forked from byoshiwara/mfg
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathglossary.xml
More file actions
1387 lines (1384 loc) · 77.5 KB
/
glossary.xml
File metadata and controls
1387 lines (1384 loc) · 77.5 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<?xml version="1.0" encoding="UTF-8" ?>
<!-- <mathbook><book> -->
<appendix xml:id="glossary" xmlns:xi="http://www.w3.org/2001/XInclude">
<title>Glossary</title>
<p>
Abbreviations used in this glossary: <term>n</term> (noun), <term>v</term> (verb), <term>adj</term> (adjective)
</p>
<paragraphs>
<p>
<dl>
<li><title>absolute value</title>
<p>
<term>n</term>, the distance on the number line from a number to <m>0</m>. For example, the absolute value of <m>-7</m> is <m>7</m>. This fact is expressed by the equation <m>\abs{-7} = 7</m>.
</p></li>
<li><title>absolute value equation</title>
<p>
<term>n</term>, an equation in which the variable occurs between the absolute value bars.
</p></li>
<li><title>absolute value inequality</title><p>
<term>n</term>, an inequality in which the variable occurs between the absolute value bars.
</p></li>
<li><title>algebraic expression</title><p>
<term>n</term>, a meaningful combination of numbers, variables, and operation symbols. Also called an <term>expression</term>.
</p></li>
<li><title>algebraic fraction</title><p>
<term>n</term>, a fraction whose numerator and denominator are polynomials. Also called a <term>rational expression</term>.
</p></li>
<li><title>algebraic solution</title><p>
<term>n</term>, a method for solving equations (or inequalities) by manipulating the equations (or inequalities). Compare with <term>graphical solution</term> and <term>numerical solution</term>.
</p></li>
<li><title>allometric equation</title><p>
<term>n</term>, an equation showing the (approximate) relationship between a living organism's body mass and another of the organism's properties or processes, usually given in the form <m>y = k (\text{mass})^p</m>.
</p></li>
<li><title>altitude</title><p>
<term>n</term>, (i) the distance above the ground or above sea level; (ii) the vertical distance between the base and the opposite vertex of a triangle, pyramid, or cone; (iii) the distance between parallel sides of a parallelogram, trapezoid, or rectangle. Also called <term>height</term>.
</p></li>
<li><title>amortization</title><p>
<term>n</term>, the payment of a debt through regular installments over a period of time.
</p></li>
<li><title>amount</title><p>
(in an interest-bearing account), <term>n</term>, the sum of the principal that was invested and all the interest earned.
</p></li>
<li><title>amplitude</title><p>
<term>n</term>, the vertical distance between the midline and the maximum value of a sinusoidal function.
</p></li>
<li><title>annuity</title><p>
<term>n</term>, sequence of equal payments or deposits made at equal time intervals.
</p></li>
<li><title>approximation</title><p>
<term>n</term>, an inexact result.
</p></li>
<li><title>area</title><p>
<term>n</term>, a measure of the two-dimensional space enclosed by a polygon or curve, typically expressed in terms of square units, such as square meters or square feet, etc.
</p></li>
<li><title>ascending powers</title><p>
<term>n</term>, an ordering of the terms of a polynomial so that the exponents on the variable are increasing, such as in the polynomial <m>1 + x + x^2</m>.
</p></li>
<li><title>associative law of addition</title><p>
<term>n</term>, the property that when adding three or more terms, the grouping of terms does not affect the sum. We express this formally by saying that if <m>a</m>, <m>b</m>, and <m>c</m> are any numbers, then <m>(a + b) + c = a + (b + c)</m>.
</p></li>
<li><title>associative law of multiplication</title><p>
<term>n</term>, the property that when multiplying three or more factors, the grouping of factors does not affect the product. We express this formally by saying that if <m>a</m>, <m>b</m>, and <m>c</m> are any numbers, then <m>(a \cdot b) \cdot c = a \cdot (b \cdot c)</m>.
</p></li>
<li><title>asymptote</title><p>
<term>n</term>, a reference line (or curve) towards which the graph of an equation tends as the value of x and/or y grows or diminishes without bound.
