Click on a term to go to the resources for that unit.
Note: The help for unit may not explicitly discuss the associated term at this time.
Absolute value function, horizontal shifts, 463
horizontal stretching and compression, 466-468
rules and tables, 442-443,445, 463
vertical stretching and shrinking, 449-452
vertical translation, 442-443
Addition, associative property of, 194, 274
commutative property of, 194, 274
Addition Rule for mutually exclusive events, 404-415,
Adjacency matrices 270, 305, row 274
Adjacency matrix, 19, 37, 55, 356,
Affirming the hypothesis, 276,
Algebra, 25-45, 170-186,
Algebraic equations, rewriting in equivalent forms, 15,
Algebraic expressions, common mistakes when writing, 195
not equivalent, using graph to show, 204
Algebraic operations, 187-224,
Algebraic properties, 194,
Algebraic reasoning, 240-252, in geometry, 243-247
in statistics, 243-247
to find center and radius of a circle, 252
to minimize distance, 559
distance matrix, for creating, 343-344
for Delaunay triangulation, 550, 554
Traveling Salesperson Problem, for analyzing, 348-349, 360
Algorithm 257, 281, vs. formula 380
Amplitude, 429,
Analytic proof, 328,
Angle Bisector Algorithm, 320,
Angle Construction Algorithm,320,
Angles, 282-287, adjacent, 281
alternate exterior, 283
alternate interior, 283
bisecting, 308, 320
central versus inscribed,324
central, measure of, 296
congruent, 305
corresponding, 283
exterior, on same side of transversal, 283
included, 313
inscribed versus central, 324
inscribed, measures of, 296
interior, on same side of transversal, 283
linear pair of, 279, 281
Linear Pair Property, 280
reasoning about, 279-282
supplementary, 281
vertical, 279, 281
Angular velocity, 417, 419, 548,
Animation, computer, 149-164, coordinates of a point, 164
matrix representation of a 180¾ rotation about the origin, 150
matrix representation of a 45¾ counterclock-wise rotation, 151-153
matrix representation of a 90¾ counterclockwise rotation, 151
stretching and shrinking,154-164
Area 35, 62, 92, 106, 135, 151, 355, 356, circle 136, 359, 372
Area model for probability,472,
Area, maximizing, 555-556,
Arguments, good, 264
reasoned, 260-296
synthetic proofs, 312
valid, 264
Arithmetic growth, 506, and linear models, 507
recursive formula versus function formula, 506-507
Arithmetic sequence, 506, 515, equations, 507
function formula, 507
interpreting formulas, 508
recursive formula, 506
sum of terms, 512
Arrow's Theorem, 102-105, fairness conditions, 103-104
Association and causation, 197-210, Kendall's rank correlation coefficient, 185
Spearman's rank correlation coefficient,173-175
Associative property, determining if new operations have, 207
of addition, 194, 274
of multiplication, 194
Associative property of multiplication for real numbers, 50,
Assumptions, identifying, 261-265,
Asymptotes, and inverse functions, 440
horizontal, 433
vertical, 433
Average run length, 412,
Average, properties of operation, 205,
Back-to-back stem-and-leaf plot 32,
Best-edge algorithm, 323, for Traveling Sales-person Problem, 349
Bias in surveys, sources of,121-124, information collection, 122-123
nonresponse, 123
sample selection, 122
wording of survey, 122
Binomial distribution, 492, histogram for, 492-493
Binomials, geometric illustration proof for multiplying two, 250,
Borda count vote-analysis method, 98,
Box plot 52, 106, combining 62
Braces, minimum number for rigid grid, 333-334,
Brand-switching matrix,, 27-30, 49-50, 55
Brute force method, 350, 351, , 357
Calculator, matrix capability, 29, 53
using to find trigonometric ratios, 398-399
Cause-and-effect relationship, , 197-210
Cause-and-effect relationship, 564,
Ceiling function, 185,
Census, 117, when to take, 117
Chaos, 533, 541,
Chord, 296, 322,
Circle, and algebraic reasoning, 252
average area, 132
average radius, 132
centered at origin, equation for, 304-305
coordinates of points on unit, 445
equation of, 248
