The following list of learning goals is designed to give you some guidance at what topics are important from the various sections we will cover from the book.  These goalss 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.

MATH115 CHAPTER P (Prerequisites) LEARNING GOALS

Section P.1 Algebraic Expressions and Real Numbers
1) Evaluate an algebraic expression
2) Understand set builder and roster notation
3) Understand unions and intersections of sets
4) Know the subsets of the real numbers (irrational, rational, integer, natural, and whole)
5) Work with the number line
6) Understand absolute value
7) Understand the properties of real numbers

Section P.2 Exponents and Scientific Notation
1) Be able to work with the properties of exponents
2) Be able to simplify exponential expressions
3) Convert from scientific notation to decimal notation
4) Convert from decimal notation to scientific notation

Section P.3. Radicals and Rational Exponents
1) Be able to evaluate square roots
2) Add and subtract square roots
3) Rationalize denominators
4) Work with nth roots
5) Work with rational exponents

 Section P.4 Polynomials
1) Determine the degree of a polynomial
2) Write a polynomial in either ascending or descending powers of the variable
3) Add or subtract polynomials
4) Multiply polynomials
5) Use the FOIL method
6) Use special product formulas

Section P. 5 Factoring Polynomials
1) Determine the greatest common factor
2) Factor by grouping
3) Factor trinomials
4) Factor using special formulas for squares and cubes
5) Factor using the general factoring techniques

Section P.6 Rational Expressions
1) Understand domain and range
2) Simplify rational expressions
3) Add, subtract, multiply, or divide rational expressions
4) Simplify a complex rational expressions

Section P.7 Equations
1) Solve linear equations in one variable
2) Solve rational equations
3) Solve a formula for one of its variables
4) Solve absolute value equations
5) Solve quadratic equations by factoring
6) Solve a quadratic equation by completing the square
7) Use the quadratic formula
8) Solve radical equations (check for extraneous solutions)

Section P.8 Modeling with Equations
1) Convert a word problem to an equation
2) Use equations to solve word problems
3) Use the Pythagorean theorem

Section P.9 Linear Inequalities and Absolute Value Inequalities
1) Use interval notation
2) Solve linear inequalities
3) Solve absolute value inequalities

MATH115 CHAPTER 1 FUNCTIONS AND GRAPHS LEARNING GOALS

Section 1.1 Graphs and Graphing Utilities
1) Plot points in the Cartesian (rectangular) coordinate system
2) Graph equations in the rectangular coordinate system
3) Determine intercepts of a graph

Section 1.2 Basics of Functions and Their Graphs
1) Find the domain and range of a relation
2) Determine whether a relation is a function
3) Evaluate a function
4) Graph functions
5) Understand the vertical line test
6) Identify the domain and range of a function from its graph

Section 1.3 More on Functions and Their  Graphs
1) Work with the difference quotient [f(x + h) – f(x)]/h
2) Work with the difference quotient [f(x) ? f(a)] /(x – a)
3) Work with piecewise functions
4) Identify intervals where a graph is increasing or decreasing
5) Understand even and odd symmetry
6) Understand the greatest integer function

Section 1.4 Linear Functions and Slope
1) Determine the slope of a non-vertical line
2) Work with equations of vertical or horizontal lines
3) Use the point-slope formula
4) Use the slope-intercept formula

Section 1.5 More on Slope
1) Determine if lines are parallel, perpendicular or neither
2) Understand the average rate of change of a function

Section 1.6 Transformations of Functions
1) Recognize graphs of some common functions
2) Recognize when graphs shift vertically
3) Recognize when graphs shift horizontally
4) Use reflection to graph a function
5) Graph functions involving more than one transformation

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

Section 1.7 Combinations of Functions; Composite Functions
1) Understand the arithmetic operations (+, ? , ? , ?) with two functions f(x) and g(x)
2) Work with composite functions such as f(g(x))
3) Write a function as a composition of functions

Section 1.8 Inverse Functions
1) Determine if two functions are inverses of one another
2) Determine the inverse of a function
3) Determine if the graph of a function is one to one by applying the horizontal line test

Section 1.9 Distance and Midpoint Formulas; Circles
1) Find the distance between two points
2) Find the midpoint of a line segment
3) Write the equation of a circle in standard form
4) Find the center and radius of a circle in standard form
5) Graph a circle that is in standard form using the center and radius as a guide

MATH115 CHAPTER 2 POLYNOMIAL AND RATIONAL FUNCTION  LEARNING GOALS

Section 2.2 Quadratic Functions
1) Graph a quadratic function in standard form
2) Graph quadratic functions by finding the axis of symmetry, vertex, y intercept, x intercepts, and using symmetry to include five points on the graph
3) Determine for what x value a minimum or maximum is obtained
4) Determine the minimum or maximum value of a quadratic
5) Work with word problems involving maximization or minimization of a quadratic

Section 2.3 Polynomial Functions and Their Graphs
1) Determine whether a given graph is that of a polynomial of specified degree
2) Use factoring to find zeroes of polynomials (x – intercepts)
3) Graph polynomial functions by determining their behavior near each x intercept and its end behavior
Note: polynomials should be smooth (no cusps), unbroken curves with at most n-1 turning points where n is the degree of the polynomial.  It should also approach + or - infinity at the extreme values of x.

