career tech ap calculus
TRANSCRIPT
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AP CALCULUS
The Calculus objectives that follow are meant as a framework forCareerTech Centers and educators. They should aide in alignment ofcurriculum, supply additional resources, and assist in the assignment ofhigh school calculus academic credit.A committee of Mathematicsinstructors compiled the list of necessary objectives that all CareerTechstudents should master upon completion of the course. CareerTech
upper division math courses demonstrate the Content and ProcessStandards of the National Council of Teachers of Mathematics (NCTM)and the Process Standards of Oklahoma Priority Academic Student Skills(PASS). Students are expected to problem solve, do reasoning andproofs, demonstrate mathematical communication, connect and linkmathematical ideas to real-world and other disciplines, and usemathematical representations for modeling, interpreting, andcommunicating. Technology will be integrated into the course in order toprepare students for real-world situations.
Course Description:
This is a college preparatory course that offers extreme rigor in aspecialized field of study. It will enable the student to be successful onthe Advanced Placement AB Calculus exam and/or in college calculus.Topics covered will be: limits, differentiation, and basic integrationtechniques. An emphasis will be placed on real world applications asthey relate to the various engineering fields as well as development ofproblem-solving skills. Prerequisites for the course are: Algebra I,Algebra II, Geometry, Trigonometry/Pre-Calculus
Requirements for College Admission Status (Title 70 O.S. 11-103.6)These courses are to be taught by a highly qualified teacher with anOklahoma Advanced Mathematics teaching certification. The studentsshould be in the eleventh or twelfth grade or if a sophomore, they shouldbe in a Focused Field of Career Study program. The course will have at aminimum, but may exceed, a duration of 120 hours within a school year.
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CalculusSyllabus
Objective NCTM Standard OklahomaPASS
ProcessStandard
I. Preparation forCalculus
A. Sketch the graph ofan equation
AlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
B. Find the intercepts
of a graph
Algebra
Measurement
1.1, 1.2, 2.1, 2.2, 5.1,
5.2C. Test a graph forsymmetry with respectto an axis and theorigin
Number & OperationsAlgebraMeasurementGeometryData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 3.3,3.4, 5.1, 5.2
D. Find the points ofintersection of twographs
Algebra 1.1, 1.2, 2.1, 2.2, 5.1,5.2
E. Interpret
mathematical modelsfor real-life data
Number & Operations
AlgebraMeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,
3.1, 3.3, 4.1, 4.3, 5.1,5.2, 5.3
F. Find the slope of aline passing throughtwo points
AlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
G. Write the equationsof a line with a givenpoint and slope
Number & OperationsAlgebra
1.1, 1.2, 2.1, 2.2, 5.1,5.2
H. Interpret slope as aratio or as a rate in areal-life application
Number & OperationsAlgebraMeasurement
Data Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.1, 3.3, 4.1, 4.3, 5.1,
5.2, 5.3
I. Sketch the graph ofa linear equation inslope-intercept form
Algebra 1.1, 1.2, 2.1, 2.2, 5.1,5.2
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J. Write equations oflines that are parallelor perpendicular to agiven line
Number & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
K. Use function
notation to representand evaluate afunction
Number & Operations
AlgebraMeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,
5.2
L. Find the domainand range of afunction
Number & OperationsAlgebraMeasurement
Data Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,5.2
M. Sketch the graphof a function
AlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
N. Identify differenttypes oftransformations offunctions
Number & OperationsAlgebraData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,5.2
O. Classify functionsand recognizecombinations offunctions
Number & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
P. Fit a linear modelto a real-life data set
Number & OperationsAlgebraMeasurement DataAnalysis & Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.1, 3.3, 4.1, 4.3, 5.1,
5.2, 5.3
Q. Fit a quadraticmodel to a real-lifedata set
Number & OperationsAlgebraMeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.1, 3.3, 4.1, 4.3, 5.1,
5.2, 5.3
R. Fit a trigonometricmodel to a real-life
data set
Number & OperationsAlgebra
MeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.1, 3.3, 4.1, 4.3, 5.1,
5.2, 5.3
II. Limits and TheirProperties
A. Understand whatcalculus is and how itcompares to pre-
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,4.4, 5.1, 5.2
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calculus
B. Understand thatthe tangent lineproblem is basic tocalculus
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,4.4, 5.1, 5.2
C. Understand thatthe area problem isalso basic to calculus
Number & OperationsData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,4.4, 5.1, 5.2
D. Estimate a limitusing a numerical orgraphical approach
Number & OperationsData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,5.2
