10804115College Technical Mathematics 1
Course Information
Description
Topics include: solving linear, quadratic, and rational equations; graphing; formula rearrangement; solving systems of equations; percent; proportions; measurement systems; computational geometry; right and oblique triangle trigonometry; and operations on polynomials. Emphasis will be on the application of skills to technical problems. This course is the equivalent of successful completion of College Technical Mathematics 1A and College Technical Mathematics 1B.
Total Credits
5
Prior Learning Assessment
  • Exam-College Developed Challenge Exam
Course Competencies
  1. Perform basic operations with real numbers
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    perform the arithmetic operations in proper sequence
    simplify expressions using the laws of exponents
    evaluate numeric expressions containing exponents
    convert numbers between decimal notation and scientific and/or engineering notation·
    perform arithmetic operations with numbers in scientific notation
    calculate powers and roots with numbers in scientific notation
    express angles in radian, degree, or revolution measurement
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. show work in a clear and logical manner, verify the solution, solution is within stated range and reflects appropriate accuracy or precision, solution is labeled with appropriate units)

  2. Solve linear equations
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    solve linear equations in one variable
    rearrange a formula to solve for an indicated first-degree variable
    represent unknown(s) with a variable and translate English phrases into equations
    substitute given number for variables into formula or equation
    apply skill to technical problems
    utilize appropriate technology
    apply the process for solving technical problems according to the problem-solving criteria (i.e. 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. Solve problems using percent and proportion
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    perform conversions among fractions, decimals, and percent
    write an equation representing the problem
    solve the 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)

  4. Solve variation problems
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    identify the type of variation
    write the variation equation
    solve direct variation problems
    solve inverse variation problems
    solve joint and combined variation problems
    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. Perform operations on polynomials
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    add, subtract, multiply, and divide polynomials
    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. Factor algebraic expressions
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    factor using the greatest common factor
    factor binominals and trinominals
    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 quadratic equations over the set of real numbers
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    identify coefficients of a quadratic equation in standard form
    select appropriate method for solving second degree equations
    generate the equation which satisfies the conditions of the problem
    solve second degree equation using the selected method
    select relevant solution(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)

  8. Perform operations with rational expressions
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    add, subtract, multiply, and divide rational expressions
    apply skill to an applied technical problem
    simplify complex fractions
    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. Solve rational equations
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    apply multiplication property to clear all denominators
    solve equations
    identify extraneous 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)

  10. Graph algebraic functions
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    determine ordered pairs from a given graph
    differentiate a function from a relation
    utilize function notation
    identify range and domain of a given function
    graph linear and quadratic functions on the Cartesian plane
    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. Relate the equation of a line to its graph
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    calculate the distance between two points
    calculate the slope of a line given two points on the line
    determine the slope of a line parallel to a given line
    determine the slope of a line perpendicular to a given line
    write the equation of a line using the slope-intercept form, the point-slope form, or the two-point 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)

  12. Solve systems of equations
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    solve systems of two and three equations or formulas
    check all solutions in the system
    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. Convert units of measure
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    convert within SI (metric)
    convert within USCS (United States Customary System)
    convert between USCS and SI units
    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. Compute angle measures, length of sides, perimeter, and area of plane geometric figures
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    calculate the measure of the specified angle(s) of polygons
    calculate the circumference, perimeter, and area of plane figures including composite figures
    calculate a specified side of similar polygons
    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. Calculate surface area, volume, and weight/mass
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    calculate the surface area of solids
    calculate the volume of solids
    you identify the density of a given material
    calculate the weight/mass of a solid or liquid
    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)

  16. Solve right triangles
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    use the angle-sum principle to compute the third angle of a triangle
    use the Pythagorean Theorem to compute a side of a right triangle
    use sine, cosine, and tangent ratios to compute sides and/or angles of right triangles
    apply skill to technical problems such as vectors
    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)

  17. Solve oblique triangles
    Assessment Strategies
    in an oral, written, or graphic product
    Criteria
    use the Law of Cosines, Law of Sines, and right triangle methods when appropriate
    relate angle in standard position to its reference angle
    apply skill to technical problems such as vectors
    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)