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MAT122 - Technical Math 2
Catalog Description: Emphasizes solutions to systems of linear equations, solutions and applications of quadratic equations, laws of sines and cosines, graphs of trigonometric functions, complex numbers, exponential and logarithmic functions, linear inequalities, and direct and inverse variation. Not open for credit to students who have credit in MAT 140 or higher. Prerequisite: MAT121 with a grade of C or higher.
Lecture: 3 hrs.
Course Learning Outcomes (CLOs):
Upon successful completion of this course as documented through writing, objective testing, case studies, laboratory practice, and/or classroom discussion, the student will be able to:
1. Given a linear equation, graph it by hand using its slope and y-intercept.
2. Given a system of either two or three linear equations, determine the number of solutions and the solution(s) itself (if any exist) using:
b. substitution or addition method.
3. Given a quadratic equation:
a. solve it by factoring.
b. solve it by completing the square.
c. solve it by taking square roots.
d. solve it using the quadratic formula.
e. graph the quadratic (parabola).
4. Given an oblique triangle, solve it using the law of sines and/or law of cosines.
5. Given a trigonometric equation involving sine and cosine of the form y = a sin(bx + c) or y = a cos (bx + c), graph it by hand.
6. Given a complex number with a negative radicand, rewrite it in rectangular form.
7. Given two or more complex numbers:
a. add, subtract, multiply, and/or divide them.
b. graph each complex number.*
c. change the complex number from rectangular form to polar form.*
d. change the complex number from polar form to rectangular form.
8. Rewrite an exponential equation as a logarithmic equation and a logarithmic equation as an exponential equation.
9. Given a logarithmic expression, rewrite it as a single logarithm and expand a single logarithm as the sum/difference/multiple of logarithms.
10. Use a calculator to find the value of common logarithms and natural logarithms.
11. Solve a logarithmic equation.
12. Given an inequality of one variable:
a. graph it on the number line.
b. solve it algebraically.
13. Given a direct or inverse relationship between two quantities:
a. write the appropriate equation.
b. solve for the constant of proportionality.
c. given a value for one of the quantities, use the equation and the constant of proportionality to find the value of the other quantity.
* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.
I. Systems of Linear Equations; Determinants
A. Linear Equations
B. Solving Systems of Two Equations Graphically
C. Solving Systems of Two Equations Algebraically
D. Solving Systems of Two Equations Using Determinants
E. Solving Systems of Three Equations Algebraically
F. Solving Systems of Three Equations Using Determinants
II. Quadratic Equations
A. Solving Quadratic Equations by Factoring
B. Solving Quadratic Equations by Completing the Square
C. Solving Quadratic Equations Using Quadratic Formula
D. Graphing Quadratic Equations
III. Vectors and Oblique Triangles
A. Solving a Triangle Using the Law of Sines
B. Solving a Triangle Using the Law of Cosines
IV. Graphs of the Trigonometric Functions
A Graphs of y = a sin x and y = a cos x
B. Graphs of y = a sin bx and y = a cos bx
C. Graphs of y = a sin (bx + c) and y = a cos (bx + c)
V. Complex Numbers
A. Basic Definition
B. Basic Operations with Complex Numbers
C. Graphical Representation of Complex Numbers
D. Polar Form of a Complex Number
VI. Exponential and Logarithmic Functions
A. Introduce Exponential and Logarithmic Functions
B. Properties of Logarithms
C. Logarithms to the Base 10
D. Natural Logarithms
E. Exponential and Logarithmic Equations
A. Properties of Inequalities
B. Solving Linear Inequalities
Effective Term: Fall 2013