MAC1147 - Precalculus Algebra and Trigonometry

Topical Outline with Specific Course Objectives

  1. Introduction of Functions, the Properties, Graphs, and Inverses
    1. Analyze and interpret functions using graphs, tables, and equations.
    2. Determine domain and range both algebraically and graphically.
    3. Demonstrate an understanding of both composition and decomposition of functions. 
    4. Construct the inverse of a function, including trigonometric functions, both graphically and algebraically when feasible. 
    5. Demonstrate an intuitive understanding of functions including limits, continuity, increasing, decreasing, maximum and minimum values, and concavity.
    6. Demonstrate an understanding of transformations graphically, symbolically, and numerically. 
    7. Graph and write equations for piecewise-defined functions. 
  2. Polynomial and Rational Functions
    1.  Identify multiplicities of zeros and their effect on the graph.
    2. Use formal limit definitions and limit notation to define the end behavior and vertical and horizontal asymptotes for functions given in numerical, graphical, and symbolic forms. 
    3. Demonstrate mastery of the logarithmic properties by applying them in a variety of settings. 
    4. Determine when a rational function has a hole and the point at which it occurs.
  3. Exponential and Logarithmic Functions 
    1. Create graphs and write equations for exponential and logarithmic functions given sufficient information. 
    2. Use formal limit definitions and limit notation to define the end behavior and vertical and horizontal asymptotes for functions given in numerical, graphical, and symbolic forms. 
    3. Demonstrate mastery of the logarithmic properties by applying them in a variety of settings.
    4. Understand the inverse relationship and use it to solve exponential and logarithmic equations.
    5. Use exponential, logarithmic, and related functions in science based applications. 
  4. Trigonometric Functions 
    1. Demonstrate an understanding of the trigonometric functions as functions of real numbers. 
    2. Analyze and interpret trigonometric functions using graphs, tables and equations. 
    3. Discuss the scientific basis for radian measure. 
    4. Model real-world applications using trigonometric functions. 
    5. Apply radian measure to arc length and area. 
  5. Solving Equations and Inequalities 
    1. Solve non-linear equations and inequalities numerically, graphically, and symbolically. 
    2. Recognize when a solution is approximate and have a rough idea of its accuracy. .
    3. State exact solutions in proper mathematical form.
  6. Conic Sections
    1. Identify and graph a conic section from its equation. 
    2. Find the equation of a conic section from its description. 
    3. Identify the attributes of a conic section. 
  7. Matrices 
    1. Perform basic matrix algebra and demonstrate knowledge of the commutative properties.
    2. Use expansion by cofactors to compute the determinant of matrices up to dimension 4x4.  
    3. Construct the inverse of a matrix using row operations. 
    4. Use matrices and determinants to solve linear systems of equations. 
  8. Sequences and Series 
    1. Recognize arithmetic and geometric sequences and series in summation or iterative notation. 
    2. Demonstrate an understanding of sequences and series notation by expanding a given formula and by creating a formula for a given expansion. 
    3. Find the sum of a finite series. 
  9. Additional Topics 
    1. Apply the Binomial Theorem. 
    2. Demonstrate an understanding of Proof by Induction. 
    3. Demonstrate the ability to find unknown angles and side lengths of right and non-right triangles using trigonometry. 
    4. Solve applications using solutions of triangles. 
  10. Trigonometric identities and conditional trigonometric equations 
    1. Verify and apply trigonometric identities. 
    2. Solve trigonometric equations numerically, graphically, and algebraically. 
  11. Vector algebra and polar coordinates
    1. Demonstrate an understanding of vectors, their graphical representation and vector algebra. 
    2. Sketch and identify graphs in polar coordinates.
    3. Convert rectangular equations to polar form and vice versa.
  12.  Parametric equations 
    1. Sketch and identify graphs using parametric equations. 
    2. Convert rectangular equations to parametric form and vice versa. 

Evaluation:  Each instructor will determine the specific criteria for determining the final course grade.  These criteria will be delineated in the first day handout provided to each student.  Each instructor will give a comprehensive final exam during the assigned final exam period. 

Commonality:  All instructors will use the same textbook and cover all topics in the topical outline.  All students will participate in at least two technology based lab activities.  A computer lab with mathematical software is provided to facilitate collaboration and the use of technology.   

Department Policies

  • Graphing Calculator not allowed on proctored tests or final exam
  • Comprehensive Final
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