Download 2.1 Algebraic Expressions and Combining Like Terms I. Algebraic

 2.1 Algebraic Expressions and Combining Like Terms I.
Algebraic expression A. Evaluating an algebraic expression Exs B. Coefficient C. Like Terms More exs 2.2 The Additive Property of Equality I.
Def II.
Exs 2.3 The Multiplicative Property of Equality I.
Def. II.
Exs 2.4 Combining Properties to Solve Linear Equations I.
Exs II.
Steps 2.6 Literal Equations and Applications 2.7 Applications of Linear Equations 2.9 Linear Inequalities 3.1 Natural Number Exponents I.
Product Law Exs. II.
Exs. Power to a Power Law III.
Product to a Power Law Quotient Law Exs. IV.
Exs. V.
Exs. Quotient to a Power Law 3.2 Integer Exponents I.
Zero Exponent Negative Exponent Exs. II.
Exs. III.
Quotient Law Scientific Notation Exs. IV.
Exs. 3.3 Adding and Subtracting Polynomials I.
Degree of a monomial Exs. II.
Degree of a polynomial Exs. I.
3.4 Multiplying Polynomials Distributive Property 3.5 The FOIL Method and Special Products of Binomials I.
Difference of Two Squares II.
Square of a Binomial 3.6 Dividing Polynomials 4.1 The Greatest Common Factor I.
Definition II.
Finding the GCF of a Group of Numbers 4.2 Factoring the Difference of Two Squares and Perfect Square Trinomials I.
Difference of Two Squares II.
Perfect Square Trinomials 4.3 Factoring Trinomials with a Leading Coefficient of 1 4.4 Factoring General Trinomials 4.5 Factoring by Grouping I.
Factoring by Grouping II.
Factoring Trinomials (Alternative Method) 4.6 Factoring the Sum and Difference of Two Cubes I.
Sum and Difference of Two Cubes 4.7 Factoring Summary 4.8 Solving Quadratic Equations By Factoring I.
Quadratic Equation II.
Zero Product Theorem III.
Steps (Solving Quadratic Equation By Factoring) 4.9 Applications of a Quadratic Equation I.
Number Problems II.
Geometric Problems III.
Physics Problems 5.1 Reducing to Lowest Terms I.
Definition: Any expression that can be written as the quotient of two polynomials, where the denominator is not equal to zero, is called a rational expression. II.
Reduction Property of Fractions 5x 8 y 2 z 6
Ex.1 5 4 9 4x y z
Ex.2 2 x 2  3x  35
x 2  4x  5
Ex.3 x 2  4 x  21
9  x2
5.2 Multiplying and Dividing Rational Expressions I. Multiplication Property of Fractions II. Division Property of Fractions Exs. 5.3,5.4 Adding and Subtracting Rational Expressions 1. Like denominators a. Combine Expressions (Add/Subtract) b. Simplify/Reduce i.
2 6
 11 11
ii.
x
3
 2
x  x  12 x  x  12
2
2. Unlike denominators a. Factor denominators b. Find the Least Common Denominator (LCD) c. Combine Expressions (Add/Subtract) d. Simplify/Reduce i.
1 5

18 24
ii.
x 1
x2
 2
6x  7 x  2 2x  7 x  3
2
5.6 Equations Involving Rational Expressions (7‐Step Method) 1.
Rational Equations (equations involving rational expressions and operations) a. 7‐Step Method i. Reduce (Factor) expressions ii. Multiply both sides of equation by Least Common Denominator (LCD) iii. Eliminate Grouping Symbols (Parentheses) iv. Isolate the Unknown v. Factor equation vi. Solve equation vii. Check for extraneous solutions b. Ex. Ex) 3x  1
3
2x  5
 2
 2
x  4 x  3 x  x  12 x  3x  4
2
1) 2) 3) 4) 5) 6) 7) Remember My Education Is For Skillful Calculations Reduce Multiply Eliminate Isolate Factor Solve Check 6.1 Solutions of Linear Equations in Two Variables I.
Linear Equation in Two Variables 6.2 The Cartesian Coordinate System I.
Ordered Pair: II.
Cartesian Coordinate System/rectangular coordinate system: III.
Origin: IV.
X‐axis V.
Y‐axis VI.
Quadrants: VII.
Solution to an equation in two variables: 6.3 Graphing Linear Equations I.
T‐tables II.
X‐intercepts and y‐intercepts 7.1 Solve a Linear System by Graphing Exs. Graphing Method (Steps) Type Of Solution 7.2 The Substitution Method Exs. Substitution Method 7.3 The Elimination Method Exs. Elimination Method 7.4 Applications of Linear Systems Steps 8.1 Radicals I.
Square Root of a Number Principal Square Root II. If n is a positive even integer and a is a real number, then n
an  a If n is a positive odd integer and a is a real number, then Ex.3 Ex.4 n an  a Ex.5 Ex1. Ex2. III.Let m and n be positive integers and a be a real number; then m
n
a  a or a
n
m
m
n

 a
n
m
Provided that n a is a real number. 1. 2. Ex.6 Ex.7 Ex.8 8.2 Simplifying Radical Expressions I.
Multiplication Property of Radicals Let n be a natural number; then ab  a  b provided that both a and b are not both negative. Exs. II. Simplifying a Square Root 1. 2. 3. Exs. III.Division Property of Radicals Let n be a natural number; then Exs. a
a

provided that both a and b are not negative and b  0 . b
b