</p></li>
<li><title>augmented matrix (for a linear systterm with <m>n</m> variables in standard form),</title><p>
<term>n</term>, the matrix obtained by making each row of the matrix correspond to an equation of the systterm, with the coefficients of the variables filling the first <m>n</m> columns, and the last (that is, the <m>n + 1</m>) column having the constants.
</p></li>
<li><title>axis</title><p>
<term>n</term>, (<term>plural</term> <term>axes</term>), a line used as a reference for position and/or orientation.
</p></li>
<li><title>axis of symmetry</title><p>
<term>n</term>, a line that cuts a plane figure into two parts, each a mirror image of the other.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>back substitution</title>
<p>
<term>n</term>, a technique for solving a triangular systterm of linear equations.
</p></li>
<li><title>bar graph</title><p>
<term>n</term>, a picture of numerical information in which the lengths or heights of bars are used to represent the values of variables.
</p></li>
<li><title>base</title><p>
<term>n</term>, (i) a number or algebraic expression that is used as a repeated factor, where an exponent indicates how many times the base is used as a factor. For example, when we write <m>3^5</m>, the base is <m>3</m>. (ii) The bottom side of a polygon. (iii) The bottom face of a solid.
</p></li>
<li><title>base angles</title><p>
<term>n</term>, the angles opposite the equal sides in an isosceles triangle.
</p></li>
<li><title>binomial</title><p>
<term>n</term>, a polynomial with exactly two terms.
</p></li>
<li><title>binomial expression</title><p>
<term>n</term>, a sum of two unlike terms, such as <m>\sqrt{3}+\sqrt{2} </m>.
</p></li>
<li><title>build (a fraction)</title><p>
<term>v</term>, to find an equivalent fraction by multiplying numerator and denominator by the same nonzero expression.
</p></li>
<li><title>building factor</title><p>
<term>n</term>, an expression by which both numerator and denominator of a given fraction are multiplied (in order to build the fraction).
</p></li>
<li><title>cartesian coordinate systterm</title><p>
<term>n</term>, the grid that associates points in the coordinate plane to ordered pairs of numbers.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>cartesian plane</title><p>
<term>n</term>, a plane with a pair of coordinate axes. Also called a <term>coordinate plane</term>.
</p></li>
<li><title>change in (a variable)</title><p>
<term>n</term>, the final value (of the variable) minus the starting value.
</p></li>
<li><title>change of variables</title><p>
<term>n</term>, (i) a <term>transformation</term> of data, (ii) substitution of a new variable for a variable expression, for example, replacing <m>t^2</m> with <m>x</m> so that the equation <m>y = at^2 + b</m> becomes <m>y = ax + b</m>.
</p></li>
<li><title>circle</title><p>
<term>n</term>, the set of all points in a plane at a fixed distance (the <term>radius</term>) from the center.
</p></li>
<li><title>circumference</title><p>
<term>n</term>, the distance around a circle.
</p></li>
<li><title>closed interval</title><p>
<term>n</term>, a set of numbers, denoted by <m>[a, b]</m>, which includes all the numbers between <m>a</m> and <m>b</m> as well as the numbers <m>a</m> and <m>b</m> thtermselves, where <m>a</m> and <m>b</m> are real numbers and <m>a \lt b</m>. Or the set of numbers denoted by <m>(-\infty, b]</m>, which includes the real number <m>b</m> and all numbers less than <m>b</m>, or the set of numbers denoted by <m>[a, \infty)</m>, which includes the real number <m>a</m> and all numbers greater than <m>a</m>.
</p></li>
<li><title>coefficient</title><p>
<term>n</term>, the numerical factor in a term. For example, in the expression <m>32a + 7b</m>, the coefficient of <m>a</m> is <m>32</m> and the coefficient of <m>b</m> is <m>7</m>.
</p></li>
<li><title>coefficient matrix (for a linear systterm with n variables in standard form)</title><p>
<term>n</term>, the matrix of <m>n</m> columns obtained by making each row of the matrix correspond to an equation of the systterm, with the coefficients of the variables filling the <m>n</m> columns (and the constants are not represented in the matrix).
