# 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) Find Leading Term and Leading Coefficient

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) Add Polynomials

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) Add Fractions

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

**Chapter 6 Objectives: Radical Equations**

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) Identify Radicand

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) Graph Radical Function

Objective: (6.1) Simplify Radical Expression

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) Multiply Radicals

Objective: (6.3) Divide Radicals

Objective: (6.3) Simplify Rational Expression Under Radical I

Objective: (6.3) Simplify Rational Expression Under Radical II

Objective: (6.4) Add or Subtract Like Radicals

Objective: (6.4) Add or Subtract Unlike Radicals (Two Terms)

Objective: (6.4) Add or Subtract Unlike Radicals (Three Terms)

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 Radical Equation (One Radical)

Objective: (6.6) Solve Radical Equation (Two Radicals)

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

**Chapter 7 Objectives: Quadratic Equations**

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) Graph 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 Quadratic Inequality

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