# MATH 117

**Chapter 2.** *Combining Algebra and Geometry* [1.5 Weeks]

2.1 - (Cover very quickly.) The coordinate plane: coordinates, graphs of equations, distance formula, length, perimeter, circumference.

2.2 – (Cover very quickly.) Lines: slope, equation of a line, parallel/perpendicular lines, midpoints.

2.3 – Quadratic Expressions and Conic Sections: completing the square, quadratic formula, circles, ellipses, hyperbolas. Foci for ellipses/hyperbolas optional.

2.4 – (Cover very quickly.) Area: squares, rectangles, parallelograms, triangles, trapezoids, stretching, circles and ellipses.

**Chapter 3.** *Functions and their Graphs* [2.5 Weeks]

3.1 – Functions: definition, graphs, domain, range, tables.

3.2 – Function transformations and graphs: vertical/horizontal shifts, stretches, flips, combinations of transformations, even/odd functions.

3.3 – Composition of Functions: definition, importance of order, decomposing functions, composing 3 or more functions, transformations as functions.

3.4 – Inverse Functions: definition, one-to-one functions, domain/range of inverse functions, composition of a function and its inverse, importance of notation.

3.5 – A graphical approach to inverse functions: graph of inverse functions, horizontal line test, increasing/decreasing function, inverses via tables.

**Chapter 4.** *Polynomial and Rational Functions* [2.5 Weeks]

4.1 – Integer exponents: positive integer exponents, properties of exponents, negative integer exponents.

4.2 – Polynomials: degree, algebra of polynomials, zeros, factorization, behavior as *x* approaches positive/negative infinity, graphs.

4.3 – Rational functions: definition, algebra of rational functions, polynomial division, behavior as *x* approaches positive/negative infinity, graphs.

4.4 – Complex numbers: complex number system, arithmetic/algebra of complex numbers, conjugates, division, relation to zeros and factorization.

**Chapter 5.** *Exponents and Logarithms* [3 Weeks]?

5.1 – Exponents and exponential functions: roots, rational exponents, real exponents, exponential functions.

5.2 – Logarithms as inverses of exponential functions: logarithms with arbitrary base, common logarithms, number of digits, logarithm of a power, decay/half-life problems.

5.3 – Applications of Logarithms: logarithm of products/quotients, change of base, Richter scale, decibels. Apparent magnitude and sound intensity optional.

5.4 – Exponential growth: functions with exponential growth, population growth, compound interest.

**Chapter 6.** *e and the Natural Logarithm* [2 Weeks]

6.1 – Defining *e* and ln: estimating area using rectangles, definitions of *e* and ln, properties of ln.

6.2 (Optional) – Approximations of *e* and ln, and an area formula.

6.3 – Exponential growth revisited: continuous compounding of interest, continuous growth rates, doubling time.

**Chapter 7.** *Systems of Equations* [1 Week]

7.1 – Equations and systems of equations: solving an equation, solving a system graphically, solving a system by substitution.

7.2 – Solving systems of linear equations: linear equations and number of solutions, systems of linear equations, Gaussian elimination.

There is one required book for this course:

Axler, Sheldon. *Precalculus: A Prelude to Calculus, 2nd Edition* Paperback w/ Wileyplus ISBN: 978-1-118-55625-2. Hoboken, NJ: Wiley, 2012.

Many instructors do require WileyPLUS. If your section is using WileyPLUS, it is important that you buy a bundle that includes a WileyPLUS access code since you will need it in order to submit homework. A WileyPLUS access code includes an online electronic version of the textbook. You can obtain an access code in one of three ways:

- Buy a new copy of the text bundled with WileyPLUS access code from the bookstore.
- Buy a
*Precalculus: A Prelude to Calculus 2E*access code directly from the publisher’s website. - Buy a Precalculus: A Prelude to Calculus 2E WileyPLUS access code directly from the bookstore.

If you go for option (2) or (3) above, then you will only have access to the book electronically through WileyPLUS. Whether you have purchased an access code or not, all students have immediate and free access to register for our class WileyPLUS page. **Free trial access expires two weeks after the semester starts.**

### Center for Tutoring and Academic Excellence

The Center for Tutoring & Academic Excellence offers free collaborative learning opportunities that include small group tutoring and tutor-led study halls to Loyola students. To learn more or request tutoring services, visit the Center for Tutoring & Academic Excellence online at http://www.luc.edu/tutoring.

### Loyola Math Club Tutoring

The Loyola Math Club offers free tutoring to students in Math 117 (and other courses). Further details regarding the important information of where and when will be posted once announced.

WileyPLUS is an online, interactive environment for teaching and learning. As part of the required text for MATH 117, you are asked to purchase an access code for WileyPLUS. This access code is active for up to one year, and you will therefore be able to use WileyPLUS next semester (if you take MATH 118) at no additional cost. Many sections of MATH 117 will use WileyPLUS as a required homework component of the final course grade.

Follow the steps below to register for your section in WileyPLUS:

- Go to the WileyPLUS homepage.
- In the Students section of the homepage, click on the
**Get started**button. - Enter
**LOYOLA UNIV - CHICAGO**as the school name and click**Find**. - Click the plus sign next to
**PRECALCULUS/MATH 117**to expand the section list. - Click on your section.
- Create a WileyPLUS account or log in using an existing account.
- If you have purchased a hard copy of the text with the access code, enter your code to register for the course. Otherwise you can purchase a code (for $55.00).

**Note: All students may register for WileyPLUS immediately, even if you have not received your copy from the bookstore at the start of the semester. If you have not received an access code by January 28, you will no longer have access to WileyPLUS.**

Mathematica is a powerful computing environment that is designed for use in engineering, mathematics, finance, physics, chemistry, biology, and a wide range of other fields. Loyola students and faculty can download and install the latest copy of Mathematica for free. You must be logged on to Loyola VPN, and then visit the following ITS webpage, https://digitalmedia.luc.edu/News/NewsItem/View/4/mathematica-version-9-downloads-available.

## Other Useful Loyola Sites

- Sakai (Online Course Materials)
- Tutoring Center
- Get
*Mathematica*for***free***through myITS - WebWork