E. Learn differentways that a limit canfail to exist
Number & OperationsData Analysis &ProbabilityMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
F. Study and use aformal definition of alimit
Number & OperationsData Analysis &ProbabilityMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
G. Evaluate a limitusing properties oflimits
Number & OperationsData Analysis &ProbabilityMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
H. Develop and use astrategy
Data Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,5.2
I. Evaluate a limitusing dividing out andrationalizingtechniques
Number & OperationsData Analysis &ProbabilityMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
J. Evaluate a limitusing the SqueezeTheorem
Number & OperationsData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,5.2
K. Determinecontinuity at a pointand continuity on anopen interval
Number & OperationsData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,5.2
L. Determine one-sided limits andcontinuity on a closedinterval
Number & OperationsData Analysis &ProbabilityMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
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M. Use properties ofcontinuity
Number & OperationsData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,5.2
N. Understand and
use the IntermediateValue Theorem
Number & Operations
Data Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,
5.2
O. Determine infinitelimits from the left andfrom the right
Number & OperationsData Analysis &ProbabilityMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
P. Find and sketch thevertical asymptotes ofthe graph of a function
Data Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,5.2
III. Differentiation
A. Find the slope ofthe tangent line to acurve at a point
Number & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
B. Use the limitdefinition to find thederivative of a function
Number & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
C. Understand therelationship betweendifferentiability andcontinuity
Number & OperationsAlgebraMeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
D. Find the derivativeof a function using theConstant Rule
Number & OperationsAlgebraMeasure Data Analysis& Probability ment
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
E. Find the derivativeof a function using thePower Rule
Number & OperationsAlgebraMeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
F. Find the derivativeof a function using theConstant Multiple Rule
Number & OperationsAlgebraMeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
G. Find the derivativeof a function using theSum and Difference
Number & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
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Rules Data Analysis &Probability
H. Find the derivativeof the sine functionand of the cosine
function
Number & OperationsAlgebraMeasurement
Data Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
I. Use derivatives tofind rates of change
Number & OperationsAlgebraMeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
J. Find the derivativeof a function using theProduct Rule
Number & OperationsAlgebraMeasurementData Analysis &
Probability
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
K. Find the derivativeof a function using theQuotient Rule
Number & OperationsAlgebraMeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
L. Find the derivativeof a trigonometricfunction
Number & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
M. Find a higher-order derivative of afunction
Number & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
N. Find the derivativeof a compositefunction using theChain Rule
Number & OperationsAlgebraMeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
O. Find the derivativeof a function using theGeneral Power Rule
Number & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
P. Simplify thederivative of a functionusing algebra
Number & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
Q. Find the derivativeof a trigonometricfunction using theChain Rule
Number & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
R. Distinguish Number & Operations 1.1, 1.2, 2.1, 2.2, 2.3,
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between functionswritten in implicit andexplicit forms
AlgebraMeasurement
3.3, 4.2, 5.1, 5.2
S. Use implicitdifferentiation to find
the derivative of afunction
Number & OperationsAlgebra
Measurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
T. Find a related rate Number & OperationsAlgebraMeasurementData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
U. Use related rates tosolve real-life problems
Number & OperationsAlgebraMeasurementData Analysis &
Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.1, 3.3, 4.1, 4.3, 5.1,
5.2, 5.3
IV. Applications ofDifferentiation
A. Understand thedefinition of extrema ofa function on aninterval
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
B. Understand thedefinition of relativeextrema of a functionon an open interval
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
C. Find extrema on aclosed interval
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,5.1, 5.2
D. Understand anduse Rolles Theorem
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