equation of, center not at origin, 252, 475
survey, 125-126
theorem about, 322
Circumference 136, and area 369
Closed-form formula for a sequence, 525,
Coefficients in standard quadratic form related to factored form, 211,
Coefficients of variables, 107,
Combinations, 110,
Combined recursive formulas, 510, and linear function iteration, 546-547
and recursive formulas for arithmetic and geometric sequences, 510
function formula, 523, 542
Combined variation, 10, 427,
Common difference, 508,
Commutative property, determining if new operations have, 207
of addition, 194, 274
of multiplication, 194
Commutative property of, multiplication for matrices, 43
Commutative Property of Addition 239,
box plots and histogram 53, 59, 61
compared to recursive 435, exponential 425, 441
Compasses, 319,
Complete bipartite graph, 357,
Complete graphs, 516-518,
Composite transformation, 140, similar shapes, 142
similarity transformation, 143
Compound statement, 278,
Computer software, matrix, capability of, 29, 53
Computer-generated graphics, , 80-108, 138
Conclusion, 267,
Condorcet vote-analysis method, 97-98,
Confidence intervals, 153-164, 90%, 156
and sample size, 159
box plot charts to find, 155
likely populations, 154-159
margin of error, 156
properties of, 157
Congruent triangles, 297-324, consequences of, 305
definition, 305
theorems, 306, 309
connection to tables and equations 186,
Consistent fairness condition, 103,
Constraints, 64, inequalities, 69
Contrapositive, 277,
Converse, 277, 285, and Venn diagram, 274
Coordinate plane, calculating, distances in, 82-83
Coordinate proof, 328,
Correction term, 35,
Correlation coefficient, 563-564, and standardized scores, 379
effect of outliers, 564
formulas for, 379
Correlation coefficients and, influential point in, 193
Pearson's correlation coefficient r, 188-196
Cosine graphs, equations of, 433-434
scatterplots and tables, 432-433
Cosine ratio, 27,
Cosines, Law of, 32-36, 298, coordinate proof of, 314
proof of, 245, 251
to find angle measures, 34
to find length, 34
versus Pythagorean Theorem, 35
when to use, 35
Counterexamples, use of, 268,
Critical Path Method (CPM) 310,
Cube 151, intersection with plane 339
Cubic equations, solving, 299,
Cubic functions, patterns in graphs of, 426
rules, 446
table patterns, 446
vertical translation, 446
Cylinder 332, surface area 375
Dart, 330,
Decisive fairness condition, 103,
Deductive reasoning, 269, 271, to establish a relationship, 270
versus inductive, 275
Degree, 421, per minute, converting from rpm, 417
Delaunay triangulation, 550,, 554
algorithms for, 550
Dependent variable 175, 178, 188,
Detachment, law of, 276,
Diagram, marking, 308,
Dice, rolling doubles, 457-459
Digraph of pairwise-comparison method, 110-111,
Digraph, 19, 37, 342, paths, 37, 343
Dijkstra's algorithm, 359-360,
Direct variation relationships, 426, and sequential change, 503-504
Direct variation, models of,, 256-259, 541-542
Discrete dynamical systems, 491,
Dissection of shapes, 314,
Distance matrix, 326, row sums of the, 327
Distance, minimum, 558-561, ways to find, 559
Distances, and pantograph images,374-375
computing with computer graphics, 81-87
Distributive property, diagrams illustrating, 206
multiplication of linear factors using, 210
of multiplication over addition, 194
of multiplication over subtraction, 194
Distributive property for multiplication over addition for matrices, 41, 52,
Distributive Property of, Multiplication over Addition 239
Division, 215-218,
Divisor, 275,
Dodecahedron, 345, 468, vertex-edge graph for, 346
Domain, 177, 438, practical, 177
theoretical, 177
Doyle Log Rule, 546,
Earliest finish time (EFT) 299, 308,
Earliest start time (EST) 308,
Enlargement factors 160, 170, 176,
Equality, properties of, 15, 37, 62, to solve equations, 37
to solve proportions, 39
Equation 76, 119, 121125, 138, 140, 142, 147,
Equations, algebraic, rewriting in equivalent forms, 15
equivalent, 228
linked, 46-62
