College algebra covers equations, inequalities, functions, graphs, polynomials, rational expressions, exponents, logarithms, and sequences. You’ll use those ideas to solve problems, interpret graphs, and model situations such as growth and compound interest. Here’s what Math 111 covers chapter by chapter and how it compares with other math courses.
What does college algebra cover?
College algebra asks you to work with expressions, solve equations, and explain what the results mean. You’ll move between formulas, graphs, and word problems rather than treating each as a separate skill.
For example, to solve x² − 5x + 6 = 0, factor it as (x − 2)(x − 3) = 0. The zero-product property gives x = 2 or x = 3. In a quadratic function, those solutions also identify where its graph crosses the x-axis.
You’ll also learn to watch for restrictions. The expression (x² − 1)/(x − 1) simplifies to x + 1, but the original expression is still undefined at x = 1.
What does Math 111 cover?
The UPI Study College Algebra course organizes Math 111 into ten chapters. The syllabus below lists their lessons and hours, followed by the assignment and final exam.
| # | Chapter | Lessons | Hours |
|---|---|---|---|
| 1 | Algebraic Foundations | Real Numbers and Their Properties — number sets, absolute value, order of operations, properties of real numbers; Integer Exponents and Scientific Notation — product, quotient, power, zero, and negative exponent rules; scientific notation; Radicals and Rational Exponents — nth roots, simplifying radicals, rationalizing denominators, converting between radical and rational exponent notation; Simplifying Radical Expressions — product and quotient rules for radicals, adding and subtracting radicals, multiplying radical expressions | 4 |
| 2 | Polynomials & Factoring | Operations on Polynomials — addition, subtraction, multiplication, special products (FOIL, difference of squares, perfect square trinomials); Factoring: GCF and Grouping — greatest common factor, factoring by grouping; Factoring Trinomials — leading coefficient of 1 and a ≠ 1, trial-and-error and AC methods; Special Factoring Formulas — difference of squares, sum and difference of cubes | 5 |
| 3 | Rational & Radical Expressions | Simplifying Rational Expressions — identifying excluded values, reducing to lowest terms; Multiplying and Dividing Rational Expressions — factoring to cancel common factors; Adding and Subtracting Rational Expressions — finding the LCD, combining fractions; Complex Fractions — simplifying by LCD method and division method | 5 |
| 4 | Linear Equations & Inequalities | Linear Equations in One Variable — solving, checking solutions, equations with fractions; Formulas and Applications — literal equations, solving for a variable; applied word problems (distance, rate, mixture, geometry); Linear Inequalities — solving, graphing on a number line, interval notation; Compound Inequalities — AND (intersection) and OR (union) compound inequalities | 5 |
| 5 | Systems of Linear Equations | Systems of Two Linear Equations — graphing method, substitution method, elimination method; consistent, inconsistent, dependent systems; Applications of 2×2 Systems — mixture, rate, investment, and geometry word problems; Systems of Three Linear Equations — solving 3×3 systems by elimination and back-substitution; Systems of Linear Inequalities — graphing feasible regions, identifying vertices | 4 |
| 6 | Quadratic Equations & Functions | Solving Quadratic Equations by Factoring — zero product property, checking solutions; Square Root Property and Completing the Square — solving equations of the form x² = k; completing the square method; The Quadratic Formula and Discriminant — deriving and applying the quadratic formula; using discriminant to determine number and type of solutions; Quadratic Functions and Parabolas — standard form y = ax² + bx + c; vertex form y = a(x−h)² + k; vertex, axis of symmetry, direction of opening, intercepts | 5 |
| 7 | Functions & Their Graphs | Relations, Functions, and Function Notation — definition, vertical line test, evaluating f(x), difference quotient; Domain and Range — finding algebraically and from graphs; interval notation; Graphs of Basic Functions — linear, absolute value, square root, cube root, quadratic; identifying and sketching; Piecewise-Defined Functions — evaluating and graphing | 7 |
| 8 | Polynomial & Rational Functions | Polynomial Functions and End Behavior — degree, leading coefficient, end behavior, turning points; Zeros of Polynomial Functions — real zeros, multiplicity, graphs touching vs. crossing the x-axis; Polynomial Division and the Remainder Theorem — long division, synthetic division, Remainder and Factor Theorems; Rational Functions and Their Graphs — vertical asymptotes, horizontal asymptotes, oblique asymptotes, holes, graphing strategy | 5 |
| 9 | Exponential & Logarithmic Functions | Exponential Functions — definition, base restrictions, graphs and transformations, natural base e, compound interest formula; Logarithmic Functions — definition as inverse of exponential, converting between forms, evaluating log and ln; Properties of Logarithms — product, quotient, power rules; change-of-base formula; expanding and condensing; Solving Exponential and Logarithmic Equations — algebraic methods, checking extraneous solutions | 5 |
| 10 | Sequences & Series | Sequences and Recursive Definitions — explicit and recursive formulas, generating terms; Arithmetic Sequences and Series — common difference, nth term, sum of first n terms; Geometric Sequences and Series — common ratio, nth term, sum of finite geometric series; Infinite Geometric Series — condition for convergence (|r| < 1), sum formula, applications | 5 |
| ASSIGNMENT | 5 | ||
| FINAL EXAM | 3 |
- Algebraic Foundations: Review real numbers, exponent rules, scientific notation, and radicals.