Section 2.6 Rational Functions and Their Graphs
1) Find the vertical asymptotes of a rational function
2) Find the horizontal asymptotes of a rational function
3) Determine whether the graph will cross the horizontal asymptote

Section 2.4 Polynomial and Rational Inequalities
1) Solve polynomial inequalities by using the critical point table approach
2) Solve rational inequalities by using the critical point table approach

MATH115 CHAPTER 3 EXPONENTIAL & LOGARITHMIC FUNCTIONS  LEARNING GOALS

Section 3.1 Exponential Functions
1) Estimate the value of 2^10x by 10^3x
2) Graph exponential functions of the form a^x
3) Graph exponential functions of the form e^x
4) Work with compound interest formulas

Section 3.2 Logarithmic Functions
1) Convert logarithms to exponential form and vice versa
2) Evaluate logarithms
3) Graph logarithmic functions
4) Work with common or natural logarithms

Section 3.3 Properties of Logarithms
1) Use the properties of logarithms
            logPQ =  logp + logQ,   log P/Q = logP – logQ,   log P^n = nlogP
2) Express simple logarithms involving sums differences or coefficients as a single logarithm and vice versa

Section 3.4 Exponential and Logarithmic Equations
1) Use like bases to solve exponential equations
2) Use definition of logarithms to solve logarithmic equations  (watch out for the possibility of an extraneous solution)

Section 3.5 Exponential Growth and Decay; Modeling Data
 1) Model exponential growth or decay
 

MATH115 CHAPTER 4 TRIGONOMATRIC FUNCTIONS  LEARNING GOALS

Section 4.1 Angles and Radian Measure
1) Convert degrees to radians or radians to degrees
2) Draw angles in standard position
3) Understand coterminal angles
4) Determine arc lengths

Section 4.2 Trigonometric Functions of Angles
1) Work with sine, cosine, and tangent
2) Work with the reciprocals  trigonometric functions cosecant, secant and cotangent
3) Determine any of the six trigonometric function values at a given point on the unit circle
4) Know the domain and range for sine and cosine functions
5) Understand even and odd trigonometric function relationships
6) Understand periodic properties of sine and cosine functions

Section 4.3 Right Triangle Trigonometry
1) Use the Pythagorean Theorem
2) Determine the six trigonometric functions using opposite, adjacent, hypotenuse as guides (SOH CAH TOA)
3) Evaluate the trigonometric functions for special angles (30, 45, and 60 degrees)
4) Understand angle of elevation(depression) problems

Section 4.4 Trigonometric Functions of Any Angle
1) Evaluate any of the six trigonometric functions at any angle in standard position
2) Evaluate any of the six trigonometric functions at radian measures corresponding to the quadrantal angles (lying on an axis).
3) User reference angles to determine the trigonometric function values at a point

Section 4.5 Graphs of Sine and Cosine Functions
1) Graph AsinBx or AcosBx using the fact that the amplitude is |A| and the period is two pi divided by B
2) Graph sine or cosine graphs that involve a phase shift as well Asin(Bx – C) and Acos(Bx – C)

Section 4.8 Applications of Trigonometric Functions
1) Determine the angle measurements of a right triangle
2) Solve a right triangle

MATH115 CHAPTER 5 ANALYTIC TRIGONOMETRY  LEARNING GOALS

Section 5.1 Verifying Trigonometric Identities
1) Work with the Pythagorean identities
2) Prove trigonometric identities  using the fundamental trigonometric identities as a short cut

Section 5.2 Sum and Difference Formulas
1) Use the sum and difference formulas for sines and cosines
2) Use the addition formulas for tangents

Section 5.3 Double-Angle, Power Reducing, and Half-Angle Formulas
1) Use the double-angle formulas for sine, cosine, and tangent
2) Find exact values using the formulas (your calculator gives approximations)
3) Work with the power reducing formulas
4) Work with the half-angle formulas

Section 5.5 Trigonometric Equations
1) Find all solutions in a given interval for a trigonometric equation
2) Solve trigonometric equations with multiple angles
3) Solve trigonometric equations that are factorable
4) Use identities to change the original form of the equation into one more easily solved

MATH115 CHAPTER 6 ADDITIONAL TOPICS IN TRIGONOMETRY  LEARNING GOALS

Section 6.1 The Law of Sines
1) Use the Law of Sines with a SAA triangle
2) Use the Law of Sines with an ASA triangle
3) Use the Law of Sines with an SSA triangle

Section 6.2 The Law of Cosines
1) Use the Law of Cosines with a SAS triangle
2) Solve a SS triangle with both Laws