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 goals 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.

MATH010 CHAPTER 1  Algebra and Problem Solving Learning Goals

Section 1.1 Some Basics of Algebra
1) Recognize key words for translating word problems into equations
2) Be able to evaluate algebraic expressions
3) Understand exponential notation
4) Know the order of operations
5) Know the subsets of the real numbers (irrational, rational, integer, natural, whole)

Section 1.2 Operations and Properties of Real Numbers
1) Evaluate absolute values of numbers or expressions
2) Add or subtract real numbers
3) Multiply or divide real numbers
4) Use the properties of real numbers

Section 1.3 Solving Equations
1) Recognize equivalent equations
2) Use the addition and multiplication principles for equations
3) Recognize like terms and how to combine them
4) Understand types of equations (identity, contradiction, and conditional)

Section 1.4 Introduction to Problem Solving
1) Use a general step strategy for problem solving with algebra
2) Always remember to check that your solution makes sense

Section 1.5 Formulas, Models, and Geometry
1) Be able to solve a formula for a specified variable
2) Work with general mathematical models
3) Know some general formulas for areas, distance, triangles, etc

Section 1.6 Properties of Exponents
1) Work with exponential expressions [be careful of the difference between -x^2 and (-x)^2]
2) Be able to apply the product, quotient, and power rules for exponents
3) Understand a zero exponent
4) Work with integer exponents

Section 1.7 Scientific Notation
1) Convert between decimal form and scientific notation
2) Use scientific notation to help simplify expressions
 

MATH010 CHAPTER 2 Graphs, Functions, and Linear Equations Learning Goals

Section 2.1 Graphs
1) Plot ordered pairs
2) Given the graph of an ordered pair determine its coordinates
3) Determine if a particular ordered pair is a solution to an equation
4) Plot a linear, quadratic or other graph by selecting x values and then determining y

                  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 at least five points on the graph
• Otherwise plot a sufficient number of key points to determine the appearance of the graph

Section 2.2 Functions
1) Determine if a relation is a function
2) Use the vertical line test to determine if a graph is that of a function
3) Find the domain or range of functions
4) Evaluate a function at a specific value of the variable
5) Understand function notation

Section 2.3 Linear Functions: Slope, Graphs, and Models Objectives
1) Find the y-intercept of a linear function
2) Determine the slope of a line through two given points
3) Work with slope intercept form of line [y = mx + b]

Section 2.4 Another Look at Linear Graphs
1) Find the x and y intercepts of a linear equation to aid in graphing
2) Recognize the equations for vertical or horizontal lines
3) Be able to graph a vertical or horizontal line
4) Understand how to work with the standard for of a linear equation (Ax + By = C)

Section 2.5 Other Equations of Lines
1) Work with point slope form of a line
2) Understand when to lines are parallel (they have the same slope)
3) Understand when two lines are perpendicular (their slopes are negative reciprocals)

Section 2.6 The Algebra of Functions
1) Find the sum of two functions f(x) and g(x)
2) Find the difference of two functions f(x) and g(x)
3) Find the product of two functions f(x) and g(x)
4) Find the quotient of two functions f(x) and g(x)
 

MATH010 CHAPTER 3 Systems of Linear Equations and Problem Solving Learning Goals

Section 3.1 Solving Systems of Linear Equations in Two Variables
1) Determine if an ordered pair is a solution to a system of linear equations
2) Solve a linear system of equations by graphing
3) Determine if a system is dependent, inconsistent or independent and consistent
* Note: Your solution is an ordered pair (x, y)

Section 3.2 Solving by Substitution or Elimination
1) Solve a linear system of equations by substitution
2) Solve a linear system of equations by elimination

Section 3.3 Solving Applications: Systems of Two Equations
1) Solve application problems such as the mixture problem which involve a system of linear equations
 

MATH010 CHAPTER 4 Inequalities and Problem Solving Learning Goals

Section 4.1 Inequalities and Applications
1) Solve linear inequalities and show solution on a number line
2) Use interval notation
3) Understand the addition and multiplication principles for inequalities

Section 4.2 Intersections, Unions, and Compound Inequalities
1) Understand unions and intersections of sets
2) Work with compound inequalities
3) Use interval notation to state domains

Section 4.3 Absolute Value Equations and Inequalities
1) Solve absolute value equations
2) Solve absolute value inequalities
   * Often students forget that here are two cases to consider with these problems

Section 4.4 Inequalities in Two Variables
1) Solve a system of linear inequalities by graphing
2) Algebraically find any corner points for the system
*Often students forget that they must shade the appropriate half-plane for each inequality

Section 4.5 Applications Using Linear Programming
1) Understand the concepts of objective function and constraints
2) Understand how to minimize/ maximize the objective function of an LP (use corner points)
 

MATH010 CHAPTER 5 Polynomials and Polynomial Functions Learning Goals

Section 5.1 Introduction to Polynomials and Polynomial Functions
1) Evaluate a polynomial at a specific value for the variable
2) Determine if an expression is that of a polynomial
3) Determine the degree of a polynomial or coefficients of its terms
4) Write polynomials in descending or ascending order (typically descending order is used)
5) Add or subtract polynomials by combining like terms