E. Understand anduse the Mean ValueTheorem
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
F. Determine intervals
on which a function isincreasing ordecreasing
Data Analysis &
ProbabilityAlgebraNumbers & Operations
1.1, 1.2, 2.1, 2.2, 2.3,
3.3, 4.2, 5.1, 5.2
G. Apply the FirstDerivative Test to findrelative extrema of afunction
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.1, 3.3, 4.1, 4.3, 5.1,
5.2, 5.3
H. Determine intervals Data Analysis & 1.1, 1.2, 2.1, 2.2, 2.3,
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on which a function isconcave upward ordownward
ProbabilityAlgebraNumbers & Operations
3.1, 3.3, 4.1, 4.3, 5.1,5.2, 5.3
I. Find any points ofinflection of the graph
of a function
Data Analysis &Probability
Algebra
1.1, 1.2, 2.1, 2.2, 2.3,3.1, 3.3, 4.1, 4.3, 5.1,
5.2, 5.31.1, 1.2, 2.1,2.2, 2.3, 3.1, 3.3, 4.1,
4.3, 5.1, 5.2, 5.3
J. Apply the SecondDerivative Test to findrelative extrema of afunction
Data Analysis &ProbabilityAlgebraNumbers & Operations
1.1, 1.2, 2.1, 2.2, 2.3,3.1, 3.3, 4.1, 4.3, 5.1,
5.2, 5.3
K. Determine (finite)limits at infinity
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
L. Determine the
horizontal asymptotesof the graph of afunction
Data Analysis &
ProbabilityAlgebraNumbers & Operations
1.1, 1.2, 2.1, 2.2, 2.3,
3.3, 4.2, 5.1, 5.2
M. Determine infinitelimits at infinity
Data Analysis &ProbabilityAlgebraNumbers & Operations
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
N. Analyze and sketchthe graph of a function
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
O. Solve appliedminimum andmaximum problems
Data Analysis &ProbabilityAlgebraNumbers & Operations
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
P. Approximate a zeroof a function usingNewtons Method
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
Q. Understand theconcept of a tangentline approximation
Data Analysis &ProbabilityAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
R. Compare the value
of the differential, dy,with the actual changein y, delta y
Data Analysis &
ProbabilityAlgebraNumbers & Operations
1.1, 1.2, 2.1, 2.2, 2.3,
3.3, 4.2, 5.1, 5.2
S. Estimate apropagated error usinga differential
Data Analysis &ProbabilityAlgebraNumbers & Operations
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
T. Find the differential Data Analysis & 1.1, 1.2, 2.1, 2.2, 2.3,
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of a function usingdifferentiationformulas
ProbabilityAlgebraNumbers & Operations
3.3, 4.2, 5.1, 5.2
V. Integration
A. Write the general
solution of adifferential equation
Numbers & Operations
MeasurementAlgebra
1.1, 1.2, 2.1, 2.2, 5.1,
5.2
B. Use indefiniteintegral notation forantiderivatives
Numbers & OperationsMeasurementAlgebra
1.1, 1.2, 2.1, 2.2, 5.1,5.2
C. Use basicintegration rules tofind antiderivatives
Numbers & OperationsMeasurementAlgebra
1.1, 1.2, 2.1, 2.2, 5.1,5.2
D. Find a particularsolution of adifferential equation
Numbers & OperationsMeasurementAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
E. Use sigma notationto write and evaluate asum
Numbers & OperationsMeasurementAlgebra
1.1, 1.2, 2.1, 2.2, 5.1,5.2
F. Understand theconcept of area
Numbers & OperationsMeasurementAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
G. Approximate theareas of a plane region
Numbers & OperationsMeasurementAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
H. Find the area of aplane region usinglimits
Numbers & OperationsMeasurementAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
I. Understand thedefinition of aRiemann sum
Numbers & OperationsMeasurementAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2
J. Evaluate a definiteintegral using limits
Numbers & OperationsMeasurementAlgebraData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
K. Evaluate a definite
integral usingproperties of definiteintegrals
Numbers & Operations
MeasurementAlgebraData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,
3.3, 4.2, 5.1, 5.2, 5.3
L. Evaluate a definiteintegral using theFundamental Theorem
Numbers & OperationsMeasurementAlgebra
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
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of Calculus Data Analysis &Probability
M. Understand anduse the Mean Value
Theorem for Integrals
Numbers & OperationsMeasurement
AlgebraData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
N. Find the averagevalue of a functionover a closed interval
Numbers & OperationsMeasurementAlgebraData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,5.2
O. Use patternrecognition to evaluatean indefinite integral
Numbers & OperationsMeasurementAlgebra
Data Analysis &Probability
1.1, 1.2, 2.1, 2.2, 5.1,5.2
P. Use a change ofvariables to evaluatean indefinite integral
Numbers & OperationsMeasurementAlgebraData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
Q. Use the GeneralPower Rule forIntegration to evaluatean indefinite integral
Numbers & OperationsMeasurementAlgebraData Analysis &
Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
R. Use a change ofvariables to evaluate adefinite integral
Numbers & OperationsMeasurementAlgebraData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
S. Evaluate a definiteintegral involving aneven or odd function
