PRE-ALGEBRA 1
CHAPTER 1: SETS
1.1 BASIC CONCEPTS OF SETS
1. Defining a Set
2. Representing Sets Vid 1 , Vid 2 ,
3. Number of Elements of a Set
4. Comparing Sets
5. Types of Sets
6. Subsets
-Subsets Including or Not Including Distinct Elements Vid 1 ,
-Subsets With Distinct Number of Elements Vid 1 ,
1.2 OPERATIONS ON SETS
1. UNION OF SETS
2. INTERSECTION OF SETS
3. COMPLEMENT OF A SET
4. DIFFERENCE OF TWO SETS
5. SURVEY PROBLEMS about sets union, intersection, difference, complement Vid 1 , Vid 2 , Vid 3 ,
CHAPTER 2: NUMERATION SYSTEMS
2.1 NUMERATION SYSTEMS
A. ANCIENT NUMERATION SYSTEMS
1. Introduction
2. The Egyptian Numeration System
3. The Babylonian Numeration System
4. The Roman Numeration System
5. The Mayan Numeration System
6. The Hindu-Arabic Numeration System
B. THE DECIMAL PLACE VALUE SYSTEM
C. EXPONENTIAL NOTATION
D. EXPANDED NOTATION IN THE DECIMAL SYSTEM
1. Powers of Ten
2. Expanded Notation
2.2 ARITHMETIC IN OTHER BASES
A. THE BASE 5 COUNTING SYSTEM
1. Converting Base 5 Numbers to Base 10
2. Converting Base 10 Numbers to Base 5
B. THE BINARY (BASE 2) COUNTING SYSTEM
1. Converting Base 2 Numbers to Base 10
2. Converting Base 10 Numbers to Base 2
CHAPTER 3: NATURAL NUMBERS
3.1 NATURAL NUMBERS
A. THE CONCEPT OF NATURAL NUMBERS
1. Natural Numbers
2. Whole Numbers
3. The Order of Natural Numbers
4. Betweenness in N
B. ADDITION OF NATURAL NUMBERS
1. Concept of Addition
2. Addition on a Number Line
3. Properties of Addition in N
C. SUBTRACTION OF NATURAL NUMBERS
1. Concept of Subtraction
2. Subtraction on a Number Line
3. Properties of Subtraction in N
D. MULTIPLICATION OF NATURAL NUMBERS
1. Concept of Multiplication
2. Multiplication on a Number Line
3. Multiplying Powers of Ten
4. Properties of Multiplication in N
E. DIVISION OF NATURAL NUMBERS
1. Concept of Division
2. Division with Remainder
3. Zero in Division
4. Properties of Division in N
F. MIXED OPERATIONS
1. Order of Operations
2. The Sum of Consecutive Natural Numbers
3. Written Problems
CHAPTER 4: DIVISIBILITY, GREATEST COMMON FACTOR AND LEAST COMMON MULTIPLE
4.1 DIVISION OF NATURAL NUMBERS
A. RULES OF DIVISIBILITY
1. The Division Algorithm
2. Divisibility Rules
B. FACTORS AND DIVISORS OF NATURAL NUMBERS
4.2 FACTORIZATION OF NATURAL NUMBERS
A. PRIME NUMBERS AND COMPOSITE NUMBERS
1. Prime Numbers
2. Composite Numbers
B. PRIME FACTORIZATION OF NATURAL NUMBERS
1. Prime Factors
2. Prime Factorization
C. NUMBER OF FACTORS OF A NATURAL NUMBER
4.3 GREATEST COMMON FACTOR AND LEAST COMMON MULTIPLE
A. GREATEST COMMON FACTOR (GCF)
1. Common Factors
2. Greatest Common Factor (GCF)
3. Relatively Prime Numbers
4. Written Problems
B. LEAST COMMON MULTIPLE (LCM)
1. Common Multiple
2. Least Common Multiple
3. Written Problems
4. Properties of the Greatest Common Factor and the Least Common Multiple
CHAPTER 5: INTEGERS
5.1 INTEGERS
1. Understanding Integers
2. Integers on the Number Line
3. The Order of Integers
5.2 ADDITION OF INTEGERS
A. ADDITION IN Z
B. PROPERTIES OF ADDITION IN Z
1. Closure Property
2. Commutative Property
3. Associative Property
4. Identity Element
5. Inverse Element
5.3 SUBTRACTION OF INTEGERS
A. SUBTRACTION IN Z
B. PROPERTIES OF SUBTRACTION IN Z
1. Closure Property
2. Commutative Property
3. Associative Property
4. Identity Element
5.4 MULTIPLICATION OF INTEGERS
A. MULTIPLICATION IN Z
B. PROPERTIES OF MULTIPLICATION IN Z
1. Closure Property
2. Commutative Property
3. Associative property
4. Identity Element
5. Null Element
6. The Distributive Property of Multiplication Over Addition
7. The Distributive Property ofMultiplication Over Subtraction
