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Elkhorn Public Schools |
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Math |
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Mathematics - AP Calculus |
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Equality/Inequality: Problem Solving
The learner will be able to
use and obtain solutions to problems involving equations and inequalities.
| Strand |
Scope |
Source |
| Equality/Inequality |
Reinforce |
NE: Standards, February 6, 1998, Grade 12, 12.6.2 |
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Problem Solving: Represent
The learner will be able to
illustrate a problem in a variety of formats.
| Strand |
Scope |
Source |
| Problem Solving |
Master |
NE: Standards, February 6, 1998, Grade 12, 12.6.4 |
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Algebraic Concepts: Analyze/Represent
The learner will be able to
study and illustrate, through calculator use, situations and number patterns by applying tables, graphs, and equations.
| Strand |
Scope |
Source |
| Algebraic Concepts |
Reinforce |
Elkhorn High School |
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Algebraic Concepts: Explain
The learner will be able to
explain the idea of unit rate, ratio, and slope in the context of rate of change.
| Strand |
Scope |
Source |
| Algebraic Concepts |
Master |
Elkhorn High School |
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Limits
The learner will be able to
calculate limits using algebra.
| Strand |
Scope |
Source |
| Problem Solving |
Master |
Elkhorn High School(a) |
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Exponential Growth/Decay: Real Life
The learner will be able to
identify the significance of exponential growth and decay to real life scenarios.
| Strand |
Scope |
Source |
| Algebraic Concepts |
Master |
NE: Standards, February 6, 1998, Grade 12, 12.6.4 |
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Functions: Recognize
The learner will be able to
recognize the attributes of families of functions.
| Strand |
Scope |
Source |
| Absolute Value |
Master |
NE: Standards, February 6, 1998, Grade 12, 12.6.4 |
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Functions: Apply/Solve
The learner will be able to
use and obtain solutions to problems applying functions.
| Strand |
Scope |
Source |
| Algebraic Concepts |
Reinforce |
NE: Standards, February 6, 1998, Grade 12, 12.6.4 |
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Problem Solving: Theoretical/Applied
The learner will be able to
apply numbers in equivalent forms, radicals, exponents, scientific notation, absolute values, fractions, decimals, percents, ratios and proportions, order of operations, and properties of real numbers to obtain solutions to theoretical and applied problems.
| Strand |
Scope |
Source |
| Algebraic Concepts |
Reinforce |
NE: Standards, February 6, 1998, Grade 12, 12.2.1 |
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Analyze graphs
The learner will be able to
analyze graphs to predict and to explain the behavior of a function.
| Strand |
Scope |
Source |
| Absolute Value |
Master |
Elkhorn High School(a) |
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Asymptotes
The learner will be able to
understand asymptotes in terms of graphical behavior.
| Strand |
Scope |
Source |
| Absolute Value |
Master |
Elkhorn High School(a) |
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Pattern: Apply/Solve
The learner will be able to
use and obtain solutions to problems applying patterns.
| Strand |
Scope |
Source |
| Patterns: Problem Solving |
Reinforce |
NE: Standards, February 6, 1998, Grade 12, 12.6.4 |
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Equivalent Forms: Express Numbers
The learner will be able to
convey the equivalent forms of numbers by applying exponents, radicals, scientific notation, absolute values, fractions, decimals, and percents.
| Strand |
Scope |
Source |
| Numeration |
Reinforce |
NE: Standards, February 6, 1998, Grade 12, 12.1.2 |
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Solutions: Justify Reasonableness
The learner will be able to
provide justification for the reasonableness of a solution.
| Strand |
Scope |
Source |
| Numeration |
Reinforce |
NE: Standards, February 6, 1998, Grade 12, 12.2.2 |
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Continuous Functions
The learner will be able to
use the MEAN Value Theorem and the Extreme Value Theorem to understand the graphs of continuous functions.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School(a) |
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Graph behavior
The learner will be able to
understand the relationship between the increasing and decreasing behavior of the function and the sign of its derivative.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School(a) |
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Limits: Estimate
The learner will be able to
estimate limits from graphs or tables of data.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn Public Schools.; NE: Standards, February 6, 1998, Grade 12, 12.5.2 |
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Derivatives: Concavity
The learner will be able to
apply derivatives to determine whether curves are concave or convex at a given point.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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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 |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Derivatives: Implicit Differentiation
The learner will be able to
apply the concept of implicit differentiation in many different problem types originating in a variety of curriculum areas.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Derivatives: Velocity/Acceleration/Speed
The learner will be able to
use derivatives in solving for velocity, acceleration, and speed.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Apply Calculus Concepts: Derivative
The learner will be able to
use the definition of derivative in situations involving average, instantaneous, and/or related rates of change.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Derivatives: Problem Solving
The learner will be able to
solve problems using derivatives and include tangent and normal lines to a curve, curve sketching, velocity, acceleration, related rates of change, differentials and linear approximations, and optimization problems.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Derivatives: Algebraic Functions
The learner will be able to
determine the higher order derivatives of algebraic, exponential, logarithmic, trigonometric, and inverse trigonometric functions.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Integration: Riemann Sums
The learner will be able to
determine the value of the Riemann Sum over a given interval.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Definite Integral: Riemann Sums
The learner will be able to
apply Riemann Sums and the Trapezoidal Rule to calculate an approximate value for a definite integral.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Definite Integral: Limit of Riemann Sums
The learner will be able to
rewrite definite integrals as the limit of Riemann Sums and vice-versa.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Definite Integral: Problem Solving
The learner will be able to
use the concept of definite integral to obtain solutions to problems including area between curves, volumes of solids of revolution about the axes or lines parallel to the axes using disc/washer and shell methods, and volumes of solids with known cross-sectional areas.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School.; NE: Standards, February 6, 1998, Grade 12, 12.4.1 |
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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 accumulated change of the quantity over the interval using the Fundamental Theorem of Calculus: the integral from a to b of f'(x)dx = f(b) - f(a).
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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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 |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Antiderivatives: Distance/Velocity
The learner will be able to
use antiderivatives in determining distance and velocity when acceleration and initial conditions are given.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Differential Equations: Solve
The learner will be able to
obtain solutions to separable differential equations and apply them as models.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn High School |
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Derivatives/Antiderivatives
The learner will be able to
learn the derivative defined as the limit of the difference quotient.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn Public Schools |
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Communication
The learner will be able to
demonstrate an understanding of the objectives of this course in oral and written form.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Reinforce |
Elkhorn High School.; NE: Standards, February 6, 1998, Grade 12, 12.2.2 |
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equations
The learner will be able to
use slope fields to determine a family of possible solutions for a differential equation.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn Public Schools(a) |
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equation 1
The learner will be able to
solve separable differential equations and use them in modeling.
| Strand |
Scope |
Source |
| Calculus/Trigonometry |
Master |
Elkhorn Public Schools(a) |
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Coordinate Geometry: Describe Objects
The learner will be able to
use coordinate geometry to explain objects algebraically.
| Strand |
Scope |
Source |
| Acute/Right/Obtuse Angles |
Master |
NE: Standards, February 6, 1998, Grade 12, 12.4.4 |
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