Course Description
MAT1033 / MAT1033C – Intermediate Algebra is a 3-credit lecture course in the Mathematics: Other Mathematics taxonomy of Florida's Statewide Course Numbering System (SCNS). The course reinforces and develops algebra skills as a bridge between developmental mathematics and college-level algebra. Topics include sets and set notation; operations with polynomial and rational expressions; radicals and rational exponents; linear equations, inequalities, and systems with applications; absolute value equations; quadratic equations; graphing of linear equations and inequalities; and applications of these algebraic skills to problems drawn from science, business, geometry, and other disciplines.
MAT1033 is offered at 42 Florida public institutions and transfers as equivalent across the state. The course occupies a unique position in Florida's mathematics sequence: it is the standard bridge course between MAT0028 (Elementary Algebra, developmental) and MAC1105 (College Algebra, gen-ed). MAT1033 typically does NOT satisfy the General Education Core Mathematics requirement and typically does NOT satisfy Gordon Rule at most Florida public universities and many state colleges (UCF and others explicitly classify it as elective credit only). Students must verify their target institution's policies. Per Florida Senate Bill 1720 (2013) and State Board Rule 6A-10.0315, students who entered 9th grade in a Florida public high school in 2003-2004 or later and earned a standard Florida diploma, plus active-duty military students, are exempt from common placement testing and developmental education and may enroll directly in MAT1033 without first completing MAT0022/0028.
Learning Outcomes
Required Outcomes
Upon successful completion of this course, students will be able to:
- Define the sets of real numbers (natural, whole, integer, rational, irrational, real); apply proper set notation; recognize subset relationships.
- Evaluate formulas used in other disciplines (science, business, statistics, geometry) involving routine operations with real numbers.
- Solve linear equations, including equations containing fractions; solve literal equations and formulas for given variables.
- Solve linear and compound linear inequalities, including those containing fractions; express solutions using interval notation, set-builder notation, and graphically on a number line.
- Solve absolute value equations and inequalities; represent solutions using set notation and graphically.
- Translate real-world problems into mathematical equations or inequalities and then solve the problem; interpret solutions in context.
- Simplify algebraic expressions using the rules of exponents (positive, negative, and zero exponents).
- Multiply and divide algebraic expressions in scientific notation; convert between standard and scientific notation.
- Perform operations with polynomial expressions: addition, subtraction, multiplication (including special products), and long and synthetic division.
- Apply factoring techniques: greatest common factor; factoring by grouping; factoring trinomials of forms ax² + bx + c; difference of squares; sum and difference of cubes; perfect-square trinomials.
- Perform operations with rational expressions: simplification; multiplication and division; addition and subtraction with common and unlike denominators; complex fractions.
- Solve rational equations; identify extraneous solutions; apply rational equations to work, distance/rate/time, and other applications.
- Simplify radical expressions; perform operations with radicals; rationalize denominators; convert between radical form and rational exponent form.
- Solve radical equations; identify extraneous solutions.
- Solve quadratic equations by factoring, by the square root property, by completing the square, and by the quadratic formula; solve equations quadratic in form.
- Graph linear equations and inequalities in two variables; identify slope, x- and y-intercepts; write equations of lines in slope-intercept and point-slope forms; recognize parallel and perpendicular relationships.
- Solve systems of linear equations in two variables by graphing, substitution, and elimination methods; apply systems to real-world applications.
- Apply function notation at an introductory level; identify the domain of basic algebraic functions; evaluate functions.
Optional Outcomes
Depending on institutional emphasis, students may also:
- Solve systems of three linear equations in three variables using elimination methods.
- Apply introductory variation concepts (direct, inverse, joint variation).
- Use graphing technology (Desmos, GeoGebra, graphing calculators) to verify algebraic results and visualize functions.
- Use online homework and tutoring platforms (Pearson MyLab Math, ALEKS, MyMathLab) for adaptive practice and remediation.
- Apply algebraic skills to workforce and academic context-specific problems (business break-even analysis, geometric measurement problems, science formulas).
Major Topics
Required Topics
- Real Numbers and Sets: Set notation; the real number line; subsets of the real numbers; absolute value; interval notation; properties of real numbers (commutative, associative, distributive); operations with real numbers.
- Linear Equations and Inequalities in One Variable: Solving linear equations and equations with fractions; solving literal equations; solving and graphing linear inequalities; compound inequalities; absolute value equations and inequalities; applications and word problems.
- Exponents and Polynomials: Rules of exponents (positive, negative, zero); scientific notation; polynomial vocabulary; addition, subtraction, multiplication of polynomials (including special products: (a + b)(a - b), (a + b)², etc.); polynomial division (long and synthetic).
