MATH 115 at the University of Maryland Global Campus is a three-credit pre-calculus course. UMGC describes an explication of equations, functions and graphs, with topics including polynomials, rational functions, exponential and logarithmic functions, trigonometry and analytical geometry.
Because it combines material that other schools split into two courses, the pace is brisk. Students who keep a summary of each function family and practice mixed sets do best.
Course at a Glance
| Item | Details |
|---|---|
| University | University of Maryland Global Campus |
| Course code | MATH 115 |
| Credits | 3 |
| Level | Undergraduate |
| Alternative to | The MATH 107 and MATH 108 series |
| Credit rule | Credit for only one of MATH 107, MATH 108 or MATH 115 |
| Restriction | Not open to students who have completed MATH 140 or any course for which MATH 140 is a prerequisite |
| Typical work | Problem sets and modeling tasks (general; check your term) |
What MATH 115 Covers
| Area | Skill |
|---|---|
| Equations and inequalities | Solving and checking solutions |
| Polynomial and rational functions | Zeros, asymptotes and graphs |
| Exponential and logarithmic functions | Modeling growth and solving equations |
| Trigonometry | Functions, identities and equations |
| Analytical geometry | Conics and related graphs |
| Mathematical modeling | Translating, solving and interpreting applied problems |
Key Concepts Explained
Logarithmic Equations
Combine logarithms, rewrite in exponential form and solve, then check for extraneous solutions.
Example: log2(x) + log2(x - 2) = 3 becomes x(x - 2) = 8, so x^2 - 2x - 8 = 0 and x = 4 or x = -2. Since x = -2 makes a logarithm undefined, the only solution is x = 4.
Factor Theorem
If p(a) = 0 then x - a is a factor of p(x). For p(x) = x^3 - 6x^2 + 11x - 6, p(1) = 0, so x - 1 is a factor.
Modeling
Choose a function family from the pattern in the data, find its parameters, then interpret them in context, including any limit on where the model can be trusted.
Typical Assignments and How to Approach Them
| Assignment type | What it tests | How to approach it |
|---|---|---|
| Function analysis problems | Reading structure from equations | List domain, zeros, asymptotes and end behavior before sketching |
| Equation solving | Technique and checking | Isolate, apply the inverse, then verify |
| Trigonometry tasks | Identities and equations | Use reference angles and quadrant signs |
| Applied modeling | Translating a situation | Define variables, choose the model, interpret the result |
MATH 115 or the Two-Course Route
UMGC offers MATH 115 as an alternative to taking MATH 107 and MATH 108 separately, and it allows credit for only one of these routes. Either one satisfies the prerequisite for MATH 140 Calculus I. Check your degree plan or ask an advisor which fits your program.
Pacing a Combined Course
Because MATH 115 covers so much, treat each function family as its own mini-unit with a summary sheet: equation, graph shape, key features and one worked example. Review those sheets weekly so earlier units stay fresh when you reach trigonometry.
A Worked Growth Question
How long does 1,000 take to double at 5% growth a year? Solve 1.05^t = 2 by taking logs: t = ln 2 / ln 1.05, about 0.6931/0.04879, which is about 14.2 years.
Check: 1.05^14.2 is about 2.0. Always test a logarithmic answer by substituting back.
Function Families Summary
A single summary table is the best revision tool for a combined course. Add an example graph beside each row.
| Family | Key features to know |
|---|---|
| Polynomial | Degree, end behavior, zeros and multiplicity |
| Rational | Vertical and horizontal asymptotes, holes |
| Exponential | Base, growth versus decay, horizontal asymptote |
| Logarithmic | Domain restriction, vertical asymptote, inverse relationship |
| Trigonometric | Period, amplitude, phase shift |
A Short Self-Test
These questions sample the main strands of the course. Aim to explain each answer, not only state it.
- Find the zeros of x^3 - 4x.
- State the vertical and horizontal asymptotes of (2x)/(x - 1).
- Solve 2^x = 10 using logarithms.
- Evaluate sin(pi/6) and cos(pi/3).
- Describe how y = log(x + 2) differs from y = log(x).
Managing the Pace
Because MATH 115 covers algebra, functions and trigonometry in one term, falling behind in an early week is costly. Do the practice for each topic within a day or two of the lesson, and leave a short weekly slot for revisiting earlier topics. When a topic feels shaky, redo its worked examples from scratch rather than rereading them.
Where Students Get Stuck
- Extraneous roots. Check log and rational equations.
- Mixing up inverse functions. Remember exponentials and logarithms undo each other.
- Trig modes. Check degrees versus radians.
- Volume of material. Spread practice across the week.
Study Tips for MATH 115
- Summarize each function family on one page.
- Do mixed review every week.
- Graph by hand before trusting software.
- Redo errors without notes.
How We Help with MATH 115
Send the problem set, your notes and your working. A maths tutor can explain each method, prepare fully worked solutions to study from, or check your steps.
GradeEssays is independent and not affiliated with University of Maryland Global Campus. Our work is a study and reference aid: use it to understand the method, then complete and submit your own work under UMGC's academic integrity policy.
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Frequently Asked Questions
UMGC lists MATH 115 as an alternative to the two-course series and permits credit for only one route.
UMGC says it is not open to students who have completed MATH 140 or any course for which MATH 140 is a prerequisite.
MATH 140 Calculus I lists MATH 108 or MATH 115 as its prerequisite.
Polynomials, rational functions, exponential and logarithmic functions, trigonometry and analytical geometry.
It covers more in one course, so the pace is faster.
Yes. We review the steps and explain corrections.