- Polynomials & Factoring: Perform polynomial operations and choose factoring methods.
- Rational & Radical Expressions: Simplify and combine expressions while identifying excluded values.
- Linear Equations & Inequalities: Solve equations, inequalities, and applications, including absolute value problems.
- Systems of Linear Equations: Solve systems using graphs, substitution, and elimination; graph systems of inequalities.
- Quadratic Equations & Functions: Solve quadratics, analyze parabolas, and use the quadratic formula.
- Functions & Their Graphs: Work with domain, range, transformations, composition, and inverse functions.
- Polynomial & Rational Functions: Analyze zeros, end behavior, asymptotes, and holes.
- Exponential & Logarithmic Functions: Solve equations and model growth, decay, and interest.
- Sequences & Series: Find terms and sums of arithmetic and geometric sequences, and use sigma notation.
For a review of formulas you may encounter along the way, see the algebra formulas cheat sheet.
What level is college algebra?
College algebra generally builds on high school Algebra 1 and Algebra 2 or intermediate algebra. It revisits familiar skills such as factoring and solving equations, then applies them to a wider range of functions and graphs.
A course may overlap with precalculus, particularly in its treatment of functions. Precalculus often adds substantial trigonometry and is designed to prepare students for calculus; exact content varies. See college algebra vs. precalculus for help comparing the two.
The Complete Resource for College Algebra
UPI Study has a full resource page built specifically for college algebra — covering which courses count and how to get started at $250 per course with no deadlines. Your college decides how credits transfer.
See College Algebra →Is finite math the same as college algebra?
No. College algebra focuses heavily on equations and functions, while finite math often draws from topics such as systems, matrices, probability, and counting. The subjects can overlap, and a finite math syllabus may vary by institution.
Neither is automatically easier. If you enjoy manipulating expressions and graphing functions, college algebra may feel more familiar; if you prefer probability and discrete problems, you may prefer finite math. Compare the actual syllabuses and your program’s requirements.
How hard is Math 111?
Difficulty depends largely on your comfort with earlier algebra and on the course itself. Fractions, negative exponents, factoring, and equation solving are useful skills to review before starting.
Practice each method on paper and check solutions in the original equation. If a word problem is challenging, define the variable first, write an equation from the given relationships, and then interpret the answer in context.
What math is after college algebra?
Precalculus or another math course may follow college algebra, depending on your program and institution. Some paths lead toward calculus; others may call for statistics or a different quantitative course.
Check the course sequence and prerequisites for your intended major before choosing your next class. A course number alone does not tell you what every institution requires.
Which colleges list College Algebra on an equivalency chart?
These colleges show College Algebra (Math 111) on their equivalency charts with UPI Study. Open a college for its full chart.
| College | Equivalent course | Credits | Status |
|---|---|---|---|
| CSU | MAT 1302 – College Algebra | 3 | Recommended by UPI Study — the college confirms on evaluation |
| Crestpoint | College Algebra | 3 | Recommended by UPI Study — the college confirms on evaluation |
| Dunlap-Stone | MATH-110-S College Algebra | 3 | Recommended by UPI Study — the college confirms on evaluation |
| Gracelyn | MATH 1394 College Algebra | 3 | Recommended by UPI Study — the college confirms on evaluation |
| Indiana Tech | MA 1030 – Applied Algebra | 3 | Recommended by UPI Study — the college confirms on evaluation |
| Maestro | UPI Recommended | 3 | Recommended by UPI Study — the college confirms on evaluation |
| Newlane | MATH101 College Algebra | 3 | Recommended by UPI Study — the college confirms on evaluation |
| Nexford | Math Elective (Gen Ed) | 3 | Recommended by UPI Study — the college confirms on evaluation |
See the rest of the equivalency on the College Algebra course page, or open a college above for its full chart. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
Frequently Asked Questions about College Algebra
Math 111 is College Algebra at UPI Study, but course numbers are not universal. Check the title and description in your institution’s catalog.
Math 111 is a course number whose meaning depends on the institution. It can identify a college algebra course, so read the course description to confirm its topics.
College algebra often reviews and builds on topics from Algebra 1 and Algebra 2. It may revisit equations and factoring while extending work with functions and graphs.
College algebra overlaps with parts of precalculus, especially functions and their graphs. It does not necessarily cover a full precalculus syllabus, which often includes substantial trigonometry.
Math 111 can be challenging if earlier algebra skills are rusty, but difficulty varies by student and course. Reviewing fractions, exponents, factoring, and linear equations can help you prepare.
Finite math is not necessarily easier than college algebra. Compare the topics in each syllabus with your strengths and the requirements of your program.
Not necessarily; general education requirements differ by institution and program. Ask your college which courses meet your specific math requirement.
Math 111 is not necessarily precalculus; the number can refer to different courses at different institutions. Check the course title and syllabus rather than relying on the number.
Final Thoughts on College Algebra
Start by reviewing the syllabus alongside your program’s math requirements. Then try a few factoring, equation-solving, and graphing problems to see which skills you want to refresh.
The way this actually clicks
Skip step 3 and the whole thing is wasted.
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