</p></li>
<li><title>common factor (of two or more expressions)</title><p>
<term>n</term>, a quantity that divides evenly into each of the given expressions.
</p></li>
<li><title>common log or common logarithm (of a given positive number x)</title><p>
<term>n</term>, the exponent, denoted by <m>\log x</m> (or by <m>\log_{10} x</m>) for the number <m>10</m> to obtain the value <m>x</m>, that is, <m>10^{\log x} = x</m>.
</p></li>
<li><title>commutative law of addition</title><p>
<term>n</term>, the property that when adding terms, the order of the terms does not affect the sum. We express this formally by saying that if <m>a</m> and <m>b</m> are any numbers, then <m>a + b = b + a</m>.
</p></li>
<li><title>commutative law of multiplication</title><p>
<term>n</term>, the property that when multiplying factors, the order of the factors does not affect the product. We express this formally by saying that if <m>a</m> and <m>b</m> are any numbers, then <m>a\cdot b = b\cdot a</m>.
</p></li>
<li><title>compltermentary angles</title><p>
<term>n</term>, two angles whose measures add up to <m>90\degree</m>.
</p></li>
<li><title>complete the square</title><p>
<term>v</term>, to determine the appropriate constant to add to a binomial of the form <m>ax^2 + bx</m> so that the result can be written in the form <m>a(x + k)^2</m>.
</p></li>
<li><title>complex conjugate (of a complex number)</title><p>
<term>n</term>, the complex number with the same real part and opposite imaginary part; for example, the complex conjugate of <m>1 + i</m> is <m>1 - i</m>.
</p></li>
<li><title>complex fraction</title><p>
<term>n</term>, a fraction that contains one or more fractions in its numerator and/or in its denominator.
</p></li>
<li><title>complex plane</title><p>
<term>n</term>, a coordinate plane representing complex numbers, with the real parts corresponding to the values on the horizontal axis and imaginary parts corresponding to values on the vertical axis.
</p></li>
<li><title>complex number</title><p>
<term>n</term>, a number that can be written in the form <m>a + bi</m>, where <m>a</m> and <m>b</m> are real numbers and <m>i^2=-1</m>.
</p></li>
<li><title>component</title><p>
<term>n</term>, one of the values of an ordered pair or ordered triple.
</p></li>
<li><title>compound inequality</title><p>
<term>n</term>, a mathtermatical statterment involving two order symbols. For example, the compound inequality <m>1\lt x\lt 2</m> says that "<m>1</m> is less than <m>x</m>, and <m>x</m> is less than <m>2</m>."
</p></li>
<li><title>compound interest (or compounded interest)</title><p>
<term>n</term>, an interest earning agreterment in which the interest payment at a given time is computed based on the sum of the original principal and any interest money already accrued.
</p></li>
<li><title>compounding period</title><p>
<term>n</term>, the time interval between consecutive interest payments to an account that earns interest.
</p></li>
<li><title>concave down (of a graph)</title><p>
<term>adj</term>, curving so that the ends of a flexible rod would need to be bent downward (compared with a straight rod) to lie along the graph. Or equivalently, curving so that a line segment tangent to the curve will lie above the curve.
</p></li>
<li><title>concave up (of a graph)</title><p>
<term>adj</term>, curving so that the ends of a flexible rod would need to be bent upward (compared with a straight rod) to lie along the graph. Or equivalently, curving so that a line segment tangent to the curve will lie below the curve.
</p></li>
<li><title>concavity</title><p>
<term>n</term>, a description of a curve as either concave up or concave down.
</p></li>
<li><title>concentric (of circles or spheres)</title><p>
<term>adj</term>, having the same center.
</p></li>
<li><title>conditional equation</title><p>
<term>n</term>, an equation that is true for some (but not all) values of the variable(s).
</p></li>
<li><title>cone</title><p>
<term>n</term>, a three-dimensional object whose base is a circle and whose vertex is a point above the circle. The points on the segments joining the circle to the vertex make up the cone.
</p></li>
<li><title>congruent</title><p>
<term>adj</term>, having all measure(s) matching exactly. For example, two line segments are congruent when they have the same length; two triangles are congruent if all three sides and all three angles of one match exactly with the corresponding parts of the other triangle.
