The following objectives are listed in a sequence ranging from the simple to the more complex. As such, this document should not be viewed as a chronological guide to the course, although some elements naturally will precede others. These elements should be viewed as mastery goals which will be reinforced whenever possible throughout the course.

 I. Description and classification of whole numbers, integers, and rational numbers using sets and the operations among them.

1. identify and use properties of real numbers
2. simplify expressions involving real numbers
3. evaluate numerical expressions with integral exponents
4. simplify square roots of whole numbers

 II. Polynomials.

1. use the definition of a polynomial to distinguish between expressions that are polynomials and expressions that are not
2. classify polynomials by degree and number of terms
3. add, subtract, multiply, and divide polynomials (including the use of long division techniques and the distributive law)
4. simplify polynomials
5. factor polynomials (including factoring out the greatest common factor, factoring by grouping, factoring trinomials, and factoring the difference of two squares)
6. understand and use the exponent laws involving integer exponents

 III. Concepts and skills involving the analysis and graphing of linear equations and inequalities in one variable. 

1. solve linear equations and inequalities in one variable involving integral, decimal, and fractional coefficients and solutions
2. identify conditional equations, identities, and equations with no solution
3. graph the solution set of linear equations and inequalities on a number line

 IV. Application problems.

1. write and evaluate linear expressions from verbal descriptions
2. solve application problems which lead to one of the following types of equations: linear equations in one variable, linear systems of equations in two variables, quadratic equations, or rational equations
3. solve literal equations for a specified variable
4. solve application problems using ratio and proportion and variation
5. solve problems involving the Pythagorean Theorem

 V. Graphing as a tool to interpret linear equations in two variables.

1. identify the relationship between the solution of a linear equation in two variables and its graph on the cartesian plane
2. understand and use the concepts of slope and intercept
3. graph a line given either two points on the line or one point on the line and the slope of the line
4. identify the equations of the line in the standard, point-slope, or slope-intercept forms and graph their solutions
5. write an equation of a line given its graph or description (including one point on the line and the slope of the line or two points on the line)
6. solve systems of linear equations

 VI. Quadratic equations.

1. find solutions to quadratic equations and equations of higher degree using the technique of factoring
2. solve quadratic equations by using the quadratic formula

VII. Rational expressions.

1. evaluate rational expressions, avoiding division by zero
2. simplify rational expressions
3. multiply and divide rational expressions
4. add and subtract rational expressions with monomial and linear binomial denominators
5. solve rational equations with monomial and linear binomial denominators
6. simplify complex fractions with monomial secondary denominators

 VIII. Properties of and operations with square roots.

1. simplify square roots with monomial radicands (including fractional radicands with monomial numerators and denominators)
2. find products and quotients of square roots with monomial radicands
3. introduce rationalizing monomial denominators which contain the square root of a monomial

Last updated January 24, 1999. Nancy Miller and Janet Bickham