Competencies and Performance Standards-MAT 154

Performance Standards-You will demonstrate your competence on assigned activities, written exams and a two hour cumulative final exam

1. Simplify algebraic expressions.

Learning objectives-What you will learn as you master the competency:

a. Apply the rules for simplifying polynomial expressions.

b. Apply the rules for simplifying rational expressions.

c. Apply the rules for simplifying radical expressions.

Performance Standards-You will demonstrate your competence when:

o You can demonstrate the ability to simplify a variety of

     algebraic expressions

2. Apply algebraic techniques to the solution of word problems.

Learning objectives-What you will learn as you master the competency:

a. Solve linear equations and inequalities

b. Solve nonlinear inequalities

c. Solve absolute value equations and inequalities

d. Solve polynomial equations by factoring

e. Solve quadratic equations by the quadratic formula

f. Solve radical equations

g. Solve rational equations

h. Solve exponential and logarithmic equations

i. Solve systems of equations in two or more variables

j. Translate a word problem into an algebraic equation or equations

Performance Standards-You will demonstrate your competence when:

o You can demonstrate the ability to solve a variety of algebraic

      equations and inequalities

o You can demonstrate the ability to translate word problems

       into algebraic equations

3. Analyze relations, functions and their graphs.

Learning objectives-What you will learn as you master the competency:

a. Distinguish between functions and non-functions

b. Determine the domain and range of functions and non-functions

c. Use function notation

d. Determine the inverse of a function

e. Perform the basic operations with functions: addition, subtraction,

      multiplication, division and composition

f. Sketch the graphs of a variety of basic algebraic functions

Performance Standards You will demonstrate your competence with relations expressed

     in a variety of forms such as, tables, graphs, equations, sets of ordered pairs, verbal descriptions

Your performance will be successful when:

o You can demonstrate the ability to distinguish between functions and non-functions.

o You can determine the domain range and inverse of a relation

o You can read and write using function notation correctly

o You can perform the basic operations of addition, subtraction, multiplication, and

composition with functions

o You can sketch the graph of some basic algebraic functions

4. Examine polynomial and rational functions in detail.

Learning objectives-What you will learn as you master the competency:

a. Determine slope and intercepts of a linear function

b. Graph linear functions

c. Write the equation of a linear function

d. Determine the coordinates of the vertex, and the intercepts of a quadratic function

e. Graph quadratic functions

f. Determine the zeros, and the y- intercept of higher degree polynomial functions

g. Graph higher degree polynomial functions

h. Determine the asymptotes, and the intercepts of rational functions

i. Graph rational functions

Performance Standards You will demonstrate your competence when:

o You can identify the slope, intercepts, and sketch the graph of any linear function

o You can identify the vertex, intercepts, and sketch the graph of any quadratic function

o You can identify the zeros, y-intercept, and sketch the graph of higher degree polynomials

o You can identify the asymptotes, intercepts, and sketch the graph of rational functions

5. Analyze the properties, graphs, and applications of exponential and logarithmic functions.

Learning objectives-What you will learn as you master the competency:

a. Simplify exponential and logarithmic expressions

b. Solve exponential and logarithmic equations

c. Sketch the graphs of exponential and logarithmic functions

d. Apply exponential and logarithmic functions in various applications

Performance Standards You will demonstrate your competence when:

o You can simplify exponential and logarithmic expressions

o You can solve exponential and logarithmic equations

o You can sketch the graphs of exponential and logarithmic functions

o You can correctly model real world situations with exponential

      or logarithmic functions

6. Examine the equations and graphs of conic sections in detail.

Learning objectives-What you will learn as you master the competency:

a. Identify the various conic sections from equations written in general form.

b. Convert the general form of the equation of a conic section into the standard form.

c. Determine the radius and center of a circle.

d. Graph a circle.

e. Write the equation of a circle.

f. Determine the center, foci, vertices, major axis, and minor axis, of an ellipse.

g. Graph an ellipse.

h. Write the equation of an ellipse.

i. Determine the center, foci, vertices, orientation, and asymptotes of a hyperbola.

j. Graph a hyperbola.

k. Write the equation of a hyperbola.

l. Determine the vertex, focus, directrix, and orientation of a parabola.

m. Graph a parabola.

n. Write the equation of a parabola.

o. Determine the conic section from a general equation

Performance Standards-You will demonstrate your competence when:

o You can identify the conic section from an equation written in general form

o You can write the equation of a conic section in standard form

o You can identify the relevant features and sketches the graph of any conic section

7. Apply systems of equations and matrices

Learning objectives-What you will learn as you master the competency:

a. Solve systems of equations using a specified method such as: graphing,

     substitution, elimination, Row-Echelon, Gaussian, Gauss-Jordon,

     Matrix Inverses or Cramer's Rule

b. Perform basic operations with matrices

c. Sketch the graph of a system of linear inequalities

d. Solve a system of linear inequalities

Performance Standards-You will demonstrate your competence when:

o You can solve a system of equations in two variables by the following methods:

      graphing, substitution, and elimination

o You can solve a system of equations in two and three variables by these methods:

Gaussian Elimination, Row-Echelon Form, Matrix Inverse and Cramer's Rule

o You can perform matrix operations such as: adding, subtracting, multiplying, scaler

multiplication, the identity of a matrix and calculate the inverse matrix

for a 2x2 and a 3x3 matrix

o You can graph the solution of systems of linear inequalities

o You can find the best solution to a system of linear inequalities

o You can find the partial fraction decomposition of a rational expression