Integrated Mathematics: Course 1

by Dressler, Isidore; Keenan, Edward P.

• ISBN13: 9780877202288
• ISBN10: 0877202281
• Edition: 3rd
• Format: Paperback
• Copyright: 1997-06-01
• Publisher: Amsco School Pubns Inc

Table of Contents

The Real Numbers	1	(37)
The Whole Numbers	2	(4)
The Integers	6	(4)
The Rational Numbers	10	(6)
The Irrational Numbers	16	(6)
The Real Numbers	22	(3)
Number Lines and Rulers	25	(4)
Number Lines and Graphs	29	(8)
Chapter Summary	34	(1)
Vocabulary	35	(1)
Review Exercises	35	(2)
Operations and Properties	37	(36)
Operations in Arithmetic	38	(5)
Bases, Exponents, and Powers	43	(4)
Order of Operations	47	(5)
Properties of Operations	52	(7)
Properties of a Field	59	(2)
Operations in Geometry	61	(6)
Operations with Sets	67	(6)
Chapter Summary	70	(1)
Vocabulary	70	(1)
Review Exercises	71	(1)
Cumulative Review	72	(1)
Problem Solving	73	(24)
General Technique for Solving Problems	74	(1)
Guessing and Checking	75	(2)
Using a Simpler Related Problem	77	(3)
Working Backward	80	(2)
Discovering Patterns	82	(2)
Drawing Pictures and Diagrams	84	(3)
Making Lists and Charts	87	(3)
Choosing and Combining Strategies	90	(7)
Chapter Summary	93	(1)
Review Exercises	93	(2)
Cumulative Review	95	(2)
Algebraic Expressions, Geometric Formulas, and Open Sentences	97	(39)
Translating Verbal Phrases into Algebraic Language	98	(3)
Using Letters to Represent Variables	101	(2)
Algebraic Terms and Vocabulary	103	(2)
Evaluating Algebraic Expressions	105	(4)
Translating Verbal Sentences into Formulas	109	(2)
Formulas for Perimeter and Area of Polygons	111	(5)
Formulas for Circumference and Area of a Circle	116	(5)
Reasoning with Perimeter, Area, and Shaded Regions	121	(4)
Formulas for Volume of a Solid	125	(5)
Open Sentences and Solution Sets	130	(6)
Chapter Summary	132	(1)
Vocabulary	133	(1)
Review Exercises	134	(1)
Cumulative Review	135	(1)
Signed Numbers	136	(34)
The Opposite of a Directed Number	137	(1)
The Absolute Value of a Number	138	(2)
Addition of Signed Numbers	140	(7)
Subtraction of Signed Numbers	147	(4)
Multiplication of Signed Numbers	151	(4)
Division of Signed Numbers	155	(4)
Evaluating Algebraic Expressions Using Signed Numbers	159	(3)
Number Lines and Graphs Using Signed Numbers	162	(8)
Chapter Summary	167	(1)
Vocabulary	167	(1)
Review Exercises	167	(2)
Cumulative Review	169	(1)
Introduction to Solving Equations	170	(24)
Preparing to Solve an Equation	171	(3)
Solving Equations Using Addition	174	(3)
Solving Equations Using Multiplication	177	(3)
Solving Equations Using More Than One Operation	180	(2)
Writing Verbal Sentences as Equations	182	(3)
Using Equations to Solve Problems	185	(3)
Solving Percent Problems	188	(2)
More Practice In Solving Equations	190	(4)
Chapter Summary	191	(1)
Vocabulary	191	(1)
Review Exercises	192	(1)
Cumulative Review	192	(2)
Introducing Logic	194	(36)
Sentences, Statements, and Truth Values	195	(4)
Negations and Symbols	199	(4)
Conjunctions	203	(10)
Disjunctions	213	(6)
Conditionals	219	(11)
Chapter Summary	227	(1)
Vocabulary	227	(1)
Review Exercises	228	(1)
Cumulative Review	229	(1)
Using Logic	230	(35)
Compound Statements and Truth Values	231	(3)
Compound Sentences and Truth Tables	234	(3)
Biconditionals	237	(5)
Tautologies	242	(6)
