 # Algebra & Trigonometry Super Review

## Paperback(Second Edition, Revised)

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ISBN-13: 9780738611181 Research & Education Association 01/15/2013 Super Reviews Study Guides Series Second Edition, Revised 304 514,582 5.40(w) x 8.20(h) x 1.00(d) 16 Years

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Sets and Set Operations

1.1 Sets

A set is defined as a collection of items. Each individual item belonging to a set is called an element or member of that set. Sets are usually represented by capital letters, elements by lowercase letters.

A set can be described in two ways: 1) it can be listed element by element, or 2) a rule characterizing the elements in a set can be formulated.

For example, given the set A of the whole numbers starting with 1 and ending with 9, we can describe it either as A = {1, 2, 3, 4, 5, 6, 7, 8, 9} or as {the set of whole numbers greater than 0 and less than 10}. In both methods, the description is enclosed in brackets. A kind of shorthand is often used for the second method of set description; instead of writing out a complete sentence in between the brackets, we write instead

A = {k | 0 < k < 10, k is a whole number}

This is read as “the set of all elements k such that k is greater than 0 and less than 10, where k is a whole number.”

A set not containing any members is called the empty or null set. It is written either as φ or { }.

Chapter 1 Sets and Operations
1.1 Sets
1.2 Subsets
1.3 Union and Intersection of Sets
1.4 Laws of Set Operations

Chapter 2 Number Systems and Fundamental Algebraic Laws and Operations
2.1 Decimals
2.2 Number Systems
2.3 Absolute Value
2.4 Fundamental Algebraic Laws
2.5 Basic Algebraic Operations
2.6 Operations with Fractions
2.7 Imaginary and Complex Numbers

Chapter 3 Exponents and Radicals
3.1 Exponents
3.3 Scientific Notation
Quiz: Sets and Set Operations—Exponents and Radicals

Chapter 4 Polynomials and Rational Expressions
4.1 Terms and Expressions
4.2 The Polynomial
4.3 Algebraic Operations with Polynomials
4.4 Polynomial Factorization
4.5 Operations with Fractions and Rational Expressions
Quiz: Polynomials and Rational Expressions

Chapter 5 Equations
5.1 Equations
5.2 Basic Laws of Equality
5.3 Equations with Absolute Values

Chapter 6 Linear Equations and Systems of Linear Equations
6.1 Linear Equations
6.2 Linear Equations in Two Variables
6.3 Graphing the Solution Set
6.4 Systems of Linear Equations
Quiz: Equations—Linear Equations

Chapter 7 Inequalities
7.1 Inequality
7.2 Properties of Inequalities
7.3 Inequalities with Absolute Values
7.4 Inequalities in Two Variables
Quiz: Inequalities

Chapter 8 Relations and Functions
8.1 Relations and Functions
8.2 Properties of Relations
8.3 Properties of Functions
Quiz: Relations and Functions

Chapter 9 Quadratic Equations
9.4 Quadratic Equations in Two Unknowns and Systems of Equations
9.5 Solving Systems of Equations Involving Unknowns

Chapter 10 Equations of Higher Order
10.1 Methods to Solve Equations of Higher Order
10.2 Theory of Equations
10.3 Algebraic Theorems
10.4 Descartes’ Rule of Signs
Quiz: Equations of Higher Order

Chapter 11 Ratio, Proportion, and Variation
11.1 Ratio and Proportion
11.2 Variation

Chapter 12 Logarithms
12.1 Logarithms
12.2 Logarithmic, Exponential, and Power Functions

Chapter 13 Sequences and Series
13.1 Sequences
13.2 Series
Quiz: Ratio, Proportion, and Variation—Sequences and Series

Chapter 14 Permutations, Combinations, and Probability

14.1 Permutation
14.2 Combination
14.3 Probability
Quiz: Permutations, Combinations, and Probability

Chapter 15 Vectors and Matrices, Determinants, and Systems of Equations
15.1 Vectors
15.2 Matrices
15.3 Determinates
15.4 System of Equations

Chapter 16 Mathematical Induction and the Binomial Theorem
16.1 Mathematical Induction
16.2 Binomial Theorem
Quiz: Vectors, Matrices—Mathematical Induction

Chapter 17 Partial Fractions
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Chapter 18 Complex Numbers
18.1 DeMoivre’s Theorem
Quiz: Partial Fractions—Complex Numbers

Chapter 19 Trigonometry and Trigonometric Functions
19.1 Angles and Triangles
19.2 Trigonometric Ratios
19.3 Trigonometric Functions
19.4 Properties and Graphs of Trigonometric Functions; Trigonometric Identities and Formulas

Chapter 20 Solving Triangles
20.1 Laws and Formulas
20.2 Important Concepts and Theorems
Quiz: Trigonometry and Trigonometric Functions—Solving Triangles

Chapter 21 Inverse Trigonometric Functions and Trigonometric Equations
21.1 Inverse Trigonometric Functions
21.2 Trigonometric Equations

Chapter 22 Introduction to Analytic Geometry
Quiz: Inverse Trigonometric Functions—Analytic Geometry

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