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# Intermediate Algebra Learning Outcomes

Course Description:

For students with moderate algebra experience. Curriculum will include operations with linear equations,
factoring polynomials, and graphical techniques. Solutions to rational, radical, quadratic, and systems of
equations will be developed thoroughly. Culminating material will include operations with exponential and
logarithmic functions.

Learning Outcomes:

Chapter 1 Objectives: Solving Linear Equations
Objective: (1.1) Determine if Number is Solution of Equation (T/F)
Objective: (1.1) Solve Equation by Addition Principle
Objective: (1.1) Solve Equation by Multiplication Principle
Objective: (1.1) Solve Basic Equation by Both Principles
Objective: (1.1) Solve Eqn by Both Principles (Fractions)
Objective: (1.1) Solve Eqn by Both Principles (Remove Parentheses)
Objective: (1.2) Solve Formula for Specified Letter I
Objective: (1.2) Solve Formula for Specified Letter II
Objective: (1.2) Solve Apps: Formulas
Objective: (1.3) Solve Apps: Numbers
Objective: (1.3) Solve Apps: Percentages
Objective: (1.3) Solve Apps: Geometry, Other
Objective: (1.3) Solve Apps: Motion Problems
Objective: (1.4) Choose Number that is Solution of Inequality
Objective: (1.4) Write Set in Interval Notation
Objective: (1.4) Write Graph in Interval Notation
Objective: (1.4) Solve and Graph Inequality
Objective: (1.4) Solve Inequality
Objective: (1.4) Solve Apps: Inequalities
Objective: (1.5) Find Intersection or Union of Sets
Objective: (1.5) Graph Intersection and Write Interval Notation
Objective: (1.5) Solve and Graph Conjunction of Inequalities
Objective: (1.5) Solve Conjunction of Inequalities
Objective: (1.5) Solve and Graph Disjunction of Inequalities
Objective: (1.5) Solve Apps: Compound Inequalities
Objective: (1.6) Simplify Absolute-Value Expression
Objective: (1.6) Find Distance Between Two Points on Number Line
Objective: (1.6) Solve Absolute-Value Equation
Objective: (1.6) Solve Equation with Two Absolute Values
Objective: (1.6) Solve Absolute-Value Inequality

Chapter 2 Objectives: Graphs, Functions, and Applications
Objective: (2.1) Plot Points on Graph
Objective: (2.1) Determine Whether Ordered Pair is Solution
Objective: (2.1) Find Another Solution Given One
Objective: (2.1) Graph Linear Equation
Objective: (2.1) Graph Nonlinear Equation
Objective: (2.2) Determine Whether Correspondence Is a Function
Objective: (2.2) Find Function Values
Objective: (2.2) Solve Apps: Find Function Value
Objective: (2.2) Graph Function
Objective: (2.2) Determine Whether Graph Is Graph of Function
Objective: (2.2) Solve Apps: Functions and Graphs
Objective: (2.3) Find Domain or Range from Graph
Objective: (2.3) Determine Function Value from Graph
Objective: (2.3) Find x Given Graph of f(x)
Objective: (2.3) Find Domain from Equation
Objective: (2.3) Find Nonlinear Function Value
Objective: (2.4) Find Slope and y-intercept of Equation
Objective: (2.4) Find Slope of Line on Graph
Objective: (2.4) Find Slope Between Two Points
Objective: (2.4) Solve Apps: Graph and Slope
Objective: (2.5) Find Intercepts and Graph Equation
Objective: (2.5) Graph Using Slope and Intercept
Objective: (2.5) Graph Horizontal or Vertical Line
Objective: (2.5) Determine Whether Lines are Parallel/Perpendicular
Objective: (2.6) Find Equation Given Slope/Intercept
Objective: (2.6) Find Equation Given Point/Slope
Objective: (2.6) Find Equation Given Two Points
Objective: (2.6) Find Equation Given Point and Line
Objective: (2.6) Solve Apps: Equations of Lines

