STATE UNIVERSITY OF NEW YORK
COLLEGE OF TECHNOLOGY
CANTON, NY
COURSE OUTLINE
MATH 135 - TECHNICAL MATH I
Prepared by: Mary Gfeller
SCHOOL OF LIBERAL ARTS & SUPPORT SERVICES
MATHEMATICS DEPARTMENT
FEBRUARY 2006
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Technical Math I: A Comprehensive Course Outline for MATH 135 at SUNY Canton, Exams of Mathematics
An outline for math 135, technical math i, a college-level mathematics course offered at the state university of new york (suny) college of technology in canton. The course covers a range of mathematical topics, including algebra, geometry, functions and graphs, trigonometric functions, systems of linear equations, determinants, factoring, fractions, and quadratic equations. Students will learn fundamental concepts, perform calculations, and apply mathematical principles to solve problems. The course is designed for individuals who have completed beginning algebra or its equivalent and is offered in the fall semester.
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STATE UNIVERSITY OF NEW YORK
COLLEGE OF TECHNOLOGY
CANTON, NY
COURSE OUTLINE
MATH 135 - TECHNICAL MATH I
Prepared by: Mary Gfeller SCHOOL OF LIBERAL ARTS & SUPPORT SERVICES MATHEMATICS DEPARTMENT FEBRUARY 2006
MATH 135
Technical Math I A. TITLE: Technical Math I B. COURSE NUMBER: MATH 135 C. CREDIT HOURS: 4 D. COURSE LENGTH: 15 weeks E. SEMESTERS OFFERED: Fall F. HOURS OF LECUTRE, LABORATORY, RECITATION, TUTORIAL, ACTIVITY: Four hours lecture per week. G. CATALOGUE DESCRIPTION: This course is the first of a two-semester sequence of intermediate algebra and trigonometry with technical applications. Topics include: review of the fundamental concepts of algebra, units of measurement and approximate numbers, functions and graphs, trigonometry functions, vectors, complex numbers, systems of linear equations, determinants, factoring, rational expressions, quadratics, geometry, (areas and perimeters of common plane figures, volumes and surfaces of common solids). H. PRE-REQUISITES/CO-REQUISITES: Beginning Algebra (Math 100) or High School Equivalent or individuals enrolled in the Verizon Next Step Program. I. GOALS (STUDENT LEARNING OUTCOMES): see attached. J. TEXTS: Basic Technical Mathematics (8/e) by Allyn J. Washington bundled with MyMathLab, Addison-Wesley, 2001. ISBN: 0321383125. Student Solution Manual. ISBN: 0-201-38569- K. REFERENCES: Additional Instructor Materials: Instructor’s Solution Manual. ISBN: 0-201-38570- Test Gen-Eq/QuizMaster-Eq Duel Platform CD-ROM. ISBN:0-201-38575- L. EQUIPMENT: Laptop Computer, Graphing Calculator (TI-84 Plus Silver)
STUDENT LEARNING OUTCOMES
MATH 135
TECHNICAL MATH I
By the end of this course, the student will: I. Fundamental Concepts and Operations of Algebra
- Identify a number as being an natural, integer, rational, irrational and real or imaginary and locate numbers on a number line
- Determine the absolute value of a number
- Determine the order between two real numbers using <, >, =
- Find the reciprocal of a number
- Identify the additive and multiplicative identity and inverse of a number
- Determine when an expression is equal to zero, undefined, or indeterminate
- Identify fundamental laws of algebra (commutative, associative, and distributive)
- Perform basic operations with integers (addition, subtraction, multiplication, division)
- Evaluate algebraic expressions involving exponents and absolute value
- Determine the number of significant digits and round a number to a specified number of significant digits
- Use rules of exponents to simplify numerical and algebraic expressions (including zero and negative exponents)
- Change a number from scientific notation to ordinary notation (and vice versa)
- Find the nth root of a numerical expression by hand and by calculator
- Perform basic operations with polynomials (addition, subtraction, multiplication) to simplify
- Find the quotient of an algebraic expression divided by a monomial or binomial (using long division)
- Solve linear equations with variables on both sides of the equation
- Solve proportional equations
- Solve for a designated variable in a literal equation
- Evaluate formulas
- Identify an unknown in a word problem
- Translate English phrases into algebraic expressions and vice versa
- Solve word problems using algebraic models
STUDENT LEARNING OUTCOMES (continued) MATH 135 TECHNICAL MATH I II. Geometry
- Identify angles as acute, right, obtuse, straight
- Find the complement and supplement of an angle
- Find angle measures involving parallel lines and nonparallel lines
- Categorize a triangle according to length and angle measurements (scalene, isosceles, or equilateral and acute, obtuse, or right)
- Identify features of a triangle (legs, hypotenuse, median, altitude, centroid and angle bisectors)
- Find the perimeter and area of a triangle
- Use the Pythagorean Theorem to find the length a missing side in a triangle
- Determine whether two triangles are similar
- Identify types of quadrilaterals
- Find the perimeter and area of a quadrilateral
- Identify chords, secants, tangents in a circle
- Find the circumference and area of a circle
- Find areas of irregular polygons
- Identify basic geometric solids
- Find the volume and surface area of geometric solids
- Use dimensional analysis in conversion between English and metric
- Use dimensional analysis in conversion between the same measurement system III. Functions and Graphs
- Evaluate functions in the form of functional notation
- Identify the domain and range of a function
- Write word problems using functional notation
- Solve word problem algebraically
- Plot points in the rectangular coordinate system
- Find the distance between two points
- Find the slope between two points
- Identify locus of points given various conditions
- Graph functions by plotting points and by using the graphing calculator
- Use the Vertical Line Test to see if a relation is a function
- Solve word problems involving linear equations graphically
STUDENT LEARNING OUTCOMES (continued) MATH 135 TECHNICAL MATH I VII. Inequalities
- Use inequality symbols to make a statement true
- Express inequalities as verbal statements (and vice versa)
- Graph inequalities of a single variable on a number line
- Solve linear inequalities (including application problems) algebraically and graphically
- Solve nonlinear inequalities
- Solve absolute value inequalities
- Use a graphing calculator to display the solution of a system of inequalities VIII. Ratio, Proportion, and Variation
- Express a ratio in simplest form
- Find ratios given a word problem
- Solve proportion problems
- Set up equations involving direct, indirect, joint, and combined variation
- Solve equations involving direct, indirect, joint, and combined variations (including application problems)
TOPICAL OUTLINE
MATH 135
TECHNICAL MATH I
TOPICS
I. Fundamental Concepts and Operations of Algebra A. Arithmetic, Real Numbers
- Basic concepts
- Properties
- Operations B. Exponents
- Rules of exponents
- Scientific notation
- Roots and radicals C. Operations with polynomials D. Equations
- Linear
- Literal equations and formula manipulation
- Applications II. Geometry A. Basic geometric figures and definitions B. Basic geometric formulae (area, perimeter, volume, surface area) C. Basic Metric Units and Dimensions of Analysis III. Functions and Graphs A. Functions
- Linear; slope, distance formula, equations of straight lines
- Evaluating non-linear functions
- Applications B. Graphs
- Rectangular coordinate system
- Graph of a function IV. Trigonometric Functions A. Defining basic trig functions of sine, cosine, and tangent B. Values of trig functions C. Right triangles D. Applications of right triangles