multiple-variable, solving, 13
of circles with center not at origin, 252, 475
quadratic, 229-234
reasoning to solve, 225-239
systems of, 48, 60
Equivalent expressions, 192-197,
Equivalent function rules, 189,
Estimating measures of center 36,
Euler circuit, 266,
Euler circuit, 347, versus Hamiltonian circuit, 347
Euler's formula, 19,
Expected value, 486, 513-515, of a waiting-time distribution, 521-523
Explicit formula for a sequence, 525,
Exponential functions, 176, 432, 499, decay, 425
growth, 425
half-life, 425
interpreting patterns in tables and graphs, 176
rate of change, 425
vertical translation, 445
Exponential model 420481, comparing with linear 434, 467
Exponential models, 244, 544, compared to inverse variation, 256-258
compared to linear models, 238-249
compared to power models, tables, and graphs, 238-241, 244
Exponential pattern of change, closed 441
Factor, 275,
Factorial, 110, 415, notation, 110
Factoring, difference of two squares, 212-213
the quadratic, 209
Fair price, 511-515, and expected value, 513-515
Fairness conditions, 103-104, consistent, 103
decisive, 103
nondictatorship, 103
ordered, 103
relevant, 103
unanimous, 103
False alarms, 402-405, probability of, 403
Feasible, combinations, 67
points, 65, 69
set, 70, 72
Fermat's problem, 561,
Fibonacci sequence, 527,
Finding equations, using points 196
Finite differences, 515-518, table relation to function formula, 516
Five-number summary 49, 106, using technology 50
Fixed points, 535, attracting, 536
numerical iteration to find, 538
of linear function, formula, 539
repelling, 536
Floor function, 185,
Follower pulley, 370, 413, 425,
Formulas, discrete view, 505-529
recursive, 492-494, 498
Formulating definitions, 294,
Fractional power models, 289-310,
Fractional rules, finding zeroes of, 221
undefined, finding input values for, 221
Fractions, 215-218, and inverse variation rules, 215
combining two by multiplication or addition, 216
common errors in rewriting algebraic, 217
rewriting as a product or sum of terms, 216
Frequency distribution, standard deviation, 370
Frequency table, rolling doubles, 457-459
Function 101, 127, 130, rate of change 182
Function formula, 507, combined recursive formulas, 523, 542
relation to finite differences table, 516
using regression methods to find, 522
Function iteration, 530-545, and long-term behavior, 532
and NOW-NEXT equations, 531
and recursive formulas, 531
to solve linear equations, 539
to solve quadratic equations, 543
using computer or graphing calculator, 544
Function notation, advantages and disadvantages of, 185
using, 171-172, 175
Function, 170-186, absolute value, 442
ceiling, 185
composition, 186
decreasing, 439
definition, 171
exponential, 176, 425, 432
families, 431-433, 522
floor, 185
graphs and notation, 172
horizontal transformation, 462-479
increasing, 439
interpreting graphs, 173, 439
inverse power, 179
iteration, 530-545
linear, 175, 424, 432
notation, 171-172
periodic, 429
piecewise-defined, 186
quadratic, 176, 444
reflections, 446-449
square root, 433
trigonometric, 177, 183,432, 444
versus relationships, 182
vertical transformation, 441-446, 449-453
with symbolic rules, 175-179
Functions toolkit, 431-433, exponential functions, 432
linear functions, 432
power functions, 432
square root function, 433
trigonometric functions,432
Geometric construction, angle bisector, 320
congruent angle, 320
congruent triangle, 320-321
perpendicular bisector, 321
Geometric growth, 508,
Geometric reasoning,259-344, reasoned arguments, 260-296
Geometric sequences, 508, 515, interpreting recursive and function formulas, 509
sum of the terms formula, 513
writing recursive and function formulas, 509
Geometric series, sum of infinite, 528,
Geometric transformations, iterating, 544-545
method to minimize distance, 559
Geometry coordinate model of, 90,
Geometry drawing programs, 81,
Geometry, 25-45, algebraic reasoning in, 243-247
GEOXPLOR, 81, 99, 129, 149, 164,
