MATH 107 at the University of Maryland Global Campus is a three-credit course and the first of the two-course series MATH 107 and MATH 108, an alternative to MATH 115.
UMGC describes an introduction to equations and inequalities and a study of functions, including graphing polynomial, rational, exponential and logarithmic functions.
The course expects fluency in the language of algebra and use of technology for data modeling. Students tend to struggle with the pace of new function types, so the best preparation is steady practice and clear, step-by-step working.
Course at a Glance
| Item | Details |
|---|---|
| University | University of Maryland Global Campus |
| Course code | MATH 107 |
| Credits | 3 |
| Level | Undergraduate |
| Series | First course in MATH 107 and MATH 108; alternative to MATH 115 |
| Credit rule | Credit for only one of MATH 107 or MATH 115 |
| Typical work | Problem sets, graphing and modeling with technology (general; check your term) |
What MATH 107 Covers
| Area | Skill |
|---|---|
| Real and complex numbers | Operations, including the imaginary unit |
| Equations and inequalities | Linear, quadratic, absolute value and others |
| Functions and graphs | Domain, range, transformations, circles |
| Polynomial and rational functions | Zeros, asymptotes and graphs |
| Exponential and logarithmic functions | Growth, decay and inverse relationships |
| Modeling | Using technology to fit data and solve applied problems |
Key Concepts Explained
Quadratics
Factor when it is quick; use the quadratic formula when it is not. For x^2 - 5x + 6 = 0 the factors are (x - 2)(x - 3), so x = 2 or x = 3.
Absolute Value Inequalities
|x - 3| < 2 means x lies within 2 units of 3.
Example: -2 < x - 3 < 2, so 1 < x < 5.
Complex Numbers
With i squared equal to -1, multiply as with binomials and replace i squared.
Example: (2 + 3i)(1 - i) = 2 - 2i + 3i - 3i^2 = 2 + i + 3 = 5 + i.
Typical Assignments and How to Approach Them
| Assignment type | What it tests | How to approach it |
|---|---|---|
| Equation and inequality sets | Algebraic technique | Show each step, check answers by substitution |
| Graphing tasks | Reading and sketching functions | Find intercepts and asymptotes first, then plot a few points |
| Modeling tasks | Applying functions to data | Choose the model type from the pattern, then interpret the parameters |
| Applications | Translating words into equations | Define variables, write equations, solve, and answer in a sentence |
Credit Rules to Know
UMGC states that students may receive credit for only one of MATH 107 or MATH 115, and MATH 108 follows MATH 107 as the second course of the series. If you are unsure which route fits your degree, confirm with your academic advisor before enrolling.
Building a Weekly Routine
Algebra improves with frequent short sessions. Do new problems the day you learn the method, review them two days later, and mix in older topics each week. When you miss a problem, write the rule you missed beside it.
More Worked Examples
Quadratic formula: for x^2 + 4x + 1 = 0, x = (-4 plus or minus the square root of 12)/2 = -2 plus or minus the square root of 3.
Circle: x^2 + y^2 - 6x + 4y - 12 = 0. Complete the squares: (x - 3)^2 + (y + 2)^2 = 25, so the center is (3, -2) and the radius is 5.
Domain: For f(x) = the square root of (x - 2), divided by (x - 5), you need x - 2 at least 0 and x not equal to 5, so the domain is x at least 2 with x not equal to 5.
Using Technology Sensibly
UMGC notes that technology is used for data modeling. Use graphing software or a spreadsheet to explore a model, test an equation and check a graph, but still show the algebra that produces your answer.
| Task | Technology helps with | You still show |
|---|---|---|
| Solving an equation | Checking the roots on a graph | The algebraic steps |
| Fitting data | Producing a model quickly | Why that model type fits |
| Graphing | Seeing the overall shape | Intercepts and asymptotes found by hand |
A Short Self-Test
Try these without notes, then check against your lessons. They sample the course's main skills.
- Solve x^2 - 7x + 12 = 0 and check both roots.
- Solve |2x - 1| = 5.
- Write (3 - i)(2 + i) in the form a + bi.
- Find the domain of the square root of (x + 4).
- Describe the graph of y = -(x - 2)^2 + 1.
Where Students Get Stuck
- Extraneous solutions. Check roots in the original equation.
- Sign errors with inequalities. Reverse the sign only when multiplying or dividing by a negative.
- Graph shapes. Learn each function family from its key features.
- Logarithm rules. Practice until product, quotient and power rules are automatic.
Study Tips for MATH 107
- Keep a list of the function families and their graphs.
- Check every solution by substitution.
- Use technology to verify, not replace, your algebra.
- Redo missed problems a week later.
How We Help with MATH 107
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.
Every order is written from scratch, comes with free revisions within the scope of your original request, and is refunded in full if it is late.
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Frequently Asked Questions
Yes. UMGC calls it the first of MATH 107 and MATH 108, an alternative to MATH 115.
No. UMGC says credit is allowed for only one of MATH 107 or MATH 115.
Polynomial, rational, exponential and logarithmic functions, with graphing.
The catalog entry shows none.
UMGC notes that technology is used for data modeling.
Yes. We review each step and explain any corrections.