Mathematics and Technical Foundation Skills Courses

Engineering Technology Orientation, Part 1

Course #: 062002
Duration: 10 hours
What Students Learn: Preview
This study unit will provide a detailed discussion of the working engineer's and technician's reponsibilities and opportunities. Trainees will be able to use this information to start mapping out a plan for success in engineering for advancement in a rewarding career.

Objectives
When a student completes this study unit, he and she will be able to:

Recognize the impact engineers and technology have had on our lives.

Understand the general tasks technicians perform in the workplace.

Recognize why the ability to work well with teams is important to technicians.

Appreciate the importance of organization to both the engineering student and the working technician.

Contents
Engineering Technology: Engineering's Effect on History; Iron Age and the development of Steel; Steam Power and the launch of the Transportation Age; Electricity; Flight and Space; Technology's impact on the world; The Technician Today; Tools for Success: Teamwork and the ability to communicate; Solving Problems analytically; The Problem-Solving process; Defining the Root Problem; Identifying, Evaluating and Selecting the best solutions; Implementing the Solution and checking the results. Mathematically Thinking: Angles, Vectors, and Trigonometry; Statistically Speaking; Using Calculators and Computers; Units, Standards and Conversions; Using Units to solve problems accurately.

Special Notes:

This updated course replaces, Engineering Orientation, Part 1, course 4102A.

The entire course consists of study units 062002 and 062003.

Engineering Technology Orientation, Part 2

Course #: 062003
Duration: 10 hours
What Students Learn: Preview
This study unit introduces the common benefits to most careers in the engineering technologies. The concept of data is explained. Students will learn why data collection and interpretation are important to all technicians. The course will cover how engineering technicians support businesses in their continuous drive to improve quality, productivity and customer satisfaction. It covers the job responsibilities of engineering technicians in different types of businesses. Finally, it discusses how obtaining a degree in engineering technology will improve your career opportunities.

Objectives

Explain how a technician gathers data.

Explain how and why technicians use data.

Explain why the work of engineering technicians contribute to the competitiveness of a business.

Describe the job responsibilities of an engineering technician.

List some of the main industries that employ engineering technicians.

Contents
Introduction: Types of Data; Accuracy; Data Collection and Graphing; Creating Charts and Graphs; The Computer's Role in data collection and interpretation; Engineering Technician's Meeting the Needs of Industry: Competition and Productivity; Quality and the Engineering Technician; The Working Technician: Manufacturing Technology; Construction Manufacturing Technology; Civil Engineering; Electrical Engineering; Electronics Engineering; Industrial Engineering; Mechanical Engineering; Chemical Engineering: Specialists in the Product Development Cycle; The Value of getting a Degree.

Special Notes:

This new course replaces, Engineering Orientation, Part 2, course 4102B.

The entire course consists of study units 062002 and 062003.

Basic Industrial Math

Course #: Block X21
Duration: 30 hours
What Students Learn: This module of six study units offers the trainee arithmetic and basic mathematics, metric measurement, and calculator fundamentals. The Metric System is an introductory unit which includes metric conversions. Problem exercises and examples in this module are presented in on-the-job scenarios with applications drawn from the industrial context.
Components: Addition and Subtraction (186008); Multiplication and Division (186009); Fractions, Percents, Proportions, and Angles (186010); Metric System (186011); Formulas (186012); Introduction to Algebra (186013);
Special Notes: This updated course replaces lessons contained within Practical Math and Measurements, Block X01. Each study unit contains a progress examination.

Addition and Subtraction

Course #: 186008
Duration: 5 hours
What Students Learn:

Define the terms: whole number, numeral, digit, decimal, place value, addend, sum, minuend, subtrahend, and difference.
Explain the significance of the digit zero in a number.
Differentiate between concrete and abstract numbers.
Properly prepare numbers for addition and subtraction.
Perform addition and subtraction on numbers.
How to check your answers to both addition and subtraction problems.
How to use a calculator to add and subtract numbers.

