Guaranteed B+ or Better in MATH 110

Week 1 establishes the foundation for all of College Algebra by introducing functions, relations, domain, range, and function notation. You'll learn to identify functions from graphs and equations, evaluate function values, and understand the vertical line test. This week also covers linear functions, slope-intercept form, and graphing basics. Many students struggle with translating between different representations (equations, graphs, tables) and understanding what makes a relation a function. We provide detailed examples of each concept and help you master the notation that will be used throughout the entire course.

Week 2 focuses on solving linear equations and inequalities in one variable, including compound inequalities and absolute value equations. You'll learn systematic approaches to isolating variables, handling fractions and decimals, and expressing solutions in interval notation. The week also introduces applications of linear equations including distance-rate-time problems, mixture problems, and geometric applications. Students often make errors with sign changes when multiplying or dividing by negatives in inequalities, and struggle with absolute value equations that have two solutions. Our step-by-step guidance ensures you understand why each algebraic manipulation is valid and how to check your solutions.

Week 3 teaches multiple methods for solving systems of linear equations: graphing, substitution, and elimination. You'll learn when each method is most efficient and how to recognize systems with no solution or infinitely many solutions. Applications include break-even analysis, mixture problems, and rate problems involving two unknowns. The week also covers systems of linear inequalities and graphing solution regions. Common difficulties include choosing the wrong method for a given system, making arithmetic errors during elimination, and misinterpreting what the solution represents in word problems. We help you develop strategic thinking about which approach to use and provide extensive practice with real-world applications.

Week 4 introduces polynomial expressions including adding, subtracting, multiplying, and dividing polynomials. You'll master special product formulas like (a+b)², (a-b)², and (a+b)(a-b), which are essential for factoring. The week covers polynomial long division and synthetic division for dividing by linear factors. Students frequently struggle with keeping track of signs during subtraction, applying the distributive property correctly with multiple terms, and organizing work in long division. Our tutoring emphasizes systematic organization and provides memory aids for special products that will save you time on quizzes and the final exam.

Week 5 covers all factoring techniques: greatest common factor, factoring by grouping, factoring trinomials, difference of squares, and sum/difference of cubes. You'll learn to recognize which method applies to each polynomial and how to factor completely. The week also teaches solving polynomial equations by factoring and using the zero-product property. Applications include geometry problems and projectile motion. This is often the most challenging week because it requires pattern recognition and the ability to work backwards from expanded form to factored form. We provide a systematic decision tree for choosing factoring methods and extensive practice with each technique until it becomes automatic.

Week 6 focuses on rational expressions (algebraic fractions) including simplifying, multiplying, dividing, adding, and subtracting them. You'll learn to find least common denominators with polynomial denominators and solve rational equations by clearing denominators. The week covers identifying restrictions on variables and checking for extraneous solutions. Applications include work-rate problems and proportion problems. Students often struggle with finding common denominators when denominators are polynomials, making sign errors when subtracting rational expressions, and forgetting to check solutions against restrictions. Our approach emphasizes careful organization and systematic checking to avoid these common pitfalls.

Week 7 introduces radical expressions including simplifying radicals, operations with radicals, and rationalizing denominators. You'll learn properties of radicals, how to simplify radical expressions with variables, and techniques for adding and multiplying radicals. The week also covers solving radical equations and checking for extraneous solutions that arise from squaring both sides. Applications include geometry problems involving the Pythagorean theorem and distance formula. Common errors include incorrectly simplifying radicals with variables, forgetting to rationalize denominators, and failing to check solutions in the original equation. We provide clear rules for radical operations and emphasize the importance of solution verification.

Week 8 covers exponential functions, their graphs and properties, and introduces logarithms as inverse functions of exponentials. You'll learn logarithm properties including product rule, quotient rule, and power rule, and how to solve exponential and logarithmic equations. The week includes applications like compound interest, population growth, and radioactive decay. This material is crucial for higher math courses and appears heavily on the comprehensive final exam. Students often confuse logarithm properties with exponent rules and struggle with change-of-base formula. The final exam covers all material from weeks 1-8, so we provide a comprehensive review strategy focusing on the most commonly tested concepts and problem types from each unit.