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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

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Intermediate Algebra