# MATH 1710 Course Topics & Learning Outcomes

**Topics
**

Numbers, Data, and Problem Solving

Visualization of Data

Functions and Their Representations

Types of Functions and Their Rates of Change

**I. Learning Outcomes**

1. Students will demonstrate the ability to classify numbers and to interpret data

presented in visual or numeric forms.

2. Students will demonstrate the ability to convert numbers between standard and

scientific notation, and to use scientific notation in numerical computations.

3. Students will demonstrate the ability to extrapolate necessary data and information

from given application problems and to use this data and the processes of problem

solving to successfully determine solutions.

4. Students will demonstrate the ability to distinguish corresponding sets as

representations of relations or functions by the analysis of graphical, numeric, or

symbolic data .

5. Students will demonstrate the ability to identify types of functions and to determine the

domain, range, and average rate of change from their graphical, numeric, and symbolic

representations.

**Topics**

Linear Functions and Models

Equations of Lines

Linear Equations

Linear Inequalities

Piece-wise Defined Linear Functions

Linear Approximation

**II. Learning Outcomes**

1. Students will demonstrate the ability to solve linear equations, inequalities, and

compound inequalities , and to represent solutions in set , interval, and graphical

notations.

2. Students will demonstrate the ability to solve absolute value equations and inequalities.

3. Students will demonstrate the ability to graph linear functions and vertical lines, and to

determine intercept (s) and slope.

4. Students will demonstrate the ability to write the equation of a linear function given the

slope and a point on the line or given the slope and a parallel or perpendicular line.

5. Students will demonstrate the ability to graph a scatter plot of given points and to use

regression to approximate a linear model.

6. Students will demonstrate the ability to evaluate and graph piece-wise defined linear

functions.

**Topics
**

Quadratic Functions and Models

Quadratic Equations and Problem Solving

Transformations of Graphs

**III. Learning Outcomes**

1. Students will demonstrate the ability to use factoring , the square root property, and the

quadratic formula to solve quadratic equations.

2. Students will demonstrate the ability to use the discriminant and graphical

representations to determine types of solutions for quadratic equations.

3. Students will demonstrate the ability to solve applications and model data involving

quadratic equations.

4. Students will demonstrate the ability to determine maxima and minima of quadratic

functions using a graphing calculator.

5. Students will demonstrate the ability to graph quadratic functions, to identify the vertex

and axis of symmetry, and to convert between standard and vertex forms of a function.

6. Students will demonstrate the ability to solve quadratic inequalities graphically and

symbolically.

7. Students will demonstrate the ability to use vertical and horizontal shifts and vertical

stretching and shrinking in transformations of graphs.

**Topics**

Polynomial Functions and Models

Rational Functions and Models

**IV. Learning Outcomes**

1. Students will demonstrate the ability to understand and interpret data from the graphs

of polynomial functions.

2. Students will demonstrate the ability to identify the domain of a rational function.

3. Students will demonstrate the ability to determine vertical and horizontal asymptotes of

the graphs of rational functions.

**Topics
**

Combining Functions

Inverse Functions and Their Representations

Exponential Functions and Models

Logarithmic Functions and Models

Properties of Logarithms

Exponential and Logarithmic Equations

Functions and Equations of Two Variables

**V. Learning Outcomes**

1. Students will demonstrate the ability to perform arithmetic operations and

compositions of functions using graphical, numeric, and symbolic representations.

2. Students will demonstrate the ability to identify one-to-one functions and find inverse

functions symbolically.

3. Students will demonstrate the ability to determine the domains and ranges of inverse

functions and to graph inverse functions and their line of symmetry.

4. Students will demonstrate the ability to distinguish between linear and exponential

functions and to distinguish between exponential growth and decay.

5. Students will demonstrate the ability to calculate compound interest and to use

exponential models to represent growth and decay.

6. Students will demonstrate the ability to calculate logarithms.

7. Students will demonstrate the ability to solve logarithmic and exponential equations.

8. Students will demonstrate the ability to apply basic properties of logarithms and to use

the change of base formula.

**Topics**

Linear Systems of Equations and Inequalities in Two Variables

Properties and Applications of Matrices

Solutions of Linear systems Using Matrices

Inverses of Matrices

Determinants

**VI. Learning Outcomes**

1. Students will demonstrate the ability to solve systems of equations and
inequalities

graphically.

2. Students will demonstrate the ability to solve systems of linear equations by

substitution and elimination .

3. Students will demonstrate the ability to determine dimensions of matrices and
to

determine if a matrix is in row-echelon form.

4. Students will demonstrate the ability to find sums, differences , and scalar
multiples of

matrices and to determine when matrices may be multiplied and to perform matrix

multiplication.

5. Students will demonstrate the ability to represent systems of linear
equations with

matrices and to use matrices and technology to solve systems.

6. Students will demonstrate the ability to solve applications using systems of
equations.

7. Students will demonstrate the ability to use technology to find inverses of
matrices and

to solve linear systems with inverses.

8. Students will demonstrate the ability to use technology to find determinants.

**Topics**

Counting

Probability

**VII. Learning Outcomes
**

1. Students will demonstrate the ability to apply the fundamental counting principle.

2. Students will demonstrate the ability to calculate and apply permutations and

combinations.

3. Students will demonstrate the ability to calculate the probability of independent,

dependent, and compound events.

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