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School City of Hobart |
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School City of Hobart Mathematics |
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Mathematics - Calculus |
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Calculus and Pre-Calculus
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Limits and Continuity
The learner will be able to
understand the concept of limit, find limits of functions at points and at infinity, decide if a function is continuous, and use continuity theorems.
| Strand |
Source |
| Limits |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.1
The learner will be able to
understand the concept of limit and estimate limits from graphs and tables of values.
| Strand |
Source |
| Limits |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.2
The learner will be able to
find limits by substitution.
| Strand |
Source |
| Limits |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.3
The learner will be able to
find limits of sums, differences, products, and quotients.
| Strand |
Source |
| Limits |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.4
The learner will be able to
find limits of rational functions that are undefined at a point.
| Strand |
Source |
| Limits |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.5
The learner will be able to
find one-sided limits.
| Strand |
Source |
| Limits |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.6
The learner will be able to
find limits at infinity.
| Strand |
Source |
| Limits |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.7
The learner will be able to
decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior.
| Strand |
Source |
| Limits |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.8
The learner will be able to
find special limits. Example: Use a diagram to show that the limit above is equal to 1.
| Strand |
Source |
| Limits |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.9
The learner will be able to
understand continuity in terms of limits.
| Strand |
Source |
| Limits |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.10
The learner will be able to
decide if a function is continuous at a point.
| Strand |
Source |
| Applying Calculus Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.11
The learner will be able to
find the types of discontinuities of a function.
| Strand |
Source |
| Applying Calculus Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.12
The learner will be able to
understand and use the Intermediate Value Theorem on a function over a closed interval.
| Strand |
Source |
| Applying Calculus Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.1.13
The learner will be able to
understand and apply the Extreme Value Theorem: If f(x) is continuous over a closed interval, then f has a maximum and a minimum on the interval.
| Strand |
Source |
| Applying Calculus Concepts |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Differential Calculus
The learner will be able to
find derivatives of algebraic, trigonometric, logarithmic, and exponential functions. They find derivatives of sums, products, and quotients, and composite and inverse functions. They find derivatives of higher order, and use logarithmic differentiation and the Mean Value Theorem.
| Strand |
Source |
| Differential Equations |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.1
The learner will be able to
understand the concept of derivative geometrically, numerically, and analytically, and interpret the derivative as a rate of change.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
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| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.2
The learner will be able to
state, understand, and apply the definition of derivative.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.3
The learner will be able to
find the derivatives of functions, including algebraic, trigonometric, logarithmic, and exponential functions.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.4
The learner will be able to
find the derivatives of sums, products, and quotients.
Example: Find the derivative of x cos x.
.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.5
The learner will be able to
find the derivatives of composite functions, using the chain rule.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.6
The learner will be able to
find the derivatives of implicitly-defined functions.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.7
The learner will be able to
find derivatives of inverse functions.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.8
The learner will be able to
find second derivatives and derivatives of higher order.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.9
The learner will be able to
find derivatives using logarithmic differentiation.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.10
The learner will be able to
understand and use the relationship between differentiability and continuity.
| Strand |
Source |
| Differentiation |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.2.11
The learner will be able to
understand and apply the Mean Value Theorem.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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Applications of Derivatives
The learner will be able to
find slopes and tangents, maximum and minimum points, and points of inflection. They solve optimization problems and find rates of change.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.3.1
The learner will be able to
find the slope of a curve at a point, including points at which there are vertical tangents and no tangents.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.3.2
The learner will be able to
find a tangent line to a curve at a point and a local linear approximation.
Example: In the last example, find an equation of the tangent at (2, 8).
.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.3.3
The learner will be able to
decide where functions are decreasing and increasing. Understand the relationship between the increasing and decreasing behavior of f and the sign of f'.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.3.4
The learner will be able to
find local and absolute maximum and minimum points.
Example: In the last example, find the local maximum and minimum points of f(x).
.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.3.5
The learner will be able to
analyze curves, including the notions of monotonicity and concavity.
Example: In the last example, for which values of x is f(x) decreasing and for which values of x is f(x) concave upward?
.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.3.6
The learner will be able to
find points of inflection of functions. Understand the relationship between the concavity of f and the sign of f". Understand points of inflection as places where concavity changes.
Example: In the last example, find the points of inflection of f(x) and where f(x) is concave upward and concave downward.
.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.3.7
The learner will be able to
use first and second derivatives to help sketch graphs. Compare the corresponding characteristics of the graphs of f, f', and f".
Example: Use the last examples to draw the graph of f(x) = x3 - 3x.
.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.3.8
The learner will be able to
use implicit differentiation to find the derivative of an inverse function.