Numbers & OperationsMeasurementAlgebraData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
T. Approximate adefinite integral usingthe Trapezoidal Rule
Numbers & OperationsMeasurementAlgebraData Analysis &Probability
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
U. Approximate adefinite integral using
Numbers & OperationsMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
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functions Measurement
K. Integrate naturalexponential functions
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
L. Define exponential
functions that havebases other than e
Numbers & Operations
AlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,
5.2
M. Differentiate andintegrate exponentialfunctions that havebases other than e
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
N. Use exponentialfunctions to modelcompound interest andexponential growth
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
O. Use separation of
variables to solve asimple differentialequation
Numbers & Operations
AlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,
3.3, 4.2, 5.1, 5.2, 5.3
P. Use exponentialfunctions to modelgrowth and decay inapplied problems
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
Q. Use initialconditions to findparticular solutions ofdifferential equations
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
R. Recognize andsolve differentialequations that can besolved by separation ofvariables
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
S. Recognize and solvehomogeneousdifferential equations
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
T. Use a differentialequation to model and
solve an appliedproblem
Numbers & OperationsAlgebra
Measurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
U. Develop propertiesof the six inversetrigonometricfunctions
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
V. Differentiate aninverse trigonometric
Numbers & OperationsAlgebra
1.1, 1.2, 2.1, 2.2, 5.1,5.2
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function Measurement
W. Review the basicdifferentiationformulas forelementary functions
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
X. Integrate functionswhose antiderivativesinvolve inversetrigonometricfunctions
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
Y. Use the method ofcompleting the squareto integrate a function
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
Z. Review the basicintegration formulasinvolving elementary
functions
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
AA. Develop propertiesof hyperbolic functions
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
BB. Differentiate andintegrate hyperbolicfunctions
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
CC. Developproperties of inversehyperbolic functions
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
DD. Differentiate andintegrate functionsinvolving inversehyperbolic functions
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
VII. Applications ofIntegration
A. Find the area of aregion between twocurves usingintegration
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
B. Find the area of a
region betweenintersecting curvesusing integration
Numbers & Operations
AlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,
5.2
C. Describeintegration as aaccumulation process
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
D. Find the volume ofa solid of revolution
Numbers & OperationsAlgebra
1.1, 1.2, 2.1, 2.2, 5.1,5.2
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using the disk method Measurement
E. Find the volume ofa solid of revolutionusing the washermethod
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
F. Find the volume ofa solid with knowncross sections
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
G. Find the volume ofa solid of revolutionusing the shell method
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 5.1,5.2
H. Compare the usesof the disk method andthe shell method
Numbers & OperationsAlgebraMeasurement
1.1, 1.2, 2.1, 2.2, 2.3,3.3, 4.2, 5.1, 5.2, 5.3
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8/8/2019 Career Tech AP Calculus
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References and Resources
Referenced Standards
Principles and Standards for School Mathematics(4th ed.). (2005).
National Council of Teachers of Mathematics, Reston, VA
Oklahoma Priority Academic Student Skills(2003). Oklahoma StateDepartment of Education-PASS-{www.sde.state.ok.us}
Suggested Text and Supplemental Materials
Larson, Ron, Hostetler, Bob, Edwards, Bruce. (2006). Calculus withAnalytic Geometry (8thed)/Calculus of a Single Variable (8thed). Boston:Houghton Mifflin.
Larson, Ron, Hostetler, Bob, Edwards, Bruce. (2006). Calculus withAnalytic Geometry (8thed)/Calculus of a Single Variable (8thed)-Instructors Resource Guide. Boston: Houghton Mifflin.
Varberg, Dale, Edwin J. Purcell, and Steven E. Rigdon. (2007). Calculus(9 ed.) th . Boston: Pearson Prentice Hall.
Thomas, George B., Jr., and Ross L. Finney (1996). Calculus withAnalytic Geometry (9 ed.)th . Boston: Addison-Wesley.
Finney, Ross L., Franklin D. Demana, Bert K. Waits, and DanielKennedy. (2007). Calculus: Graphical, Numerical, Algebraic: AP Edition (3ed.)
rd
. Boston: Pearson Prentice Hall.