20804228Calculus with Algebra and Trigonometry I
Course Information
Description
Designed for students of mathematics, science, and engineering. Reviews algebra and trigonometry topics including absolute values, inequalities, coordinates in the plane, linear equations, polynomials, exponent, radicals, simplification of algebraic expressions, functions, transformation of functions, radian measure, angles, trigonometric functions and their graphs, and trigonometric identities. Introduces basic properties of limits, rate of change of functions, continuity, derivatives of algebraic and trigonometric functions, their products quotients and compositions, implicit differentiation and related rate problems.
Total Credits
5
Course Competencies
  1. Apply the Fundamental Concepts of Algebra
    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 on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you apply laws of exponents (including rational exponents) to simplify expressions.
    you simplify radical expressions.
    you add, subtract, mulitply, and divide polynomials.
    you factor polynomials.
    you solve absolute value equations and inqualities.
    you find the distance between two points.
    you rewrite the equation of a circle in standard form.
    you identify the center and radius of a circle from the standard form of a circle.

  2. Demonstrate an Understanding of Functions and Their Graphs
    Assessment Strategies
    by completing and submitting for evaluation all in-class and take-home quizzes, tests, projects graded assignments, and take-home quizzes, tests, projects, graded assignments, and laboratory work with passing grades according to the grading scale contained in the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you determine the domain and the range of functions from the equation or graph.
    you apply the concepts of stretching and compressing (both horizontally and vertically), reflecting, or shifting a graph.
    you define and determine the composition of two functions (understanding that function composition is non-commutative).
    you determine whether a given equation or graph represents a one-to-one function.
    you determine the inverse function of a one-to-one function.
    you demonstrate an understanding of increasing and decreasing functions.
    you determine the equation of a linear function given a point and slope or two points.
    you find the equation of a linear function through a specified point that is parallel or perpendicular to a given linear function.
    you change the form of a quadrtic function to standard form.
    you determine the vertex of a quadratic function and determine whether it is a maxima or minima from the standard form.
    you find the sum, difference and product of rational functions.

  3. Demonstrate an Understanding of Limits and Their Calculations
    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 graded scale contained on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you demonstrate an understanding of limits.
    you calculate the limit of a function symbolically using limit laws.
    you verify that the answer to a limit calculation is consistent with graphical and numerical information.
    you demonstrate an understanding of the precise definition of limit.
    you identify and explore continuous functions.
    you determine the intervals for which a function is continuous both by intuitive and symbolic methods.
    you demonstrate the connection between the concept of continuity and the concept of limit.
    you demonstrate an understanding of the connection between limit calculations and the asymptotes of a graph.

  4. Demonstrate an Understanding of Functions and Their Derivatives
    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 graded scale contained on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you understand and apply the concept of rate of change of a function.
    you define and compute the derivative of a given function by methods which include symbolic manipulation.
    you compute and interpret a velocity function given its position function.
    you make inferences and connections between the graph of a function and its derivative.
    you determine the derivative as a limit.
    you check if the answer to a derivative is consistent with the information given.

  5. Calculate Derivatives of Non-transcendental 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 graded scale contained on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you compute symbolically the derivatives of polynomials.
    you compute symbolically the derivatives of rational functions.
    you compute symbolically the derivatives of power functions with rational exponents.
    you compute symbolically the derivatives of products of functions.
    you compute symbolically the derivatives of quotients of functions.
    you compute the derivatives of compositions of functions.
    you compute a derivative implicitly.
    you compute higher order derivatives.
    you find the tangent to a given function.
    you solve related rate problems in a variety of verbally stated application.
    you demonstrate the connection of the linear approximation and differential notion to the concept of derivatives.
    you approximate the roots of a function using Newton's method
    you demonstrate the connection between Newton's method and the linear approximation

  6. Demonstrate an Understanding of Trigonometric Functions and Their Graphs
    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 graded scale contained on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you convert between degrees and radians
    you calculate the length of a circular arc and the area of a sector.
    you evaluate the trigonometric functions for degree and radian measure.
    you understand and apply the right triangle definitions of trigonometric functions to solve triangles.
    you understand how to use and derive trigonometric identities.
    you can define the inverse trigonometric functions and identify their domain and ranges.
    you evaluate inverse trigonometric functions and compositons involving them.
    you apply the Law of Sines and Law of Cosines to solve triangles.
    you use trigonmetry to compute areas.
    you use addition, subtraction, half-angle, and double-angle identities to find the exact value of trigonometric functions.
    you solve trigonometric equations
    you graph trigonometric functions

  7. Calculate Limits and Derivatives Involving Trigonmetric 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 graded scale contained on the syllabus.
    by active participation in class discussions and activities.
    Criteria
    you evaluate limits involving trigonometric functions.
    you calculate derivatives involving trigonemetric functions.
    you compute a derivative involving a trigonometric function implicitly.
    you solve related rate problems involving trigonmetric functions in a variety of verbally stated applications.