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.

Overall objectives:

A. Students will feel a sense of accomplishment in their increasing ability to use mathematics to solve problems of interest to them or useful in their chosen fields. Students will attain more positive attitudes based on increasing confidence in their abilities to learn mathematics.

B. Students will learn to understand material using standard mathematical terminology and notation when presented either verbally or in writing.

C. Students will improve their skills in describing what they are doing as they solve problems using standard mathematical terminology and notation.

1. Description and classification of whole numbers, integers, and rational numbers using sets

and the operations among them.

a. identify and use properties of real numbers

b. simplify expressions involving real numbers

c. evaluate numerical expressions with integral exponents

d. simplify square roots of perfect square whole numbers

2. Polynomials in one variable.

a. use the definition of a polynomial in one variable to distinguish between expressions that

are polynomials and expressions that are not

b. classify polynomials in one variable by degree and number of terms

c. add, subtract, multiply, and divide polynomials in one variable (including the use of long

division techniques and the distributive law)

d. simplify polynomials in one variable

e. factor polynomials (including factoring out the greatest common factor, factoring by

f. understand and use the exponent laws involving integer exponents

3. Concepts and skills involving the analysis and graphing of linear equations and inequalities

in one variable.

a. solve linear equations and inequalities in one variable involving integral, decimal, and

fractional coefficients and solutions

b. graph the solution set of linear equations and inequalities on a number line

4. Application problems.

a. write and evaluate linear expressions from verbal descriptions

b. 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

c. solve literal equations for a specified variable using only addition and multiplication

principles

4. solve application problems using ratio and proportion and direct variation
5. use given data to estimate values and to evaluate geometric and other formulas

f. solve problems involving the Pythagorean Theorem

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

a. identify the relationship between the solution of a linear equation in two variables and

its graph on the cartesian plane

b. understand and use the concepts of slope and intercept

c. graph a line given either two points on the line or one point on the line and the slope

of the line

d. identify the equations of the line in the standard, point-slope, or slope-intercept forms

and graph their solutions

e. 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)

f. solve systems of linear equations

6. Quadratic equations.

a. find solutions to quadratic equations and equations of higher degree using the

technique of factoring

b. recognize a need to use the quadratic formula to solve quadratic equations and solve

quadratic equations by using the quadratic formula when simplification of square roots

other than perfect squares is not needed

7. Rational expressions.

a. evaluate rational expressions, avoiding division by zero

b. simplify rational expressions

c. multiply and divide rational expressions

d. add and subtract rational expressions, limiting unlike denominators to monomials

e. solve rational equations with monomial denominators or proportion equations with

binomial denominators

6. simplify complex fractions with monomial secondary denominators

8. Description and classification of irrational numbers.

1. simplify perfect square radical expressions
2. recognize irrational numbers
3. use decimal approximations in applications that involve radical expressions

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Last updated January 5, 2000. Comments, questions, suggestions?