A-plus Notes for Algebra With Trigonomentry and Probability

by Yang, Rong

• ISBN13: 9780965435284
• ISBN10: 0965435288
• Format: Paperback
• Copyright: 2000-10-01
• Publisher: A-Plus Notes Learning Center

Summary

This simple, easy-to-use review has 5,000 examples and exercises, from simple to complex. It outlines the concepts, formulas and theorems in algebra, and facilitates the learning process in problem solving. Covers equations, slopes, radicals, fractional equations, quadratic equations, and logarithms.

Table of Contents

Numbers
Numbers	9	(1)
Number Properties	10	(1)
Variables	11	(1)
Simplifying Expressions	12	(1)
Addition (Sum)	13	(1)
Subtraction (Difference)	14	(1)
Multiplication (Product)	15	(1)
Division (Quotient)	16	(3)
Exercises	17	(2)
Equations and Inequalities
Polynomials	19	(1)
Words into Algebraic Expressions	20	(1)
Solving Equations in One Variable	21	(1)
Solving Word Problems	22	(1)
Inequalities in one variable	23	(2)
Combined Inequalities	25	(2)
Equations and Inequalities with Absolute Values	27	(2)
Solving Word Problems with Inequalities	29	(4)
Exercises	31	(2)
Graphs and Functions
Cartesian Coordinate Plane	33	(1)
Equations in Two Variables	34	(1)
Slope of a Line	35	(2)
Finding the Equation of a Line	37	(2)
World Problems in Two Variables	39	(2)
Functions	41	(2)
Linear Functions	43	(2)
Direct Variations and Inverse Variations	45	(2)
Relations and Functions	47	(4)
Exercises	49	(2)
Polynomials and Factoring
Laws of Exponents	51	(1)
Multiplying Two Polynomials	52	(1)
Factoring a Monomial	53	(1)
Factoring a Polynomial	54	(1)
Factoring a Quadratic Polynomial	55	(2)
Solving Equations by Factoring	57	(2)
Solving Word Problems by Factoring	59	(2)
Solving Polynomial Inequalities	61	(4)
Exercises	63	(2)
Fractional Expressions
Simplifying Quotients	65	(1)
Zero and Negative Expressions	66	(1)
Scientific Notations	67	(1)
Simplifying Rational Expressions	68	(1)
Adding and Subtracting Fractions	69	(1)
Multiplying and Dividing Fractions	70	(1)
Dividing Polynomials	71	(1)
Complex Fractions	72	(1)
Simple Fractional Equations and Inequalities	73	(1)
Fractional Equations	74	(3)
Exercises	75	(2)
Radicals and Complex Numbers
Radicals	77	(2)
Evaluating Radicals	79	(2)
Simplifying Radical Expressions	81	(1)
Solving Radical Expressions	82	(1)
Solving Equations for Rational Roots	83	(1)
Converting Repeating Decimals into Fractions	84	(1)
Imaginary Numbers	85	(1)
Complex Numbers and Conjugates	86	(3)
Exercises	87	(2)
Quadratic Equations
Solving Quadratic Equations	89	(1)
Quadratic Formula	90	(1)
Equations in Quadratic Form	91	(1)
The Discriminant	92	(1)
Finding a Quadratic Equation having the Given Roots	93	(2)
Graphing a Quadratic Equation -- Parabola	95	(2)
Graphing any Quadratic Function	97	(4)
Exercises	99	(2)
System of Equations and Synthetic Division
System of Equations in Two Variables	101	(2)
Solving Word Problems with Two Variables	103	(1)
Graphing Linear Inequalities	104	(1)
System of Equations in Three Variables	105	(2)
Synthetic Division	107	(2)
Remainder Theorem and Factor theorem	109	(2)
Solving Equation with Degree n	111	(3)
Estimating Real Roots of p(x)=0	114	(3)
Exercises	115	(2)
Analytic Geometry
Distance and Midpoint Formulas	117	(1)
Parallel and Perpendicular Lines	118	(1)
Circle	119	(1)
Parabolas	120	(1)
Ellipse	121	(2)
Hyperbolas	123	(2)
Solving System of Quadratic Equations	125	(4)
Exercises	127	(2)
Exponents and Logarithms
Exponents with Rational Powers	129	(1)
Exponents with Irrational Powers	130	(1)
Exponential and Logarithmic Functions	131	(2)
The Law of Logarithms	133	(1)
Common Logarithms	134	(1)
Formulas for Changing Base and Antilogarithms	135	(1)