Inverses, Converses, and Contrapositives	248	(9)
Drawing Conclusions	257	(8)
Chapter Summary	261	(1)
Vocabulary	262	(1)
Review Exercises	262	(2)
Cumulative Review	264	(1)
Operations With Algebraic Expressions	265	(39)
Adding Algebraic Expressions	266	(6)
Subtracting Algebraic Expressions	272	(3)
Multiplying Powers That Have the Same Base	275	(3)
Multiplying By a Monomial	278	(5)
Multiplying Polynomials	283	(4)
Dividing Powers That Have the Same Base	287	(2)
Powers With Zero and Negative Exponents	289	(3)
Using Scientific Notation	292	(5)
Dividing By a Monomial	297	(2)
Dividing By a Polynomial	299	(5)
Chapter Summary	301	(1)
Vocabulary	302	(1)
Review Exercises	302	(1)
Cumulative Review	303	(1)
First-Degree Equations and Inequalities In One Variable	304	(39)
Simplifying Each Side of an Equation Before Solving	305	(4)
Solving Equations That Have the Variable In Both Members	309	(5)
Consecutive-Integer Problems	314	(3)
Solving For a Variable In a Formula	317	(2)
Perimeter Problems	319	(3)
Solving For a Variable In Terms of Another Variable	322	(1)
Transforming Formulas	323	(2)
Properties of Inequalities	325	(5)
Finding and Graphing the Solution Set of an Inequality	330	(6)
Using Inequalities To Solve Problems	336	(7)
Chapter Summary	339	(1)
Vocabulary	340	(1)
Review Exercises	340	(2)
Cumulative Review	342	(1)
Angle Measure in Geometry	343	(32)
Points, Lines, and Planes	344	(2)
Angles, Angle Measures, and Perpendicularity	346	(4)
Pairs of Angles	350	(7)
Angles and Parallel Lines	357	(4)
Triangles and Angles	361	(6)
Triangles with Congruent Angles	367	(8)
Chapter Summary	371	(1)
Vocabulary	372	(1)
Review Exercises	372	(1)
Cumulative Review	373	(2)
Congruence and Transformations	375	(36)
Geometric Figures	376	(4)
Congruent Triangles	380	(7)
Quadrilaterals	387	(6)
Line Reflections and Line Symmetry	393	(7)
Point Reflections and Point Symmetry	400	(3)
Translations	403	(2)
Rotations	405	(6)
Chapter Summary	407	(1)
Vocabulary	408	(1)
Review Exercises	408	(1)
Cumulative Review	409	(2)
Ratio and Proportion	411	(48)
Ratio	412	(4)
Using a Ratio to Express a Rate	416	(1)
Verbal Problems Involving Ratio	417	(3)
Proportion	420	(5)
Direct Variation	425	(4)
Percent and Percentage Problems	429	(6)
Similar Polygons	435	(3)
Similar Triangles	438	(6)
Dilations	444	(4)
Ratio of Perimeters and Ratio of Areas of Similar Polygons	448	(11)
Chapter Summary	455	(1)
Vocabulary	456	(1)
Review Exercises	456	(2)
Cumulative Review	458	(1)
Probability	459	(63)
Empirical Probability	460	(7)
Theoretical Probability	467	(5)
Evaluating Simple Probabilities	472	(6)
The Probability of (A and B)	478	(3)
The Probability of (A or B)	481	(6)
The Probability of (not A); Probability as a Sum	487	(3)
The Counting Principle and Sample Spaces	490	(4)
Probabilities and the Counting Principle; Predicting Outcomes	494	(4)
Probabilities with Two or More Activities	498	(4)
Permutations	502	(4)
More About Permutations	506	(5)
Probability Without Replacement; Probability With Replacement	511	(11)
Chapter Summary	518	(1)
Vocabulary	519	(1)
Review Exercises	519	(2)
Cumulative Review	521	(1)
Statistics	522	(43)
Collecting Data	523	(2)
Organizing Data	525	(7)
The Histogram	532	(3)
The Mean, the Median, and the Mode	535	(8)
Measures of Central Tendency and Grouped Data	543	(8)
