Course Descriptions

GTM 105 - Applied Technical Mathematics

3 Credits, 3 Contact Hours
3 lecture periods 0 lab periods

Applied geometry and trigonometry. Includes a brief review of operations with integers; review of pre-algebra; systems of measurement; solving problems involving right- and oblique triangle trigonometry, perimeter, areas, surface areas, and volumes; and practical applications.

Prerequisite(s): Within the last three years: With a grade of C or better: ICS 081  or completion of module 15 in MAT 089A  or satisfactory score on the Mathematics assessment test.
Gen-Ed: Meets CTE - M&S.

1. Use ratios and proportions to solve application problems involving similar shapes, percentages, and conversion of measures between metric and US customary systems..
2.  Solve application problems using algebraic techniques such as solving linear equations and manipulating and evaluating formulas.
3. Apply angle measurement, right- and oblique-triangle trigonometry to solve application problems.      
4.  Calculate area and perimeter of polygons and circles, and volumes and surface areas of basic three-dimensional figures to solve application problems.
5. Apply concepts and techniques to practical math problems related to their specific subject areas     

A. Integer numbers

B. Fractions

C. Decimals Powers and square roots    

D. Ratios, proportions, ratios and percents

E. Dimensional analysis (includes Metric/US customary conversions) Order of operations

F.  Measurement      

1.Lengths and angles    

2. Reading of specialized instruments

II. Equations and Formulas

A. One- and two-step equations

B. Formulas

C. Application problems

III. Elements of Geometry

A. Angles

1. Practical application (e.g., perpendicularity)

2. Complement/supplement

3. Conversion (decimal degrees/degrees-minutes-seconds)

IV. Triangles and Circles

A.  Triangles

1.  Types

2.  Right triangle and Pythagorean Theorem

3.  Congruent and similar triangles

4.  Oblique triangles

B.  Circles

1.  Identifying parts

2.  Circle measurements

3.  Area

III.  Trigonometry 

A.  Right triangles

1.  Sine, cosine, and tangent

2.  Determining angles and sides

3.  Area and perimeter

VI. Plane Geometry

A.  Perimeter of polygons and circles

B.  Area of polygons and circles

V.  Solids

A.  Surface area of solids

B.  Volume of solids

VI. Program Specific Topics

A. Selected topics differentiated by programs (e.g., Cartesian plane and transformations, units of pressure, and Ohm’s Law).

GTM 105V - Applied Technical Mathematics for Aviation

3 Credits, 3 Contact Hours
3 lecture periods 0 lab periods

Applied geometry and trigonometry operations. Includes review of basic math operations, charts and graphs, review of pre-algebra, elements of geometry, plane trigonometry, and aviation practical applications.

Prerequisite(s): With a grade of C or better: ICS 081  or MAT 086 or completion of Module 15 in MAT 089A  or satisfactory score on the Mathematics assessment test.
Gen-Ed: Meets CTE - M&S.

1. Demonstrate proficiency performing basic math operations
2. Demonstrate proficiency performing power, root, and ratio calculations
3. Demonstrate proficiency performing area and volume calculations
4. Demonstrate proficiency performing aircraft weight and balance calculations

1. Review of Basic Math Operations (CLO 1, 2, 3, 8)
   1. Whole/signed numbers
      1. Add
      2. Subtract
      3. Multiply
      4. Divide
   2. Fractions
      1. Add
      2. Subtract
      3. Multiply
      4. Divide
   3. Decimals
      1. Add
      2. Subtract
      3. Multiply
      4. Divide
   4. Metric/English conversions
      1. Multiples and prefixes
      2. Conversion tables
   5. Proportions and ratios
      1. Aspect ratio
      2. Bonding adhesive mixture
      3. Proportion
   6. Formulas
   7. Percentages
      1. Determining a number which is a percentage of another
      2. Determining the percentage that one number is of another
      3. Finding the total number when part of the number and its percentage are known
   8. Aviation applications of basic math operations / weight and balance
      1. Terms and definitions
      2. Effective of CG to an aircraft
      3. Calculations
      4. Corrections
2. Charts and Graphs (CLO 7, 9)
   1. Pie charts
   2. Broken line graphs
   3. Bar graphs
   4. Continuous curve graphs
   5. Aviation applications of charts and graphs
3. Review of Pre-Algebra (CLO 4, 5)
   1. Order of operations
   2. Variables 
   3. Formulas
   4. Powers / raising a number to a given power
   5. Roots / extracting the root of a number
   6. Aviation applications of pre-algebra concepts / bend allowance
      1. Flat pattern layout
      2. Calculations
4. Elements of Geometry (CLO 6, 9)
   1. Angles
      1. Measurement
      2. Practical application
      3. Conversion
      4. Complement/supplement
   2. Measure of an area
      1. Area of a rectangle
      2. Areas of a square
      3. Area of a triangle
      4. Area of a parallelogram
      5. Area of a trapezoid
      6. Area of a circle
   3. Measure of volume
      1. Volume of a rectangle
      2. Volume of a cube
      3. Volume of a cylinder
      4. Volume of a sphere
   4. Triangles
      1. Types
      2. Pythagorean theorem
      3. Congruent
      4. Oblique
   5. Aviation applications of geometry
5. Plane Trigonometry (CLO 9)
   1. Right triangles
   2. Sine, cosine, and tangent
   3. Determining angles and sides
   4. Area and perimeter

Aviation applications of plane trigonometry