C. POWERS OF INTEGERS
1. Understanding Powers of Integers
2. Square of an Integer
3. Cube of an Integer
4. Even and Odd Powers of a Negative Integer
5. Powers of Ten
5.5 DIVISION OF INTEGERS, AND MIXED OPERATIONS
A. DIVISION IN Z
1. Understanding Division in Z
2. Dividing Integers by 1 and –1
3. Dividing Integers by Powers of Ten
B. PROPERTIES OF DIVISION IN Z
1. Closure Property
2. Commutative Property
3. Associative Property
4. Identity Element
5. Null Element
6. Distributive Property
C. MIXED OPERATIONS IN Z
CHAPTER 6: RATIONAL NUMBERS
6.1 FRACTIONS
A. CONCEPT OF FRACTION
1. Understanding Fractions
2. Terms of a Fraction
B. TYPES OF FRACTION
1. Proper (Simple) Fractions
2. Improper Fractions
3. Mixed Numbers
4. Writing an Improper Fraction as a Mixed Number
5. Writing a Mixed Number as an Improper Fraction
C. REPRESENTING FRACTIONS ON A NUMBER LINE
D. EQUIVALENT FRACTIONS
1. Equivalent Fractions
2. Enlarging a Fraction
3. Simplifying and Reducing a Fraction
4. Written Problems
6.2 RATIONAL NUMBERS
A. RATIONAL NUMBERS: THE SET Q
1. Understanding Rational Numbers
2. The Set of Positive Rational Numbers
3. The Set of Negative Rational Numbers
4. The Set of Rational Numbers
5. Showing Rational Numbers on the Number Line
B. COMPARING AND ORDERING RATIONAL NUMBERS
1. Comparing and Ordering Positive Rational Numbers
2. Comparing and Ordering Negative Rational Numbers
3. Density Property of Rational Numbers
6.3 ADDITION OF RATIONAL NUMBERS
A. ADDITION IN Q
1. Adding Rational Numbers with Common Denominators
2. Adding Rational Numbers with Different Denominators
B. PROPERTIES OF ADDITION IN Q
6.4 SUBTRACTION OF RATIONAL NUMBERS
A. SUBTRACTION IN Q
1. Subtracting Rational Numbers with Common Denominators
2. Subtracting Rational Numbers with Different Denominators
B. PROPERTIES OF SUBTRACTION IN Q
6.5 MULTIPLICATION OF RATIONAL NUMBERS
A. MULTIPLICATION IN Q
1. Multiplying Two Rational Numbers
2. Multiplying a Rational Number by an Integer
3. Multiplying Mixed Numbers
B. PROPERTIES OF MULTIPLICATION IN Q
C. POWERS OF RATIONAL NUMBERS
1. Understanding Powers of Rational Numbers
2. Even and Odd Powers of Negative Rational Numbers
6.6 DIVISION OF RATIONAL NUMBERS
A. DIVISION IN Q
B. PROPERTIES OF DIVISION IN Q
6.7 MIXED OPERATIONS
1. Mixed Operations in Q
2. Operations on Complex Fractions
CHAPTER 7: DECIMAL NUMBERS
A. THE CONCEPT OF DECIMAL NUMBER
1. Understanding Decimals and Decimal Fractions
2. Decimal Notation
3. Representing Decimals on the Number Line
4. Comparing and Ordering Decimals
B. RELATIONSHIP BETWEEN FRACTIONS AND DECIMAL NUMBERS
1. Terminating Decimals
2. Repeating Decimals
3. Rounding Decimals
CHAPTER 8: REAL NUMBERS
8.1 REAL NUMBERS
A. THE SET OF REAL NUMBERS
1. Understanding Real Numbers
2. Properties of Real Numbers
B. ABSOLUTE VALUE
1. Absolute Value
2. Properties of the Absolute Value
8.2 EXPONENTS
A. POWERS OF REAL NUMBERS
B. PROPERTIES OF EXPONENTS
C. EXPONENTIAL EQUATIONS
8.3 SQUARE ROOTS
1. Understanding Square Roots
2. Properties of Square Roots
3. Working with Pure and Mixed Radicals
4. Multiplying Square Roots
5. Rationalizing Denominators
8.4 RATIONAL EXPONENTS
A. RATIONAL EXPONENTS
1. nth Roots
2. Rational Exponents
B. PROPERTIES OF RADICALS
C. RADICAL EQUATIONS
PRE-ALGEBRA 2
CHAPTER 9: EQUATIONS AND INEQUALITIES
9.1 ALGEBRAIC EXPRESSIONS
A. ALGEBRAIC EXPRESSIONS
1. Translating Phrases into Algebraic Expressions
B. OPEN SENTENCES AND EQUATIONS
C. LINEAR EQUATIONS IN ONE VARIABLE
1. Equality and its Properties
2. Solving Linear Equations
3. Solution Strategies: Combining Like Terms
