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Jefferson County Schools |
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Jefferson County K-12 Curriculum |
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Mathematics - Calculus |
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Operations: Develop/Proficiency
The learner will be able to
develop proficiency in operations with real numbers, vectors, and matrices, by applying mental math or paper and pencil computations for simple problems, and by applying technology for the more complex problems.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Operations |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard |
Classroom
Home
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Rates: Estimate/Interpret
The learner will be able to
estimate and interpret rates of change using graphical and numerical data.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Rates |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Symbols: Manipulation
The learner will be able to
assess the meaning, usefulness, and reasonableness of the results of symbol manipulations, including those performed using technology.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Symbols |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Operations: Relationships
The learner will be able to
comprehend the relationships among operations.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Operations |
Comprehension |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard |
Classroom
Home
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Algebraic Concepts: Symbolism/Apply
The learner will be able to
apply algebraic symbolism as a tool to represent mathematical relationships.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Algebraic Concepts |
Application |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Algebraic Concepts: Apply/Symbolism
The learner will be able to
apply algebraic symbolism as a tool to describe mathematical relationships.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Algebraic Concepts |
Application |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Rate: Change
The learner will be able to
illustrate rates of change, including associated rates problems.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Rates |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Computation: Fluency
The learner will be able to
compute fluently.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Computation |
Application |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard |
Classroom
Home
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Computations: Assess/Reasonableness
The learner will be able to
assess the reasonableness of numerical computations.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Computation |
Evaluation |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard |
Classroom
Home
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Computations: Assess/Reasonableness
The learner will be able to
assess the reasonableness of the results of numerical computations.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Computation |
Evaluation |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard |
Classroom
Home
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Calculus and Pre-Calculus
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Curves: Study
The learner will be able to
study curves applying the notions of monotonicity and concavity; optimization, both absolute and relative extrema.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Curve Sketching |
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Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Definite Integral: Riemann Sum
The learner will be able to
apply Riemann sums and the Trapezoidal Rule to estimate definite integrals of functions illustrated algebraically, geometrically, and by tables of values.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Definite Integral |
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Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 51 |
Classroom
Home
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Matrices/Vectors: Comprehension
The learner will be able to
build a comprehension of the properties of, and representations for, the addition and multiplication of vectors and matrices.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Matrices |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard |
Classroom
Home
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Calculus Concepts: Differentiability
The learner will be able to
describe the relationship between differentiability and continuity.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Applying Calculus Concepts |
Comprehension |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Calculus Concepts: Antidifferentiation
The learner will be able to
apply strategies of antidifferentiation.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Applying Calculus Concepts |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 51 |
Classroom
Home
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Definite Integral: Riemann Sums
The learner will be able to
describe the relationship between a Riemann sum and a definite integral.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Definite Integral |
Comprehension |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Definite Integral: Fundamental Theorems
The learner will be able to
evaluate definite integrals by applying the Fundamental Theorem of calculus.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Definite Integral |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Definite Integral: Use
The learner will be able to
use the basic properties of definite integrals.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Definite Integral |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Differential Equation: Separable
The learner will be able to
apply separable differential equations in modeling.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Differential Equations |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 51 |
Classroom
Home
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Derivatives: Define
The learner will be able to
give the definition of the derivative as the limit of the difference quotient.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Knowledge |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Derivatives: Describe
The learner will be able to
describe the relationship of increasing and decreasing behavior of functions and the sign of first order derivatives.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Comprehension |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Derivatives: Describe
The learner will be able to
describe corresponding attributes of graphs of functions, first order and/or second order derivatives.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Comprehension |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p.50 |
Classroom
Home
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Derivatives: Mean Value Theorem
The learner will be able to
illustrate an understanding of the Mean Value Theorem and its geometric consequence.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Comprehension |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Derivatives: Concavity
The learner will be able to
describe the relationship of the concavity of functions and the sign of a second order derivative.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Comprehension |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Derivatives: Basic Rules
The learner will be able to
use basic rules for the derivative of basic functions and their sum, product, and quotient.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Derivatives: Translate
The learner will be able to
make verbal descriptions into equations involving derivatives and vice versa.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Derivatives: Points of Inflection
The learner will be able to
determine points of inflections.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Derivatives: Implicit Differentiation
The learner will be able to