Chapter 3 Objectives: Systems of Equations
Objective: (3.1) Solve System Graphically
Objective: (3.1) Classify System by Number of Solutions
Objective: (3.2) Solve System by Substitution: One Variable Alone
Objective: (3.2) Solve System by Substitution
Objective: (3.2) Solve Apps: Solve by Substitution
Objective: (3.3) Solve System by Elimination with No Multiplication
Objective: (3.3) Solve System Using Multiplication and Elimination
Objective: (3.3) Solve Apps: Solve by Elimination
Objective: (3.4) Solve Apps: Mixtures
Objective: (3.4) Solve Apps: Total Value
Objective: (3.4) Solve Apps: Motion
Objective: (3.5) Solve Sys of Eqns in 3 Vars (Consistent, Indep) I
Objective: (3.5) Solve Sys of Eqns in 3 Vars (Consistent, Indep) II
Objective: (3.6) Solve Apps: Systems of Three Equations I
Objective: (3.6) Solve Apps: Systems of Three Equations II
Objective: (3.7) Choose Ordered Pair That Is Solution of Inequality
Objective: (3.7) Graph Linear Inequality in Two Variables
Objective: (3.7) Match Inequality with Graph
Objective: (3.7) Graph Sys of Two Inequalities, Identify Vertices
Objective: (3.7) Graph Sys of Three/Four Inequalities, Identify Vertices
Objective: (3.8) Find Profit Function and Break-even Point
Objective: (3.8) Solve Apps: Determine Profit or Loss
Objective: (3.8) Find the Equilibrium Point

Chapter 4 Objectives: Polynomial Functions
Objective: (4.1) Determine Degree of Each Term of Polynomial
Objective: (4.1) Determine Degree of Polynomial
Objective: (4.1) Arrange Terms in Descending Order
Objective: (4.1) Arrange Terms in Ascending Order
Objective: (4.1) Evaluate Polynomial for Given Value
Objective: (4.1) Solve Apps: Evaluate/Add Polynomials
Objective: (4.1) Collect Like Terms
Objective: (4.1) Find Opposite of Polynomial
Objective: (4.1) Subtract Polynomials I
Objective: (4.1) Subtract Polynomials II
Objective: (4.2) Multiply Monomial and Polynomial
Objective: (4.2) Multiply Two Binomials
Objective: (4.2) Use FOIL to Multiply Binomials
Objective: (4.2) Square a Binomial
Objective: (4.2) Multiply a Sum and a Difference of Same Terms
Objective: (4.2) Find and Simplify f(a + h) or f(a + h) - f(a)
Objective: (4.3) Factor Out Common Factor
Objective: (4.3) Factor Out Factor with Negative Coefficient
Objective: (4.3) Solve Apps: Factor Out Common Factor
Objective: (4.3) Factor by Grouping
Objective: (4.4) Factor x^2 + bx + c
Objective: (4.4) Factor x^2 + bx + c (Common Factor, Higher Degree)
Objective: (4.5) Factor ax^2 + bx + c
Objective: (4.5) Factor ax^2 + bx + c with Common Factor
Objective: (4.5) Factor ax^2 + bxy + cy^2
Objective: (4.5) Factor ax^2n + bx^n + c
Objective: (4.5) Solve Apps: Factor ax^2 + bx + c
Objective: (4.6) Factor Trinomial Square
Objective: (4.6) Factor Difference of Squares
Objective: (4.6) Factor Polynomial
Objective: (4.6) Factor Sum or Difference of Cubes
Objective: (4.7) Factor Binomial by Any Method
Objective: (4.7) Factor Trinomial by Any Method I
Objective: (4.7) Factor Trinomial by Any Method II
Objective: (4.7) Factor Polynomial by Any Method
Objective: (4.8) Solve Equation Using Principle of Zero Products
Objective: (4.8) Find a Such That f(a) Is a Given Value
Objective: (4.8) Find Domain of Rational Function
Objective: (4.8) Find x-Intercepts Using Graph
Objective: (4.8) Solve Apps: Polynomial Equation

