# MATH-165: Mathematics for Calculus

School
Science, Technology, Engineering and Math
Division
Mathematics
Department
Mathematics
Course Subject
Mathematics
Course Number
165
Course Title
Mathematics for Calculus
Credit Hours
6.00
Instructor Contact Hours Per Semester
92.00 (for 15-week classes)
Student Contact Hours Per Semester
92.00 (for 15-week classes)
A-E
Pre-requisites
MATH-1094 OR MATH-110 with a grade of B- or better OR placement into MATH-115
Catalog Course Description

Topics include algebraic, graphical and numerical representations of functions, including transformations, composition and inverses of functions. Focuses on the study of polynomial, rational, root, exponential and logarithmic functions, and trigonometric and inverse trigonometric functions of real numbers. Also includes equation solving and trigonometric identities. Techniques of problem solving and applications are included throughout the course requiring the frequent usage of graphing utilities. Requires a non-graphing scientific calculator for some formal assessments and access to an online homework assessment.

### Goals, Topics, and Objectives

Goal Statement
1. To develop the advanced algebraic skills needed in college-level science and mathematics courses.
2. To develop an understanding of functions represented algebraically, graphically and numerically necessary for the study of higher level science and mathematics.
3. To develop an understanding of rational functions, exponential and logarithmic functions and trigonometric functions of real numbers and angles.
4. To develop familiarity with some mathematical and physical applications of advanced algebra and trigonometry.
5. To incorporate graphing utilities whenever appropriate to illustrate concepts and solve problems.
6. To develop in students the problem-solving skills needed to interpret, analyze and solve applied problems requiring precalculus-level skills in advanced algebra and trigonometry.
Core Course Topics
1. Functions and Their Graphs
1. Determine if an equation, graph, or table of values represents a function, and state the domain and range of the function.
2. Deter mine graphically and algebraically whether a function is even, odd, or neither.
3. Test algebraically symmetry with respect to x-axis, y-axis, and the origin.
4. Determine the local minima and local maxima of a function and the interval(s) on which the function is increasing, decreasing and/or constant, given the graph of the function and using a graphing utility.
5. Graph identity, constant, square, cubic, square root, cube root, absolute value, greatest integer, and reciprocal functions of the form 1/x and 1/(x squared), and check using the graphing utility.
6. Analyze and graph functions in terms of translations, reflections, and expansions or contractions.
7. Determine the graph of a function obtained from a series of transformations.
8. Graph piecewise-defined functions and determine their domains and ranges.
9. Form the sum, difference, product, quotient, and composition of two functions and determine their domains, given their equations or graphs.
10. Find and simplify the difference quotient of a function.
11. Relate the difference quotient and average rate of change of a function.
12. Solve absolute value equations and inequalities algebraically and graphically.
13. With the aid of a graphing utility, determine points of maximization or minimization in situations dealing with distances, areas, and volumes of various geometric figures, as well as in real-world business situations involving revenues, costs, and profits.
2. Polynomial Functions and their Graphs
1. Determine algebraically the intercepts of a polynomial function, and verify graphically.
2. Determine a polynomial function’s intercepts, extreme values, turning points, and intervals of increase and decrease by using a graphing utility.
3. Determine the end behavior of a polynomial function using the degree of the polynomial and its leading coefficient.
4. Construct a polynomial function with specified zeros.
5. Test factors of polynomial functions by using the Remainder and Factor Theorems, and factor polynomial functions to find the real zeros.
6. Solve polynomial equations by using the Rational Zeros Theorem and synthetic division in conjunction with a graphing utility.
7. Find the complex solutions of polynomial equations.
8. Solve polynomial inequalities algebraically and graphically.
3. Rational Functions
1. Find the domain of a rational function.
2. Find vertical and horizontal asymptotes and oblique asymptotes of the graph of a rational function algebraically, graphically, and numerically.
3. Find the x-intercept(s), y-intercept and coordinates of any hole(s) in the graph of a rational function.
4. Graph a rational function by hand and check it by using a graphing utility.
5. Solve rational equations and inequalities algebraically and graphically.
6. Solve application problems involving rational functions.
4. Exponential and Logarithmic Functions
1. Determine if a function is one-to-one and find its inverse if possible.
2. Define and graph basic exponential and logarithmic functions (with a strong emphasis on functions with base 10 and e) and their transformations, and identify their domains, ranges, intercepts and asymptotes both by hand and using a graphing utility.
3. Solve exponential and logarithmic equations both algebraically and graphically using a graphing utility.
4. Use exponential and /or logarithmic functions to solve problems involving compound interest and growth and decay.
5. Expand or condense logarithmic expressions using the properties of logarithms.
6. Use the change of base formula to find the logarithm of any base other than 10 or e.
5. Angles and Trigonometric Functions
1. Sketch a given angle in standard position.
2. Apply the relationship between arc length, area of a sector, central angle, and the radius of a circle and that between linear speed, angular speed, and the radius of a circle.
3. State the unit circle definitions and the domain and range of each of the six trigonometric functions for any real number t.
4. Find exact values of the six trigonometric functions of special real numbers in standard position if given partial information.
5. Evaluate the six trigonometric function of an acute angle of a right triangle.
6. Use the Reciprocal Identities, Quotient Identities, Even-Odd Identities, and the Pythagorean Identities to simplify trigonometric expressions.
7. Sketch the graphs of the of sine, cosine, and tangent trigonometric functions and their transformations both by hand and by using a graphing utility, stating their periods, amplitudes, and phase shifts if applicable.
8. Find an equation for a sinusoidal graph.
6. Analytic Trigonometry
1. Define the inverse sine, inverse cosine, and inverse tangent functions, and determine their domains and ranges.
2. Evaluate the inverse sine, inverse cosine, and inverse tangent function values exactly when possible and, if not possible, approximate using a graphing utility.
3. Use properties of inverse functions to find the exact value of certain composite functions and solve equations.
4. Determine graphically whether an equation appears to be an identity if so verify algebraically.
5. Use identities, including, Quotient Identities, Reciprocal Identities, the Pythagorean Identities, the Even-Odd Identities, the Sum and Difference Identities, the Double Angle Identities, and the Half Angle Identities for sine, cosine and tangent to simplify expressions.
6. Determine exact solutions of trigonometric equations.
7. Estimate solutions to trigonometric equations by using a graphing utility.

