# Extra Practice Problems

Though our programs are not in need of any reviewing, many parents have told us that they would like some extra problems for certain lessons. The following downloads include sets of additional practice problems for EACH lesson in the VideoText Interactive Algebra program. With this download you will be able to choose a specific lesson, and then print out extra problems for that lesson!

Note: These problems will stretch your student’s thinking. You should only use these problems if your student has already mastered the concepts and only needs extra practice.

## Unit 1

Part A – Mathematics as a Language
Lesson 1Mathematical Parts of Speech
Lesson 2Mathematical Expressions
Lesson 3Translation of Mathematical Symbols

Part B – Further Investigation of Number Symbols
Lesson 1The Development of Our Number System
Lesson 2Fraction Forms and Decimal Forms
Lesson 3Changing Fraction Forms to Decimal Forms
Lesson 4Changing Decimal Forms to Fraction Forms
Lesson 5Percent
Lesson 6Primes, Composites, and Factoring
Lesson 7Least Common Multiple
Lesson 8Greatest Common Factor

Part C – Further Investigation of Operation Symbols
Lesson 1Order of Operations
Lesson 2Properties of Operations
Lesson 3Properties of Operations with Special Numbers
Lesson 4Operations with Fractions – Multiplication
Lesson 5Operations with Fractions – Addition and Subtraction
Lesson 6Operations with Fractions – Division
Lesson 7Operations with Decimals
Lesson 8Operations with Signed Numbers – Vectors/Absolute Value
Lesson 9Operations with Signed Numbers – Addition
Lesson 10Operations with Signed Numbers – Subtraction
Lesson 11Operations with Signed Numbers – Multiplication/Division

Part D – Further Investigation of Relation Symbols
Lesson 1
Order of Numbers and the Number Line
Lesson 2 Properties of Equality
Lesson 3 Properties of Inequality

Part E – Mathematical Models
Lesson 1The Mathematics of Sets
Lesson 2The Mathematics of Functions

## Unit 2

Part A – Basic Equations and Inequalities
Lesson 1
Solution Statements and Solution Sets
Lesson 2First Type – Making Zeroes
Lesson 3Second Type – Making Ones
Lesson 4Combinations

Part B – Complications on Equations and Inequalities
Lesson 1Grouping Symbols
Lesson 2Like Terms on the Same Side
Lesson 3Placeholders on Both Sides
Lesson 4Combinations – A Suggested Hierarchy

Part C – Special Cases of Equations and Inequalities
Lesson 1
No Solution
Lesson 2Infinite Number of Solutions

Part D – Systems of Equations and Inequalities
Lesson 1 “And”
Lesson 2“Or”
Lesson 3Absolute Value “Equal To” a Number (or)
Lesson 4Absolute Value “Less Than” a Number (and)
Lesson 5Absolute Value “Greater Than” a Number (or)

Part E – Problem-Solving Using One Placeholder
Lesson 1
General Setup
Lesson 2“Number” Problems
Lesson 3“Consecutive Integer” Problems
Lesson 4“Age” Problems
Lesson 5“Geometric Figure” Problems
Lesson 6“Motion” Problems
Lesson 7“Percent” Problems

## Unit 3

Part A – Solution Set for One Open Sentence
Lesson 1
Solution Sets For Equations
Lesson 2Solution Sets For Inequalities
Lesson 3Graphing Terminology
Lesson 4Graphing Techniques for y=mx
Lesson 5Graphing Techniques for y=mx+b
Lesson 6Graphing Techniques – Intercepts

Part B – Special Cases of Solution Sets
Lesson 1
y=a, y<a, y>a
Lesson 2x=a, x<a, x>a
Lesson 3Absolute Value

Part C – Finding Relations from Solution Sets
Lesson 1Given the Slope and y-intercept
Lesson 2Given the Slope and One Solution
Lesson 3Given Two Solutions
Lesson 4Given Parallel or Perpendicular Lines and One Solution

Part D – Solution Set for a System of Two Open Sentences
Lesson 1
Graphic Solution for Equations
Lesson 2Graphic Solution for Inequalities
Lesson 3Algebraic Solution for Equations-Elimination by Addition
Lesson 4Algebraic Solution for Equations-Elimination by Substitution

Part E – Special Cases of Solution Sets for Systems
Lesson 1
No Solution – Inconsistent
Lesson 2Infinite Number of Solutions – Dependent

Part F – Problem-Solving Using Two Placeholders
Lesson 1
General Setup
Lesson 2“Number” Problems
Lesson 3“Age Problems”
Lesson 4“Geometric Figure” Problems
Lesson 5“Motion” Problems
Lesson 6“Percent” Problems
Lesson 7“Value” or “Mixture” Problems

## Unit 4

Part A – Solution Sets
Lesson 1
One Open Sentence
Lesson 2Two Open Sentences
Lesson 3Systems of Three or More Open Sentences (Algebraic Solution)

Part B – Special Cases
Lesson 1
No Solution – Inconsistent
Lesson 2Infinite Number of Solutions – Dependent