</p></li>
<li><title>conjugate</title><p>
<term>n</term>, (i) (of a complex number) the complex number with the same real part and opposite imaginary part; (ii) (of a binomial expression) the binomial expression with the same first term and opposite second term.
</p></li>
<li><title>conjugate pair</title><p>
<term>n</term>, (i) (of a complex number) a complex number and its conjugate; (ii) (of a binomial expression) the binomial expression and its conjugate.
</p></li>
<li><title>consistent (of a systterm of equations)</title><p>
<term>adj</term>, having at least one solution.
</p></li>
<li><title>consistent and independent (of a systterm of linear equations)</title><p>
<term>adj</term>, having exactly one solution.
</p></li>
<li><title>constant</title><p>
<term>adj</term>, unchanging, not variable. For example, we say that the product of two variables is constant if the product is always the same number, for any values of the variables.
</p></li>
<li><title>constant</title><p>
<term>n</term>, a number (as opposed to a variable).
</p></li>
<li><title>constant of proportionality</title><p>
<term>n</term>, the quotient of two directly proportional variables, or the product of two inversely proportional variables. Also called the <term>constant of variation</term>.
</p></li>
<li><title>constant of variation</title><p>
<em>see</em> constant of proportionality.
</p></li>
<li><title>constraint</title><p>
<term>n</term>, an equation or inequality involving one or more variables, typically specifying a condition that must be true in the given context.
</p></li>
<li><title>continuous</title><p>
<term>adj</term>, without holes or gaps. For example, a curve is continuous if it can be drawn without lifting the pencil from the page, and a function is continuous if its graph can be drawn without lifting the pencil from the page.
</p></li>
<li><title>continuous compounding</title><p>
<term>n</term>, an interest earning agreterment in which the amount in the account is <m>Pe^{rt}</m>, where <m>P</m> is the initial principal, <m>r</m> is the annual interest rate, and <m>e\approx 2.71828</m> is the base of the natural logarithm.
</p></li>
<li><title>conversion factor</title><p>
<term>n</term>, a ratio used to convert from one unit of measure to another.
</p></li>
<li><title>coordinate</title><p>
<term>n</term>, a number used with a number line or an axis to designate position.
</p></li>
<li><title>coordinate axis</title><p>
<term>n</term>, one of the two perpendicular number lines used to define the coordinates of points in the plane.
</p></li>
<li><title>coordinate plane</title><p>
<term>n</term>, a plane with a pair of coordinate axes. Also called the <term>Cartesian plane</term> or <term><m>xy</m>-plane</term>.
</p></li>
<li><title>corollary</title><p>
<term>n</term>, a mathtermatical fact that is a consequence of a previously known fact.
</p></li>
<li><title>costs</title><p>
<term>n</term>, money that an individual or group must pay out. For example, the costs of a company might include payments for wages, supplies, and rent.
</p></li>
<li><title>counting number</title><p>
<term>n</term>, one of the numbers <m>1, 2, 3, 4, \ldots</m>.
</p></li>
<li><title>cube</title><p>
<term>n</term>, (i) a three-dimensional box whose six faces all consist of squares; (ii) an expression raised to the power <m>3</m>.
</p></li>
<li><title>cube</title><p>
<term>v</term>, to raise an expression to the power <m>3</m>. For example, to cube <m>2</m> means to form the product of three <m>2</m>s: <m>2^3 = 2 \times 2 \times 2 = 8</m>.
</p></li>
<li><title>cube root</title><p>
<term>n</term>, a number that when raised to the power <m>3</m> gives a desired value. For example, <m>2</m> is the cube root of <m>8</m> because <m>2^3 = 8</m>.
</p></li>
<li><title>cubic</title><p>
<term>adj</term>, having to do with the third degree of a variable or with a polynomial of degree <m>3</m>.
</p></li>
<li><title>cylinder</title><p>
<term>n</term>, a three-dimensional figure in the shape of a soft drink can. The top and base are circles of identical size, and the line segments joining the two circles are perpendicular to the planes containing the two circles.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>decay factor</title><p>
<term>n</term>, the factor by which an initial value of a diminishing quantity is multiplied to obtain the final value.