Golden rectangle, 131,
Graph coloring 279, algorithms 281
Graphical iteration, 534-535, 544,
Graphing, connected mode, 500
dot mode, 500
Graphing calculators, 81, input, 84
complete, 516-518
to solve quadratic equations, 267, 278
transformations, 459
zeroes, 459
Gray Code, 353-354, using Hamiltonian circuits to find, 353-354, 358
Half-plane regions, 78,
Hamilton, Sir William, Rowan, 345-346
Hamiltonian circuit, 346, and Traveling Sales-person Problem, 349
Gray Codes, using to find, 353-354, 358
estimating measures of center 36
Homogeneous coordinates of a point, 164,
Horizontal line, 94, distance between points, 82-83
Horizontal shifts, graphs, 463
of absolute value functions, 463
of periodic functions, 464
of quadratic functions, 464
relation to quadratic formula, 477-479
relation to zeroes of quadratics, 477-479
symbolic rules, 463-464
tables of values, 463
Horizontal transformations, 462-479, horizontal shifts, 463-466
horizontal stretching and compressing, 466-468
Horizontal translation, 110, 111,
Horizontal translations, 463,
Hypothesis, 267, affirming the, 276
If-then statement, 265-266, and Venn diagrams, 274
symbolic representation of, 267
of segment under translation, 120
under reflection rotation, 121
indirect and inverse variation situations, 3-5, in values of direct, inverse, and combined variation, 15
Independent events, Multiplication Rule, 404-405, 410
versus mutually exclusive events, 414
Independent variable 127, 175, 178, 188,
Inductive reasoning, 267, 271, versus deductive, 275
Inequalities, constraint, 69
equivalent, 228
quadratic, 233
reasoning to solve, 225-239
writing and solving, 47-48, 54
Inequality 79, 85, 211, 219, modeling situations 212
Inequality, properties of, 62,
Infinite geometric series, 528, sum of, 528-529
Integers, theorems about, 262, 264, 270-271, 273, 275,
Intercepts, using to graph linear equations, 69,
interpreting, 157,
Interquartile range (IQR) of a, distribution, 347
effect of adding constant to data values, 351
effect of multiplying data values by a constant, 351
versus standard deviation, 350
Intersect option, 70,
Inverse functions, and asymptotes, 440
reflection across the x-axis, 446
Inverse matrix, 44, for solving systems of more than two linear equations, 74
Inverse operations, 37, 62, to solve equations, 37
to solve proportions, 39
Inverse power functions, interpreting patterns in tables and graphs, 179,
Inverse variation functions, and models, 250-264
compared to exponential models, 256-262
compared to linear models, 256-262
patterns in tables and graphs of, 254-255
Inverse variation models, 50,
Inverse, 277,
IQR and MAD 72, line plots and histograms 18
shapes of two distributions 32
stem-and-leaf plot to number line plot 24
IQR Interquartile range 49, 106, as a measure of variability 51
Isoperimetric, Quotient (IQ), 556
Theorem, 556
Iterating functions, 530-545,
Kendall's rank correlation coefficient, 185,
Kite, 330,
Koch snowflake, 521,
Kruskal's algorithm, 325, 357, versus Prim's algorithm, 338
Lateral surface area, 554,
Lattice point, 65,
Least squares regression, 211-226, 544, "best-fitting" line,216-219
slope and y-intercept formulas, 225-226
Least squares regression, 291,
Like terms, combining, 205,
Likely populations, 154-159,
Line 7679, 85, 89, 9293, 253, 265, 274,
Line segment, calculating length of, 82
Linear association, 563,
Linear combination, finding, intersection coordinates, 100
Linear combinations, 11,
Linear data patterns, connections between correlation coefficients and, 192,
Linear equalities, graphing, 70,
Linear equations, 78-79, calculator-based methods versus symbolic reasoning to solve, 238
graphing, 48
solving system of two, 70
solving system of, by substitution, 83
symbolic reasoning to solve, 226-229
using matrices to solve, 517
writing and solving, 47
Linear equations, systems of adding two equations, 98-101, and families of lines, 97-101
comparing solution methods, 63-66