Chapter 5 Objectives: Rational Equations
Objective: (5.1) Determine Numbers for Which Rational Expression is Not Defined
Objective: (5.1) Find Domain of Rational Function
Objective: (5.1) Multiply to Obtain Equivalent Rational Expression
Objective: (5.1) Simplify Rational Expression
Objective: (5.1) Multiply Rational Expressions
Objective: (5.1) Divide Rational Expressions
Objective: (5.1) Divide Rational Expressions
Objective: (5.2) Find LCM of Numbers
Objective: (5.2) Find LCM of Rational Expressions
Objective: (5.2) Add or Subtract Rational Exprns (Like Denominators)
Objective: (5.2) Add or Subtract Rational Exprns (Opposite Denominators)
Objective: (5.2) Add or Subtract Rational Exprns (Unlike Denominators)
Objective: (5.2) Simplify Combined Add/Subt of Rational Expressions
Objective: (5.3) Divide Polynomial by Monomial
Objective: (5.3) Divide Polynomial by Binomial I
Objective: (5.3) Divide Polynomial by Binomial II
Objective: (5.3) Divide Using Synthetic Division
Objective: (5.4) Simplify Complex Rational Expression
Objective: (5.4) Simplify Complex Rational Expression II
Objective: (5.5) Solve Rational Equation I
Objective: (5.5) Solve Rational Equation II
Objective: (5.5) Find Values of x for Which f(x) Has Given Value
Objective: (5.6) Solve Apps: Work
Objective: (5.6) Solve Apps: Proportions
Objective: (5.6) Solve Apps: Motion
Objective: (5.7) Solve Rational Formula for Letter
Objective: (5.8) Find Equation for Direct Variation
Objective: (5.8) Solve Apps: Direct Variation
Objective: (5.8) Find Equation for Inverse Variation
Objective: (5.8) Solve Apps: Inverse Variation
Objective: (5.8) Find Equation for Other Variation
Objective: (5.8) Solve Apps: Combined Variation

Objective: (6.1) Find Square Roots of Numbers
Objective: (6.1) Find Principal Square Root of Number
Objective: (6.1) Find Approximate Square Root
Objective: (6.1) Find Square Root Function Value
Objective: (6.1) Find Domain of Radical Function
Objective: (6.1) Solve Apps: Radical Function Value
Objective: (6.1) Simplify Cube Root Expression
Objective: (6.1) Find Higher Root Function Value
Objective: (6.1) Simplify Odd/Even Root Expression
Objective: (6.2) Rewrite Without Rational Exponents
Objective: (6.2) Rewrite With Rational Exponents
Objective: (6.2) Write Without Negative Rational Exponent
Objective: (6.2) Use Laws of Exponents to Simplify
Objective: (6.2) Use Rational Exponents to Simplify
Objective: (6.2) Write as a Single Radical Expression
Objective: (6.3) Simplify Rational Expression Under Radical I
Objective: (6.3) Simplify Rational Expression Under Radical II
Objective: (6.4) Multiply Radical Expressions I
Objective: (6.4) Multiply Radical Expressions II
Objective: (6.5) Rationalize Denominator (One Term)
Objective: (6.5) Rationalize Denominator (Binomial)
Objective: (6.6) Solve Apps: Radical Equations
Objective: (6.7) Find Missing Right Triangle Side
Objective: (6.7) Solve Apps: Pythagorean Theorem
Objective: (6.8) Write Imaginary Number as bi or a + bi
Objective: (6.8) Add or Subtract Complex Numbers
Objective: (6.8) Multiply Complex Numbers
Objective: (6.8) Simplify Power of i
Objective: (6.8) Simplify Binomial with Power of i
Objective: (6.8) Divide Complex Numbers
Objective: (6.8) Decide if Complex Number is Solution