Multiplication and Division

Course #: 186009
Duration: 5 hours
What Students Learn:

Define the terms: factor, multiplicand, multiplier, partial product, dividend, divisor, quotient, and remainder.

Recognize the various signs used for multiplication and division.

Properly prepare numbers for multiplication and division.

Perform multiplication and division on whole numbers and decimals.

How to check your answers to both multiplication and division problems.

How to find the average of a group of numbers.

How to use a calculator to multiply and divide numbers.

Fractions, Percents, Proportions, and Angles

Course #: 186010
Duration: 5 hours
What Students Learn:

Define the terms: fraction, proper fraction, improper fraction, lowest common denominator, percent, ratio, and proportion.

How to add, subtract, multiply, and divide fractions and decimals.

How to change fractions to decimals and decimals to fractions.

Solve problems involving percent.

How to use a protractor to measure angles.

Lay out templates for checking angles.

How to use a calculator to solve percent problems and to convert fractions to decimals.

Metric System

Course #: 186011
Duration: 5 hours
What Students Learn:

Name the base units most commonly used in the metric system.

Identify metric prefixes and their values.

Apply conversion factors to increase or decrease metric base units.

Estimate lengths in metric units.

Express temperature in degrees Celsius.

Define the terms: mass, density, force, torque, and pressure. Identify the metric units used to measure each one.

How to use a calculator to convert one metric unit to another.

Formulas

Course #: 186012
Duration: 5 hours
What Students Learn:

Explain the use of letters in formulas.

Prepare and use formulas to solve problems.

The use of formulas to calculate the perimeter of a triangle and rectangle, distance, area of a triangle, rectangle, and circle, volume of a pyramid, current in a circuit, and volume of a sphere.

How to use a calculator to find square root and solve formulas.

Transform and solve an equation.

Perform basic arithmetic operations with signed terms.

Substitute given numerical values for letters in a formula and find the unknown quantity.

Special Notes: This updated course replaces 2468.

Introduction to Algebra

Course #: 186013
Duration: 5 hours
What Students Learn:

Define the terms: term, constant, coefficient, exponent, monomial, trinomial, and polynomial.

Identify and combine like terms in an expression.

Multiply and divide terms containing exponents.

Remove parentheses from an expression and simplify the expression.

Perform basic arithmetic operations with signed terms.

Introduction to Algebra, Geometry, and Trigonometry

Course #: Block X02
Duration: 72 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn: This twelve lesson block is for those trainees requiring more advanced math subjects. The subject of algebra is covered in detail and the subjects of geometry and trigonometry are introduced in a practical manner.
Because math skills vary widely, a placement test is available to determine the trainee's specific knowledge of the various areas. Test X0250: Introduction to Algebra, Geometry, and Trigonometry is divided into four sections: lessons X0201 through X0204; lessons X0205 through X0208; lessons X0209 through X0210; and lessons X0211 and X0212.
Components: Algebra: Monomials and Polynomials (X0201); Algebra: Factoring (X0202); Algebra: Addition and Subtraction of Fractions (X0203); Algebra: Multiplication and Division of Fractions (X0204); Algebra: Linear Equations (X0205); Algebra: Simultaneous Linear Equations (X0206); Algebra: Determinants (X0207); Algebra: Quadratic Equations (X0208); Algebra: Exponents (X0209); Algebra: Radicals and Imaginary Numbers (X0210); Applied Geometry (X0211); Practical Trigonometry (X0212); Progress Examination Booklet (X0220); Progress Examination (X0221); Progress Examination (X0222); Progress Examination (X0223); Progress Examination (X0224); Placement Test: Introduction to Algebra, Geometry, and Trigonometry (X0250);

Algebra: Monomials and Polynomials

Course #: X0201
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Remove grouping symbols from algebraic expressions, dividing by a monomial when indicated.

Multiply binomials by monomials, trinomials, and other inomials.

Calculate the square root and the third power of given monomials.

Find special products involving binomials.