Section 5.2 Multiplication of Polynomials
1) Multiply a monomial by a polynomial
2) Multiply a binomial by a binomial (FOIL)
3) Square a Binomial
4) Recognize that (A + B)(A – B) leads to a difference of squares
5) Multiply polynomials
6) Work with function notation

Section 5.3 Common Factors and Factoring by Grouping
1) Find the greatest common factor
2) Factor the greatest common factor from an expression
3) Factor four terms by grouping

Section 5.4 Factoring Trinomials
1) Factor trinomial by trial and error
2) Factoring trinomials where the lead coefficient is not a “1”

Section 5.5 Factoring Perfect-Square Trinomials and Difference of Squares
1) Recognize and be able to factor perfect square trinomials
2) Factor difference of squares (sum of squares is not factorable)

Section 5.6 Factoring Sums or Differences of Cubes
1) Factor a sum of cubes
2) Factor a difference of cubes

Section 5.7 Factoring: A General Strategy
1) Combine all the factoring techniques of the previous sections to factor an expression
2) If there are 2 terms look for sums or differences of squares or cubes
3) If there are 4 terms try grouping in pairs or possibly look for a trinomial to be involved
4) If there are 3 terms look for perfect square trinomials otherwise use trial and error

Section 5.8 Applications of Polynomial Equations
1) Use factoring, in particular the zero-product property to solve equations
 

MATH010 CHAPTER 6 Rational Expressions, Equations, and Functions Learning Goals

Section 6.1 Rational Expressions and Functions: Multiplying and Dividing
1) Find the domain of rational expressions (set the denominator equal to zero to find the restrictions on the domain
2) Simplify rational expressions by factoring and reducing
3) Multiply rational expressions and simplify
4) Divide rational expressions and simplify

Section 6.2 Rational Expressions and Functions: Adding and Subtracting
1) Add or subtract rational expressions with a common denominator
2) Find the least common denominator
3) Add or subtract rational expressions with unlike denominators

Section 6.3 Complex Rational Expressions
1) Simplify complex fractions (I suggest that you rewrite the expressions as numerator divided by denominator and then work with the two components separately to make the problem a little more manageable)

Section 6.4 Rational Equations
1) Solve proportions
2) Solve rational equations
3) Work with similar triangles
4) Perform checks of your solutions for extraneous solutions

Section 6.5 Solving Applications Using Rational Equations Solving
1) Solve work word problems ( Determine how much of a job is completed per hour as a start)
2) Solve number problems involving rational expressions

Section 6.6 Division of Polynomials
1) Divide a polynomial by a monomial
2) Use long division to divide a polynomial by another polynomial

Section 6.7 Synthetic Division
1) Use synthetic division to divide polynomials

Section 6.8 Formulas, Applications, and Variation
1) Solve rational equations for a specified variable
2) Solve direct, inverse, and joint variation problems
 

MATH010 CHAPTER 7 Exponents and Radicals Learning Goals

While we are not formally covering the sections in this chapter,  I will be giving you a handout
Containing some key concepts you should understand from this chapter which include:

1) Find square roots, cube roots, and nth roots of perfect nth powers
2) Change rational expressions to exponential ones and vice versa
3) Simplify radical expressions with fractional exponents
4) Apply rules of exponents to rational and negative exponents
5) Simplify radicals
6) Add or subtract radicals by combining coefficients of like radicals
7) Simplify the products of radicals
8) Rationalize the denominator
9) Know when you have simplified a radical completely (each variable only appears once, no reducing can be done, all powers are less than the index, and no radical is left in the denominator)
 

MATH010 CHAPTER 8 Quadratic Functions and Equations Learning Goals

Section 8.1 Quadratic Equations
1) Use the square root property to solve equations
2) Solve quadratic equations by completing the square

Section 8.2 The Quadratic Formula
1) Use the quadratic formula to solve quadratic equations
2) Recognize when there are no real solutions

Section 8.3 Applications Involving Quadratic Equations
1) Solve application problems involving quadratic equations
2) Solve equations that are in quadratic form (can include using substitution)

Section 8.6 Quadratic Functions and Their Graphs
1) Graph quadratics a(x – h)^2 + k by finding the axis of symmetry, the vertex, any x intercepts, and the y intercept.
2) Understand translation  and reflection of parabolas (up, down, left, right, or upside down)
3) Include five points with the graph using symmetry to guide you

Section 8.6 More About Graphing Quadratic Functions
1) Graph quadratics ax^2 + bx +c by finding the axis of symmetry, the vertex, any x intercepts, and the y intercept.
 

Section 7.7 The Distance and Midpoint Formulas

Section 10.1 Conic Sections: Parabolas and Circles
1) Work with parabolas of the form x = a(y – k)^2 + h (opens left or right)
2) Find the distance between two points
3) Find the midpoint between two points
4) Determine the equation of a circle centered at the origin with a radius of r
5) Determine equations of circles centered at (h, k)
6) Graph a circle

Section 11.1 Sequences and Series
1) Find the general term of a sequence
2) Use the sigma notation
3) Work with arithmetic sequences
4) Work with basic geometric sequences