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5/12/2015
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MAC1106 Integrated College and Precalculus Algebra MAC1106 Integrated College and Precalculus Algebra Course Description: This course is intended for students preparing for MAC2311 and will cover topics found in MAC1105 & MAC1140. Students will learn how to analyze linear, quadratic, polynomial, rational, radical, absolute value, composite, inverse, piecewise, exponential, and logarithmic functions; conic sections; systems of equations/inequalities; matrices/determinants; sequence & series; Binomial Theorem; applications of mathematical modeling such as optimization problems, and exponential growth/decay. Prerequisite: MAT1033 with a minimum grade of B. ( 5 hr. lecture ) Prerequisite: MAT1033
Course Competency
Learning Outcomes
Competency 1: The student will demonstrate knowledge of absolute value equations and inequalities by:
2. Numbers / Data 3. Critical thinking
1. Solving absolute value equations.2. Solving absolute value inequalities. Competency 2: The student will demonstrate knowledge of systems of linear equations and inequalities by:
2. Numbers / Data 3. Critical thinking
1. Solving systems of linear equations in three variables (with or without technology).2. Solving applications involving systems of linear equations3. Solving systems of linear and nonlinear equations and inequalities. Competency 3: The student will demonstrate knowledge of complex numbers by: 1. Simplifying radicals that represent imaginary numbers.2. Adding, subtracting, multiplying, and dividing complex numbers. Competency 4: The student will demonstrate knowledge of quadratic equations and functions by:
2. Numbers / Data 3. Critical thinking 2. Numbers / Data 3. Critical thinking
1. Using the discriminant to identify the types of solutions for quadratic equations.2. Graphing quadratic function and identifying the vertex, xintercept, yintercept and the axis of symmetry of the graph.3. Finding the maximum or minimum value of a quadratic function.4. Finding the maximum or minimum value of a quadratic function in quadratic models.5. Solving equations that are quadratic in form. Competency 5: The student will demonstrate knowledge of functions from a numerical, graphical, verbal and analytic perspective by:
2. Numbers / Data 3. Critical thinking
1. Distinguishing if a given relation is a function.2. Evaluating using functional notation.3. Using the vertical line test to determine if a graph represents a function.4. Identifying the domain and range of relations and functions.5. Recognizing and graphing nonlinear relations.6. Adding, subtracting, multiplying and dividing functions.7. Forming compositions of functions.8. Finding the inverse of a function.9. Graphing a function http://www.curricunet.com/mdc/reports/Competencies.cfm?courses_id=39605
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and its inverse function.10. Evaluating and graphing piecewisedefined functions. Competency 6: The student will demonstrate knowledge of polynomial and rational functions and inequalities by: 1. Graphing polynomial functions.2. Graphing rational functions.3. Solving polynomial inequalities and graphing their solution set.4. Solving rational inequalities and graphing their solution set. Competency 7: The student will demonstrate knowledge of absolute value, radical and power functions by: 1. Finding the domain and range of these functions.2. Graphing these functions and transformations. Competency 8: The student will demonstrate knowledge of exponential and logarithmic functions by:
2. Numbers / Data 3. Critical thinking 2. Numbers / Data 3. Critical thinking 2. Numbers / Data 3. Critical thinking
1. Graphing exponential and logarithmic functions.2. Identifying the domain and range of exponential and logarithmic functions.3. Applying properties of logarithms to expand logarithmic expressions.4. Applying properties of logarithms to write logarithmic expressions as a single logarithm.5. Solving exponential and logarithmic equations.6. Applying modeling techniques to solve problems of exponential growth and decay. Competency 9: The student will demonstrate knowledge of equations in two variables by: 1. Recognizing and graphing equations that represent circles 2. Writing the equation of the circle given the center and radius. 3. Determining the distance between two points Competency 10: The student will demonstrate knowledge matrices and determinants by: 1. Defining matrices and dimensions of matrices. 2. Performing algebraic operations on matrices. 3. Evaluating determinants. 4. Solving linear systems using Cramer’s Rule. Competency 11: The student will demonstrate knowledge of sequences and series by: 1. Defining sequences and series (including arithmetic and geometric). 2. Writing the Nth term, An, of a sequence.3. Finding the sums of series (including arithmetic and geometric).4. Defining sequences by using the general term or a recursive formula. 5. Using the summation notation properties to express and evaluate sums. Competency 12: The student will demonstrate knowledge of mathematical induction by: 1. Proving that a given formula is the true through the Principle of Mathematical Induction. Competency 13: The student will demonstrate knowledge of the Binomial Theorem by: 1. Expanding a Binomial using the Binomial Theorem.
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2. Numbers / Data 3. Critical thinking 2. Numbers / Data 3. Critical thinking 2. Numbers / Data 3. Critical thinking
2. Numbers / Data 3. Critical thinking 2. Numbers / Data 3. Critical thinking
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Competency 14: The student will demonstrate an understanding of polynomial functions by:
1. Analyzing the graph of a polynomial function, its behavior near its zeros and its end behavior. 2. Using appropriate theorems of polynomials to factor a polynomial function and find all its zeros.3. Stating the Fundamental Theorem of Algebra.4. Using appropriate rules or theorems to determine the existence, location, and classification of the zeros of a polynomial function.5. Using the appropriate theorems of polynomials to build a polynomial function given its zeros or its graph. Competency 15: The student will demonstrate knowledge of rational functions by:
2. Numbers / Data 3. Critical thinking
2. Numbers / Data 3. Critical thinking
1. Graphing rational functions which have asymptotes including vertical, horizontal and oblique.2. Analyzing the behavior of the graph of a rational function about a point of discontinuity.3. Analyzing the end behavior of the graph of a rational function in which the degree of the numerator is greater than the degree of the denominator plus one. Competency 16: The student will demonstrate knowledge of conic sections by:
2. Numbers / Data 3. Critical thinking
1. Identifying conic section as the result of intersecting a plane with a cone.2. Writing an equation for a parabola, ellipse or hyperbola in standard form given sufficient information about the conic.3. Graphing a parabola, ellipse or hyperbola in standard form given sufficient information about the conic or given its equation.4. Solving application problems involving parabolas, ellipses, and hyperbolas. 5. Identifying the different conic sections. 6. Graphing the different conic sections.
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