MATH 17

Course Description

College Algebra and Trigonometry (MATH 17) is one of the foundation courses that is still being offered in UP Mindanao. Since 2018, students in any Bachelor of Science program in UP Mindanao take this course as a prerequisite to Calculus courses offered in the succeeding semesters. While it is a refresher course to students who already took Algebra and Trigonometry in their senior high school, MATH 17 offers a fresh look on how we perceive the world mathematically and attempts to anchor it to the needs of the students’ respective degree programs.

In this course, we will explore the world of numbers, letters, symbols, and operations through topics ranging from sets and real numbers to applying trigonometric functions in real-world problems. We will also traverse the Cartesian plane through various equations, functions, and their graphs. Most of the topics will be attributed to “looking for the x” by utilizing a variety of techniques allowed in Algebra. This, in turn, allows us to search for the missing values in problems we encounter in real life through various applications tailored to your course. You will demonstrate your problem-solving skills with exercises, quizzes, and exams administered online or in paper, depending on your needs and preferences. It is highly recommended for you to interact and discuss with your instructors and fellow MATH 17 students as we relearn Algebra and Trigonometry together.

Course Learning Outcomes

By the end of the semester, students would have gained an understanding and mastery of the language of algebra and trigonometry. Specifically, they would be able to

1) recognize the sets of complex numbers and their properties;

2) manipulate algebraic and trigonometric expressions by using different operations;

3) describe the nature of algebraic and trigonometric equations and function; and

4) demonstrate various operations in solving solutions of algebraic and trigonometric equations.

Course Outline

I. Sets and Set of Complex numbers

A. Sets (basic notation, relations, and operations)

B. The Real Number System

C. Set of Complex Numbers

II. Algebraic Expressions

A. Integer Exponents

B. Polynomials and Operations Between Them

C. Rational Expressions

D. Rational Exponents and Radicals

III. Equations and Variations

A. Linear and Quadratic Equations

B. Equations with Rational Expression, Radicals, and Absolute Values

C. Variations and Real-world Applications

IV. Cartesian Coordinate Plane and Inequalities

A. Two-dimensional Coordinate System

B. Graphs of Equations

C. Inequalities

D. Graphs of Inequalities

V. Systems of Equations

A. Systems of Linear Equations in Two Variables

B. Systems of Linear Equations in Three Variables

C. Systems of Nonlinear Equations

VI. Functions

A. Functions and Its Properties

B. Polynomial Functions

C. Inverse of Functions

D. Exponential/Logarithmic Functions

VII. Trigonometric Functions

A. Right Triangle Approach on Trigonometric Functions

B. Unit Circle Approach

C. Angle; Circular Functions and Graphs

VIII. Trigonometric Equations

A. Trigonometric Properties

B. Trigonometric Identities

C. Equations Involving Trigonometric/inverse Functions

IX. Applications of Trigonometry

A. Solving Triangles

B. Polar Form of Complex Numbers

C. Applications of Trigonometric Functions