Covers analytic geometry, functions and their graphs, algebraic and graphical solutions of equations and inequalities, graphs and zeros of polynomial functions, conic sections, linear and polynomial modeling, systems of equations and inequalities, sequences and series, and the Binomial Theorem. Includes techniques of problem solving and applications. Requires a graphing calculator, with the TI-84 Plus series recommended, and access to an online homework management system.

### Goals, Topics, and Objectives

- To develop the advanced algebraic skills needed in college-level science and mathematics courses.
- To provide an introduction to functions.
- To develop familiarity with some mathematical and physical applications of advanced algebra and analytic geometry.
- To incorporate graphing calculators whenever appropriate to illustrate concepts and solve problems.
- To develop in students the problem-solving skills needed to interpret, analyze, and solve applied problems requiring college-level algebraic skills.

- Solution of Equations and Inequalities
- Solve linear equations and linear inequalities in one variable algebraically and graphically.
- Solve quadratic equations and inequalities algebraically and graphically.
- Solve rational equations and inequalities algebraically and graphically.
- Solve radical equations algebraically and graphically.
- Solve absolute value equations and inequalities algebraically and graphically.
- Solve polynomial equations and inequalities algebraically and graphically.

- Characteristics of Functions and their Graphs
- Determine if an equation, graph, or table of values represents a function, and state the domain and range of the function.
- Determine graphically and algebraically whether a function is even, odd, or neither.
- Test algebraically symmetry with respect to x-axis, y-axis, and the origin.
- Determine graphically if a function is increasing, decreasing, or constant.
- Determine the location of maxima and minima using a graphing utility.

- Basic functions and their transformations.
- Graph identity, constant, square, cubic, square root, cube root, absolute value, greatest integer, reciprocal functions of the form 1/x and 1/(x squared), and piecewise-defined functions by hand, and check using the graphing utility.
- Analyze and graph functions in terms of translations, reflections, and expansions or contractions.
- Determine the graph of a function obtained from a series of transformations.

- Operations on Functions
- Find the sum, difference, product, quotient, and composition of two functions and their domains given their equations or graphs.
- Evaluate composite functions.
- Find and simplify the difference quotient of a function.

- Linear Functions and their Graphs
- Graph linear functions by hand, and check using a graphing utility.
- Find the intercepts of a linear function algebraically and graphically.
- Determine the slope of a line joining two points in the plane, and determine the slope of a line given its equation.
- Produce a graph of a linear function by using slope and a point on a line.
- Write equations of lines satisfying specified sets of conditions.
- Write equations of parallel and perpendicular lines satisfying specified sets of conditions.
- Estimate the equation of the line of best fit for a set of bivariate data algebraically and by using a regression program in a graphing utility.
- Solve applied problems involving the line of best fit for a set of bivariate data.

- Quadratic Functions and their Graphs
- Graph quadratic functions by hand and check using a graphing utility.
- Find the intercepts of quadratic functions algebraically and graphically.
- Identify the vertex and axis of symmetry of a quadratic function both algebraically and by using a graphing utility.
- Determine the maximum or minimum value of a quadratic function both algebraically and by using a graphing utility.
- Solve applied maximum and minimum problems both algebraically and by using a graphing utility.
- Determine a quadratic model for a given set of data using a graphing utility.

- Quadratic Equations and Inequalities
- Solve quadratic equations algebraically using factoring, the square root property, and the quadratic formula, and verify solutions graphically.
- Perform basic arithmetic operations on complex numbers, and solve quadratic equations with complex solutions.
- Determine the number and type of solutions to a quadratic equation using the discriminant.
- Solve equations that are quadratic in form algebraically, and verify solutions using a graphing utility.
- Solve inequalities involving quadratic functions algebraically, and verify solutions using a graphing utility.

- Polynomial Functions and their Graphs
- Determine algebraically the intercepts of a polynomial function, and verify graphically.
- Determine a polynomial function’s intercepts, extreme values, turning points, and intervals of increase and decrease by using a graphing utility.
- Determine the end behavior of a polynomial function using the degree of the polynomial and its leading coefficient.
- Construct a polynomial function with specified zeros.

- Polynomial Equations and Inequalities
- Test factors for polynomial functions by using the Remainder and Factor Theorems, and factor polynomial functions to find the real zeros.
- Solve polynomial equations by using the Rational Zeros Theorem and synthetic division in conjunction with a graphing utility.
- Find the complex solutions of polynomial equations.
- Solve polynomial inequalities algebraically and graphically.

- Analytic Geometry and Conic Sections
- Find the distance between two points in the coordinate plane by means of the distance formula, and find the midpoint of the segment joining the points.
- Complete the square to write equations of circles, parabolas, ellipses, and hyperbolas in standard form.
- Determine the center and radius from the equation of the circle, and use these to sketch its graph by hand.
- Write the equation of a circle satisfying a set of specified conditions.
- Determine the vertex, focus, and directrix from the equation of a parabola, and use these to sketch its graph.
- Write the equation of a parabola given information about its vertex, focus, or directrix.
- Determine the center, foci, vertices, and the lengths of the major and minor axes from the equation of an ellipse, and use these to sketch its graph.
- Write the equation of an ellipse given information about its center, foci, vertices, or major and minor axes.
- Determine the center, foci, vertices, asymptotes, and the lengths of the conjugate and transverse axes from the equation of a hyperbola, and use these to sketch its graph.
- Write the equation of a hyperbola given information about its center, foci, vertices, asymptotes, or the lengths of the conjugate and transverse axes.
- Graph conic sections using a graphing utility.
- Solve applied problems involving parabolas, ellipses, and hyperbolas.

- Systems of Equations and Inequalities
- Solve 2 x 2 and 3 x 3 systems of linear equations by the methods of substitution and elimination.
- Classify systems of equations as inconsistent, consistent, or dependent, and represent solutions of dependent systems.
- Solve applied problems by using a system of linear equations.
- Represent the solution of a system of linear inequalities graphically.
- Solve systems of nonlinear equations graphically and algebraically.

- Sequences and Series
- Write terms of a sequence given its general term.
- Write the terms of a sequence using a recursive definition.
- Determine if a sequence is arithmetic, geometric, or neither.
- Given an arithmetic or geometric sequence of terms, write a general formula for the nth term of the sequence.
- Expand a sum of terms represented by summation notation, and express a finite sum in terms summation notation.
- Find the sum of a finite number of terms of a sequence using properties of sequences, and, in particular, find finite sums of arithmetic and geometric sequences.
- Find the sum of a geometric series if it exists.
- Expand powers of binomials.

### Assessment and Requirements

- All students will be required to complete a comprehensive final examination that assesses the learning of all course objectives. This exam must be weighted in a manner so that this exam score is worth a minimum of fifteen percent (15%) of the final course grade. In selected semesters this exam may be a common exam administered to all sections of Math 115.
- All students will be required to complete online homework. This online homework must be weighted in such a manner so that it is worth between six percent (6%) and twelve percent (12%) of the final course grade.
- Additional assessment of student achievement may include assignment, quizzes, and exams.
- Application problems must not only be included on chapter exams but also on the final exam.

- A graphing calculator is required of each student and the Mathematics Department recommends and uses the TI-84 Series.
- Access to an online homework management system is also required.
- Application problems must be covered in all mathematics courses. Every section in any course outline that includes application problems must be covered.

### Credit for Prior College-Level Learning

50, CLEP College Algebra exam, taken at any certified Testing Center, such as HFC’s Workforce & Professional Development’s Testing Center (313) 317-6600.

A student may receive credit for Math-115 by earning a minimum score of 50 on the CLEP College Algebra exam.