### Assessment and Requirements

• All students will be required to complete a comprehensive final examination that assesses the learning of all course objectives. This final 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 final exam may be a common final exam administered to all sections of Math-165.
• All students will be required to complete at least two proctored on-campus exams. The cumulative value of those exams must be at least 40% of a student’s final grade.
• 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 assignments, quizzes, and exams.
• For proctored in-person formal assessments (quizzes, tests, and exams) the only technology students can use is a non-graphing scientific calculator. Quizzes, tests, and exams may have non-calculator parts. Class projects and informal assessments will require students to use a free graphing application to support learning.
• Application problems must not only be included on chapter exams but also on the final exam.
General Course Requirements and Recommendations
• A non-graphing scientific calculator is required for formal assessments.
• Free graphing applications may be used to support learning for informal assessments and class work.
• Application problems must be covered in all mathematics courses. Every section in any course outline that includes application problems must be covered.

### Outcomes

General Education Categories
• Mathematics
MTA Categories
• Category 3: Mathematics
• Category 3: Mathematics (College Algebra Track)
Satisfies Wellness Requirement
No

### Credit for Prior College-Level Learning

Options for Credit for Prior College-Level Learning
Other Exam
Minimum Score on Other Exam
50 on the CLEP Precalculus exam
Other Exam Details

A student may receive credit by earning a minimum score of 50 on the CLEP Precalculus exam.

### Approval Dates

Effective Term
Fall 2024
ILT Approval Date
AALC Approval Date
Curriculum Committee Approval Date
Review Semester
Fall 2024