Exponential Growth and Decay	136	(3)
Exercises	137	(2)
Sequences, Series, Binomial Expansions
Arithmetic Sequences	139	(1)
Geometric Sequences	140	(1)
Arithmetic Series	141	(1)
Geometric Series	142	(1)
Infinite Geometric Series	143	(1)
Pascal's Triangle	144	(1)
Binomial Theorem	145	(4)
Exercises	147	(2)
Matrices and Determinants
Matrices	149	(1)
Matrix Addition and Subtraction	150	(1)
Matrix Multiplication	151	(1)
Applications of Matrices	152	(1)
Determinants	153	(2)
Expansion of determinants	155	(2)
The Inverse of Matrix	157	(2)
Solving Systems with Matrices	159	(2)
Cramer's Rule	161	(4)
Exercises	163	(2)
Probability and Statistics
Basic Counting Principals	165	(1)
Permutations	166	(1)
Combinations	167	(2)
Permutation with Repeating Selections	169	(1)
Permutations with Elements Alike	170	(1)
Sample Spaces and Events	171	(1)
Probability	172	(1)
Sets and Venn Diagrams	173	(2)
Probability of Mutual Exclusive Events	175	(1)
Probability of Independent Events	176	(1)
Frequency Distributions	177	(2)
The Normal Distribution	179	(4)
Exercises	181	(2)
Trigonometric Functions
Angles and Degree Measures	183	(1)
Radian Measure of angles	184	(1)
Basic Trigonometric Functions	185	(1)
Sin&thetas; and cos&thetas;	186	(1)
Tables of Trigonometric Functions	187	(1)
Reference Angles	188	(1)
Other Trigonometric Functions	189	(2)
Graphs of Sin x and Cos x	191	(2)
Graphs of Tan x and Cot x	193	(1)
Graphs of Sec x and Csc x	194	(1)
Trigonometric Identities	195	(4)
Exercises	197	(2)
Applications of Trigonometry
Solving Right Triangles	199	(1)
The Area of a Triangle	200	(1)
The Law of Sines	201	(1)
The Law of Cosines	202	(1)
Solving Ambiguous Triangles	203	(2)
Sum and Difference Formulas	205	(2)
Double--Angle Formulas	207	(1)
Half--Angle Formulas	208	(1)
Trigonometric Equations	209	(1)
Complex Numbers in Trigonometry	210	(3)
Exercises	211	(2)
Other Topics
Solving Equations Having Absolute Values	213	(2)
Greatest Integer Functions	215	(1)
Inverse Functions f-1	216	(3)
Inverse Trigonometric Functions	219	(3)
Composition of Functions f ˆ g	222	(1)
Even and Odd Functions	223	(2)
Identifying the Graph of y = f(x)	225	(2)
Descartes' Rule of Signs	227	(2)
Relationships between Roots and Coefficients	229	(1)
Distance Formulas	230	(1)
Angles between Lines or Planes	231	(2)
Eccentricity and Latus Rectum of Quadratic Equations	233	(2)
Degenerate Cases of Quadratic Equations	235	(1)
Fractional Inequalities	236	(1)
Solving Inequalities by Completing the Square	237	(1)
Inequalities involving Absolute Values	238	(2)
Transformations of Graphs	240	(2)
Upper and Lower Bounds on p(x)=0	242	(1)
Decomposing Rational Expressions	243	(3)
Graphing Rational Functions	246	(4)
Rotation of Axes	250	(2)
Graphing a General Quadratic Equations	252	(3)
Identifying the graph without a rotation of axes	255	(2)
Finding the Nth term of a sequence	257	(2)
Natural Logarithms	259	(2)
Parametric Equations	261	(3)
Polar Coordinate Planes	264	(2)
Graphing Polar Equations	266	(3)
Complex Numbers in Polar Coordinates	269	(3)
Limits	272	(3)
Continuity	275	(2)
Mathematical Induction	277	(2)
Vectors	279	(4)
Mathematical Logic	283	(20)
Appendix
1: Comparable Chart of measures	303	(1)
2: Table of Roots	304	(1)
3: Common Logarithms	305	(2)
4: Natural Logarithms	307	(2)
5: Area under the Standard Normal Curve	309	(2)
6: Formulas in Basic Trigonometry	311	(2)
7: Table of Trigonometric Functions (&thetas; in decimal degrees)	313	(4)
8: Table of Trigonometric Functions (&thetas; in degrees and minutes)	317	(4)
9: Table of trigonometric Functions (&thetas; in radians)	321	(2)
Answers to the Chapter Exercises	323	(24)
Order Form	347