Divide one polynomial by another polynomial of lower degree.

Algebra: Factoring

Course #: X0202
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Find the prime factors of certain binomials and trinomials.

Factor a given trinomial.

Use the Factor Theorem to factor a given polynomial.

Use factoring to find the roots of an equation.

Divide one polynomial by another polynomial of lower degree.

Find the lowest common multiple of several polynomials.

Algebra: Addition and Subtraction of Fractions

Course #: X0203
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Recognize equivalent algebraic fractions.

Perform additions and subtractions involving algebraic fractions.

Reduce an algebraic fraction to its lowest terms.

Find the least common denominator for a group of algebraic fractions.

Algebra: Multiplication and Division of Fractions

Course #: X0204
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Perform multiplications and divisions involving algebraic fractions.

Reduce an algebraic fraction to its lowest terms.

Find the least common denominator for a group of algebraic fractions.

Solve equations involving fractions or decimals.

Simplify complex fractions.

Algebra: Linear Equations

Course #: X0205
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Recognize equations expressing mixture problems and other word problems.

Solve number problems, digit problems, and age problems.

Recognize the graph of a linear equation, given the graph or a set of points.

Algebra: Simultaneous Linear Equations

Course #: X0206
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Recognize essential steps in the solving of simultaneous linear equations by addition, subtraction, comparison, graphing, and clearing of fractions.

Identify the classification of a system of equations.

Solve a system of linear equations.

Solve interest problems, lever problems, and work-sharing problems.

Algebra: Determinants

Course #: X0207
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Evaluate a second-order determinant and expand a third-order determinant.

Recognize the standard form to be used in solving simultaneous equations by determinants.

Recognize determinants that represent the solutions of simultaneous equations in two or three unknowns.

Algebra: Quadratic Equations

Course #: X0208
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Recognize the graphical solution of two equations.

Solve and recognize steps in the solution of systems of quadratic equations and systems of a quadratic and linear equation.

Solve a fourth-degree polynomial equation in quadratic form.

Use the quadratic formula to solve a quadratic equation, calculate the discriminant of a quadratic equation, and point out what can be known from a given discriminant.

Write a quadratic equation which has given roots.

Solve word problems involving quadratic equations.

Algebra: Exponents

Course #: X0209
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Demonstrate an understanding of the meaning of a fractional exponent.

Apply the rules for positive and negative exponents in multiplication, division, and raising to powers.

Use radicals to convert fractional exponents and use fractional exponents to convert radicals.

Write a given number in standard form.

Algebra: Radicals and Imaginary Numbers

Course #: X0210
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Simplify several radicals and then add like terms.

Rationalize the denominator of a fraction and eliminate an imaginary number from the denominator of a fraction.

Solve an equation containing several square roots.

Multiply, divide, and raise to powers terms containing radicals.

Applied Geometry

Course #: X0211
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Recognize characteristics of angles and closed plane figures.

Distinguish between common geometric solids.

Apply the Pythagorean theorem.

Calculate perimeters and areas of a polygon, circle, and ellipse.

Apply the formula for area and volume of geometric solids.

Practical Trigonometry

Course #: X0212
Duration: 6 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn:

Define trigonometric functions.

Use trigonometric tables and apply interpolation.

Solve right triangles.

Apply the laws of sines and cosines in solving oblique triangles.

Logarithms

Course #: 5254
Duration: 10 hours
Course Prerequisites: Basic Industrial Math (Block X21); Practical Measurements (Block X22);
What Students Learn: Table of Common Logarithms; Table of Useful Numbers; Exponents; Logarithms of Numbers; Determination of Characteristics of a Logarithm; Determination of Mantissa of a Logarithm; Proportional Parts; Determination of Antilogarithms; Multiplication by Use of Logarithms; Division by Use of Logarithms; Finding Powers and Roots by Logarithms; Cologarithms; Hyperbolic Logarithms.