Part C – Problem-Solving Using Three or More Placeholders
Lesson 1“Number Problems”
Lesson 2“Age” Problems
Lesson 3“Geometric Figure” Problems
Lesson 4“Value” or “Mixture” Problems

## Unit 5

Part A – Exponent Notation
Lesson 1
Definition and Terminology
Lesson 2Operations with Powers
Lesson 3Extensions of Operations with Powers
Lesson 4Special Cases of Powers
Lesson 5Scientific Notation

Part B – Polynomials
Lesson 1
Algebraic Expressions
Lesson 2Definition and Terminology
Lesson 3Operations with Polynomials – Addition and Subtraction
Lesson 4Operations with Polynomials – Multiplication
Lesson 5Operations with Polynomials – Division

Part C – Solving Equations and Inequalities by Factoring
Lesson 1Principle of Zero Products
Lesson 2Special Products – Common Factor
Lesson 3Special Products – Difference of Squares
Lesson 4Special Products – Perfect Square Trinomial
Lesson 5Special Products – General Trinomial
Lesson 6 Special Products – Four-Term Polynomial
Lesson 7Special Products – Sum or Difference of Cubes
Lesson 8General Factoring Strategy
Lesson 9Synthetic Division
Lesson 10Literal Equations

Part D – Problem-Solving with Higher-Order Relations
Lesson 1
“Number” Problems
Lesson 2“Consecutive Integer” Problems
Lesson 3“Geometric Figure” Problems
Lesson 4“Formula” Problems

## Unit 6

Part A – Operations
Lesson 1
Simplifying
Lesson 2Multiplying
Lesson 3Dividing
Lesson 5Complex Forms

Part B – Solving Open Sentences
Lesson 1Equations (Arithmetic Case)
Lesson 2Equations (Algebraic Case)
Lesson 3Inequalities (Algebraic Case)
Lesson 4Literal Equations

Part C – Problem-Solving with Algebraic Fractions
Lesson 1
“Fraction” Problems
Lesson 2“Work” Problems
Lesson 3“Motion” Problems
Lesson 4“Direct Variation” Problems
Lesson 5“Inverse Variation” Problems
Lesson 6“Mixed Variation” Problems

## Unit 7

Part A – Rational Numbers as Exponents
Lesson 1
Fractions and Exponents
Lesson 2Odd and Even “Kth” Roots

Part B – Operations with Radical Expressions
Lesson 1
Multiplying
Lesson 2Simplifying with Perfect Powers
Lesson 3Dividing and Simplifying
Lesson 6Rationalizing Denominators

Part C – Solving Radical Equations
Lesson 1
Lesson 2Equations with Two Radical Expressions

Part D – Problem-Solving with Relations Containing Radical Expressions
Lesson 1
The “Distance” Relation
Lesson 2“Formula” Problem

Part E – The Complex Numbers as a Mathematical System
Lesson 1
Imaginary and Complex Numbers
Lesson 3Multiplication
Lesson 4Division

## Unit 8

Part A – Solving Quadratic Equations of the Form
Lesson 1
Suppose a = 0, b = 0, or c = 0
Lesson 2Suppose a, b, c = 0
Lesson 4Checking Solutions

Part B – Equations that are Quadratic in Form
Lesson 1
Higher Integer Order
Lesson 2Lower Rational Order, Greater Than Zero
Lesson 3Integer Order Less Than Zero

Part C – Problem-Solving with Quadratic Relations
Lesson 1
“Geometric Figure” Problems
Lesson 2“Pythagorean Theorem” Problems
Lesson 3“Work” Problems
Lesson 4“Motion” Problems

## Unit 9

Part A – Parabolas – The Quadratic Function
Lesson 1
– Origins
Lesson 2The Graph of y=ax2
Lesson 3The Graph of y=(x-h)2
Lesson 4The Graph of y=x2+k
Lesson 5The Graph of y=a(x-h)2+k
Lesson 6Intercepts

Part B – Circles
Lesson 1
Standard Form
Lesson 2Not Standard Form

Part C – Ellipses
Lesson 1
Standard Form
Lesson 2Not Standard Form

Part D – Hyperbolas
Lesson 1
Standard Form
Lesson 2Not Standard Form

Part E – Solving Systems of Relations
Lesson 1
One First-Degree and One-Second Degree
Lesson 2Two Second-Degree

Part F – Problem-Solving with Non-Linear Systems
Lesson 1
“Number” Problems
Lesson 2“Geometric Figure” Problems

## Unit 10

Part A – Exponential Functions
Lesson 1
Graphs of Solution Sets for f(x)=ax
Lesson 2 Graphs of Solution Sets for f(y)=ay

Part B – Logarithmic Functions
Lesson 1Logarithmic Functions as Inverses of Exponential Functions
Lesson 2Graphs of Solution Sets for f(x)=logax

Part C – Operations with Logarithms
Lesson 1Properties of Logarithms
Lesson 2Finding Logarithms
Lesson 3Computation

Part D – Solving Open Sentences
Lesson 1Exponential Equations
Lesson 2 – Logarithm Equations