Math 102
This course aims to strengthen and solidify foundational quantitative skills and algebraic concepts students in non-STEM programs such as business, education, or the social sciences or for students seeking additional preparation for more advanced math courses. Following a comprehensive review of essential mathematical topics including operations with integers, fractions, decimals, percentages, exponents and radical expressions, the course will focus on algebraic concepts such as solving linear equation and inequalities, absolute value equations, systems of equations, functions, polynomials, factoring and solving quadratic equations.
Throughout the course, students will develop their analytical reasoning and problem-solving skills while building core mathematical competencies. In addition to promoting confidence in mathematical thinking, this course fosters critical quantitative skills for academic success across disciplines.
Learning outcomes
At the conclusion of this course students should have the ability to:
- Demonstrate proficiency in basic arithmetic operations involving integers, fractions and decimals and percentages without the use of a calculator
- Solve algebraic equations using systematic, step-by step methods
- Develop problems solving and algebraic skills to support success in more advanced math courses or for non-STEM disciplines that require mathematical proficiency such as business, education or the social sciences.
- Apply a variety of problem-solving strategies including numerical, graphical and algebraic techniques to solve complex, multi -step problems and real-world problems
- Develop analytical thinking skills and ability to interpret mathematical information in applied problems and effectively communicate problems solving process and solutions.
Key topics include:
- Arithmetic fundamentals
- Integers: operations with integers- addition/subtraction, multiplication/division, exponents and order of operations
- Fractions: addition/subtraction, multiplication/division, mixed and improper fractions
- Decimals and percent: arithmetic with decimals, converting decimals to percent, converting percent to fractions and decimals, scientific notation
- Applied problems with percent: solving basic percent equations, percent increase and decrease, mark-up and discount problems, simple interest problems
- Radical expressions and applied problems, distance formula
- Translating verbal expressions into algebraic expressions and applied problems
- Solving Linear equations and absolute value equations
- Applied problems: uniform motion problems
- Solving Inequalities: solving inequalities in one variable, compound inequalities, absolute value inequalities
- Graphing linear equations in two variables
- Introduction to functions and evaluating function values
- Determining equations of lines
- Slopes and intercepts, parallel and perpendicular lines
- Graphing Inequalities in two variables.
- Solving systems of linear equations in two variables
- Using graphing, elimination and substitution methods
- Polynomials functions: performing operations on polynomial expressions
- Quadratic functions
- Factoring polynomials, including special factoring
- Solving quadratic equations by factoring
- Rational expressions and simplifying with rules of exponents
Math 103
This course continues where Math 102 leaves off, covering more intermediate algebra concepts, as well as an emphasis on elementary functions. This course is intended to give students the proficiency in algebra necessary to succeed in Math 120. Students will also be introduced to many of the same elementary functions they will encounter in Math 120 and some basic applications. Hopefully this exposure will help them when more challenging applications become the focus in Math 120.
Key topics include:
• Rational Expressions: Reducing, Multiplication/Division, Addition/Subtraction, Complex Fractions, Equations with Rational Expressions, Applications
• Radicals & Rational Exponents: Simplifying, Addition/Subtraction, Multiplication/Division, Solving Square Root Equations, Applications
• Quadratic Equations: Solving by Factoring, Taking Square Roots, Completing the Square, Quadratic Formula, Applications, Quadratic in Form Equations, Non-Linear Inequalities
• Measurement & Geometry: Unit conversion, Angles, Lines, Areas, Volumes, Pythagorean Theorem, Similar Triangles
• Introduction to Functions: Definition, Evaluation, Domain, Range, Function Notation, Graphs, Vertical Line Test
• Linear Functions: Slopes, Finding Equation of Lines, Applications, Parallel & Perpendicular Lines, Applications
• Quadratic Functions: Intercepts, Vertex, Applications
• More on Functions: Algebra of Functions, One-to-One Functions, Inverse Functions
• Exponential & Logarithmic Functions: Evaluation, Graphs, Exponential vs Logarithmic Forms, Solving Exponential & Logarithmic Equations, Applications
• Trigonometry: Degrees, Radians, Arc Length, Right Triangle Trig, Law of Sines & Cosines
• Miscellaneous: Circles, Non-Linear Inequalities, Non-Linear Systems of Equations (More Conic Sections if time permits)