Pre-calculus: Quick Access to the Important Facts and Concepts

by Woodward, Ernest

• ISBN13: 9780878918775
• ISBN10: 0878918779
• Format: Paperback
• Copyright: 1992-06-01
• Publisher: Research & Education Assn

Summary

Reviews sets, numbers, operations and properties, coordinate geometry, fundamental algebraic topics, solving equations and inequalities, functions, trigonometry, exponents and logarithms, conic sections, matrices and determinants.

Table of Contents

Sets, Numbers, Operations, and Properties	1	(7)
Sets	1	(1)
Real Numbers and Their Components	2	(1)
Real Number Properties of Equality	2	(1)
Real Number Operations and Their Properties	3	(3)
Complex Numbers	6	(2)
Coordinate Geometry	8	(13)
Real Numbers and the Coordinate Line	8	(1)
Cartesian Coordinates	9	(1)
Lines and Segments	10	(4)
Symmetry	14	(2)
Intercepts and Asymptotes	16	(2)
Parametric Equations	18	(1)
Polar Coordinates	19	(2)
Fundamental Algebraic Topics	21	(8)
The Arithmetic of Polynomials	21	(1)
Factoring	22	(1)
Rational Expressions	23	(3)
Radicals	26	(3)
Solving Equations and Inequalities	29	(14)
Solving Equations in One Variable	29	(1)
Solving Inequalities	30	(1)
Solving Absolute Value Equations and Inequalities	31	(2)
Solving Systems of Linear Equations	33	(5)
Cramer's Rule (In the Case of Two Equations)	35	(1)
Inverse of Matrices	36	(1)
The Method of Substitution	37	(1)
Solving Systems of Linear Inequalities and Linear Programming	38	(2)
Solving Equations Involving Radicals, Solving Rational Equations, and Solving Equations in Quadratic Form	40	(3)
Functions	43	(14)
Functions and Equations	43	(3)
Combining Functions	46	(2)
Inverse Functions	48	(1)
Increasing and Decreasing Functions	49	(1)
Polynomial Functions and Their Graphs	50	(2)
Rational Functions and Their Graphs	52	(2)
Special Functions and Their Graphs	54	(3)
Trigonometry	57	(14)
Trigonometric Functions	57	(7)
Inverse Trigonometric Functions	64	(1)
Trigonometric Identities	64	(1)
Triangle Trigonometry	65	(2)
Solving Trigonometric Equations	67	(1)
The Trigonometric Form of a Complex Number	68	(3)
Exponents and Logarithms	71	(7)
Integer Exponents	71	(1)
Rational Number Exponents	72	(1)
Exponential Functions	72	(1)
Logarithms	73	(3)
Logarithmic Functions	76	(2)
Conic Sections	78	(10)
Introduction to Conic Sections	78	(1)
The Circle	79	(1)
The Ellipse	80	(3)
The Parabola	83	(2)
The Hyperbola	85	(3)
Matrices and Determinants	88	(8)
Matrices and Matrix Operations	88	(2)
Determinants	90	(2)
The Inverse of a Square Matrix	92	(4)
Miscellaneous Topics	96
The Fundamental Counting Principle, Permutations, and Combinations	96
The Binomial Theorem	97
Sequences and Series	97
Mathematical Induction	99
Zeros of a Polynomial	100