Practical Geometry

Course #: 5983A-B
Duration: 20 hours
Course Prerequisites: Introduction to Algebra, Geometry, and Trigonometry (Block X02);
What Students Learn: PART 1 (5983A). Points, Lines, Surfaces, and Angles; Perpendicular and Parallel Lines; Triangles; Quadrilaterals; Other Polygons.
PART 2 (5983B). The Circle; Arcs and Areas of Figures Bounded by Them; Solids; Areas and Volumes of Unusual Figures.

Special Notes: Covers subject at an advanced, in-depth level.

Plane Trigonometry

Course #: 2309A-B
Duration: 60 hours
Course Prerequisites: Practical Geometry (5983A-B); Introduction to Algebra, Geometry, and Trigonometry (Block X02);
What Students Learn: PART 1 (2309A). Solving a Triangle; Deriving Trigonometric Functions; Trigonometric and Geometric Identities; Values for the Trigonometric Functions; Using the Table of Natural Trigonometric Functions; Interpolation; Solving the Right Triangle; Solving the Right Triangle by Using Logarithms.
PART 2 (2309B). Angles and Their Measurement; Degrees and Radians; Rectangular Coordinates; The Trigonometric Formulas; Finding the Values of the Functions of Angles; Reduction Formulas; Solving the Oblique Triangle; Law of Tangents; Using Half-Angle Formulas; Area of a Triangle; Radius of an Inscribed Circle; Radius of a Circumscribed Circle.

Special Notes: Covers subject at an advanced, in-depth level.

Linear Surveying

Course #: 6670
Duration: 10 hours
Course Prerequisites: Plane Trigonometry (2309A-B); Logarithms (5254);
What Students Learn: Methods of Measurement; Tapes and Accessories; Description of Geodimeter and Tellurometer; Use of Tape; Adjustment of Taped Distances; Use of Geodimeter; Use of Tellurometer; Simple Field Problems; Survey of Tract with Tape.

Leveling

Course #: 6671
Duration: 10 hours
Course Prerequisites: Plane Trigonometry (2309A-B); Logarithms (5254); Introduction to Algebra, Geometry, and Trigonometry (Block X02);
What Students Learn: The Engineer's Level; Definitions; Construction of Levels; Setting Up Level; Leveling Rods; Reading the Rod; Operations of Direct Leveling; Forms for Level Notes; Precision in Leveling; Adjustments of Levels; Profiles; Barometric Leveling.

Transit Surveying

Course #: 5460A-C
Duration: 30 hours
Course Prerequisites: Linear Surveying (6670); Leveling (6671);
What Students Learn: PART 1 (5460A). Meridians; Magnetic Declination; Azimuth of Lines; Bearings of Lines; Angles Between Lines; The Engineer's Transit; Reading Vernier; Reading Compass; Optical-Reading Theodolites; Adjustments of a Transit.
PART 2 (5460B). Operations with Transit; Measurement of Direct Angles; Measurement of Deflection Angles; Details of Transit Surveys; Field Problems; Surveying by Triangulation; Trigonometric Leveling.
PART 3 (5460C). Computations involving Latitudes and Departures; Balancing Closed Traverses; Errors of Closure; Computation of Omitted Measurements; Plotting Traverse by Lengths and Directions of Courses; Plotting Traverse by Latitudes and Departures; Computation of Area; Problems on Partitioning Tracts of Land.

Drafting Kit

Course #: 1200M
Duration: 0 hours
What Students Learn: This drawing board includes a straight-edge rather than a separate T-square, a setup preferred by professionals. The drawing instruments are tools trainees will use on the job. The drafting outfit includes: one set of drawing instruments, one 18" x 24" drawing board/straight-edge combination, one 6" protractor, one 10" 300/600 triangle, one 8" 450 triangle, one 12" architect's scale, one 12" engineer's scale, one 300 mm metric scale, one irregular curve, one lettering guide, one erasing shield, one roll >" drafting tape, two mechanical pencils, two tubes of lead, one lead pointer, one pink eraser, and one pad 25 sheets of 15" x 20" transparent paper.

