20804229Math Analysis
Course Information
Description
This course covers skills needed for success in Calculus and many application areas at the baccalaureate level. Algebra topics include the real and complex number systems, polynomials, exponents, radicals, solving equations and inequalities, relations and functions, systems of equations and inequalities, graphing, and conic sections. Trigonometry topics include the unit circle, trigonometric functions, graphs, identities, equations, inverse functions, solutions of triangles, complex numbers, polar coordinates, and vectors.
Total Credits
5
Course Competencies
  1. Analyze the features of a graph of a given function or relation
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    differentiate between symmetry about the x-axis, the y-axis, and the origin
    determine the domain and range of a relation or function
    determine the inverse function of a 1-1 function
    specify the relation between the domain and the range of a function and its inverse
    apply basic transformations to the elementary functions
    differentiate among elementary functions

  2. Solve linear and quadratic equations and inequalities
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    relate the solution of an equation to the x-intercept of a graph of the function and to the root (or zero) of the function
    use appropriate notation when writing solutions of inequalities
    solve quadratic equations using more than one method
    use modeling techniques to solve applied problems

  3. Analyze the properties of linear and quadratic functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    graph quadratic functions
    determine the composition of two functions
    create new functions by using function operations
    apply transformations as compositions of functions
    determine the characteristics of a quadratic function
    find zeros of quadratic functions algebraically and graphically
    convert between standard and vertex form of a quadratic function

  4. Analyze polynomials
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    find zeros of polynomial functions
    determine whether a function is increasing or decreasing on an interval
    determine the end-behavior of a polynomial function
    use graphical methods to estimate the roots of a polynomial equation
    identify local and global extrema
    apply the intermediate value theorem
    determine the number of roots of a polynomial equation using the fundamental theorem of algebra
    determine the number of roots of a polynomial function using the fundamental theorem of algebra
    determine all solutions to polynomial equations including complex solutions

  5. Analyze rational functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    identify removable discontinuities
    graph rational functions
    perform arithmetic operations with rational expressions
    determine the domain of rational functions
    determine all asymptotes
    solve rational equations

  6. Analyze radical functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    solve radical equations
    graph radical functions
    verify solutions to identify extraneous roots
    determine the domain of radical expression

  7. Analyze exponential and logarithmic functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    define the exponential function with an arbitrary base
    graph an exponential function with an arbitrary base
    model exponential functions to real life applications
    solve exponential equations
    define logarithmic functions with an arbitrary base
    identify the inverse relationship between the logarithmic function and the exponential function
    graph a logarithmic function with an arbitrary base
    solve logarithmic equations

  8. Solve algebraic systems
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    solve nonlinear systems of equations
    solve systems of linear equations in three or more variables
    use systems of three equations to solve applied problems
    graph systems of linear inequalities
    graph systems of nonlinear equations

  9. Analyze conic sections
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    identify all conic sections based on a graph
    identify all conic sections based on an equation
    analyze the characteristics of all conic sections
    sketch the graph of all conic sections given their equations

  10. Analyze trigonometric functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    graph angles in standard position given degree measure
    solve problems involving special right triangles
    use reference angles to find exact values of trigonometric functions in any quadrant
    find the exact value of a trigonometric function given a point on the terminal side of an angle
    find the exact value of a trigonometric function given a right triangle
    use reciprocal identities
    use quotient identities
    use Pythagorean identities
    use even-odd identities
    use cofunction identities

  11. Evaluate the trigonometric functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    identify exact values of trigonometric functions
    find approximate values of trigonometric functions using a calculator
    solve right triangles using inverse trigonometric functions
    solve right triangles using trigonometric functions

  12. Apply the unit circle and radian measure
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use the concept of a reference angle
    graph angles in standard position givenradian measure
    relate radian measures to real numbers
    convert between radian measures anddegree measures of angles
    find exact and approximate values of trigonometric functions given in radian measure
    analyze the unit circle

  13. Analyze graphs of trigonometric functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    sketch graphs of basic trigonometric functions
    apply transformations to the graphs of trigonometric functions
    identify domains and ranges given trigonometric functions
    identify domains and ranges given graphs of trigonometric functions
    find equations from graphs of trigonometric functions

  14. Analyze inverse trigonometric functions
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    define the inverse trigonometric functions
    identify domains and ranges of inverse trigonometric functions
    evaluate the inverse trigonometric functions
    evaluate the composition of trigonometric and inverse trigonometric functions

  15. Manipulate trigonometric identities
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use identities to evaluate trigonometric functions
    use trigonometric identities to verify other identities
    apply sum and difference identities
    apply double-angle and half-angle identities
    apply sum-to-product and product-to-sum identities

  16. Solve trigonometric equations
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    solve equations involving trigonometric expressions of a single angle
    solve equations involving trigonometric expressions of multiple angles
    use correct notation to express infinite and finite solution sets of trigonometric equations

  17. Solve oblique triangles
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    use the Law of Sines to solve oblique triangles
    use the Law of Cosines to solve oblique triangles
    solve application problems involving oblique triangles

  18. Complete vector operations
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    define a vector
    define unit vectors i and j
    identify the horizontal and vertical components of a vector
    find the magnitude of a vector
    find the direction of a vector
    perform vector addition
    perform scalar multiplication of vectors
    compute dot product of vectors
    determine if two vectors are perpendicular
    find the angle measure between two vectors

  19. Complete operations with complex numbers in trigonometric form
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    convert complex numbers between rectangular form and trigonometric form
    graph complex numbers in trigonometric form and rectangular form
    find products of complex numbers written in trigonometric form
    find quotients of complex numbers written in trigonometric form

  20. Analyze the polar coordinate system
    Assessment Strategies
    Oral, Written, Graphic and/or Skill Assessment
    Criteria
    identify points in the polar coordinate system
    translate between rectangular coordinates and polar coordinates for a given point
    convert an equation between polar form and rectangular form
    explore graphs of equations in polar form