  # Intermediate Algebra

## PREREQUISITE(S):

1 year H.S. algebra, department permission, or MAT 063.

## COURSE DESCRIPTION:

A review of elementary algebra along with new topics including exponents and radicals, functions and graphs, quadratic equations , inequalities and systems of equations.

## COURSE COMPETENCIES:

During this course, the student will be expected to:

1. Solve first and second degree equations/inequalities.
1.1 Solve first degree equations using the properties of equality.
1.2 Solve first degree inequalities using the properties of inequalities.
1.3 Solve second degree equations by factoring.
1.4 Solve second degree equations by the square root method.
1.5 Solve second degree equations by completing the square.
1.6 Solve second degree equations by using the quadratic formula.
1.7 Solve equations reducible to quadratic form.

2. Solve absolute value linear equations/inequalities.

3. Solve fractional equations/inequalities.

4. Solve exponential equations.
4.2 Solve exponential equations that do not require the use of logs.
4.3 Solve exponential equations that do require the use of logs.
4.4 Solve logarithmic equations.

5. Write models for verbal problems that result in first degree equations/inequalities.

6. Write models for verbal problems that result in second degree equations.

7. Demonstrate an understanding of the real number system.
7.1 Calculate with rational numbers using order of operations .
7.2 Graph sets of real numbers on a number line.
7.3 Use the properties of real numbers: commutative, associative, distribute, identities, inverses, closure, and order.
7.4 Use scientific notation.

8. Simplify an algebraic expression.
8.1 Use the rules of exponents to simplify an expression.
8.2 Use the properties of real numbers to simplify an expression.

9. Perform the basic arithmetic operations with polynomials .
9.1 Classify polynomials according to number of terms.
9.3 Subtract polynomials.
9.4 Multiply polynomials.
9.5 Divide polynomials.
9.6 Factor polynomials .
9.6.1 By factoring out the greatest common factor .
9.6.2 By grouping.
9.6.3 Factor trinomials by inspection.
9.6.4 Factor trinomials by using the special cases of: difference of two squares ; perfect square of sum; perfect square of difference; difference of two cubes; and sum of two cubes.

10. Perform the basic arithmetic operations with rational expressions.
10.1 Express rational algebraic expressions in simplest form.
10.2 Find sums, differences, products and quotients of rational algebraic expressions.
10.3 Simplify a complex fraction .

11. Perform the basic arithmetic operations with expressions containing rational exponents or radicals.
11.1 Express the square root of a negative number as a complex number.
11.2 Perform the basic arithmetic operations with expressions containing complex numbers.
11.3 Use the rules of exponents to simplify expressions containing rational exponents.
11.4 Perform the basic arithmetic operations with expressions containing rational exponents.
11.5 Convert an expression from radical to exponential notation and vice versa.
11.7 Perform the basic arithmetic operations with expressions containing radical expressions.

12. Graph linear equations/inequalities and quadratic equations.
12.1 Graph linear equations.
12.2 Write the equation of a line.
12.3 Graph linear inequalities.
12.4 Graph circles, parabolas, ellipses centered at the origin, hyperbolas centered at the origin.
12.5 Identify the type of conic section by inspecting its equation.

13. Solve systems of linear equations/inequalities and nonlinear systems of equations.
13.1 Solve linear systems of equations by the elimination method.
13.2 Solve linear systems of equations by the substitution method.
13.3 Solve linear systems of equations by Cramer's Rule.
13.4 Solve systems of linear inequalities by graphing.
13.5 Solve nonlinear systems of equations by graphing, elimination, or substitution.

14. Demonstrate an understanding of functions, function notation, inverse functions, and properties of logarithms.
14.1 Define a function.
14.2 Determine the domain and range of a variety of functions.
14.3 Construct a graph of functions including: linear functions, quadratic functions, polynomial functions, square root functions, and absolute value functions.
14.4 Given two functions, construct the sum, difference, product, quotient and composition of the functions.
14.5 Evaluate a given function.
14.6 Determine the inverse of a function.
14.7 State the relationship of a logarithmic function to an exponential function.
14.8 Use a table to find common logarithms and antilogs.
14.9 Apply the basic properties of logs when approximating computations of products, quotients, roots and powers.

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