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Apply mathematical problem solving skills.
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate.
by active participation in class discussions and activities.
Criteria
the learner shows work in a clear and logical manner
the learner verifies a solution
the learner verifies that the solution is within the stated range and reflects appropriate accuracy or precision
the learner labels the solution with appropriate units
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Demonstrate knowledge of functions.
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate.
by active participation in class discussions and activities.
Criteria
the learner computes distance between two points in a plane
the learner identifies the components of a function: independent variable, dependent variable, domain, and range
the learner determines if a relation is a function
the learner computes the inverse of a function
the learner determines intervals over which a function is increasing, decreasing, or constant
the learner performs translations of functions
the learner graphs linear functions
the learner writes the equation of a linear function from given data
the learner solves quadratic functions
the learner graphis quadratic functions
the learner determines the extrema of a quadratic function
the learner determines the behavior of a polynomial function
the learner determines the location of the asymptotes of a rational function
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Demonstrate knowledge of limits and continuity.
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate.
by active participation in class discussions and activities.
Criteria
the learner completes all assignments, laboratories, quizzes and tests on limits and continuity
the learner computes limits
the learner knows and applies the rules for calculating limits
the learner determines when a limit goes to infinity
the learner determines limits at infinity
the learner knows the relationships between infinite limits and asymptotes
the learner knows what it means for a function to be continuous
the learner determines if a function is continuous
the learner demonstrates the connection between continuity and limits
the learner checks work for consistency with given information
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Analyze exponential and logarithmic functions - solve exponential and logarithmic equations.
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate.
by active participation in class discussions and activities.
Criteria
the learner completes all assignments, laboratories, quizzes, and tests on exponential and logarithmic functions
the learner defines base and exponent
the learner applies the laws of exponents
the learner defines and graphs the exponential functions
the learner applies exponential functions to such problems as exponential growth and decay, half-life, interest, annuities, and mortgages
the learner defines logarithmic functions with a variety of bases
the learner applies the laws of logarithms
the learner defines the common logarithmic function and the natural logarithmic function
the learner produces the graph of a logarithmic function
the learner evaluates logarithms using the change of base formula
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Determine the derivative of a function.
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate.
by active participation in class discussions and activities.
Criteria
the learner determines the slope of a secant line through a graph
the learner determines the slop of a tangent line at a point on a graph
the learner approximates derivatives from data using a difference formula
the learner knows the difference between average rate of change and instantaneous rate of change
the learner computes velocity, speed, and acceleration
the learner understands the relationship between the derivative and velocity and acceleration
the learner performs marginal analysis
the learner determines derivatives using the power rule
the learner determines derivatives of logarithmic functions
the learner determines derivatives of exponential functions
the learner uses differential equations as models for exponential growth and decay
the learner computes symbolically the derivative of polynomials, rational functions, and power functions with rational exponents
the learner computes the derivatives of products, quotients, and compositions of functions
the learner computes derivative implicitly
the learner computes higher order derivatives
the learner solves problems involving related rates
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Use derivatives to solve optimization problems.
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate.
by active participation in class discussions and activities.
Criteria
the learner determines critical values of a function using the first derivative test
the learner determines the extrema of a function
the learner determines points of inflection and concavity using the second derivative test
the learner uses analytic methods to sketch and interpret a graph of a function
the learner uses the extreme value theorem to determine extrema on an interval
the learner solves applied optimization problems
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Apply basic integration methods.
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate.
by active participation in class discussions and activities.
Criteria
the learner determines antiderivatives
the learner determines basic indefinite integrals
the learner solves initial value problems
the learner integrates using substitution
the learner integrates by parts
the learner by using the method of partial fractions
the learner determine definite integrals
the learner knows and applies the properties of the definite integral
the learner knows how to compute the area of a region as a sum of sub regions
the learner uses the fundamental Theorem of Calculus to integrate
the learner uses the integration to determine the total function given a marginal function
the learner determines the area between two functions
the learner determines the average value of a function
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Solve applied integration problems.
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate.
by active participation in class discussions and activities.
Criteria
the learner solves equilibrium problems
the learner determines present and future value of revenue streams
the learner solves separable differential equations
the learner solves problems involving the logistical growth
the learner computes improper integrals
the learner determines convergence of improper integrals
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Apply the method of calculus to functions of several variables.
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate.
by active participation in class discussions and activities.
Criteria
the learner generalizes the rectangular planar coordinate system into three dimensional space
the learner computes distance in three dimensional space
the learner determines if a surface is a function
the learner determines the equation of a plane in space
the learner computes symbolically the partial derivatives of multivariable functions
the learner computes the equation of a tangent plane to a surface in space
the learner solves applied problems involving partial derivatives
the learner analyzes multivariable functions for maxima and minima
the learner analyzes multivariable functions for saddle points
the learner models data using the method of least squares
the learner solves constrained optimization problems using Lagrangian multipliers
the learner tests for optimality of solutions in a constrained optimization problem
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Solve differential equations.
Assessment Strategies
by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
by demonstrating correct and accurate use of the scientific calculator on all assignments, quizzes, tests, projects, and laboratory work when appropriate.
by active participation in class discussions and activities.
Criteria
the learner recognizes a differential equation
the learner determines the order of a differential equation
the learner uses Euler's Method to approximate the solution of a differential equation
the learner determines the steady-state solution to a differential equation
the learner solves applied problems involving differential equations