- Factoring: Greatest common factor; factoring by grouping; factoring trinomials of the form x² + bx + c and ax² + bx + c (a ≠ 1); difference of squares; sum and difference of cubes; perfect-square trinomials; choosing the appropriate factoring strategy.
- Rational Expressions and Equations: Simplifying rational expressions; multiplying and dividing rational expressions; finding least common denominators; adding and subtracting rational expressions; complex fractions; solving rational equations and identifying extraneous solutions; applications (work problems, distance-rate-time, mixture).
- Radicals and Rational Exponents: Square roots and nth roots; properties of radicals; simplifying radicals; rational exponents; operations with radicals; rationalizing denominators (including binomial denominators); solving radical equations.
- Quadratic Equations: Solving by factoring; the square root property; completing the square; the quadratic formula; the discriminant and nature of roots; equations quadratic in form (substitution); applications (geometry, projectile motion, area).
- Graphing Linear Equations and Inequalities in Two Variables: The Cartesian plane; plotting points; graphing linear equations using intercepts and slope-intercept form; calculating slope; horizontal and vertical lines; parallel and perpendicular lines; writing equations of lines (slope-intercept, point-slope, standard); graphing linear inequalities; introduction to systems by graphing.
- Systems of Linear Equations: Solving 2-variable systems by substitution and elimination; consistent, inconsistent, and dependent systems; applications (mixture, value, motion, geometry).
- Introduction to Functions: Function notation f(x); evaluating functions; domain of common algebraic functions (polynomial, rational, radical); using function notation in modeling problems.
Optional Topics
- Three-Variable Systems: Solving 3x3 systems by elimination; applications.
- Variation: Direct, inverse, and joint variation; constant of variation; applications.
- Graphing Technology: Using Desmos, GeoGebra, or TI-84 graphing calculators to verify algebraic results.
- Conic Sections (Introduction): Some courses include a brief introduction to circles, parabolas, and other conics in standard form.
- Introduction to Function Transformations: Vertical and horizontal shifts of basic graphs.
Resources & Tools
- Standard Textbooks: Intermediate Algebra by Lial, Hornsby, McGinnis (Pearson — widely adopted in Florida); Introductory and Intermediate Algebra by Bittinger, Beecher, Johnson (Pearson); Intermediate Algebra by Blitzer (Pearson); Intermediate Algebra by Sullivan and Struve (Pearson); Beginning and Intermediate Algebra by Tussy and Gustafson (Cengage); OpenStax Intermediate Algebra 2e (free, open-access at openstax.org).
- Online Homework Platforms: Pearson MyLab Math (most common in Florida); ALEKS (used at UCF and other institutions); WebAssign; Hawkes Learning; MyMathLab.
- Required Calculator: Scientific calculator at most institutions (TI-30 series or equivalent). Some institutions allow but do not require a graphing calculator (TI-84 Plus). Some online or hybrid sections require specific calculators.
- Free Online Tools: Desmos (desmos.com — free graphing calculator and equation editor); GeoGebra (geogebra.org); Wolfram Alpha for symbolic verification; Symbolab for step-by-step solutions; Microsoft Math Solver.
- Tutoring and Practice Resources: Free college tutoring centers (most Florida State Colleges have dedicated math tutoring labs); Khan Academy Algebra (free, comprehensive); Paul's Online Math Notes (tutorial.math.lamar.edu); Patrick Just Math Tutorials; Professor Leonard's Algebra video series.
- Florida-Specific Resources: Florida General Education Course requirements; Florida SCNS course descriptions; institution-specific syllabi and learning outcomes documents (most Florida institutions publish detailed MAT1033 outcomes online).
Career Pathways
MAT1033 is the bridge course that prepares students for college-level mathematics across many pathways:
- Bridge to College Algebra – MAT1033 is the standard prerequisite for MAC1105 (College Algebra), which IS a Gen-Ed Core Mathematics course. Successful completion of MAC1105 fulfills the gen-ed math requirement for transfer to Florida public universities.
- Bridge to Liberal Arts Mathematics – MAT1033 satisfies prerequisites for MGF1106 (Mathematics for Liberal Arts I) and MGF1107 (Mathematics for Liberal Arts II), both of which are Gen-Ed Core Mathematics options for students whose majors do not require a calculus or statistics path.
- Bridge to Statistics – MAT1033 satisfies prerequisites for STA2023 (Elementary Statistics), the most common gen-ed statistics option.
- Career and Technical Programs – Many A.S. and workforce programs require MAT1033 or higher, including business, healthcare, technology, and engineering technology programs.
