graph, extrema, u-sub
--U6 FRQ PtA2 by: Mr. Romero
U6 FRQ PtB:
Unit 7 MCQ & FRQ (updated 4/19/23)
#1 particular solution
#2 decoding word problem
#3 decoding differential word problems
#4 decoding differential word problems
#5 testing solutions to differential equations
#6 testing differential equations solutions
#7 testing solutions for Diff Eq
#8 slope fields
#9 analyzing slope fields
#10 slope fields
#11 general solution
#12 particulate solution two ways
#13 particular solution
#14 particular solution weird variables
#15 hard particular solution
#16 identifying expo models
#17 recognizing expo functions
#18 exponential function word problem
U7 FRQ PtA: differential equations, tangent line approximation
U7 FRQ PtB1:slope field, second derivative, particular solution
U7 FRQ PtB2: sketching a solution, tangent line, particular solution
Unit 8 MCQ & FRQ
PtA (checked 4/19/23)
#1 Average value
#2 Net change
#3 Area between curves
#4 Two areas between two curves
#5 Average value with geometry
#6 Average value and laws of integrals
#7 Position
#8 Displacement and total distance
#9 Total distance
#10 Quantity using definite integral
#11 Definite integral with geo
#12 Vertical area between curves
#13 Integral with respect to y
#14 Area of two regions
#15 Two areas between two curves
PtB
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
#11
#12
#13
#14
#15
#16
#17
#18
U8 FRQ PtA: Given a rate function find displacement, total distance, acceleration etc.
U8 FRQ PtB:
FRQ Review Section
pdf of them grouped by topic: Newton Book
Area and Volume
--NB5 2002 Calc AB FRQ1
Net Change
--NB26 2002 Calc AB FRQ2
Charts with Riemann Sums, MVT, Ave. Rate/Values
--NB41 1999 Calc AB BC FRQ3
Analyzing Graph of f' (writing a function in integral form)
--NB54 2004 Calc AB FRQ4
Slope Fields with differential Equations
Related Rates
--NB70 2002 Calc AB FRQ6 (light house)
--NB71 2002 Calc AB FRQ5 (cone)
Accumulation Functions (writing a function in integral form)
--NB77 1999 Calc AB FRQ5
--NB78 2001 Calc AB FRQ3
--NB80 2002 Calc AB FRQ4
--2009B #2
Implicit Differentiation
--NB93 2001 Calc AB FRQ6
Particle Motion
--NB96 1999 Calc AB FRQ1
Charts of f, f', f''
--NB108 2007 Calc AB FRQ3
Functions/Misc.
--NB115 2003 Calc AB FRQ6
Curve Sketching
--2005 Calc AB FRQ4
2019 FRQs
#1 Rate equations, total amounts, extrema
#2 Trapezoidal sum, total distance, displacement
#3 Rate graph, integration, limits
#4 Cylinder, related rates
#5
#6 Tangent line, chain rule, L'Hopital's, Squeeze