MATH 18 - Precalculus Mathematics
Course Description
MATH 18 (Precalculus Mathematics) is one of the foundation courses offered by the
Division of Physical Sciences and Mathematics. This serves as a prerequisite course to
MATH 53 (Calculus I). The goal of this course is for the students to develop higher-level
precalculus skills that will better prepare them to undertake the series of calculus
courses.
In this course, we will cover some preliminary topics on the real number system and
properties of the set of real numbers. We will then discuss algebraic and transcendental
functions, systems of equations and inequalities, and the conics and other plane curves.
The detailed outline of topics is presented on the next page of this guide. This course
might have a long coverage but studying all these topics will be of great help in building
a strong foundation in basic mathematical skills. Not only it will equip you with essential
arithmetic skills, but also it will help you hone your critical thinking and problem-solving
abilities by applying your learning in some real-world scenarios.
Course Learning Outcomes
After completion of the course, the student should be able to:
- Discuss the real number system, Cartesian and polar coordinate systems, various types of
algebraic and
transcendental functions together with their properties and graphs, matrices and determinants, and
vectors.
- Simplify expressions containing various functions using known rules, operations, and
identities.
- Solve various types of equations and inequalities, including systems of equations and inequalities,
analytically and/or graphically.
- Perform operations on functions, vectors, matrices, determinants, and parametrization of curves.
- Characterize analytically and graphically the various types of conics and polar curves.
- Use the concepts and tools discussed in class to model and solve situational problems.
Course Outline
UNIT 1. Preliminaries
- The Real Number System, Properties of the Set of Real Numbers
- Inequalities and Intervals; Quadratic, Rational, and Absolute Value Inequalities
- Two-Dimensional Coordinate System, Slope and Distance
- Forms of Equations of Lines
- Relations and Functions, Types of Functions
- Operations on Functions, Inverse of a Function
UNIT 2. Algebraic Functions
- Absolute Value Functions, Piecewise-defined Functions
- Polynomial Functions; Factors and Real Zeros of Polynomials
- Rational Functions and Rational Power Functions, Asymptotes
UNIT 3. Transcendental Functions
- Circular Functions and Identities, Reduction Formulas, Product-Sum Formulas
- Modeling with Circular Functions: Simple Harmonic Motion and Other Periodic Phenomena
- Inverse Circular Functions, Trigonometric Equations, and Inequalities
- Oblique Triangles and the Laws of Sines and Cosines, Area of a Triangle
- Natural Exponential and Natural Logarithmic Functions, Exponential Growth and Decay
- Hyperbolic Functions and Identities, Inverses of Hyperbolic Functions
- Vectors in Two Dimensions, Vector Operations, Dot Product
UNIT 4. System of Equations and Inequalities
- Matrices; Algebra of Matrices; Inverse of a 2x2 Matrix
- Determinants (up to order 3) and Its Properties
- Systems of Linear Equations, Cramer's Rule, Modeling Applications
- Partial Fraction Decomposition
- System of Nonlinear Equations
- System of Inequalities with Linear Programming Application
UNIT 5. Conics and Other Plane Curves
- The General Second-Degree Equations in Two Variables, Conic Sections
- Translation and Rotation of Axes
- The Polar Coordinate System, Conics in Polar Coordinates
- Special Polar Graphs (Cardioid, Limacon, Lemniscate, Spiral, Rose)
- Simultaneous Polar Equations
- Parametric Equations of Plane Curves