.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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|
C.3.9
The learner will be able to
solve optimization problems.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.3.10
The learner will be able to
find average and instantaneous rates of change. Understand the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed, and acceleration.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.3.11
The learner will be able to
find the velocity and acceleration of a particle moving in a straight line.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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|
C.3.12
The learner will be able to
model rates of change, including related rates problems. Example: A boat is heading south at 10 mph. Another boat is heading west at 15 mph toward the same point. At these speeds, they will collide. Find the rate that the distance between them is decreasing 1 hour before they collide.
| Strand |
Source |
| Problem Solving |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
Integral Calculus
The learner will be able to
define integrals using Riemann Sums, use the Fundamental Theorem of Calculus to find integrals, and use basic properties of integrals. They integrate by substitution and find approximate integrals.
| Strand |
Source |
| Definite Integral |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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C.4.1
The learner will be able to
use rectangle approximations to find approximate values of integrals.
| Strand |
Source |
| Definite Integral |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
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|
C.4.2
The learner will be able to
calculate the values of Riemann Sums over equal subdivisions using left, right, and midpoint evaluation points.
| Strand |
Source |
| Definite Integral |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.4.4
The learner will be able to
understand the Fundamental Theorem of Calculus: Interpret a definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval, that is f'(x)dx = f(b) - f(a).
| Strand |
Source |
| Definite Integral |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.4.3
The learner will be able to
interpret a definite integral as a limit of Riemann Sums.
Example: Find the values of the Riemann Sums over the interval [0, 3] using 12, 24, etc., subintervals of equal width for f(x) = x2 evaluated at the midpoint of each subinterval. Find the limit of the Riemann Sums.
.
| Strand |
Source |
| Definite Integral |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.4.5
The learner will be able to
use the Fundamental Theorem of Calculus to evaluate definite and indefinite integrals and to represent particular antiderivatives. Perform analytical and graphical analysis of functions so defined.
| Strand |
Source |
| Definite Integral |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.4.6
The learner will be able to
understand and use these properties of definite integrals.
| Strand |
Source |
| Definite Integral |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.4.7
The learner will be able to
understand and use integration by substitution (or change of variable) to find values of integrals.
| Strand |
Source |
| Definite Integral |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.4.8
The learner will be able to
understand and use Riemann Sums, the Trapezoidal Rule, and technology to approximate definite integrals of functions represented algebraically, geometrically, and by tables of values.
| Strand |
Source |
| Definite Integral |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
Applications of Integration
The learner will be able to
find velocity functions and position functions from their derivatives, solve separable differential equations, and use definite integrals to find areas and volumes.
| Strand |
Source |
| Integration |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.5.1
The learner will be able to
find specific antiderivatives using initial conditions, including finding velocity functions from acceleration functions, finding position functions from velocity functions, and applications to motion along a line.
Example: A bead on a wire moves so that its velocity, after t seconds, is given by v(t) = 3 cos 3t. Given that it starts 2 cm to the left of the midpoint of the wire, find its position after 5 seconds.
.
| Strand |
Source |
| Derivatives/Antiderivatives |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.5.2
The learner will be able to
solve separable differential equations and use them in modeling.
| Strand |
Source |
| Integration |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.5.3
The learner will be able to
solve differential equations of the form y' = ky as applied to growth and decay problems.
Example: The amount of a certain radioactive material was 10 kg a year ago. The amount is now 9 kg. When will it be reduced to 1 kg? Explain your answer.
.
| Strand |
Source |
| Integration |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.5.4
The learner will be able to
use definite integrals to find the area between a curve and the x-axis, or between two curves.
| Strand |
Source |
| Integration |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.5.5
The learner will be able to
use definite integrals to find the average value of a function over a closed interval.
| Strand |
Source |
| Integration |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.5.6
The learner will be able to
use definite integrals to find the volume of a solid with known cross-sectional area.
Example: A cone with its vertex at the origin lies symmetrically along the x-axis. The base of the cone is at x = 5 and the base radius is 7. Use integration to find the volume of the cone.
.
| Strand |
Source |
| Integration |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
C.5.7
The learner will be able to
apply integration to model and solve problems in physics, biology, economics, etc., using the integral as a rate of change to give accumulated change and using the method of setting up an approximating Riemann Sum and representing its limit as a definite integral.
Example: Find the amount of work done by a variable force.
.
| Strand |
Source |
| Integration |
IDOE |
| |
Unit Instructional Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
| |
Unit Assessment Resources |
| |
| · |
Calculus of a Single Variable, Houghton-Mifflin (McDougall-Littell) (Larson), Mathematics Book Adoption [Textbook]. |
|
|
|