Special Notes: The Drafting Kit must be used for the study of all texts that teach drafting techniques, in which the trainee is required to prepare drawings or architectural plates. Refer to the special notes of the individual print course when this kit is required.

Geometrical Drawing

Course #: 5544A-B
Duration: 110 hours
What Students Learn: Geometrical Terms; Lines, Angles, Triangles, Quadrilaterals, Circles, Ellipse, and Parabola, Solids; Drawing Equipment: Paper, Drawing Board, T-Square, Triangles, Scales, Compasses, Dividers, Protractor, Irregular Curve and Drafting Machine; Ruling; Straight Lines; Care of Drawing Instruments; Protecting Drawings; Erasing; Styles of Lettering; Relative Widths and Spacing of Letters; Vertical Single-Stroke Lettering; Inclined Single-Stroke Lettering; Five Drawing Plates Consisting of 26 Problems.

Special Notes: Covers subject at an advanced, in-depth level.
Includes 5 plates, and requires drafting kit.

Topographic Surveying

Course #: 5461A-B
Duration: 20 hours
Course Prerequisites: Transit Surveying (5460A-C);
What Students Learn: PART 1 (5461A). Determination of Distances by Stadia; Instrument Constants; Formulas for Stadia Distances; Stadia Reduction Table; Beaman Stadia Arc; Field Operations in Stadia Work-Transit-Stadia Surveys for Locating Topography; Indirect Leveling by Stadia; Accuracy of Stadia Work.
PART 2 (5461B). Plane-Table Surveying; Locating Points from Plane Table; Plotting Position of Plane Table; Field Methods for Locating Topography; Accuracy of Plane-Table Work; Topographic Maps; Methods of Control; Locating Topography by Side-Shot Method; Locating Topography by Cross-Section Method.

Mapping

Course #: 5462A-B
Duration: 80 hours
Course Prerequisites: Geometrical Drawing (5544A-B); Practical Measurements (Block X22);
What Students Learn: PART 1 (5462A). Two Drawing Plates; Scale of Map; Azimuths and Bearings of Lines; Plotting Angles; Planning Maps' Locating Points on Traverses; Plotting Open Traverses; Plate 1801, Plotting Closed Traverses; Routes involving Circular Curves; Plate 1802, Plotting Route Centerlines.
PART 2 (5462B). Two Drawing Plates; Preparation of Topographic Maps; Conventional Symbols; Location of Contours; Plotting Topographic Details; Plate 1803, Topographic Symbols and Contours; Plotting Cross Sections and Profiles; City and Village Maps; Plate 1804, Map of a Portion of Southport; Laying of Tints.

Special Notes: Includes 4 plates and requires drafting kit.

Highway Curves

Course #: 6812A-B
Duration: 20 hours
Course Prerequisites: Transit Surveying (5460A-C);
What Students Learn: PART 1 (6812A). Elements of Highway Routes; Tangents and Horizontal Curves; Grades and Vertical Curves; Radius and Degree of Simple Curves; Procedure for Locating Points on Simple Curves; Measurement of Distances on Curves; Field Layout for Simple Curves; Special Problems Relating to Simple Curves; Problems on Relocation of Route.
PART 2 (6812B). Compound and Reverse Curves; Transition Curves; Superelevation on Curve; Spiral Curve; Deflection Angles for Spiral; Coordinates for Spiral; Minimum Length of Spiral; Field Layout of Spiral; Spiral Joining Two Curves; Vertical Parabolic Curves; Elevations on Vertical Curves.

Hydrographic Surveying

Course #: 5751
Duration: 10 hours
Course Prerequisites: Topographic Surveying (5461A-B);
What Students Learn: Preparatory Surveys; Control Surveys; Triangulation and Topography; Shore Stations; Control Buoys; Taking Soundings; Equipment for Measuring Depth; Locating and Observing Soundings; Plotting Soundings; Boat Sheet; Smooth Sheet; Volume of Body of Water; Adjustments of the Sextant.

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