# INTRODUCTION TO TECHNICAL MATHEMATICS

The purpose of this course is to develop an intuitive
feeling for mathematical methods without

emphasizing mathematical rigor. The graphing calculator is incorporated into the
study of algebra,

geometry, trigonometry, and graphing techniques to solve practical problems from
various technologies.

A comprehensive departmental final exam testing the degree of mastery of the
following course

objectives is required as well as proficiency in using a graphing calculator.

1. Approximate Numbers and Measurements

1.1 Review arithmetic involving decimals, fractions, and percents.

1.2 Perform arithmetic operations on approximate numbers and express the results
in the

proper accuracy or precision format.

1.3 Make reductions (changes) to units of measurement within the customary
system and

reductions to units of measurement within the metric system.

1.4 Make conversions between the customary and metric systems of measurement.

1.5 Apply the algebra of dimensional analysis to geometric problem solving.

1.6 Express measurements as a ratio in proper form.

2. Operations on Real Numbers

2.1 Review evaluating given expressions and formulas by applying the correct
priority of

operations.

3. Equation Solving Techniques

3.1 Review solving linear equations in one variable.

3.2 Review solving literal equations and formulas for a single variable.

3.3 Review setting up and solving proportions.

3.4 Solve problems involving direct, inverse, and/or joint variation.

3.5 Review solving quadratic equations by factoring.

4. Exponents and Radicals

4.1 Review simplifying exponential expressions with integer exponents.

4.2 Convert numbers from decimal notation to scientific notation and vice versa.

4.3 Perform arithmetic operations using scientific notation.

4.4 Review simplifying square root radical expressions.

4.5 Simplify higher root radical expressions.

5. Polynomials

5.1 Review adding and subtracting polynomials.

5.2 Multiply polynomials.

6. Factoring

6.1 Review the following factoring techniques: Factor a monomial GCF from a
polynomial,

factor the difference of two squares, and factor trinomials of the form ax^{2} + bx
+ c.

7. Rational Expressions

7.1 Review simplifying rational expressions.

7.2 Review multiplying and dividing rational expressions.

7.3 Review adding and subtracting rational expressions with like denominators.

7.4 Add and subtract rational expressions with unlike denominators.

8. The Cartesian Coordinate System

8.1 Review graphing linear equations in two variables by plotting points.

8.2 Review slope and its relationship to horizontal, vertical, parallel and
perpendicular lines.

8.3 Review graphing linear equations using the slope and y-intercept.

8.4 Graph quadratic functions of the form y = ax^{2} + bx + c by plotting points.

9. Geometry

9.1 Review the definitions of plane figures: triangle, parallelogram, square,
rectangle,

trapezoid and circle.

9.2 Review area and perimeter of triangles, squares and rectangles.

9.3 Review radius, diameter, circumference and area of circles.

9.4 Find the volume of a rectangular solid, sphere, prism and cylinder.

9.5 Review the difference between a line, line segment and ray.

9.6 Review the definitions of types of angles: acute, obtuse, right, straight,
complementary,

supplementary, vertical, corresponding, interior and exterior.

9.7 Review finding measures of angles when two parallel lines are cut by a
transversal by

using alternate interior angles, alternate exterior angles and corresponding
angles.

10. Trigonometry

10.1 Review the use of the Pythagorean Theorem.

10.2 State the sine, cosine and tangent ratios in terms of opposite side,
adjacent side and

hypotenuse of a right triangle.

10.3 Use special triangles (30°-60°-90°, 45°-45°-90°) to find sine, cosine, and
tangent ratios

of special angles.

10.4 Find any angle or side of a right triangle given one acute angle and one
side, or two

sides.

10.5 Solve applications involving right triangles.