</p></li>
<li><title>decimal</title><p>
<term>adj</term>, having to do with a base-<m>10</m> numeration systterm.
</p></li>
<li><title>decimal place</title><p>
<term>n</term>, the position of a digit relative to the decimal point. For example, in the number <m>3.14159</m>, the digit <m>4</m> is in the second decimal place, or hundredths place.
</p></li>
<li><title>decimal point</title><p>
<term>n</term>, the mark "." that is written between the whole number part and the fractional part of a decimal number. For example, the decimal form of <m>1 \frac{3}{10}</m> is <m>1.3</m>.
</p></li>
<li><title>decreasing</title><p>
<term>adj</term>, (i) (of numbers) moving to the left on a number line: Positive numbers are decreasing when getting closer to zero, and negative numbers are decreasing when they move farther from <m>0</m>; (ii) (of a graph) having decreasing values of <m>y</m> when moving along the graph from left to right; (iii) (of a function) having a decreasing graph.
</p></li>
<li><title>degree</title><p>
<term>n</term>, a measure of angle equal to <m>\frac{1}{360}</m> of a complete revolution.
</p></li>
<li><title>degree</title><p>
<term>n</term>, (i) (of a monomial) the exponent on the variable, or if there are more than one variable, the sum of the exponents of all the variables; (ii) (of a polynomial) the largest degree of the monomials in the polynomial.
</p></li>
<li><title>dtermand equation</title><p>
<term>n</term>, an equation that gives the quantity of some product that consumers are willing to purchase in terms of the price of that product.
</p></li>
<li><title>denominator</title><p>
<term>n</term>, the expression below the fraction bar in a fraction.
</p></li>
<li><title>dependent</title><p>
<term>adj</term>, (of a systterm of equations) having infinitely many solutions.
</p></li>
<li><title>dependent variable</title><p>
<term>n</term>, a variable whose value is determined by specifying the value of the independent variable.
</p></li>
<li><title>descending powers</title><p>
<term>n</term>, expressed with the term with the highest degree written first, then the term with the second highest degree, etc.
</p></li>
<li><title>diagonal</title><p>
<term>n</term>, (i) a line segment joining one vertex of a quadrilateral to the opposite vertex; (ii) a line segment joining opposite corners of a box; (iii) the entries of a matrix whose row number match the column number, that is, the <m>(1, 1), (2, 2), \ldots , (n, n)</m> entries
</p></li>
<li><title>diameter</title><p>
<term>n</term>, (i) a line segment passing through the center of a circle (or sphere) with endpoints on the circle (sphere); (ii) the length of that line segment.
</p></li>
<li><title>difference</title><p>
<term>n</term>, the result of a subtraction. For example, the expression <m>a - b</m> represents the difference between <m>a</m> and <m>b</m>.
</p></li>
<li><title>difference of squares</title><p>
<term>n</term>, an expression of the form <m>a^2 - b^2</m>.
</p></li>
<li><title>dimension</title><p>
<term>n</term>, (i) (of a matrix) the numbers of rows and columns respectively of the matrix, also called the <term>order</term> of the matrix. For example, a matrix with dimension <m>2</m> by <m>3</m> (or <m>2\times 3</m>) has two rows and three columns; (ii) a measurterment defining a geometric figure, for example, the length and width are dimensions of a rectangle.
</p></li>
<li><title>direct variation</title><p>
<term>n</term>, a relation between two variables in which one is a constant multiple of the other (so that the ratio between the two variables is the constant), or in which one is a constant multiple of a positive exponent power of the other variable.
</p></li>
<li><title>directed distance</title><p>
<term>n</term>, the difference between the ending coordinate and the starting coordinate of points on a number line; the directed distance is negative if the ending value is smaller than the starting value. For example, the directed distance from <m>5</m> to <m>2</m> is <m>2 - 5 = -3</m>.
</p></li>
<li><title>directly proportional</title><p>
<term>adj</term>, describing variables related by direct variation.
