Integrated Math 3

by McDougal, Littell

• ISBN13: 9780395644485
• ISBN10: 0395644488
• Format: Hardcover
• Copyright: 1994-11-01
• Publisher: McDougal Littell/Houghton Mifflin

Table of Contents

What Students Are Saying	xiv
Course Preview	xvi
Unit 1 Modeling Problem Situations
Community Planning
Algorithms	3	(6)
Writing, using, and comparing step-by-step procedures for solving mathematical and real-world problems
Using Systematic Lists	9	(7)
Exploring inequalities related to triangles. Using organized lists as a strategy for solving many types of problems
Using Statistics	16	(7)
Using statistics, line graphs, box-and-whisker plots, and scatter plots to analyze data, to compare data sets, and to reach conclusions
Using Graphs and Equations	23	(6)
Solving real-world problems modeled by two or more linear equations by graphing and by using algebra. Solving problems involving income and expenses
Using Systems of Equations	29	(8)
Solving systems of linear equations and real-world problems using algebra, graphs, and matrices. Exploring ways that planes can intersect
Using Diagrams	37	(8)
Using network diagrams and matrices to organize and analyze information involving connections and groupings
Maximizing and Minimizing	45	(8)
Using formulas, graphs, and network diagrams to maximize or minimize quantities in real-world situations
Linear Programming	53	(16)
Using systems of inequalities to model and solve real-world problems
Review and Assessment	62	(4)
Unit 2 Exploring and Applying Functions
Bicycling	66	(3)
What is a Function?	69	(8)
Using graphs, tables, and equations to represent functions. Modeling everyday situations with functions
Linear Functions	77	(8)
Finding the domain, the range, and an equation of a linear function. Using linear functions to model real-world data
Piecewise and Absolute Value Functions	85	(9)
Writing, graphing, and applying functions that have different equations for different portions of the domain
Quadratic Functions	94	(7)
Using equations of the form f(x) = ax2 + bx + c and their graphs to solve real-world problems
Polynomial Functions	101	(9)
Writing, evaluating, and applying direct variation functions and polynomial functions. Using zeros of a function in graphing
Radical Functions	110	(9)
Exploring and applying functions that involve radicals. Solving equations containing radicals
Rational Functions	119	(7)
Evaluating, graphing, and applying rational functions
Combining Functions	126	(13)
Exploring and applying functions that are formed by combining two functions
Review and Assessment	133	(3)
Unit 3 Logical Reasoning and Methods of Proof
Justice	136	(3)
Implications and Proof	139	(8)
Exploring the relationship between an if-then statement and its converse, inverse, and contrapositive. Writing synthetic proofs
Coordinate and Synthetic Proof	147	(6)
Writing and comparing coordinate and synthetic proofs. Exploring properties of isosceles triangles and isosceles trapezoids
Another Look at Definitions	153	(6)
Analyzing and writing definitions in mathematical and everyday situations. Understanding relationships among quadrilaterals
Angles in Polygons	159	(6)
Find the measures of interior and exterior angles of both regular and nonregular polygons. Using mathematical induction in proofs
Inscribed Polygons	165	(7)
Exploring polygons inscribed in a circle, central angles, arcs, and the perpendicular bisector of a chord of a circle
Arcs and Angles	172	(7)
Investigating and applying relationships between inscribed angles and arcs of circles
Indirect Proof	179	(8)
Using indirect proofs in geometric, algebraic, and everyday contexts. Proving and using theorems about tangents to a circle
Circumscribed Polygons	187	(5)
Exploring relationships between circumscribed polygons and inscribed circles. Finding the area of a circumscribed polygon
Polyhedra	192	(15)
Investigating properties of space figures whose faces are polygons. Identifying semiregular polyhedra and the five regular polyhedra
Review and Assessment	200	(4)
Unit 4 Sequences and Series
Investing	204	(3)
Exploring Patterns	207	(9)
Recognizing and continuing patterns. Graphing sequences and deciding if an infinite sequence appears to have a limit
Sequences	216	(6)
Finding and using formulas for sequences related to algebraic, geometric, and everyday situations
Using Recursive Formulas	222	(6)
Writing and applying formulas for sequences in which each term is found by using the preceding term(s). Using technology to find limits of sequences
Arithmetic and Geometric Sequences	228	(9)
Writing and applying explicit and recursive formulas for sequences. Finding geometric means
Arithmetic Series and Sigma Notation	237	(7)
Finding the sum of a finite arithmetic series. Representing and evaluating a series with compact notation
Geometric Series	244	(7)
Finding the sum of a finite geometric series. Writing geometric series arising from everyday situations and finding their sums
Infinite Series	251	(16)
Recognizing when an infinite series has a sum. Finding the sum of an infinite geometric series
Review and Assessment	260	(4)
Unit 5 Exponential and Logarithmic Functions
Music	264	(3)
Exponential Growth and Decay	267	(8)
Using graphs and recursion with exponential growth and decay functions to model and solve real-world problems
Negative Exponents	275	(6)
Exploring exponential functions with negative exponents. Using these functions to model and solve real-world problems