effects of multiplying each term by a constant, 98-99
intercepts, using to graph, 69
inverse matrices for solving more than two, 73-74
limitations of using matrices to solve, 70
linear regression procedure to graph, 69-70
matrix equations for solving more than two, 73-74
substitution method of solving, 73
Linear factors, 209, multiplication of, using the distributive property, 210
Linear function iteration, 534-537, and combined recursive formulas, 546-547
to find fixed points, 535
Linear functions, 432, and long-term behavior of function iteration, 535-536
graphs, 424
interpreting patterns in tables and graphs, 175
rate of change, 424
reflection across the x-axis, 446
symbolic expressions, 424
tables of values, 424
vertical translation, 445
Linear inequalities, 78-79, calculator-based methods versus symbolic reasoning to solve, 238
graphs of, 78
solving systems of, by graphing, 79
Linear model 158, comparing with exponential 434, 467
nonpositive rate of change 184
Linear models, and arithmetic growth, 507
and patterns in table of values and shape of graph, 50
discrete view, 505-529
interpreting, 53
Linear models, 244, 546, compared to exponential models, 238-249
compared to inversevariation models,256-258
compared to powermodels, tables, andgraphs, 238-249
Linear Pair Property, 280,
Linear programming, 63-85, finding best feasible points, 74-77
linear equations and inequalities, 78-79
using an algebraic model, 68-73
Linear regression, finding equations using 197
Linear regression procedure, 69-70,
Linear velocity, 417, 548,
Lines in 3-dimensional space, 293,
Lines, intersecting, reasoning about, 279-282
theorems about, 295
Linkages, and similarity, 373-376
using quadrilaterals in,370-376
Linked equations, 46-62,
Linked variables, 2-24, patterns in indirect and inverse variation situations, 3-5
patterns in values of direct/inverse combined variation, 14-16
rates and times, combining, 11-14
List and Line Plot calculator feature, 122,
Logistic equations and long-term behavior, 532, 541,
Long-term behavior, additional amount added/subtracted, 490
and function iteration, 532
and logistic equations, 532
increase/decrease rate, 490
influence on, by initial conditions, 489-490
initial population, 489
Lower control limit (LCL), 389,
Majority winner vote-analysis method, 97,
Margin of error, 135, 156, 160-161,
Markov process, 55, states, 55
Mathematical modeling 252, 291,
and systems of linear equations, 59-78
to model sequential change, 499-500
to solve a system of three linear equations, 517
Matrix addition, 10-12,42, 158, addition of numbers versus, 42
Matrix addition, properties of, 205,
Matrix equation, for solving systems of more than two linear equations, 73-74
Matrix models, building and using,2-25
Matrix multiplication, 12, 26-58, 159, and zero property of multiplication, 45
distributive property for matrices, 41, 52
versus multiplication of real numbers, 43
Maximums and transformations, 458,
Mean, effect of adding constant to data values, 352-353
effect of multiplying data values by constant, 352
Mean absolute deviation, (MAD), 348
effect of adding constant to data values, 351
effect of multiplying data values by constant, 351
versus standard deviation, 350
Mean absolute deviation (MAD) 64, 66, 73, 106, comparing to mean error 178
Mean absolute error 167, as distance 169
comparing to mean absolute deviation 178
Mean of population symbol (µ), 363,
indirect, 400, 545
Median 16, 3336, 71, 92, 94, 106, as second quartile 49
Median, 109, of a triangle, 108
Median-fit procedure, 291,
Median-median line, 291,
Midline of the graph, 438,
Midpoint Connector Theorems,332,
Midpoint formula, 19,
Midpoint of a segment,, 85-86, 93
Midrange, properties of, 249,
Minimal spanning tree, and Traveling Salesperson Problem, 349
nearest-neighbor algorithm, 324
Minimums and transformations, 458,
Minor arc, 324,
Modified box plot, 137,
Modified runoff vote-analysis method, 106,
