COLLEGE ALGEBRA
* DENOTES OPTIONAL MATERIAL
Bold and Italicized items denote course competencies agreed upon by
the Kansas Core Outcomes Project
Chapter P PREREQUISITES:
FUNDAMENTAL CONCEPTS OF ALGEBRA Section: P.1 – P.6
Outcomes: The student will review concepts of real numbers, exponents,
radicals, and basic rules of algebra. |
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Specific Competencies
Demonstrate the ability to: |
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*P.1 |
Evaluate algebraic expressions. |
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*P.1 |
Use mathematical models. |
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*P.1 |
Find the intersection of two sets. |
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*P.1 |
Find the union of two sets. |
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*P.1 |
Recognize subsets of the real
numbers. |
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*P.1 |
Use inequality symbols . |
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*P.1 |
Evaluate absolute value. |
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*P.1 |
Use absolute value to express
distance. |
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*P.1 |
Identify properties of the real
numbers. |
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*P.1 |
Simplify algebraic expressions. |
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*P.2 |
Use the product, quotient,
zero-exponent, negative exponent, and power rules for
exponents. |
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*P.2 |
Use the power of a quotient. |
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*P.2 |
Simplify exponential expressions. |
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*P.2 |
Use scientific notation. |
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*P.3 |
Evaluate square roots. |
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*P.3 |
Simplify radical expressions using
the product rule and quotient rule |
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*P.3 |
Add and subtract square roots. |
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*P.3 |
Rationalize denominators. |
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*P.3 |
Evaluate and perform operations with
higher roots. |
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*P.3 |
Understand and use rational
exponents. |
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*P.4 |
Add, subtract, and multiply
polynomials . |
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*P.4 |
Use FOIL in polynomial
multiplication. |
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*P.4 |
Use special products in polynomial
multiplication. |
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*P.4 |
Perform operations with polynomials
in several variables. |
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*P.5 |
Factor out the greatest common factor
of a polynomial. |
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*P.5 |
Factor by grouping. |
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*P.5 |
Factor trinomials. |
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*P.5 |
Factor the difference of squares. |
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*P.5 |
Factor perfect square trinomials. |
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*P.5 |
Factor the sum and
difference of two cubes. |
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*P.5 |
Use a general strategy for factoring
polynomials. |
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*P.5 |
Factor algebraic expressions
containing fractional and negative exponents. |
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*P.6 |
Specify numbers that must be excluded
from the domain of a rational expression. |
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*P.6 |
Simplify rational expressions. |
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*P.6 |
Multiply and divide rational
expressions. |
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*P.6 |
Add and subtract rational
expressions. |
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*P.6 |
Simplify complex rational
expressions. |
Chapter 1 EQUATIONS AND
INEQUALITIES Section: 1.1 – 1.7
Outcomes: The student will learn to solve and use linear, quadratic and
polynomial equations, equations involving
radicals, fractions or absolute values; find intercepts , zeros, and
graphical solutions ; perform
operations with complex numbers and use mathematical models to solve
real world application
problems. |
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Specific Competencies
Demonstrate the ability to: |
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1.1 |
Plot points in the rectangular
coordinate system. |
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1.1 |
Graph equations in the rectangular
coordinate system. |
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1.1 |
*Interpret information about a
graphing utility’s viewing rectangle or table. |
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1.1 |
Use a graph to determine intercepts. |
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1.1 |
Interpret information given by
graphs. |
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1.2 |
Solve linear equations in one
variable. |
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1.2 |
Solve linear equations containing
fractions. |
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1.2 |
Solve rational equations with
variables in the denominators . |
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1.2 |
Recognize identities, conditional
equations, and inconsistent equations. |
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1.2 |
Solve applied problems using
mathematical models. |
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1.3 |
Use linear equations to solve
problems. |
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1.3 |
Solve a formula for a variable. |
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*1.4 |
Add and subtract complex numbers. |
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*1.4 |
Multiply complex numbers. |
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*1.4 |
Divide complex numbers. |
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*1.4 |
Perform operations with square roots
of negative numbers. |
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1.5 |
Solve quadratic equations by
factoring, square root property, completing the square, and
the quadratic formula.. |
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1.5 |
Use the discriminant to determine the
number and type of solutions. |
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1.5 |
Determine the most efficient method
to use when solving a quadratic equation |
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1.5 |
Solve problems modeled by quadratic
equations |
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1.6 |
Solve polynomial equations by
factoring. |
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1.6 |
Solve equations involving
radicals. |
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1.6 |
Solve equations with rational
exponents. |
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1.6 |
Solve equations that are quadratic
in form. |
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1.6 |
Solve equations involving absolute
value. |
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1.6 |
Solve problems modeled by equations. |
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1.7 |
Use interval notation. |
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1.7 |
Find intersections and unions of
intervals. |
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1.7 |
Solve linear inequalities. |
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1.7 |
Recognize inequalities with no
solution or all real numbers as solutions. |
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1.7 |
Solve compound inequalities. |
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1.7 |
Solve absolute value inequalities. |
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