# MATH 147 Precalculus

### Credits

### General Education Competency

GEM Mathematical Ways of Knowing## MATH 147Precalculus

Please note: This is not a course syllabus. A course syllabus is unique to a particular section of a course by instructor. This curriculum guide provides general information about a course.

## I. General Information

### Department

Mathematics & Engineering

## II. Course Specification

### Course Type

### General Education Competency

### Credit Hours Narrative

### Grading Method

### Repeatable

## III. Catalog Course Description

This is a single course equivalent to College Algebra (MATH 143) plus Trigonometry (MATH 144). Credit hours are not granted in both MATH 143 and MATH 147 nor in both MATH 144 and MATH 147. NOTE: For convenience of the student schedule, Math 143 and Math 144 may be taken concurrently in lieu of Math 147.

## IV. Student Learning Outcomes

Upon completion of this course, a student will be able to:

## V. Topical Outline (Course Content)

Linear equations (solve all types, simple to complex, model data and solve application problems) Formulas (solve problems using formulas, isolate a specified variable) Quadratic equations (solve by factoring, by taking square roots, by completing the square, using the quadratic formula, solve application problems) Solve other types of equations (polynomial, radical, absolute value, equations that are quadratic in form, equations with rational exponents) Inequalities with one variable (graph and solve linear, compound, absolute value, quadratic and rational inequalities) Lines (find slope, graph, write equation, model data, use idea of parallel and perpendicular) Circles (equation, center, radius, graph, convert equation to standard form) Functions (definition, domain, range, use vertical line test, evaluate, intervals for increasing and decreasing, odd, even, symmetry, model data) Graph and analyze common functions (quadratic, cubic, square root, absolute value, step, greatest integer) Transformations and combinations of functions (vertical shifts, horizontal shifts, reflections, vertical stretching and shrinking, add, subtract, multiply, divide, composition, inverse) Quadratic functions (graph, standard form, vertex, intercepts, model data, solve application problems) Polynomial functions (end behavior, leading coefficient test, graph, Remainder Theorem, Factor Theorem, find all zeros) Rational functions (vertical asymptotes, horizontal asymptotes, slant asymptotes, intercepts, graph, solve application problems) Variations (direct, inverse, joint, combined) Exponential functions and equations (evaluate, graph, transform, solve equations, model data and solve application problems) Logarithmic functions and equations (log notation, properties of logs, evaluate, graph, solve log equations, change bases, model data and solve application problems) Systems of equations (linear equations in two variables, linear equations in three variables, nonlinear equations in two variables, application problems) Systems of inequalities (linear, nonlinear, linear programming) Conic sections (analyze and graph ellipses, hyperbolas and parabolas, find vertices, foci, axis of symmetry, directrix, eccentricity and asymptotes as applicable, model data and solve application problems) Binomial theorem (expand binomial raised to a power, find one specified term) Angles (standard position, positive angle, negative angle, degree measure in degrees-minutes-seconds as well as decimal degrees, radian measure, coterminal angles, reference angles, supplementary, complementary) Trig functions in right triangles (trig function definitions using opposite side, adjacent side and hypotenuse of right triangle; exact trig values of 30(-60(-90( and 45(-45(-90( triangles; use calculator to evaluate trig function values in degrees and radians; solve right triangles including application problems) Trig functions of any angle (use the x-y-r definitions to find trig function values, signs of the trig functions within each quadrant, find and use reference angles) Trig functions of real numbers (use the unit circle to find trig function values, properties of the trig functions (domain, range, symmetries, period) Basic trig identities (Reciprocal, Quotient or Ratio, Pythagorean, rearrange basic identities, simplify trig expressions) Graph the trig functions (period, amplitude, graph sin, cos, tan, cot, csc and sec functions without the use of a graphing calculator and using a graphing calculator, transformations of the basic trig graphs (horizontal and vertical shifts, vertical stretch/shrink, change of period, graph using addition of ordinates, given the graph of a trig function write the equation) Inverse trig functions (restrictions on the domain and range, how graph of inverse is related to trig function graph, find exact values using triangles, evaluate composition of a trig function and an inverse trig function, evaluate inverse trig functions using a calculator) Verify trig identities (include techniques of changing all to sin and cos, factoring, multiplying by a conjugate, etc., use graphs to decide if a given equation is an identity, then prove algebraically) Use trig identities (Sum and Difference Identities for sin, cos, tan, Cofunction Identities, Double-Angle Identities, Half-Angle Identities, Product to Sum Identities, Sum to Product Identities) Solve trig equations Applications of trig (Linear velocity, angular velocity, arc length, area of a sector, Law of Sines, Law of Cosines, area of a triangle, trigonometric form of complex numbers (compute absolute value, product, quotient), DeMoivre’s Theorem) Parametric equations (eliminate the parameter, graph) Polar coordinates and equations (convert to and from rectangular form, graph)