Modus ponens, 276,
Multiple variable equations, solving, 13,
Multiple-variable models, 1-90, algebra, 25-45
geometry, 25-45
linear programming, 63-85
linked equations, 46-62
linked variables, 2-24
trigonometry, 25-45
Multiplication Rule for independent events, 404-405,
Multiplication Rule, 471-484, for three or four independent events, 475
Multiplicative inverse, 44,, 256
Mutually exclusive events, Addition Rule,404-411
definition, 409
versus independent events, 414
Nearest-neighbor algorithm, 324, for Traveling Salesperson Problem, 360
Negation of a simple statement, 276,
Network, finding the best, 320-339, connected, 322-323
NEXT 112, 119, 183, 276, 289, 422,
n-gon, formula for sum of measures of exterior angles, 295,
Nondictatorship fairness condition, 103,
Nonlinear systems of equations, solving, 51, 54,
Normal distribution, 362-383, and percentile rank, 369-375
characteristics, 363-371
deviation, 363-371
equation of a curve, 381
overall shape, 367-368
relation to distribution of its standardized values, 378
standardizing scores, 371-375
using sums to create, 399
Normally distributed, 363,
NOW-NEXT 112, 119, 183, 276, 289, 422,
NOW-NEXT equations, 438, and transformations, 460-461
for sequential change, 489-491
function iteration, 531
subscript notation, 492
NOW-NEXT, 29, 245, 468, 491, 506,
Number line plot 1618, 24, 27, 29, 34, 52, 66, 68, 96,
Number theory, 275,
Numerical iteration to find fixed points, 538,
Objective function, 69,
Opinion poll, 116,
Opposite of a difference, 199,
Opposite of a sum, 199,
Optimization problems, 552,
Ordered fairness condition, 103,
Outcomes, sample, as proportions, 146
as totals, 146
likely versus unlikely, 140-143, 147
Outlier 16, effect on mean or median 36
Outlier, 347, effect on mean and standard deviation, 353, 357
Out-of-control processes, 394-395,
Out-of-control signals, 385-393, due to mean changing, 385
due to standard deviation changing, 385
false alarms, 402-405
tests, 390-392
Output, 177,
Pairwise-comparison vote-analysis method, 97-98, 110-111,
Pantographs, 373-376, and coordinate systems, 379
and distances scale factor for, 375-376
Parabola, finding vertex of, 211,
Parallel 329, rate of change 183
Parallel Lines Property, 285,
Parallel lines, 282-287, theorems, 283, 285,290
Parallelogram linkage, 371-373,
Parallelograms, 325-339, definition, 326, 336
properties of, 244
reasoning about, 326-330
rhombus, 330
theorems, 317, 327-328
Parameters and patterns in tables and graphs, 431,
Paths in adjacency matrices, 37, critical, 51
Percentile rank and normal distribution, 369-375, interpreting z-score to find, 374
table, 373
Perimeter 107, 135, 356, area 360
Perimeter, minimizing, 557,
Period, 429,
Periodic change, 428-430,
Periodic change, patterns of, 436-442,
Periodic functions, 43, and vertical translation,444
changing amplitude, 450
from function rule, 467
from graph, 466
horizontal shifts, 464
reflection across the x-axis, 446
symbolic rules, 429, 464
Permutations, 110, 415,
Perpendicular, symmetry plane 337, 338
Perpendicular Bisector Algorithm, 321,
Perspective drawing 343344, 347,
Piecewise-defined function, 186,
Plane 334, intersection with cube 339
Plane, coordinate model, 80-108,
Plane, tiling the, 553,
Plot over time, 384, 387,
Plurality winner vote-analysis, compared to sequential elimination method, 114
method, 97
Point 251, 252, 254, 255, 259260, 265, 288, 294,
Point of inflection, 382,
Points-for-preferences vote-analysis method, 98,
Point-slope equation of a line, 19,
Polygon, angle measures of regular, 554
area/perimeter of regular, 553
formula for sum of measures of angles, 295
rigid, 297
Polygons, determining classification, 89
Polynomial, higher-degree, 212
perfect cube, factoring, 220
quadratic, 212
standard form, 196
Polynomial functions,, discrete view, 505-529
Population, 117,
possible roots of, 232, reasoning to solve, 229-234
roots and quadratic formula, 237
