| Course Goals |
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1.
The learner will apply principles of number theory by:
- Recognizing integers, rational numbers, irrational numbers, real numbers, and complex numbers
- Identifying properties of real numbers, fractions, exponents, rational exponents, radicals, and complex numbers
- Performing operations involving real numbers, fractions, exponents, rational exponents, radicals, and complex numbers
- Define, list properties of, and manipulate logarithms
2.
The learner will manipulate and solve various types of algebraic equations and inequities by:
- Recognizing linear, quadratic, cubic, radical, exponential, logarithmic, and absolute value equations and inequities
- Determining and checking the solution set of linear, quadratic, cubic, radical, exponential, logarithmic, and absolute value equations and inequalities
- Applying the quadratic formula to find roots of quadratic equations
- Forming and solving applied problems using linear, quadratic, cubic, radical, exponential, logarithmic, and absolute value equations and inequalities
3.
The learner will produce graphical representations of various functions by:
- Plotting points on a Cartesian coordinate system
- Finding the distance between and midpoint of a pair of points
- Identifying the x and y intercepts of a graph
- Determining the center and radius of circles from their equations
- Graphing equations in two variables
- Graphing rational functions
4.
The learner will demonstrate a proficiency in dealing with functions by:
- Differentiating between relations and functions
- Finding the inverse of a function
- Finding the domain and range of functions
- Graphing linear, quadratic, exponential, logarithmic, and other transcendental functions
- Finding the slope of and equation for linear functions
- Stating the standard form of linear and quadratic functions
- Putting functions in standard form and determining if they are increasing or decreasing or have maximum or minimum values
- Transforming functions
- Finding the composite of more than one function
- Determining if a function is one-to-one
5.
The learner will demonstrate a proficiency in dealing with complex numbers by:
- Dividing polynomials by complex numbers
- Applying the conjugate pair theorem to find the roots of a polynomial
- Applying the Complete Factorization Theorem
6.
The learner will understand and apply the remainder and factor theorems to solve higher order equations by:
- Dividing polynomials
- Using synthetic division to divide polynomials
- Determining the real roots of a polynomial using the remainder theorem
- Determining the real roots of a polynomial using the factor theorem
- Analyzing polynomials, using Descartes' Rules of Signs, to determine the number of real roots they have
- Finding all the roots of polynomials
7.
The learner will develop polynomial manipulation skills by:
- Identifying polynomials
- Performing operations of polynomials
- Factoring polynomials, including special rules involving squares and cubes
- Performing operations on rational expressions
- Simplifying rational expressions
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