PENNSYLVANIA COLLEGE OF TECHNOLOGY
School of Integrated Studies
Mathematics Department Syllabus
Technical Algebra & Trigonometry II
MTH 125
Course Description
Study of intermediate algebra and trigonometry, designed to prepare students for course work in their technical majors. Topics include factoring, algebraic fractions and equations, quadratic equations, trigonometric functions and graphs, radicals, complex numbers, exponential and logarithmic functions and graphs, nonlinear systems, and inequalities. Emphasis on problem solving and technical application as well as the use of technology. Not designed to prepare students for calculus. 3 Credits (3 lecture- 0 Lab)
Prerequisite(s): MTH 124.
Course Rationale
This course is designed primarily for students enrolled in technical programs that need additional applied algebra and trigonometry skills. This course emphasizes concepts and applications that connect topics as well as make the mathematics meaningful. Also, it provides students with a broad base of mathematical knowledge that better prepares them for solving real problems in a variety of contexts and for interpreting those results. This course will better prepare students in terms of their problem-solving skills and depth of knowledge.
Required Material:
Technical Mathematics, Ewen, Gary & Trefzger, 2 nd
ed., Pearson Prentice Hall, 2005.
For success in college-level mathematics classes at Penn College, students must know how to use a graphing calculator. All students are required to purchase the TI-83 Plus/TI-
84-Plus calculator. The instructor in this course will use the TI-84 Plus calculator for class demonstration.

Required Student Outcomes
Upon successful completion of the course, the student should be able to demonstrate the following competencies:
1.
Factor algebraic expressions, and use factoring techniques in applications.
2.
Simplify algebraic fractions, and solve equations with fractions and applied problems
involving algebraic fractions.
3.
Solve quadratic equations and associated practical applications.
4.
Apply the Law of Sines and the Law of Cosines to solve oblique triangle problems and applications.
5.
Graph sine and cosine functions by plotting points and by using appropriate technology.
6.
Simplify more complex algebraic expressions involving exponents and radicals.
7.
Perform basic operations on complex numbers.
8.
Graphically solve exponential and logarithmic equations, including growth and decay problems.
9.
Solve nonlinear systems of equations graphically.
10.
Solve linear inequalities algebraically and graphically.
11.
Engage in substantial mathematical problem solving at an intermediate algebraic and trigonometric level.
12.
Model real-world situations in a technical environment.
13.
Read, write, listen to, and speak mathematics.
14.
Use appropriate technology to enhance his/her mathematical thinking and understanding, to solve mathematical problems, and to judge the reasonableness of his/her results.
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Course Outline:
Unit
1
Sections
5.1 – 5.8
Topics
Factoring and Algebraic Equations
2 7.1 – 7.4, 17.1 Quadratic Equations & Inequalities
3 8.1 – 8.5, 14.1 Exponents and Radicals & Complex Numbers
4
11.1 – 11.4,
12.1, 12.2
Oblique Triangles & Graphing the Trigonometric Functions
5 9.1, 9.2, 20.7 Exponentials and Logarithms& Systems of Quadratic Equations
Course Competencies:
1 Factor algebraic expressions and use factoring techniques in applications. Also, work with algebraic fractions, and solve fractional equations and applied problems requiring algebraic fractions. a) Factor expressions by removing common factors and solve associated application problems by factoring. b) Factor binomials that are the difference of two squares and factor binomials that are the difference of two squares and solve associated application problems by factoring. c) Factor binomials that are the sum and difference of two cubes and solve associated application problems by factoring. d) Use factoring techniques in applications. e) Factor the perfect square trinomial and solve associated application problems by factoring. f) Factor expressions by grouping. g) Determine the values of the variables that result in undefined fractions with paper and pencil and by graphing on the calculator. h) Reduce algebraic fractions. i) Add, subtract, multiply, and divide algebraic fractions and solve associated application problems by factoring. j) Simplify complex fractions and solve associated application problems by factoring. k) Solve fractional equations and applied problems requiring fractional equations. l) Solve literal equations, formulas, and word problems arising from literal equations and formulas.
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Course Competencies (continued):
2 Solve quadratic equations and associated practical problems by a variety of techniques. a) Solve quadratic equations by factoring, completing the square, the quadratic formula, and the calculator by using PolySmlt. b) Solve word problems that result in quadratic equations. c) Graph quadratic equations and solve quadratic equations graphically. d) Solve equations of higher degree using PolySmlt on the calculator. e) Interpret complex solutions as no real solutions. f) Solve linear inequalities algebraically and graphically.
3 Work with algebraic expressions involving exponents and radicals. Also, perform basic operations on complex numbers in rectangular form with paper and pencil and using the calculator, and graph complex numbers. a) Use the law of exponents to simplify and combine expressions having integral exponents. b) Verify exponent and radical results with the calculator. c) Simplify radicals by removing perfect powers, by rationalizing the denominator, and by reducing the index. d) Add, subtract, multiply, and divide radicals. e) Solve radical equations and associated applications. f) Simplify radicals having negative radicands with paper and pencil and with the calculator. g) Evaluate powers of j with paper and pencil and with the calculator. h) Add, subtract, multiply, and divide complex numbers in rectangular form with paper and pencil and with the calculator. i) Solve quadratic equations that have complex roots with PolySmlt on the calculator.
4 Apply the Law of Sines and the Law of Cosines to solve oblique triangle problems and applications. Also, graph sine and cosine functions by plotting points and using the graphing calculator.
5 a) Solve oblique triangles using the Law of Sines. b) Solve oblique triangles using the Law of Cosines. c) Solve application problems requiring oblique triangles. d) Find the amplitude, period, frequency, and phase shift for a sine or cosine wave. e) Graph the sine and cosine functions with paper and pencil and with the calculator. f) Write a sine or cosine function given the amplitude, period, and phase shift
Solve exponential and logarithmic equations, and growth and decay problems. Also, solve a system of nonlinear equations. a) Graph the exponential and logarithmic functions using the calculator. b) Solve the exponential and logarithmic equations with paper and pencil and with the calculator. c) Solve exponential growth and decay problems. d) Solve a system of nonlinear equations by graphing on the calculator. e) Solve a system of nonlinear equations using the substitution method and the addition-subtraction method and with the calculator.
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