solving using factoring, 231
solving using the quadratic formula, 231
Power functions, 432,
Power models, tables, and, compared to exponential models, 239-240, 244-245
compared to linear models, 239-240, 244-245
graphs, 238-241, 541-542
Powers, 238, 300-302, fractional exponents and rules, 302
Preference table, 94,
Preferential voting, 93-96,
Present value, 502,
Prime number, 268,
Prim's algorithm, 337-338, versus Kruskal's algorithm, 338
Probabilities, adding, 410
multiplying, 410
using simulation to find,411-412
Probability, multiplying, 472-477
Probability distributions, 485-509, 486-488, 498, 548
Probability of A and B, 266,
Process of Mathematical Modeling 291,
Program Evaluation and Review Technique (PERT) 310,
Program-planning algorithm, 84, 93,
Proof, algebraic, 240-246
analytic, 328
synthetic, 312, 328
using coordinates, 313, 328
Proof presentation, if-then statements, 265-266, 274
paragraph form, 265
pictorally, 265
Properties of equality, 15, 37, 62, to solve equations, 37
to solve proportions, 39
properties of, 351, and variability, 349
relation to normal distribution, 363
sample (s), 364
using calculator to find, 349
versus range, 350
Proportions, 322,
Pythagorean Theorem, 26, 28, proof of, 244-245
Quadratic equations, and function iteration, 543
calculator-based methods versus symbolic reasoning to solve, 238
completing the square, 224
factoring the difference of two squares, 212-213
perfect square, 213, 223
Quadratic equations, solving,, 278-280, 546
number/existence of solutions, 281
Quadratic formula, proof of, 242, 479
relation to horizontal shifts, 477-479
Quadratic functions, 208, and vertical translation, 444
factored form, 458
finding maximum/minimum point, 209
finding vertex by symbolic reasoning, 232
graph, relation to formula calculations, 231
horizontal shifts, 464
interpreting patterns in tables and graphs, 176, 426
reflection across the x-axis, 446
rules and tables, 444
standard polynomial form, 458
using zeroes to write symbolic rules, 232, 464
vertical stretching and shrinking, 451
Quadratic inequalities, calculator-based methods versus symbolic reasoning to solve, 238
reasoning to solve, 229-234
solving without calculator or graph, 239
Quadratic models, 265-288, 546, parabola, 277
patterns in graphs and tables, 270, 274-277
using tables and graphs to solve equation, 267
Quadratic polynomials, 212,
Quadrilateral, 336, equilic, 338
theorems about, 328, 332
tree, 336
Quadrilateral, 87-91, 102, flexible, 368-383
Radian, 421, measure, 421-423, 441
relationship to revolution, 421
Radicals, 289-310, adding expressions, 298
Random sample, 126,
Randomized response technique, 133-134,
Range, 177, 438, practical, 177
theoretical, 177
versus standard deviation, 350
Rank correlation, 171-185, matrix, 178
Rates and times, combining, 11-14, rate-time-amount relations, 12
Ratio 16, 24, 27, 36, 69, 70,77, 83, 93, 176, 180, 194,
Reasoned arguments, 260-296,
Reasoning, 225-239, about angles, 279-282
about congruent triangles, 297-324
about intersecting lines, 279-282
about linear equations, 226-229
about linear inequalities, 226-229
about quadratic equations, 229-234
about quadratic inequalities, 229-234
about similar triangles, 297-324
algebraic, 240-252
deductive, 269-271
inductive versus deductive, 275
inductive, 267, 271
symbolic, 226, 232, 241
with congruence conditions, 316-319
with similarity conditions, 316-319
Rectangle, definition, 329, 335
golden, 131
properties, 247
theorems about, 316, 328, 333, 335
Rectangle, drawing with computer graphics, 81,
Rectangular coordinate system, 95,
Rectangular probability distribution, 496,
Recursion, 488-504, mode on calculator/computer, 492
Recursive form, exponential 422, 441
Recursive form compared to closed 435,
Recursive formulas, 506, and function iteration, 531-533
and functions, 530
combined, 510
general form, 494
interpreting, 493
long-term trends, 498
spreadsheets, 501
using patterns in a table,503
