College Math & Statistics Objectives

Math114 College Math & Statistics
Instructor: Dr. Carla C. Morris
TEXT: Mathematical Applications for the Management, Life, and Social Sciences by Harshbarger and Reynolds
(ninth edition)

The following list of objectives is designed to give you some guidance at what topics are important from the various sections we will cover from the book. These objectives are some of the key concepts that will be discussed for each section. When you take exams in this course you must show me your work to earn full credit for a problem. Correct answers with no work shown will be penalized. Partial credit will be given on problems therefore showing your work is vital to your grade and it also allows me to better determine where your weakness may be if you need assistance with any of the material.

MATH114 CHAPTER 0 OBJECTIVES

SECTION 0.1 SETS
1) Understand the subsets of real numbers
2) Work with unions, intersections, subsets, elements, and complements of sets
3) Be able to work with Venn Diagrams

SECTION 0.2 THE REAL NUMBERS
1) Work with number lines
2) Use interval notation
3) Work with order of operations
4) Understand absolute values of variable expressions

SECTION 0.3 INTEGRAL EXPONENTS
1) Work with the laws of exponents including positive integer, zero, and negative exponents

SECTION 0.4 RADICALS AND RATIONAL EXPONENTS
1) Work with radicals
2) Convert radicals to expressions with rational exponents and vice versa
3) Simplify radicals and expressions with rational exponents such as such as x^(m/n)
4) Determine the nth roots of expressions including fractions

SECTION 0.5 OPERATIONS WITH ALGEBRAIC EXPRESSIONS
1) Determine the degree of a polynomial
2) Determine whether an expression is a polynomial
3) Add or subtract polynomials
4) Multiply polynomials
5) Divide polynomials using long division
6) Use the special products to multiply expressions

SECTION 0.6 FACTORING
1) Factor sums or differences of squares or cubes (I will give you cube formulas)
2) Factor trinomials (Trial and error)
3) Factor four term expressions by using grouping

SECTION 0.7 ALGEBRAIC FRACTIONS
1) Simplify algebraic fractions by factoring the numerator and denominator and then reducing
2) Multiply or divide fractions
3) Add/subtract fractions by finding the least common denominator

MATH114 CHAPTER 1 OBJECTIVES

SECTION 1.1 SOLUTIONS OF LINEAR EQUATIONS IN ONE VARIABLE
1) Solve linear equations in one variable
2) Solve fractional equations (You can multiply by LCD to eliminate the fractions if you do not feel comfortable working with fractions)

SECTION 1.2 FUNCTIONS
1) Understand what a relation is
2) Determine if a relation is a function
3) Determine if a graph is a function by using the vertical line test
4) Understand function notation and how to evaluate a function at a particular point
5) Find sums, differences, products, and quotients of two functions f(x) and g(x)
6) Work with composite functions such as f(g(x))

SECTION 1.3 LINEAR FUNCTIONS
1) Be able to determine the x and y intercepts of linear functions
2) Graph a linear function

Your graphs should adhere to the following guidelines:

The x and y axis is to be labeled (or whatever variables are used)
A scale is to be included even if you mean for each block to count as one unit
Linear equations should be determined by at least three points (the third being a double check of your work).
Quadratics should include a vertex, axis of symmetry, y intercept, x intercepts, and have at least five points on the graph
Otherwise plot a sufficient number of key points to determine the appearance of the graph

3) Find the slope of a line
4) Know the relationship that exists between parallel and perpendicular lines
5) Find the equation of a line given certain information (Forms of a line include standard, point slope, and slope intercept. A vertical line takes the form x = a,
while a horizontal line takes the form y = b)

* Note: section 2.4 will be covered next (see Chapter 2) objectives

SECTION 1.5 SOLUTIONS OF SYSTEMS OF LINEAR EQUATIONS
1) Find solutions of a system of linear equations by graphing
2) Find solutions of a system of linear equations by substitution
3) Find solutions of a system of linear equations by elimination
4) Understand the three types of systems (consistent and independent, dependent, and inconsistent)
Note: The solution if it exists should be given in the form of an ordered pair (x, y)

SECTION 1.6 APPLICATIONS OF FUNCTIONS IN BUSINESS AND ECONOMICS
1) Understand the fundamentals of break-even analysis
2) Understand the fundamentals of market equilibrium

MATH114 CHAPTER 4 OBJECTIVES (note we are covering this chapter before chapter 2)

SECTION 4.1 LINEAR INEQUALITIES IN ONE VARIABLE
1) Show half-open, open, or closed intervals on a number line
2) Work with interval notation
3) Solve linear equations in one variable

SECTION 4.2 LINEAR INEQUALITIES IN TWO VARIABLES
1) Graph a linear inequality by deciding if the line should be solid or dashed and also which half-plane is to be shaded
2) Graph a system of linear inequalities and determine the solution to the system

SECTION 4.3 LINEAR PROGRAMMING; GRAPHICAL METHODS
1) Find the maximum or minimum of an objective function given a system of linear inequalities as the constraint set.
This is to be done by first determining the corner points of the feasible region.

