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Mar 26, 2023
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# MATH 1450 - Pre-Calculus Algebra and Trigonometry

This course provides an introduction to the fundamental operations of algebra, graphs, equations, inequalities, systems of equations, matrices, exponents, logarithms, an introduction to the theory of equations, the basic trigonometric functions and applications of these functions in the solution of equations, right triangles, oblique triangles, vectors, complex numbers, conics, and graphs.

Credits: 6

Instructional Method Lecture

General Education Requirement: Basic Math
Comments: This course may be used for the quantitative reasoning requirement at UW.

Prerequisites:
MATH 0930 Intermediate Algebra with a “C” or better OR Math Level IV Placement

Minimum Student Competencies
Upon completion of MATH 1450 Pre-Calculus Algebra and Trigonometry, the student will:

1. Solve first-degree equations for all real and complex roots.
2. Solve second-degree equations for all real and complex roots utilizing the quadratic formula, completing the square, and factoring.
3. Solve higher-degree equations for all real and complex roots utilizing technology and synthetic division.
4. Solve first-degree, second degree, and higher degree inequalities for all solutions utilizing technology.
5. Graph linear functions on the Cartesian Coordinate System using techniques to find intercepts and symmetry.
6. Graph non-linear functions and relations on the Cartesian Coordinate System using techniques to find intercepts, local extremum, asymptotes, and symmetry.
7. Solve real world problems including growth, decay, and other business/science applications utilizing logarithmic and exponential functions.
8. Solve exponential and logarithmic equations.
9. Evaluate the composition of two functions.
10. Calculate the inverse of a function.
11. Solve square and non-square systems of equations involving two or more variables using graphing, substitution, elimination, and matrix methods.
12. Solve application problems involving one or several variables including motion, mixing, work, growth, decay, and optimization.
13. Utilize the basic functions and capabilities of a graphing calculator.
14. Solve word problems involving circles and rotational motion.
15. Solve right triangle problems applying trigonometric principles.
16. Synthesize the best model for periodic behavior that includes shifts, reflections, or non-rigid transformations of algebraic or trigonometric graphs.
17. Prove trigonometric identities are true using reciprocal, Pythagorean, quotient, double angle, co-function, sum/difference, power-reducing, sum-to-product, product-to-sum, and half-angle identities.
18. Solve trigonometric equations.
19. Solve for missing information on oblique triangles using the law of sines and law of cosines.
20. Solve problems applying vector mechanics.
21. Write the trigonometric form of a complex number.
22. Solve problems by graphing appropriate conic, polar, or parametric models.
23. Synthesize concepts related to the four basic conics: circles, ellipses, parabolas, and hyperbolas by graphing, writing, and identifying equations.