MATH 1710 - Precalculus Algebra

3 sem hrs cr

This course includes a study of functions and their graphs, with emphasis on linear, quadratic, polynomial, rational, exponential, and logarithmic functions; equations, inequalities, and systems; matrices; conic sections; sequences and series; and probability. Prerequisite: Exemption from or completion of MATH 1003  or an ACT Math sub-score of 19 or higher and one high school credit in each algebra I, algebra II, and geometry; exemption from or completion of ENGL 0810  and READ 0810  

Students may not receive credit for both MATH 1710 and MATH 1730 .

In rare and unusual circumstances, a course prerequisite can be overridden with the permission of the Department Lead for the discipline.

This course may include proctored exams which must be completed on campus or at an instructor approved proctoring center which may require additional costs to the student. Please consult your instructor for additional details.

  Formerly/Same As (Formerly MATH 1130)

Transfer (UT) or Non-Transfer Course (UN): UT

By the end of the course, students will be able to…

• satisfy mathematics requirements for the various options under the University Parallel and Business Technology majors.
• provide fundamental preparation for calculus and other advanced mathematics courses.
• reinforce and strengthen algebraic skills gained in high school or MATH 1003.

Course Objectives

Throughout the course, students will have the opportunity to…

• review solving linear equations.
• review solving quadratic equations.
• review solving rational equations.
• use the distance formula, the midpoint formula, and the Pythagorean Theorem.
• find the center and radius of circle from equation and find circle equations from center and radius.
• identify a function, specify its domain and range, and use function notation.
• determine intervals over which a function is increasing, decreasing, and constant.
• identify equations of lines, graph lines, and find slopes of lines.
• write equation of lines.
• determine intervals over which a function is continuous.
• graph basic functions and piecewise functions.
• perform function operations and function compositions.
• identify equations of quadratic functions, put equations into standard form, and recognize vertex and other characteristics of graphs from standard form.
• use synthetic division and Remainder Theorem to find the remainder when a polynomial is divided by a binomial of the form (x-k).
• use the Rational Zeros Theorem, Number of Zeros Theorem, and Conjugate Zeros Theorem to find the zeros of polynomial functions.
• use end behaviors, x-intercepts, y-intercept, and test points to sketch graphs of polynomial functions.
• find vertical, horizontal, and slant asymptotes for rational functions and use asymptotes, intercepts, and test points to sketch graphs of rational functions.
• identify one-to-one functions.
• find inverses of one-to-one functions.
• graph exponential functions.
• solve exponential equations using properties of exponents.
• graph logarithmic functions.
• apply properties of logarithms.
• apply Change of Base Theorem to evaluate logarithms.
• solve logarithmic equations.
• solve problems resulting in exponential and logarithmic equations.
• solve linear systems of equations using graphing, substitution, and elimination.
• solve linear systems using Gauss-Jordan method.
• solve non-linear systems of equations using graphing, substitution, and elimination.
• solve systems of linear inequalities by graphing.
• put equation of a vertical or horizontal parabola into standard form; graph; and identify vertex, axis, focus, and directrix.
• write equations of parabolas.
• put equation of a vertical or horizontal ellipse into standard form; graph; and identify center, vertices, endpoints of minor axis, and foci.
• write equations of ellipses.
• put equation of a vertical or horizontal hyperbola into standard form; graph; and identify center, vertices, foci, and equations of asymptotes.
• write equations of hyperbolas.
• distinguish equations of circles, parabolas, ellipses, and hyperbolas from a collective listing.
• determine the terms of a sequence.
• evaluate the summation notation.
• identify an arithmetic sequence and determine common difference, specific terms, general term, and sums of associated arithmetic series.
• identify a geometric sequence and determine common ratio, specific terms, general term, and sums of associated geometric series.
• compute sums of infinite convergent geometric series.
• perform binomial expansions.
• evaluate factorials, permutations, and combinations.
• apply Fundamental Principle of Counting and permutations and combinations to solve problems.
• apply basic concepts of probability.