MATH 114 Applied Algebra, Geometry, and Trigonometry (5 credits)
Distribution Area Fulfilled Natural Sciences; Quantitative and Symbolic Reasoning; General Transfer Elective
Prerequisite MATH 098 or equivalent with a grade of at least 2.0, or placement test score above MATH 098.
Course Description
Linear, quadratic, logarithmic, exponential, and trigonometric functions and their applications. Interpretation and display of information using rectangular, polar, and logarithmic coordinate systems. Right triangle and unit circle trigonometry. Vector operations using real and complex numbers. Solutions to systems of linear equations.
Course Content
A. Families of functions, including polynomial functions, exponential functions, logarithmic functions, and trigonometric functions.
B. Solutions to a variety of equations related to the functions stated in A.
C. Solutions to systems of linear equations.
D. Introduction to logarithmic and polar coordinate systems.
E. Introduction to vector algebra.
F. Introduction to complex numbers and vector operations with complex numbers.
G. Unit analysis and unit conversions within and between systems of measurement (e.g. US - SI)
H. Solutions to right triangles.
I. Law of cosines and law of sines.
Student Outcomes
1. Perform basic algebraic manipulation with polynomials, rational expressions, geometric formulas, and exponential and logarithmic expressions.
2. Solve linear, quadratic, rational, exponential, logarithmic, and trigonometric equations.
3. Interpret, in the context of the problem, a variety of data in table and in graphical form.
4. Perform unit analysis and unit conversions within and between measurement systems. (e.g., US - SI, degrees - radians, Kelvin - Rankine - Farenheit - Celsius)
5. Perform basic operations with scientific notation and engineering notations and use significant figures appropriately.
6. Solve systems of equations using Cramer’s Rule and matrix algebra.
7. Display and interpret graphical information for the functions listed in 1.
8. Find solutions to vector problems graphically and algebraically.
9. Apply metric prefixes (Kilo, Hecta, Deca, deci, centi, milli) appropriately to complete problems.
10. Display and interpret graphical information in rectangular, polar, and logarithmic coordinate systems.
11. Use the appropriate formula(s) to solve right triangles.
12. Use law of cosines and law of sines appropriately to solve non-right triangles.
13. Apply complex number using unit-circle trigonometry.
14. Perform the basic (add, subtract, multiply, and divide) mathematical operations on complex numbers.
15. Perform vector operations with complex numbers.
16. Link algebraic, numeric, and graphical solutions with each other.
17. Solve and analyze application problems that involve concepts covered in this course and in previous courses.
18. Communicate methods of solutions and solutions to problems for the clarity of the receiver.
19. Interpret the solution in the context of the problem and evaluate the reasonableness of the solution.
20. Participate actively and responsibly in all course activities.
21. Use technology appropriately to solve problems.
Degree Outcomes
Quantitative & Symbolic Reasoning: Graduates utilize mathematical, symbolic, logical, graphical, geometric, or statistical analysis for the interpretation and solution of problems in the natural world and human society.
Critical, Creative and Reflective Thinking: Graduates will evaluate, analyze, synthesize, and generate ideas; construct informed, meaningful, and justifiable conclusions; and process feelings, beliefs, biases, strengths, and weaknesses as they relate to their thinking, decisions, and creations.
Lecture Contact Hours 50
Lab Contact Hours 0
Clinical Contact Hours 0
Total Contact Hours 50
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