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Jefferson County Schools |
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Jefferson County K-12 Curriculum |
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Mathematics - Calculus AP |
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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 |
|
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 |
|
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 |
|
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 |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
Classroom
Home
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Connecting: Functions/Geometric/Analytic
The learner will be able to
understand the correlation between the geometric and analytic information of a function.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Connecting |
Comprehension |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB.; I |
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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Definite Integral: Rate of Change
The learner will be able to
determine the definite integral of the rate of change of a quantity over an interval as the change of the quantity over the interval: the integral from a to b of f'(x)dx = f(b) - f(a).
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Definite Integral |
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Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Definite Integral: Riemann Sums
The learner will be able to
compute the values of Riemann Sums over equal subdivisions applying left, right, and midpoint evaluation points.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Definite Integral |
|
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Definite Integral: Apply
The learner will be able to
apply integrals to illustrate concrete, social, or economic scenarios to include determining the area of a region and the distance traveled by a particle along a line.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Definite Integral |
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Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Integration: Understanding/Methods
The learner will be able to
apply an understanding of integration and methods of integration to obtain applied problem solutions.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Integration |
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Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Integration: Use/Model/Solve
The learner will be able to
use integration to model and obtain solutions to problems in other areas outside of mathematics applying the integral as a rate of change to give accumulated change and applying the method of setting up and approximating Riemann Sum and illustrating its limit as a definite integral.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Integration |
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Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Derivatives: Comprehend
The learner will be able to
comprehend the idea of the derivative geometrically, numerically, and analytically.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
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Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
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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Intermediate Value Theorem: Comprehend
The learner will be able to
comprehend the Intermediate Value Theorem on a function over a closed interval.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Applying Calculus Concepts |
Comprehension |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB.; I |
Classroom
Home
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Extreme Value Theorem: Comprehend
The learner will be able to
comprehend the Extreme Value Theorem.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Applying Calculus Concepts |
Comprehension |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB.; I |
Classroom
Home
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Applying: Fundamental Theorem
The learner will be able to
illustrate particular antiderivatives both graphically and analytically applying the Fundamental Theorem.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Applying Calculus Concepts |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Curves: Examine/Monotone/Concave
The learner will be able to
examine curves as well as the ideas of monotonicity and concavity of the curve.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Curve Sketching |
Analysis |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Definite Integral: Average Value
The learner will be able to
use concepts of the definite integral to calculate the average value of a function.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Definite Integral |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Definite Integral: Volume/Known Areas
The learner will be able to
use concepts of the definite integral to calculate the volume of a solid of revolution where the cross-sectional area is a known value.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Definite Integral |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Definite Integral: Interpret/Riemann
The learner will be able to
interpret the definite integral as the limit of Riemann Sums over subdivision of equal size.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Definite Integral |
Analysis |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Differential Equations: Solve
The learner will be able to
obtain solutions to separable differential equations.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Differential Equations |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Differential Equation: Solve
The learner will be able to
obtain solutions to differential equations of the form y' = ky as applied to growth and decay problems.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Differential Equations |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Integration: Substitution/Variables
The learner will be able to
integrate by substitution of variables, including substituting for the limits of integration in a definite integral.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Integration |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
Classroom
Home
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Derivatives: Comprehend
The learner will be able to
comprehend the relationship of the concavity of functions and the sign of the second order derivative.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Comprehension |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
Classroom
Home
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Derivatives: Basic Rules
The learner will be able to
apply the basic rules for the sum, difference, and product of functions.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
Classroom
Home
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Derivatives: Determine/Power Function
The learner will be able to
determine the derivative of a power function.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
Classroom
Home
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Derivatives: Inverse Trigonometric
The learner will be able to
calculate the derivatives of inverse trigonometric functions.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
Classroom
Home
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Derivative: Slope of a Curve/Point
The learner will be able to
determine the slope of a curve at a point, including points at which there are vertical tangents and no tangents.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
Classroom
Home
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Derivatives: Determine/Tangent
The learner will be able to
determine tangent lines to a curve at a point and a local linear approximation.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
Classroom
Home
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Derivatives: Determine
The learner will be able to
apply implicit differentiation to determine derivatives of inverse functions.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Application |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB, III |
Classroom
Home
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Derivatives: Compare
The learner will be able to
make comparisons of the corresponding attributes of the graphs of f, f', and f".
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Analysis |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
Classroom
Home
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Derivatives: Compare/Characteristics
The learner will be able to
compare the characteristics of the graphs of the function and the first derivative of the function.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Analysis |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
Classroom
Home
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Derivative: Interpret/Rate of Change
The learner will be able to
interpret the derivative as a rate of change in different applied contexts including velocity, speed, and acceleration.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Derivatives/Antiderivatives |
Analysis |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
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: Describe/Understanding
The learner will be able to
describe an understanding of the limiting process.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Limits |
Comprehension |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB.; I |
Classroom
Home
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Limits: Infinity
The learner will be able to
explain asymptotic behavior in terms of limits involving infinity.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Limits |
Comprehension |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB.; I |
Classroom
Home
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Limits: Comprehend/Rate of Change
The learner will be able to
comprehend instantaneous rate of change as the limit of average rate of change.
| Strand |
Bloom's |
Scope |
Source |
Activities |
| Limits |
Comprehension |
Master |
Advanced Placement Tests (AP), 2000, Calculus AB, II |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB.; I |
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 |
Advanced Placement Tests (AP), 2000, Calculus AB.; I |
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 ab | |