Quartiles, Percentiles, and Cumulative Frequency	551	(14)
Chapter Summary	562	(1)
Vocabulary	562	(1)
Review Exercises	563	(1)
Cumulative Review	564	(1)
Graphing Linear Functions and Equations	565	(36)
Solutions of Open Sentences in Two Variables	566	(4)
Graphing Linear Functions Using Their Solutions	570	(4)
Graphing a Line Parallel to an Axis	574	(1)
The Slope of a Line	575	(6)
The Slope-Intercept Form of a Linear Equation	581	(3)
Graphing Linear Functions Using Their Slopes	584	(2)
Writing an Equation of a Line	586	(2)
Graphing Direct Variation	588	(3)
Graphing First-Degree Inequalities in Two Variables	591	(5)
Graphs Involving Absolute Value	596	(5)
Chapter Summary	598	(1)
Vocabulary	598	(1)
Review Exercises	599	(1)
Cumulative Review	600	(1)
Systems of Linear Open Sentences in Two Variables	601	(22)
Using a Graph to Solve a System of Linear Equations	602	(4)
Using Addition to Solve a System of Linear Equations	606	(5)
Using Substitution to Solve a System of Linear Equations	611	(2)
Using Systems of Equations to Solve Verbal Problems	613	(5)
Graphing the Solution Set of a System of Inequalities	618	(5)
Chapter Summary	620	(1)
Vocabulary	621	(1)
Review Exercises	621	(1)
Cumulative Review	622	(1)
Special Products and Factors	623	(22)
Factors and Factoring	624	(4)
Common Monomial Factors	628	(2)
The Square of a Monomial	630	(1)
Multiplying the Sum and the Difference of Two Terms	631	(1)
Factoring the Difference of Two Squares	632	(2)
Multiplying Binomials	634	(2)
Factoring Trinomials	636	(5)
Factoring a Polynomial Completely	641	(4)
Chapter Summary	642	(1)
Vocabulary	643	(1)
Review Exercises	643	(1)
Cumulative Review	644	(1)
Algebraic Fractions, and Equations and Inequalities Involving Fractions	645	(33)
The Meaning of an Algebraic Fraction	646	(1)
Reducing Fractions to Lowest Terms	647	(3)
Multiplying Fractions	650	(3)
Dividing Fractions	653	(2)
Adding or Subtracting Fractions That Have the Same Denominator	655	(2)
Adding or Subtracting Fractions That Have Different Denominators	657	(5)
Solving Equations Containing Fractional Coefficients	662	(5)
Solving Inequalities Containing Fractional Coefficients	667	(4)
Solving Fractional Equations	671	(2)
Equations and Formulas Involving Several Variables	673	(5)
Chapter Summary	675	(1)
Vocabulary	676	(1)
Review Exercises	676	(1)
Cumulative Review	677	(1)
Operations with Radicals	678	(26)
Radicals and the Rational Numbers	679	(5)
Radicals and the Irrational Numbers	684	(5)
Finding the Principal Square Root of a Monomial	689	(2)
Simplifying a Square-Root Radical	691	(2)
Addition and Subtraction of Radicals	693	(3)
Multiplication of Square-Root Radicals	696	(2)
Division of Square-Root Radicals	698	(6)
Chapter Summary	701	(1)
Vocabulary	702	(1)
Review Exercises	702	(1)
Cumulative Review	703	(1)
Quadratic Equations	704	(29)
The Standard Form of a Quadratic Equation	705	(1)
Solving a Quadratic Equation by Factoring	705	(5)
Solving Incomplete Quadratic Equations	710	(3)
Solving a Quadratic Equation by Using The Quadratic Formula	713	(4)
The Theorem of Pythagoras	717	(6)
Using Quadratic Equations to Solve Problems	723	(4)
The Graph of a Quadratic Function	727	(6)
Chapter Summary	729	(1)
Vocabulary	730	(1)
Review Exercises	730	(1)
Cumulative Review	731	(2)
Index	733