apply the concept of implicit differentiation to determine the derivative of an inverse function.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Antiderivatives: Determine
The learner will be able to
determine specific antiderivatives applying initial conditions including applications to motion along a line.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 51 |
Classroom
Home
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Derivatives: Rate of Change
The learner will be able to
make an interpretation of the derivative as an instantaneous rate of change.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Analysis |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49 |
Classroom
Home
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Derivatives: Interpret
The learner will be able to
interpret the derivative as a rate of change in many different applied contexts.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Analysis |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Complex Numbers: Comprehend/Solutions
The learner will be able to
comprehend complex numbers as solutions to quadratic equations that do not have real solutions.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Complex Numbers |
Comprehension |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard |
Classroom
Home
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Limits: Algebraic
The learner will be able to
calculate limits applying algebra.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Limits |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49 |
Classroom
Home
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Limits: Approximate/Graphs/Tables
The learner will be able to
approximate limits from graphs or tables of data.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Limits |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49 |
Classroom
Home
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Matrices: Comprehend/Real Numbers
The learner will be able to
comprehend matrices as systems that have some of the properties of the real number system.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Matrices |
Comprehension |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard |
Classroom
Home
|
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Vectors: Comprehend/Real Numbers
The learner will be able to
comprehend vectors as systems that have some of the properties of the real number system.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Vectors |
Comprehension |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Number and Operations Standard |
Classroom
Home
|
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Differentiation: Chain/Implicit
The learner will be able to
apply the chain rule and implicit differentiation.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Differentiation |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 50 |
Classroom
Home
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Scatterplots: Understand
The learner will be able to
understand scatterplots.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Scatterplots |
Comprehension |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard |
Classroom
Home
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Scatterplots: Create
The learner will be able to
create a scatterplot to display data.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Scatterplots |
Synthesis |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Data Analysis and Probability Standard |
Classroom
Home
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Recursion/Iteration: Apply/Relationships
The learner will be able to
apply symbolic expressions, including iterative and recursive forms, to illustrate relationships that come from various scenarios.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Recursion |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Functions/Relations: Comprehend
The learner will be able to
comprehend relations and functions and choose, proficiently perform conversions, and use different representations of them.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Functions/Relations |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Function/Relation: Apply/Representation
The learner will be able to
apply many different symbolic representations, including recursive and parametric equations, for functions and relations.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Functions/Relations |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Exploring: Graphs/Technology
The learner will be able to
study the graphs of polynomial, rational, radical, and transcendental functions applying suitable technology.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Exploring |
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Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49 |
Classroom
Home
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Functions: Comprehend/Compare
The learner will be able to
comprehend and make comparisons of the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Functions |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Functions: Apply/Explicit and Recursive
The learner will be able to
apply explicitly and recursively defined functions in order to generalize patterns.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Functions |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Functions: Comprehend/Apply
The learner will be able to
comprehend and apply transformations (such as arithmetically combining, composing, and inverting commonly used functions) by applying technology to perform such operations on more complex symbolic expressions.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Functions |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Functions: Predict/Describe
The learner will be able to
predict and describe the observed local and global behavior of a function.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Functions |
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Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49 |
Classroom
Home
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Functional Relationships: Recognize
The learner will be able to
recognize essential quantitative relationships in a scenario and find the class or classes of functions that might model the relationships.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Functional Relationships |
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Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Derivatives: Illustrate
The learner will be able to
illustrate the idea of the derivative geometrically, numerically, and analytically.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49 |
Classroom
Home
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Graphing: Understand/Asymptotes
The learner will be able to
illustrate an understanding of asymptotes in terms of graphical behavior.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Graphing Functions |
Application |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49 |
Classroom
Home
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Exploring: Study/1 Variable Functions
The learner will be able to
study functions of one variable by exploring rates of change, intercepts, zeros, asymptotes, and local and global behavior.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Exploring |
Analysis |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
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Representations: Interpret
The learner will be able to
make interpretations of representations of functions of two variables.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Representations of Functions |
Analysis |
Master |
National Council of Teachers of Mathematics (NCTM), 2000, Grade 12, Algebra Standard |
Classroom
Home
|
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Limits: Continuity
The learner will be able to
illustrate a comprehension of continuity in terms of limits.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Limits |
Comprehension |
Master |
TN: Curriculum Framework (9-12), January 30, 1998, Calculus, p. 49 |
Classroom
Home
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Limits: Explain/Asymptotic
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