versus function formula,507
Reflections, 441, 446-449, across the x-axis, 446-449
symbolic rules and data patterns, 446
Regression equations, using calculator to get, 459,
Regression line, 564, effect of outliers, 564
Regular polygon angle measure 387,
Relevant fairness condition, 103,
Residual in a regression line, 214,
Revolutions, per minute, converting to degrees per minute, 417
Rhombus linkage, 391, of two and of three, 382
Rhombus, 330,
Right triangles, theorems about, 290, 312, 315, 342,
Right-side view, 3-D drawing 341,
Rigid grid, minimum number, of braces for, 333-334
Rigid transformations, 110, coordinate model, 120
versus size transformations, 135
Rigidity, 333-334, and connected graphs, 334
and vertex-edge graphs, 333-334
RMS-plot, 563,
Root mean squared error (RMS), 563,
Roots of a quadratic equation,232, 237,
Rotational symmetry, 109, 412,
Rotations, 116-119, 180¾, 116-119
matrix representation of, 150-153
rpm, converting to degrees per minute, 417,
Runoff vote-analysis method, 97, compared to sequential elimination method, 114
s (standard deviation), 364,
Sample size, and 90% box plots, 146
and width of confidence intervals, 159
importance of considering, 146
relative width of box plot versus, 150
Sample, 115-134, outcomes, 146-147
random, 126
selecting, 124-12
simple random, 126
Sampling distributions, 135-152, 90% box plot, 137, 140, 142, 144-145
definition, 136
intervals of likely sample outcomes, 140-143
likely outcomes versus unlikely outcomes, 136-137
modified box plot, 137
simulation using random number generator or table, 136
standard box plot charts,144-146
Scalar multiplication, 12, 50, 160,
Scale drawings versus vertex-edge drawings, 355,
Scale factor, 298,
Scatterplots, 171, matrix, 177
Segments, congruent, 305
perpendicular bisectors of, 321
Semi-regular tessellation 392,
Sequences, arithmetic, 506
determining type, 509
Fibonacci, 527
geometric, 508
Sequential change, and direct variation, 503-504
discrete dynamical systems, 491
mathematical models, 489
matrices, 499-500
NOW-NEXT equations, 489-491
using recursion, 488-504
using subscript notation, 491-494, 498
Sequential-elimination vote analysis method, 114, compared to plurality method, 114
compared to runoff method, 114
Series, 515,
Shape of a distribution 1618,
Shapes of constant width, 431,
SHORTCUT software, 344, 360, row sums computed by, 344
Shortest paths, 340-362, and Traveling Sales-person Problem, 349
in visibility graphs, 552
Side, included, 313,
Sierpinski, carpet, 509
triangle, 520
Sigma (S) notation, 525,
Similar figures, properties of, 298-304
theorems, 300-302, 304
Simple random sample, 126,
Sine graph, equations, 433-434
relationship to cosine graph, 439
scatterplots and tables of, 433
Sine ratios, 27,
Sines, Law of, 28-31, 298, ambiguous case for, 306
proof of, 245, 251
to find angle measures, 30
to find length, 30
when to use, 31
Size transformation, 267,
Size transformations, and pantographs, 380
area of figures and composition of, 141
distances, to measure indirectly, 134-135
matrix representations for, 154-156
negative numbers as magnitudes, 132
similarity transformation, 143
successively applying two, with center at origin, 140
versus rigid transformations, 135
without use of coordinates, 147
Skew lines, 293,
Slope 182, 186, 207, 216, 369,
Slope and y-intercept of a line,, formula, 242
Solving inequalities 212, 219,
Solving systems of linear equations 227,
Spanning tree, 332, and rigidity, 334
Spearman's rank correlation, coefficient, 173-175
sum of squared differences, 175
versus Pearson's correlation coefficient, 206
Sphere, circumference formula, 426
surface area formula, 426
volume formula, 426
Spreadsheets, 501,
Square matrix, 8, 43, symmetric, 20
Square root function, 433,
Square root of a matrix,, finding, 58
Square root, 290, radical symbol, 290
Square, drawing with computer graphics, 81,
Squares, definition, 335
length of a diagonal of, 248