MATH 1250: Basic Mathematics for Science & Engineering – Syllabus and Learning Outcomes

Course Overview

This course provides a comprehensive foundation in algebra and trigonometry, preparing students for introductory calculus. The curriculum covers essential topics such as polynomial, rational, and radical expressions, equations and inequalities, functions and their properties, exponential and logarithmic functions, and the fundamentals of trigonometry.

Textbook and Software

• Textbook: Algebra & Trigonometry with Interactive Assignments, 4th edition by Kirk Trigsted (ISBN-13: 9780137876808)

• Access: Online MyLab section (access code required; physical textbook optional)

• Homework, practice tests, and tests are administered through MyLab.

Course Content and Learning Outcomes

The course is structured around five major tests, each covering specific sections and topics. Below is a summary of the main topics and subtopics, organized by test modules.

Test 1: Algebraic Foundations

• Rational Exponents, Radicals, and Rationalization (Section R.6)

  • Definition and manipulation of rational exponents

  • Properties of radicals

  • Rationalizing denominators

• Factoring Polynomials (Section R.7)

  • Common factoring techniques (GCF, difference of squares, trinomials, grouping)

• Rational Expressions (Section R.8)

  • Simplifying, multiplying, and dividing rational expressions

• Linear Equations (Section 1.1)

• Quadratic Equations (Section 1.4)

• Other Types of Equations (Section 1.6)

• Linear Inequalities (Section 1.7)

Test 2: Functions and Graphs

• Lines (Section 2.3)

  • Equations of lines, slope, intercepts

• Relations and Functions (Section 3.1)

  • Definition of functions, domain and range

• Algebra of Functions and Compositions (Section 3.5)

• Inverse Functions (Section 3.6)

• Quadratic Functions (Section 4.1)

• Graphs of Polynomial Functions (Section 4.3)

Test 3: Advanced Algebraic and Transcendental Functions

• Polynomial Division (Section 4.4)

• Rational Functions and Their Graphs (Section 4.6)

• Polynomial and Rational Inequalities (Section 1.9)

• Exponential Functions (Section 5.1)

• Logarithmic Functions (Section 5.2)

• Properties of Logarithms (Section 5.3)

• Exponential and Logarithmic Equations (Section 5.4)

Test 4: Introduction to Trigonometry

• Introduction of Angles (Section 6.1)

  • Degree and radian measure

• Right Triangle Trigonometry (Section 6.4)

• Trigonometric Functions of General Angles (Section 6.5)

• Graphs of Sine, Cosine, and Tangent (Sections 7.1/7.3)

Test 5: Trigonometric Identities and Equations

• Inverse Trigonometric Functions (Sections 7.4/7.5)

• Trigonometric Identities (Section 8.1)

• Trigonometric Equations (Section 8.5)

Grading Policy

Grade	Percentage Range	Point Range
A	90 to 100%	630 to 700
A-	88% to less than 90%	616 to less than 630
B+	86% to less than 88%	602 to less than 616
B	80% to less than 86%	560 to less than 602
B-	78% to less than 80%	546 to less than 560
C+	76% to less than 78%	532 to less than 546
C	70% to less than 76%	490 to less than 532
C-	68% to less than 70%	476 to less than 490
D	60% to less than 68%	420 to less than 476
F	Less than 60%	Less than 420

Calculation: Percentage = (Points Earned) / (Points Available) × 100

Course Policies

• Attendance: Strict attendance policy with penalties for excessive absences.

• Homework: Completed online; lowest grade dropped; late work accepted for partial credit until a specified date.

• Tests: Five major tests; lowest test grade dropped (except final exam); no make-up tests.

• Final Exam: Comprehensive and mandatory.

• Calculators: Only basic, four-function calculators provided by the instructor are allowed during tests.

• Cheating: Strictly prohibited; violations result in a zero that cannot be dropped and academic discipline.

• Disability Access: Accommodations available through the university's SDS office.

Summary of Key Mathematical Topics

• Algebraic Manipulation: Factoring, rational expressions, solving equations and inequalities.

• Functions: Definitions, operations, compositions, inverses, and graphing.

• Polynomial and Rational Functions: Division, graphing, asymptotes, and inequalities.

• Exponential and Logarithmic Functions: Properties, equations, and applications.

• Trigonometry: Angles, right triangles, trigonometric functions, graphs, identities, and equations.

Additional info: This syllabus aligns closely with standard Precalculus topics and learning outcomes, as outlined in the provided chapter titles. Students are expected to master foundational algebraic and trigonometric concepts in preparation for calculus.