MATH114 CHAPTER 2 OBJECTIVES

SECTION 2.1 QUADRATIC EQUATIONS
1) Solve quadratic equations by factoring
2) Solve quadratic equations by using the quadratic formula
3) Solve quadratic equations by applying the square root property

SECTION 2.2 QUADRATIC FUNCTIONS: PARABOLAS
1) Determine the maximum or minimum value of a quadratic function.
2) Be able to graph a quadratic (parabola) by determining the axis of symmetry, vertex, y intercept, and x intercepts.
Your graph should have at least five points to help determine the shape of the graph.

SECTION 2.3 BUSINESS APPLICATIONS OF QUADRATIC FUNCTIONS
1) Find the point(s) of intersection of supply and demand curves that involve quadratics
2) Find the point(s) of intersection where R(x) = C (x) or profit is zero (Break even)

SECTION 2.4 SPECIAL FUNCTIONS AND THEIR GRAPHS
1) Be able to graph cubics, square roots, absolute values, and 1/x
2) Be able to work with piecewise graphs
3) Determine the shifts of graphs (up, down, left, or right)

MATH114 CHAPTER 5 OBJECTIVES

SECTION 5.1 EXPONENTIAL FUNCTIONS
1) Evaluate a^x or e^x on a calculator for specific values of x
2) Graph exponential functions of the form y = a^x or y = e^x

SECTION 5.2 LOGARITHMIC FUNCTIONS AND THEIR PROPERTIES
1) Write an exponential function as a logarithmic function
2) Write a logarithmic function as an exponential function
3) Work with common or natural logarithmic functions
4) Work with the properties of (natural or common) logarithms
                              ln(xy) = lnx + lny
                              ln(x/y) = lnx – lny
                              ln(x^r) = rlnx
5) Express simple logarithms involving sums, differences or coefficients as a single logarithm and vice versa

SECTION 5.3 SOLUTIONS OF EXPONENTIAL EQUATIONS; APPPLICATIONS OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS
1) Work with simple exponential growth and decay models

MATH114 CHAPTER 6 OBJECTIVES

SECTION 6.1 SIMPLE INTEREST; SEQUENCES
1) Work with simple interest problems to determine the interest or future value of an investment
2) Determine a given term of a sequence whose equation for the nth term is given
3) Work with arithmetic sequences

SECTION 6.2 COMPOUND INTEREST; GEOMETRIC SEQUENCES
1) Work with compounding interest n times a year
2) Work with compounding continuously
3) Find a particular term of a geometric sequence whose formula for the nth term is given
4) Find the sum of the first n terms of a geometric sequence

MATH 114 TRIGONOMETRY HANDOUT

RIGHT TRIANGLE TRIGONOMETRY
1) Be able to use the Pythagorean theorem
2) Know the six trigonometric functions definitions in terms of opposites, adjacent, and hypotenuses of a right triangle
3) Work with angle of elevation problems

UNIT CIRCLE TRIGONOMETRY
1) Be able to convert radians to degrees and vice versa
2) Find the value of a trigonometric function for an angle given the reference angle information

MATH114 CHAPTER 7 OBJECTIVES

SECTION 7.1 PROBABILITY; ODDS
1) Find the probability of a single event. We will work with coin toss, die toss experiments and drawing a card from a standard deck of 52 cards.
2) Find the sample space
3)Find the odds an event occurs or does not occur
4) Work with complements of events
Note: all probabilities must lie between 0 and 1 inclusively

SECTION 7.5 COUNTING; COMBINATIONS AND PERMUTATIONS
1) Work with factorials
2) Apply the fundamental counting principle
3) Understand how to work with combinations and permutations

SECTION 7.6 PERMUTATIONS, COMBINATIONS, AND PROBABILITY
1) Find the probability of certain events by using permutations and combinations as appropriate

MATH114 CHAPTER 8 OBJECTIVES

SECTION 8.2 DESCRIPTIVE STATISTICS
1) Work with bar charts and histograms (frequency, relative frequency, relative frequency percentage)
2) Work with the summation operator
3) Work with the measures of central tendency (mean, median, mode)
4) Work with the measures of dispersion (range, variance, standard deviation)
5) Understand the difference between a population and a sample
6) Work with grouped data

SECTION 8.4 NORMAL PROBABILITY DISTRIBUTION
1) Find normal probabilities
2) Work with given z scores
3) Use the mean and standard deviation information to determine a z-score

MATH 114 REGRESSION HANDOUT
1) Determine the least squares regression line given a set of ordered pairs (You will be given the formulas to find slope and intercept here.
It is up to you to be able to understand the various summation operators that will be used.