</p></li>
<li><title>discriminant</title><p>
<term>n</term>, (for the quadratic polynomial <m>ax^2 + bx + c</m>) the quantity <m>b^2 - 4ac</m>.
</p></li>
<li><title>distributive law</title><p>
<term>n</term>, the property that for any numbers <m>a</m>, <m>b</m>, and <m>c</m>, <m>a(b + c) = ab + ac</m>.
</p></li>
<li><title>divisor</title><p>
<term>n</term>, a quantity that is divided into another quantity. For example, in the expression <m>a\div b</m>, the divisor is <m>b</m>.
</p></li>
<li><title>domain</title><p>
<term>n</term>, the set of all acceptable inputs for a function or equation.
</p></li>
<li><title>doubling time</title><p>
<term>n</term>, (of exponential growth) the time required for a quantity to double in size.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>eltermentary row operation</title><p>
<term>n</term>, one of the three following operations: (1) an exchange of two rows, (2) multiplying all entries of a row by a nonzero constant, (3) adding a multiple of any row to another row.
</p></li>
<li><title>elimination</title><p>
<term>n</term>, a method for solving a systterm of equations that involves adding together the equations of the systterm or multiples of the equations of the systterm.
</p></li>
<li><title>termpirical model</title><p>
<term>n</term>, an equation whose graph (approximately) fits a given set of data (but gives no information about the physical processes involved).
</p></li>
<li><title>entry</title><p>
<term>n</term>, a value in a matrix, often identified by specifying location by row and column.
</p></li>
<li><title>equation</title><p>
<term>n</term>, a mathtermatical statterment that two expressions are equal, for example, <m>1 + 1 = 2</m>.
</p></li>
<li><title>equation in two variables</title><p>
<term>n</term>, an equation that involves two variables.
</p></li>
<li><title>equilateral</title><p>
<term>adj</term>, (of a polygon) having all sides of equal length.
</p></li>
<li><title>equilibrium point</title><p>
<term>n</term>, the point where the graphs of the supply and dtermand equations intersect
</p></li>
<li><title>equivalent</title><p>
<term>adj</term>, representing the same value.
</p></li>
<li><title>equivalent equations</title><p>
<term>n</term>, equations that have the same solutions.
</p></li>
<li><title>equivalent expressions</title><p>
<term>n</term>, expressions that have the same value for all permissible values of their variables.
</p></li>
<li><title>error tolerance</title><p>
<term>n</term>, the allowable difference between an estimate and the actual value.
</p></li>
<li><title>evaluate</title><p>
<term>v</term>, to determine the value of an expression when the variable in the expression is replaced by a number.
</p></li>
<li><title>exact</title><p>
<term>adj</term>, not simply close, but with absolutely no deviation from an intended value.
</p></li>
<li><title>exact solution</title><p>
<term>n</term>, the exact value of a solution, i.e., not an approximation.
</p></li>
<li><title>exponent</title><p>
<term>n</term>, the expression that indicates how many times the base is used as a factor. For example, when we write <m>3^5</m>, the exponent is <m>5</m>, and <m>3^5 = 3\times 3\times 3\times 3\times 3</m>.
</p></li>
<li><title>exponential decay</title><p>
<term>n</term>, a manner of decreasing characterized by a constant decay factor for any fixed specified interval of time, or equivalently, modeled by a function <m>f</m> with the form <m>f(t) = ab^t</m>, where <m>a</m> and <m>b</m> are positive constants and <m>0 \lt b\lt 1</m>.
</p></li>
<li><title>exponential equation</title><p>
<term>n</term>, an equation containing a variable expression as an exponent.
</p></li>
<li><title>exponential function</title><p>
<term>n</term>, a function <m>f</m> which can be put in the form <m>f(x) = ab^x</m>, where <m>a</m> is a nonzero constant and <m>b\ne 1</m> is a positive constant.
</p></li>
<li><title>exponential growth</title><p>
<term>n</term>, growth characterized by a constant growth factor for any fixed specified interval of time, or equivalently, modeled by a function <m>f</m> with the form <m>f(t) = ab^t</m>, where <m>a</m> and <m>b</m> are positive constants and <m>b\gt 1</m>.
