MATH 1730 - Precalculus

5 sem cr hrs

This course includes a study of functions and their graphs with emphasis on linear, quadratic, polynomial, rational, exponential, logarithmic, and trigonometric functions; equations, inequalities, and systems; matrices; conic sections; sequences and series; probability, trigonometric applications of right and oblique triangles, linear and angular velocities, vectors, graphical representation of trigonometric functions, inverse trigonometric functions, identities and conditional equations, composite angle formulas, and other selected topics. Prerequisite: Exemption from or completion of MATH 1003  or ACT Math sub-score of 21 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 nor may they receive credit for both MATH 1720  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.

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.
• be prepared for calculus and other advanced mathematics courses.
• solve multiple higher-order algebraic equations.
• utilize graphical representations of functions in consequential manners.
• perform computations and interpret graphs involving the six trigonometric functions for angles given in radians and degrees.
• solve right and oblique triangles.
• verify identities and solve equations through applications of the fundamental identity relationships.
• apply trigonometric forms to operations on complex numbers.
• graph the six trigonometric functions and certain variations.

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 given equations 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 the 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-intercepts, 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.
• write the equation of a vertical or horizontal parabola in standard form; graph; and identify vertex, axis, focus, and directrix.
• write equations of parabolas.
• write the equation of a vertical or horizontal ellipse in standard form; graph; and identify center, vertices, endpoints of minor axis, and foci.
• write equations of ellipses.
• write the equation of a vertical or horizontal hyperbola in 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.
• define the six trigonometric functions in terms of x, y, and r using the distance formula, the rectangular coordinate system, and the Pythagorean Theorem.
• compute trig function values for 30’, 45’, 60’, 0’, 90’, 180’, and 270’.
• use a calculator to find angles for trig functions and functions for angles;
• reduce trigonometric functions of positive or negative angles to functions of the acute related angle.
• solve right triangles using trigonometric functions.
• solve application problems involving angles of elevation and depression, bearing, and vectors.
• solve oblique triangles using Law of Sines and Law of Cosines.
• find areas of triangles.
• convert angles measures from radians to degrees and degrees to radians.
• solve applications problems involving arc length and linear and angular velocities.
• verify trig identities using the basic Pythagorean, quotient, and reciprocal trig relationships.
• evaluate the trig function values for the sum and difference of two angles and for double angles and half angles.
• solve conditional trigonometric equations.
• graph the six basic trigonometric functions.
• graph variations of the six trig functions including changes in amplitude, wavelength, phase shifts and vertical shifts.
• graph and perform operations with the inverse trigonometric functions.
• convert parametric equations to rectangular form and sketch using a graphing calculator.
• convert polar coordinates to rectangular coordinates and rectangular coordinates to polar coordinates and graph polar equations.
• compute polar forms for complex numbers and multiply, divide, and raise to powers complex numbers in polar form.