Download Study Guide for EXAM 1 Appendix I and Chapter 1 (1.1-1.4)

Study Guide for EXAM 1
Appendix I and Chapter 1 (1.1-1.4)
Math 106, Fall 2011
APPENDIX I
Language, Notation, and Numbers of Mathematics
Sets of numbers and graphing real numbers
Order property of real numbers
Absolute value of a real number- (piecewise) definition, & geometric interpretation
Practice Exercises pp. A7 (19, 21, 23, 25, 31, 33, 35)
Exponents, Scientific Notation and a Review of Polynomials
Properties of exponents
Addition, subtraction and product of polynomials
Special polynomial products
Binomial conjugates: ( A B )( A B )
Binomial squares: ( A B) 2
A2
A2
B2
2 AB B 2
Practice Exercises pp. A21 (17, 25, 31, 35, 37, 43, 105, 109)
Factoring Polynomials
Factoring the greatest common factor and factoring by grouping
Factoring quadratic polynomials
Factoring special forms and quadratic forms
Difference of squares: A2
Perfect-square trinomial: A2
B2
( A B)( A B )
2 AB B 2
( A B) 2 and A2 2 AB B 2
Practice Exercises pp. A30 (21, 25, 29, 33, 37, 43, 55, 57)
Rational Expressions
Writing a rational expression in simplest form
Multiply and divide rational expressions
Add and subtract rational expressions
Simplify compound fractions
Rewriting formulas and algebraic expressions involving rational expressions
Practice Exercises pp. A37 (13, 15, 19, 23, 29, 35, 41, 51, 53, 55, 61)
( A B)2 .
Radicals and Radical Exponents
Simplifying radical expressions of the form n a n for a real number a
Radical exponents and radical expressions
Properties of radicals and simplifying radical expressions
Addition and subtraction of radical expressions
Pythagorean Theorem
Practice Exercises pp. A47 (11, 13, 15, 19, 23, 31, 51, 55)
CHAPTER 1
1.1 Linear Equations, Formulas, and Problem Solving
Properties of equalities
Solving linear equations
Applications
Practice Exercises 1.1 (29, 43, 63, 75, 81)
1.2 Linear Inequalities in One Variable
Set notation, and interval notation
Unions and intersections of sets
Properties of inequalities
Solving inequalities- solutions in set notation, interval notation, and graphs
Applications
Practice Exercises 1.2 (23, 27, 31, 41, 43, 49, 51, 55, 59, 65, 75, 83)
1.3 Absolute Value Equations and Inequalities
Properties of absolute values
Using distance to understand absolute value equations and inequalities
Solving equations and inequalities with absolute values
Applications
Practice Exercises 1.3 (13, 19, 29, 37, 41, 49, 53, 59, 63)
1.4 Complex Numbers
Identifying and simplifying imaginary and complex numbers
Adding, subtracting, multiplying and dividing polynomials
Practice Exercises 1.4 (15, 25, 35, 37, 43, 53, 61, 65, 77)