- Workforce and Life Skills Application – Algebra skills support careers across virtually every Florida industry — business analytics, financial services, healthcare measurement, technical trades, manufacturing quality control, and small-business ownership.
Important pathway note: Students intending to major in business, science, engineering, mathematics, or any STEM field should view MAT1033 as a stepping stone, not a destination. The college-level math requirement at Florida public universities for these majors is MAC1105 at minimum, with MAC2233 (Survey of Calculus) or MAC2311 (Calculus I) typically required. Students should consult their academic advisor about the proper pathway for their intended major.
Special Information
Gen-Ed and Gordon Rule Status — VERIFY AT YOUR INSTITUTION
MAT1033 typically does NOT satisfy the General Education Core Mathematics requirement and typically does NOT satisfy the Gordon Rule at Florida public universities. UCF explicitly classifies MAT1033C as a "bridge course" that may apply toward a degree as elective credit only and does not satisfy the GEP (General Education Program) or Gordon Rule. Many Florida State Colleges allow MAT1033 to count as elective credit toward A.A. and A.S. degrees but require students to complete a higher-level math course (MAC1105, MGF1106, MGF1107, or STA2023) for Gen-Ed math fulfillment. Students must verify their specific institution's and their target university's policies before relying on MAT1033 for degree progression.
Senate Bill 1720 (2013) and Developmental Education Exemption
Per Florida Senate Bill 1720 (2013) and State Board Rule 6A-10.0315, students who entered 9th grade in a Florida public high school in 2003-2004 or any subsequent year and earned a standard Florida high school diploma, AND students serving as active-duty members in any branch of the U.S. Armed Services, are exempt from common placement testing (P.E.R.T.) and from developmental education at all Florida College System institutions. These students may enroll directly in MAT1033 (or MGF1106, MGF1107) without first completing MAT0022 (Combined Pre-Algebra and Beginning Algebra) or MAT0028 (Elementary Algebra). For placement in any college-credit math course beyond MAT1033/MGF1106/MGF1107 (such as direct entry into MAC1105), exempt students will be required to take the common placement test or demonstrate readiness through SAT/ACT/ALEKS PPL scores.
Prerequisite
Students must satisfy Florida's developmental education math requirement per Rule 6A-10.0315 — through one of the following pathways:
- Successful completion of MAT0022C, MAT0028, or MAT0057 (Florida developmental algebra options) with a passing grade
- Qualifying placement score on the P.E.R.T., SAT Math, ACT Math, or ALEKS PPL placement test
- Eligible exemption per Senate Bill 1720 (Florida public high school graduate from 2003-2004 forward, or active-duty military)
Some Florida institutions have moved to corequisite remediation models in which MAT1033 is paired with a developmental support lab (sometimes designated MAT1033C with the C indicating the lab/recitation co-requisite, distinct from the typical "C" lab/lecture-integrated convention).
Course Variants
MAT1033 is offered as MAT1033 (3-credit lecture only) at most institutions and as MAT1033C (with integrated supplemental instruction or co-requisite support) at others. The two forms are equivalent for transfer purposes within Florida.
Vocational Credit
MAT1033 is unique in that it carries college credit (3 credit hours) but is generally below the level considered "college-level" for transfer to four-year programs. The course is widely used in workforce preparation, A.S. degree programs, and as a bridge for students returning to higher education after extended time away.
Workload and Time Expectations
Most institutions expect 6-9 hours of weekly out-of-class work, including online homework completion (MyLab Math or ALEKS), reading, and practice problems. Most courses include 4-5 mid-term examinations plus a comprehensive final examination. Students struggling with prerequisite skills should make heavy use of free college tutoring services, online homework hint systems, and peer study groups.
Pathway Planning
Students should consult their academic advisor early to identify the correct mathematics pathway for their intended major. The standard pathways are:
- STEM/Engineering: MAT1033 → MAC1105 → MAC1140 + MAC1114 (or MAC1147) → MAC2311 → MAC2312 → MAC2313
- Business/Social Sciences: MAT1033 → MAC1105 → MAC2233 (Survey of Calculus) and/or STA2023
- Liberal Arts/Education: MAT1033 → MGF1106 and/or MGF1107 (or MAC1105 + STA2023)
- A.S./Workforce: MAT1033 may complete the math requirement for many A.S. degrees and workforce programs.
Importance of Strong Algebra Foundations
The skills built in MAT1033 — especially factoring, rational expressions, exponent rules, and the quadratic formula — are foundational for every subsequent math course and for science courses (chemistry, physics, biology). Students who pass MAT1033 with marginal mastery often struggle in MAC1105 and beyond. Students are strongly encouraged to use tutoring resources to ensure solid mastery rather than just a passing grade.