Course Description

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Description of the course.

MAC 1105 (Basic College Algebra) is a review of Algebra designed to prepare students for MAC 1140 or MAC 1147. Content for this course includes: reviewing real and complex numbers, solving various types of equations, graphing basic functions, and exploring exponential and logarithmic functions.

WARNING: This course is designed for students who will eventually take Calculus or need MAC 1105 for their major. Students looking only to complete their general math requirement should heavily consider taking Math for Liberal Arts Majors 1 (MGF 1106).

Common paths for students taking this course are:

MAC 1105 $\rightarrow$ MAC 1140 $\rightarrow$ MAC 2233 (Survey of Calculus)
MAC 1105 $\rightarrow$ MAC 1147 $\rightarrow$ MAC 2311 (Calculus I)

Based on this split, the course content is divided into two parts: Core and Advanced. The Core content works through the foundational knowledge of College Algebra (functions) while the Advanced content prepares you for either MAC 2233 or MAC 2311. You will only complete Advanced content in preparation for one of these courses.

The specific objectives for the Core and Advanced content are written below. By the end of the course, students must show proficiency in the majority of the Core content. A and B students will show proficiency in the Core and Advanced content. Exactly how this will be determined and how your grade will be determined are described later.

Core Modules

Module 1 - Real and Complex Numbers
- Identify the subgroup of Real numbers a number belongs to.
- Identify the subgroup of Complex numbers a number belongs to.
- Apply the properties of Real numbers to simplify large expressions.
- Add/Subtract/Multiply/Divide Complex numbers.
Module 2 Linear Functions
- Construct linear functions with a slope and point or with two points.
- Convert a linear function between slope-intercept form and Standard form.
- Convert between a linear equation and the graph of a linear equation.
- Solve linear equations.
Linear Inequalities
- Describe linear inequalities.
- Convert between linear inequalities, graphs of linear inequalities, and their interval notation.
- Solve linear inequalities.
Quadratic Functions
- Construct quadratic functions with a vertex and direction of function.
- Convert between quadratic functions and their graphs.
- Factor quadratic functions with leading coefficient greater than 1.
- Solve quadratic equations.
Radical Functions
- Identify the domain of a radical function.
- Convert between radical functions and their graphs.
- Solve radical equations that lead to linear or quadratic equations.
Polynomial Functions
- Identify the end behavior of a polynomial function (in factored form).
- Identify the zero behaviors of a polynomial function (in factored form).
- Convert between polynomial functions (in factored form) and their graphs.
- Construct lowest-degree polynomial functions given their zeros.
Rational Functions
- Identify the domain of a rational function.
- Convert between basic rational functions and their graphs.
- Solve rational equations that lead to linear or quadratic equations.
Logarithmic and Exponential Functions
- Describe the domain/range of logarithmic or exponential functions.
- Convert between logarithmic and exponential forms of an equation.
- Utilize the properties of logarithmic functions to simplify expressions.
- Solve exponential equations with same or different bases.


Calculus	Biological Sciences
This set is designed to prepare you for the first concept you will encounter in Calculus: Limits.	This set is designed to prepare you for modeling real-life phenomena using functions we explored in the Core Modules.


A9 - Operations on Functions	B9 Modeling with Linear Equations
Identify the domain after operating (+, -, $\times$ , $\div$ ) on functions. Evaluate the composition of two functions. Determine whether a function is 1-1. Find the inverse of a function, if it exists.	Identify when a real-world situation would require a linear function. Describe the domain on which the model is valid. Construct a model equation for the real-life situation.


A10 - Synthetic Division	B10 - Modeling with Power Equations
Divide two polynomials using synthetic division. Determine the possible rational roots of a polynomial. Use synthetic division to complete factor a polynomial.	Identify when a real-world situation would require a direct variation equation. Identify when a real-world situation would require an inverse variation equation. Construct a model equation for the real-life situation.


A11 - Introduction to Limits	B11 - Modeling with Log or Exp Equations
Interpreting the notation for limits. Evaluate the left or right limit of a function. Evaluate the limit of a function.	Identify when a real-world situation would require a log/exp function. Describe the domain on which the model is valid. Construct a model equation for the real-life situation.


A12 - Graphing Rational Functions	B12 - Solving Modeling Problems
Use limits to determine the holes of a rational function. Use limits to determine the vertical asymptotes of a rational function. Use limits to describe he horizontal asymptotes of a rational function. Use limits to describe the oblique asymptotes of a rational function.	Determine the appropriate type of function to model the situation. Construct a model equation for the real-life situation. Solve the model equation.

Press...	...to do
left/right arrows	Move cursor
shift+left/right arrows	Select region
ctrl+a	Select all
ctrl+x/c/v	Cut/copy/paste
ctrl+z/y	Undo/redo
ctrl+left/right	Add entry to list or column to matrix
shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
ctrl+up/down	Add row to matrix
shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
norm	$\|\|\blue{[?]}\|\|$
text	$\text{\blue{[?]}}$
sym_name	$\backslash\texttt{\blue{[?]}}$
abs	$\left\|\blue{[?]}\right\|$
sqrt	$\sqrt{\blue{[?]}}$
paren	$\left(\blue{[?]}\right)$
floor	$\lfloor \blue{[?]} \rfloor$
factorial	$\blue{[?]}!$
exp	${\blue{[?]}}^{\blue{[?]}}$
sub	${\blue{[?]}}_{\blue{[?]}}$
frac	$\dfrac{\blue{[?]}}{\blue{[?]}}$
int	$\displaystyle\int{\blue{[?]}}d\blue{[?]}$
defi	$\displaystyle\int_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}d\blue{[?]}$
deriv	$\displaystyle\frac{d}{d\blue{[?]}}\blue{[?]}$
sum	$\displaystyle\sum_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
prod	$\displaystyle\prod_{\blue{[?]}}^{\blue{[?]}}\blue{[?]}$
root	$\sqrt[\blue{[?]}]{\blue{[?]}}$
vec	$\left\langle \blue{[?]} \right\rangle$
mat	$\left(\begin{matrix} \blue{[?]} \end{matrix}\right)$
*	$\cdot$
infinity	$\infty$
arcsin	$\arcsin\left(\blue{[?]}\right)$
arccos	$\arccos\left(\blue{[?]}\right)$
arctan	$\arctan\left(\blue{[?]}\right)$
sin	$\sin\left(\blue{[?]}\right)$
cos	$\cos\left(\blue{[?]}\right)$
tan	$\tan\left(\blue{[?]}\right)$
sec	$\sec\left(\blue{[?]}\right)$
csc	$\csc\left(\blue{[?]}\right)$
cot	$\cot\left(\blue{[?]}\right)$
log	$\log\left(\blue{[?]}\right)$
ln	$\ln\left(\blue{[?]}\right)$
alpha	$\alpha$
beta	$\beta$
gamma	$\gamma$
delta	$\delta$
epsilon	$\epsilon$
zeta	$\zeta$
eta	$\eta$
theta	$\theta$
iota	$\iota$
kappa	$\kappa$
lambda	$\lambda$
mu	$\mu$
nu	$\nu$
xi	$\xi$
omicron	$\omicron$
pi	$\pi$
rho	$\rho$
sigma	$\sigma$
tau	$\tau$
upsilon	$\upsilon$
phi	$\phi$
chi	$\chi$
psi	$\psi$
omega	$\omega$
Gamma	$\Gamma$
Delta	$\Delta$
Theta	$\Theta$
Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
Sigma	$\Sigma$
Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

Controls

Symbols

Settings