Intermediate Algebra

No make-up quizzes or tests are given unless a valid documented emergency. If a student
misses a lecture, it is the student’s responsibility to understand the material. Students are
encouraged to read ahead before the class in order to better understanding the material.
Questions related to the course are always welcome during the class and my office hours.
Students are responsible of checking school calendars of course addition, dropping,
graduation, final exam etc. Students should follow the school rules and policies in
disciplines. Students having any question about class rules should ask Department for
assistance.

Any test following exactly same logics and patterns as others will be suspected as
cheating. A student who cheats can expect a zero for that test, a failing grade, reprimands
from Department, and record on your transcript.

Properties of Real Numbers: Define and use the terms: set, subset, natural
numbers, rational numbers , basic axioms of equality, the properties of real
numbers, and the prime and composite numbers.

Add, subtract, multiply and divide signed numbers.

Polynomials: Define the terms: exponent, base, power, coefficient , polynomial,
degree; be able to simplify polynomial expressions and exponential expressions and
exponential expressions; be able to factor quadratics, polynomial expressions, sum
and difference of cubes , and deal with factoring by grouping; be able to evaluate an
algebraic expression for given values of the variables.

Synthetic Division .

Fractions: Be able to add, subtract, multiply, divide, and simplify algebraic fractions ;
and to simplify complex fractions .

First-Degree Equations and Inequalities -One Variable: Solve linear equalities and
inequalities in one variable; "translate" verbal problems into mathematical sentences.

Exponents, Roots and Radicals : Use laws of exponents , perform algebraic operations
and simplify expressions including integral, fractional, negative and zero exponents;
use scientific notation; change from radical form to exponential form, and
conversely; change an algebraic expression containing radicals to simplest radical
form; add, subtract, multiply and divide complex numbers.

Second-Degree Equations - On Variable: Identify a quadratic equation and select a
method for solving it by extraction of roots, factoring, completing the square,
quadratic formula ; use the discriminant to determine whether roots of a quadratic
equation are equal, real, irrational, complex; solve an equation involving radical
expressions; form a quadratic equation for which the roots are given. Solve quadratic
inequalities.

Functions and Graphs II: Graph the set of points which an algebraic function
represents, after investigating domain and range; direct, inverse and joint
variation, translating word problem into equations and solving practical problems;
graph quadratic inequalities.

Simultaneous Systems: Solve two linear equations of two unknowns by graphing ,
linear combinations, substitutions and determinants; evaluate a second or third
order determinant; solve three first degree equations on three unknowns by linear
combinations and by determinants; solve a system of a linear and a quadratic
equation or two quadratic equations by substitution or linear combinations.

Exponential and Logarithmic Functions: Sketch an exponential or logarithmic
function; change an expression form logarithmic to exponential form, and from
exponential to logarithmic form; apply the three basic laws of logarithms; use 4-
place logarithm tables to multiply, divide, find roots, and find powers ; use linear
interpolation where needed; use logarithms in compound interest problems.

2. Solve systems of linear equations and inequalities.

3. Describe and analyze the characteristics of different types of functions.

4. Solve mathematical application problems by applying critical thinking skills and
express the solution in oral or written form.

1. Solve linear equations and inequalities involving absolute value and find the
equation of a line from specified information.

2. Factor polynomials by grouping and factor the sum and difference of two cubes.

3. Use of the properties of rational and negative exponents to simplify expressions.

4. Perform the fundamental operations on rational expressions and complex
numbers.

5. Use the discriminant to determine the number and kind of solutions in a quadratic
equation.

6. Solve equations and inequalities which are quadratic or quadratic in form.

7. Solve problems involving direct and inverse variation.

8. Solve systems of linear equations in three variables by the elimination and
substitution methods and by using Cramer's Rule.

9. Graph second-degree inequalities in two variables centered at the origin.

10. Solve nonlinear systems of equations in two variables using graphical and
algebraic methods.

11. Perform the fundamental operations on functions and graph a function and its
inverse.

12. Solve exponential and logarithmic equations and related application problems.