# Intermediate Algebra

**Prerequisite Skills:** To ensure that a student will
have the most successful experience in this class, it will be assumed that the
student can (prior to enrolling in Math 20) perform with reasonable accuracy all
of the following:

• Solve linear, quadratic, literal equations,
systems of equations and linear inequalities by choosing

an appropriate method

• Graph linear equations and inequalities

• Simplify exponential expressions

• Factor general trinomials at an elementary level

• State and apply quadratic formula

• Add, subtract, multiply, and divide polynomials, square roots and
exponential expressions

• Simplify complex fractions, square roots and exponential expressions

• Solve introductory level equations with rational expressions

• Translate and solve algebraic word problems in a single variable

• Given the description of a graph of a line, write the equation of that
line

• Define and use properties of equality and inequality

• Recognize and use common mathematical language to describe mathematical
processes in either

written or verbal form

• Apply units of measurements in the solution of algebraic applications as
appropriate

**Exit Skills:** In order to pass this class and be
prepared for the subsequent courses (Math 2, Math 21, Math 26, Math 41, or Math
52), students must be able to do all of the following:

• Simplify advanced numerical and algebraic
expressions involving multiple operations

• Solve linear, quadratic, rational and absolute value inequalities, graph
their solution sets, and

express the answer in interval notation

• Solve linear equations for a designated variable

• Apply algorithms of completing the square, rationalizing the
denominator, and long division and

synthetic division of polynomials

• Solve linear, quadratic form, simple cubic, radical, rational, absolute
value, elementary

exponential, and elementary logarithmic equations

• Solve systems of linear equations in three variables using matrix row
reduction

• Graph the solution sets of systems of linear and quadratic inequalities

• Perform operations on complex numbers

• Perform operations on complex numbers

• Perform operations on functions including composition of two functions
and determine the domain

of the resulting function

• Use proper mathematical notation to evaluate functions and obtain their
inverses

• State and apply the fundamental properties of exponents and logarithms

• Demonstrate knowledge of standard vocabulary associated with graphing,
including but not limited

to slopes of lines, intercepts, vertex of parabola, asymptotes, and interplay
between graph and

functional notation

• Given its graph, determine whether a relation is a function and whether
it is one-to-one, and

determine its intercepts and domain and range

• Graph using horizontal and vertical translations and determine the
domain and range of linear,

quadratic, simple cubic, radical, reciprocal, absolute value, exponential and
logarithmic functions

• Graph circles and parabolas using horizontal and vertical translation

• Evaluate simple expressions involving summation notation

• Set up and solve practical applications of the algebraic material