10-804-116College Technical Math 2
Course Information
Description
Topics include: vectors; trigonometric functions and their graphs; identities; exponential and logarithmic functions and equations; radical equations; equations with rational exponents; dimension of a circle; velocity; sine and cosine graphs; complex numbers in polar and rectangular form; trigonometric equations; conic sections; and analysis of statistical data. Emphasis will be on the application of skills to technical problems.
Total Credits
4
Course Competencies
  1. Graph exponential and logarithmic functions
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    graph exponential functions
    graph logarithmic functions
    relate logarithmic functions to its inverse function
    graph functions on logarithmic or semi-logarithmic scales
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  2. Solve exponential and logarithmic equations
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    solve exponential equations
    solve logarithmic equations
    solve applied problems involving exponential or logarithmic equations, such as growth and decay
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  3. Perform operations with exponents and radicals
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    evaluate an expression containing rational powers on numbers with rational roots
    convert between rational powers and radical notation
    simplify radical expressions

  4. Solve equations with radicals and rational exponents
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    convert between radical and fractional exponent form
    solve radical equations involving one variable
    solve equations with fractional exponents
    verify solutions by substitution into the original equation
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  5. Use formulas involving radicals and exponents
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    choose formula when appropriate
    identify unknown value(s)
    relate the given values to the variables in the formula formed after given values are substituted into a formula that includes radical expressions
    transform a formula by isolating a variable which is contained in a radical expression
    solve equations formed after given values are substituted into a formula that includes radical expressions
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  6. Calculate unknown dimensions as related to a circle
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    calculate the length of a circular arc, given the radius and central angle
    calculate the central angle and the chord depth, given the radius and chord length of a circle
    calculate the area of a sector of a circle, given the radius and central angle
    calculate the area of a segment of a circle, given the radius, central angle, and area of sector to which the segment belongs
    calculate the length of a chord, given the radius and the angle between the chord and a tangent at one end of the chord
    calculate the angle between two tangents, given the radius of a circle and the length of the segments attached to the circle
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  7. Solve rotational, linear, and angular velocity problems
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    calculate the linear velocity of a point on the circumference of a wheel, given either the diameter or radius and the angular velocity
    calculate the angular velocity of a point on the circumference of a wheel when given either the diameter or radius and the linear velocity
    convert between radians over time and revolutions over time
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  8. Perform operations with vectors
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    determine the resultant of two or more vectors
    resolve vectors by components
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  9. Perform arithmetic operations using complex numbers in both polar and rectangular forms
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    add, subtract, multiply, and divide in rectangular form
    multiply and divide in polar form
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  10. Relate complex (rectangular) notation to polar notation
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    convert between polar and rectangular form
    use the quadratic equation to find non-real solutions
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  11. Interpret sine/cosine graphs
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    identify the amplitude from a sine or cosine wave graph
    identify the phase shift
    write the equation of a sine/cosine graph
    label amplitude, period, phase shift, and frequency for graph
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  12. Graph sine/cosine waves
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    plot a graph of sine/cosine wave from an equation
    plot a graph of sine/cosine wave given the amplitude, frequency, and phase shift
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  13. Solve trigonometric equations
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    manipulate identities
    factor trigonometric expressions
    write a trigonometric expression in terms of sine and cosine
    solve trigonometric equations with multiple solutions
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  14. Analyze the equations of conic sections and their graphs
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    determine, by inspection, whether a given second-degree equation represents a circle, ellipse, parabola, or hyperbola
    write the equation of a circle, ellipse, parabola, or hyperbola from given information
    construct a graph of any of the conic sections from equation(s)
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  15. Analyze data statistically
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    calculate measures of central tendency
    calculate measures of dispersion
    construct a graph that describes data
    interpret data in terms of statistics
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. you show work in a clear and logical manner, you verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)