Dec 02, 2023
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# MATH 130 - Precalculus

Number of Credits: 5
Precalculus is an intensive one semester course covering the same material that is included in MATH-123 Precalculus Part 1 and in MATH-124 Precalculus Part 2. MATH-130 is intended for future mathematics/science majors. Topics include relations and functions, including composite functions and inverse functions; analysis of polynomial, power, rational, exponential, logarithmic, trigonometric, inverse trigonometric, parametric, and polar functions and their graphs; right triangle trigonometry, trigonometric identities, trigonometric equations, use of trigonometric formulas in evaluating trigonometric expressions and in solving trigonometric equations, Laws of Sines and Cosines, vectors in the plane, the trigonometric form of a complex number and DeMoivre’s Theorem, linear and nonlinear systems of equations, solutions of multivariable linear systems by the use of matrices and Gaussian elimination, systems of inequalities, conics, parametric equations, polar coordinates, and polar equations. Problems will be solved through analytic, numerical, and graphical approaches with an emphasis on setting up and solving relevant application problems. Students who need to take MATH-135, Calculus of a Single Variable 1, will need to complete MATH-130, Precalculus, or both MATH-123 and MATH-124 in a year-long sequence. Credit by exam available; CLEP (Precalculus) accepted. Prerequisite: eligibility for ENGL-101; plus completion of MAT-099 with a B grade or better or a satisfactory score on the placement exam. Graphing calculator required. Credit cannot be earned in both MATH-123/124 and MATH-130. GENERAL EDUCATION

(Fall and Spring) Five hours lecture. Five Credits. Five billable hours.

GENERAL EDUCATION Category: Mathematics

Pre-requisite(s): eligibility for ENGL 101 ; plus MAT 099  with a minimum grade of B or better, or a satisfactory score on the placement exam.
Course Objectives: Upon successful completion of this course, students will be able to:

1. Evaluate, graph, and identify the domain, range and intercepts of polynomial, power, rational, exponential, logarithmic, trigonometric, and inverse trigonometric functions. (GE2)
2. Identify and graph shifts, reflections, stretches, and shrinks of functions. (GE1, GE2, GE3, GE5)
3. Find a composition of two functions, and find the domain of a composite function. (GE2)
4. Find inverses of functions analytically and graphically. (GE2)
5. Determine the zeros of polynomial functions using analytic techniques, such as synthetic division, and graphical techniques. (GE2)
6. Solve polynomial, rational, exponential, logarithmic, and trigonometric equations. (GE1, GE2, GE3, GE5)
7. Use trigonometric functions to solve right triangles. (GE2)
8. Evaluate, graph, and identify the domain, range and intercepts of inverse trigonometric functions.
9. Evaluate a composition of trigonometric and inverse trigonometric functions.
10. Prove trigonometric identities. (GE2)
11. Solve trigonometric equations. (GE2)
12. Use sum, difference, multiple-angle, half-angle, power-reducing, product-to-sum, and sum-to-product formulas to evaluate trigonometric expressions and to solve trigonometric equations. (GE2)
13. Apply the Law of Sines and the Law of Cosines to solve oblique triangles. (GE2)
14. Use polynomial, rational, exponential, logarithmic, and trigonometric function models to set up and solve application problems. (GE1, GE2, GE3, GE5)
15. Use vector components and properties of vector addition and of scalar multiplication to solve problems. (GE2)
16. Perform operations with complex numbers in both standard and trigonometric form, including the application of De Moivre’s Theorem. (GE2)
17. Solve multivariable linear and non-linear systems of equations, including the use of matrices to perform Gaussian elimination. (GE2)
18. Find standard equations of circles, parabolas, ellipses, and hyperbolas, analyze the relationships between the equations of the conics and their graphs, and solve application problems involving conics. (GE2)
19. Graph parametric equations, convert between parametric and rectangular form, and solve application problems using parametric equations. (GE2)
20. Analyze the graphs of polar equations and convert between polar and rectangular equations. (GE2)

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