Fractional Exponents	281	(7)
Exploring and applying the relationship between fractional exponents and radicals. Modeling real-world problems using exponential functions with fractional exponents
The Number e	288	(8)
Modeling real-world situations using exponential functions with base e and with logistic growth functions
Inverse Functions	296	(5)
Recognizing when a function has an inverse. Finding and graphing inverse functions
Logarithmic Functions	301	(8)
Exploring and applying the relationship between an exponential function and a logarithmic function. Using logarithms, including natural logarithms, in a variety of real-world applications
Properties of Logarithms	309	(8)
Investigating properties of logarithms, and using them to simplify and evaluate expressions and to solve problems
Exponential and Logarithmic Equations	317	(14)
Solving exponential and logarithmic equations and using these equations in real-world applications
Review and Assessment	324	(4)
Unit 6 Modeling and Analyzing Data
Cars	328	(3)
Distributions of Data	331	(7)
Exploring and analyzing types of frequency distributions. Drawing and interpreting histograms and relative frequency histograms
Standard Deviation	338	(6)
Using technology to compute the mean and standard deviation of a data set. Using statistics to compare two sets of real-world data
Normal Distributions	344	(6)
Exploring and applying properties of normal distributions
Fitting Linear Models to Data	350	(9)
Using technology to find least-squares lines and median-median lines. Interpreting the correlation coefficient
Fitting Quadratic Models to Data	359	(14)
Using technology and matrices to find quadratic models for data
Review and Assessment	366	(4)
Unit 7 Applying Probability Models
Changing the Rules	370	(3)
Simulation and Random Numbers	373	(9)
Using random numbers to perform experiments. Investigating real-world situations using simulation
Probability of Either of Two Events	382	(8)
Finding the probability of either of two events. Finding probabilities in situations with continuous outcomes and discrete outcomes
Geometric Models for Probability	390	(5)
Using area models with coordinates to find probabilities
Conditional Probability, Independent Events	395	(8)
Using tree diagrams to find probabilities under restricted conditions. Deciding if two events are independent or dependent
Expected Value	403	(7)
Finding the expected average gain or loss in real-world situations
Binomial Experiments and Decision-Making	410	(15)
Exploring probabilities in binomial experiments. Analyzing statistical decisions using significance levels
Review and Assessment	419	(3)
Unit 8 Angles, Trigonometry, and Vectors
Navigation	422	(3)
Polar Coordinates	425	(5)
Using polar coordinates and bearings to locate points in the plane
Converting Coordinates	430	(10)
Using formulas and technology to convert (x, y) to (r), and (r) to (x, y). Finding the sine, cosine, and tangent of any angle
The Geometry of Vectors	440	(6)
Solving real-world problems using graphic representations of vectors, sums of vectors, and scalar multiples of vectors
The Algebra of Vectors	446	(7)
Solving real-world problems using vectors in rectangular form
Parametric Equations	453	(6)
Solving real-world problems by using pairs of equations that define x and y in terms of a variable t
The Law of Cosines	459	(8)
Using the law of cosines to solve real-world problems
The Law of Sines	467	(16)
Using the law of sines to solve real-world problems
Review and Assessment	476	(4)
Unit 9 Transformations of Graphs and Data
Careers	480	(3)
Adding a Constant to Data	483	(6)
Exploring the effect of adding a constant to each value in a data set
Translating Graphs	489	(7)
Exploring and applying the relationship between the graph of a parent function y = f(x) and the graph of y - k = f(x - h)
Multiplying Data by a Constant	496	(5)
Exploring the effect of multiplying each data value by a constant
Stretching Graphs	501	(9)
Exploring and applying the relationship between the graph of a parent function y = f(x) and the graphs of y = f and f(x)
Multiple Transformations	510	(9)
Recognizing the effects of multiple transformations on data and graphs of functions and applying them in real-world situations
Standardizing Data	519	(7)
Using standardized values and the standard normal distribution to compare real-world data and to find percentiles
Reflecting Graphs	526	(15)
Exploring and applying the relationship between the graphs of y = f(x), y = -f(x), and y = f(-x). Combining translations, dilations, and reflections to produce new functions
Review and Assessment	534	(4)
Unit 10 Periodic Models
Cycles	538	(3)
Describing the Behavior of Functions	541	(7)
Describing graphs of real-world functions. Comparing rates of growth and decay of functions
Periodic Functions	548	(6)
Exploring periodic functions related to real-world situations
Graphs of Sine and Cosine	554	(6)
Investigating and applying the characteristics of the graphs of the sine and cosine functions
Transforming Sine and Cosine Graphs	560	(8)
Exploring and applying properties of graphs of the form y = A sin B(C) + D and y = A cos B(C) + D
Modeling with Sine and Cosine	568	(9)
Using sine and cosine functions to model real-world data
Patterns and Transformations	577	(5)
Using transformations to classify and create border patterns
Periodic Tessellations	582	(8)
Exploring ways to tile a plane with polygons
Review and Assessment	590