Objective: (7.1) Solve by Square Root Principle I
Objective: (7.1) Solve by Square Root Principle II
Objective: (7.1) Find x-Intercepts of Quadratic Function
Objective: (7.1) Solve by Completing the Square I
Objective: (7.1) Solve by Completing the Square II
Objective: (7.1) Solve Apps: Quadratic Equations
Objective: (7.2) Solve by Quadratic Formula (Exact)
Objective: (7.2) Solve by Quadratic Formula (Exact, Imaginary)
Objective: (7.2) Find x-Intercepts of Quadratic Function
Objective: (7.2) Solve by Quadratic Formula (Approx)
Objective: (7.3) Solve Apps: Geometry
Objective: (7.3) Solve Apps: Motion
Objective: (7.3) Solve Formula for Given Letter
Objective: (7.4) Use Discriminant to Identify Solutions
Objective: (7.4) Write Quadratic with Given Solutions
Objective: (7.4) Solve Equation in Quadratic Form I
Objective: (7.4) Solve Equation in Quadratic Form II
Objective: (7.4) Find x-Intercepts of Function
Objective: (7.5) Graph f(x) = ax^2 or f(x) = a(x - h)^2
Objective: (7.5) Graph f(x) = a(x - h)^2 + k
Objective: (7.5) Find Vertex of Quadratic Function
Objective: (7.5) Find Line of Symmetry of Quadratic Function
Objective: (7.5) Find Maximum or Minimum Value of Quadratic Function
Objective: (7.6) Find Vertex of Quadratic Function
Objective: (7.6) Find Maximum or Minimum Value of Quadratic Function
Objective: (7.6) Find Line of Symmetry of Quadratic Function
Objective: (7.6) Find the Intercepts of Quadratic Function
Objective: (7.7) Solve Apps: Maximum/Minimum
Objective: (7.7) Determine Function to Fit Plot
Objective: (7.7) Find Quadratic Function to Fit Data Set
Objective: (7.8) Solve Polynomial Inequality
Objective: (7.8) Solve Rational Inequality

Chapter 8 Objectives: Exponential and Logarithmic Equations
Objective: (8.1) Graph Exponential Equation
Objective: (8.1) Graph Exponential Equation with x and y Interchanged
Objective: (8.1) Solve Apps: Exponential Functions I
Objective: (8.1) Solve Apps: Exponential Functions II
Objective: (8.2) Find Inverse of Relation Descr by Set of Ord Pairs
Objective: (8.2) Graph Relation, Inverse Descr by Set of Ord Pairs
Objective: (8.2) Find Inverse of Relation Described as an Equation
Objective: (8.2) Graph Relation, Inverse Described as an Equation
Objective: (8.2) Determine if Function is One-to-One
Objective: (8.2) Find Formula for Inverse of a Function
Objective: (8.2) Graph Function and Inverse on Same Axes
Objective: (8.2) Find Composition of Functions
Objective: (8.2) Decompose Composite Function
Objective: (8.2) Use Composition to Verify Inverse (Y/N)
Objective: (8.2) Solve Apps: Inverse and Composite Functions
Objective: (8.3) Graph Logarithmic Function
Objective: (8.3) Convert Exponential Equation to Logarithmic Equation
Objective: (8.3) Convert Logarithmic Equation to Exponential Equation
Objective: (8.3) Solve Logarithmic Equation
Objective: (8.3) Find Log Value
Objective: (8.3) Find Common Logarithm on Calculator
Objective: (8.3) Evaluate 10^x
Objective: (8.4) Express Log Product as Sum of Logs
Objective: (8.4) Express Sum of Logs as Log Product
Objective: (8.4) Express Log of Power as a Product
Objective: (8.4) Express Quotient as Difference of Logs
Objective: (8.4) Express Difference of Logs as Quotient
Objective: (8.4) Convert Product/Quotient to Sum/Diff
Objective: (8.4) Convert Sum/Difference to Single Log
Objective: (8.4) Find Value of Log Expression
Objective: (8.4) Simplify Expression of Type log_a a^x
Objective: (8.4) Solve Log Equation of the Type log_a a^b = x
Objective: (8.5) Use Calculator: Find Log or Power, Base e
Objective: (8.5) Use Change-of-Base Formula to Find Log
Objective: (8.5) Graph Exponential/Log Function, Base e
Objective: (8.6) Solve Exponential Equation
Objective: (8.6) Solve Logarithmic Equation
Objective: (8.7) Solve Apps: Log Equations (Decibels)
Objective: (8.7) Use pH Formula
Objective: (8.7) Exponential Growth
Objective: (8.7) Solve Apps: Compound Interest
Objective: (8.7) Solve Apps: Exponential Decay