4. Solution Strategies: Collecting Variables on the Same Side of an Equation
9.2 INEQUALITIES
A. SOLVING INEQUALITIES IN ONE VARIABLE
1. Inequalities in One Variable
2. Graphing Inequalities on a Number Line
3. Properties of Inequality
4. Solving Inequalities
5. Written Problems
6. Compound Inequalities
9.3 LINEAR EQUATIONS IN TWO VARIABLES
A. THE COORDINATE PLANE
1. Coordinates on a Graph
2. The Rectangular Coordinate System
B. SOLVING LINEAR EQUATIONS IN TWO VARIABLES
1. Constructing a Table of Values
2. Graphing Linear Equations
3. The Intercept Method
C. SOLVING SYSTEMS OF LINEAR EQUATIONS
1. The Graphing Method
2. The Elimination Method
3. The Substitution Method
9.4 LINEAR INEQUALITIES IN TWO VARIABLES
A. GRAPHING LINEAR INEQUALITIES
B. SOLVING SYSTEMS OF LINEAR INEQUALITIES
9.5 QUADRATIC EQUATIONS
A. QUADRATIC EQUATIONS
B. SOLVING QUADRATIC EQUATIONS
1. Factoring Quadratic Equations
2. The Square Root Method
3. Completing the Square
4. The Quadratic Formula
9.6 WRITTEN PROBLEMS
1. Number and Fraction Problems
2. Age Problems
3. Work Problems
4. Percentage and Interest Problems
a. Percentage Problems
b. Interest Problems
5. Mixture Problems
6. Motion Problems
CHAPTER 10: RATIO, PROPORTION AND VARIATION
10.1 RATIO AND PROPORTION
A. RATIO
1. Ratio
2. Rate
B. PROPORTION
1. Basic Concepts
2. Properties of Proportion
3. Geometric Mean
10.2 VARIATION
A. TYPES OF VARIATION
1. Direct Variation
2. Inverse Variation
3. Joint Variation
B. VARIATION PROBLEMS
CHAPTER 11: POLYNOMIALS
11.1 POLYNOMIALS
A. ALGEBRAIC EXPRESSIONS AND POLYNOMIALS
1. Algebraic Expressions
2. Polynomials
a. Monomials
b. Types of Polynomial
3. Simplifying Polynomials
B. BASIC OPERATIONS ON POLYNOMIALS
1. Adding and Subtracting Polynomials
2. Multiplying Polynomials
3. Dividing a Polynomial by a Monomial
11.2 BINOMIAL EXPANSION AND BASIC IDENTITIES
A. BINOMIAL EXPANSION
1. Binomial Expansion Using Pascal’s Triangle
B. BASIC IDENTITIES
1. Square of a Binomial
2. Square of a Trinomial
3. Cube of a Binomial
4. Product of the Sum and the Difference of Two Terms
5. Sum of Two Cubes
6. Difference of Two Cubes
11.3 FACTORIZATION
A. FACTORIZATION METHODS
1. Taking Out a Common Factor
2. Factoring by Grouping
3. Factorization Identities
a. Squaring a Binomial
b. Factoring a Perfect Square Trinomial
c. Squaring a Trinomial
d. Difference of Two Squares a2 – b2
e. Cube of a Binomial
f. Sum or Difference of Two Cubes a3 ± b3
B. FACTORING TRINOMIALS
1. Factoring Perfect Square Trinomials
2. Completing the Square
3. Other Factoring Methods
a. Factoring trinomials of the form x2 + bx + c
b. Factoring trinomials of the form ax2 + bx + c
11.4 RATIONAL EXPRESSIONS
1. Simplifying Rational Expressions
2. Multiplying and Dividing Rational Expressions
3. Adding and Subtracting Rational Expressions
4. Complex Fractions
CHAPTER 12: MODULAR ARITHMETIC
12.1 CLOCK ARITHMETIC AND MODULAR
A. CLOCK ARITHMETIC AND MODULO
1. Clock Arithmetic
2. The Concept of Modulus
3. Clock Addition
B. OPERATIONS IN MODULAR ARITHMETIC
1. Modular Addition
2. Modular Multiplication
3. Solving Modular Equations
4. Other Operations in Modular Arithmetic
5. Applications of Modular Arithmetic
12.2 BINARY OPERATIONS
A. BASIC CONCEPT
1. Binary Operations
2. Using an Operation Table
B. PROPERTIES OF BINARY OPERATIONS
CHAPTER 13: STATISTICS
A. BASIC CONCEPTS
1. What is Statistics?
2. Collecting Data
a. Questionnaires
b. Sampling
c. Surveys
3. Summarizing Data
B. PRESENTING AND INTERPRETING DATA
1. Bar Graph
2. Line Graph
3. Circle Graph (Pie Chart)
C. MEASURES OF CENTRAL TENDENCY
1. Mean
2. Median
3. Mode
4. Range