</p></li>
<li><title>exponential notation</title><p>
<term>n</term>, a way of writing an expression that involves radicals and/or reciprocals in terms of powers that have fractional and/or negative exponents. For example, the exponential notation for <m>\sqrt{3}</m> is <m>
3^{1/2}</m>.
</p></li>
<li><title>expression</title><p>
<em>see</em> algebraic expression.
</p></li>
<li><title>extraction of roots</title><p>
<term>n</term>, a method used to solve (quadratic) equations.
</p></li>
<li><title>extraneous solution</title><p>
<term>n</term>, a value that is not a solution to a given equation but is a solution to an equation derived from the original.
</p></li>
<li><title>extrapolate</title><p>
<term>v</term>, to estimate the value of a dependent variable for a value of the independent variable that is outside the range of the data.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>factor</title><p>
<term>n</term>, an expression that divides evenly into another expression. For example, <m>2</m> is a factor of <m>6</m>.
</p></li>
<li><title>factor</title><p>
<term>v</term>, to write as a product. For example, to factor <m>6</m> we write <m>6 = 2\times 3</m>.
</p></li>
<li><title>factored form</title><p>
<term>n</term>, (i) (of a polynomial or algebraic expression) an expression written as a product of two or more factors, where the algebraic factors cannot be further factored; (ii) (of an equation of a parabola) the form <m>y = a(x - r_1)(x - r_2)</m>.
</p></li>
<li><title>feasible solution</title><p>
<term>n</term>, an ordered pair which satisfies the constraints of a linear programming problterm.
</p></li>
<li><title>FOIL</title><p>
<term>n</term>, an acronym for a method for computing the product of two binomials: <term>F</term> stands for First terms, <term>O</term> for Outer terms, <term>I</term> for Inner terms, and <term>L</term> stands for Last terms.
</p></li>
<li><title>formula</title><p>
<term>n</term>, an equation involving two or more variables.
</p></li>
<li><title>fraction bar</title><p>
<term>n</term>, the line segment separating the numerator and denominator of a fraction. In the fraction <m>\frac{1}{2} </m>, the fraction bar is the short segment between the <m>1</m> and the <m>2</m>.
</p></li>
<li><title>function</title><p>
<term>n</term>, a relationship between two variables in which each value of the input variable determines a unique value of the output variable.
</p></li>
<li><title>function of two variables</title><p>
<term>n</term>, a relationship between an output variable and an ordered pair of input variables in which each ordered pair of the input variables determines a unique value of the output variable.
</p></li>
<li><title>function value</title><p>
<term>n</term>, an output value of a function.
</p></li>
<li><title>fundamental principle of fractions</title><p>
<term>n</term>, the property that the value of a fraction is unchanged when both its numerator and denominator are multiplied by the same nonzero value. We express this formally by saying if <m>a</m> is any number, and <m>b</m> and <m>c</m> are nonzero numbers, then <m>\displaystyle{\frac{a\cdot c}{b\cdot c}=\frac{a}{b}} </m>.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>Gaussian reduction</title><p>
<term>n</term>, the process of performing eltermentary row operations on a matrix to obtain a matrix in echelon form.
</p></li>
<li><title>geometrically similar</title><p>
<term>adj</term>, having the same shape (but possibly different size).
</p></li>
<li><title>graph</title><p>
<term>n</term>, a visual representation of the values of a variable or variables, typically drawn on a number line or on the Cartesian plane.
</p></li>
<li><title>graph</title><p>
<term>v</term>, to draw a graph.
</p></li>
<li><title>graph of an equation (or inequality)</title><p>
<term>n</term>, a picture of the solutions of an equation (or inequality) using a number line or coordinate plane.
</p></li>
<li><title>graphical solution</title><p>
<term>n</term>, a method for solving equations (or inequalities) by reading values off an appropriate graph. Compare with <term>algebraic solution</term> and <term>numerical solution</term>.
</p></li>
<li><title>greatest common factor (GCF) of two or more expressions</title><p>
<term>n</term>, the largest factor that divides evenly into each expression.
</p></li>
<li><title>growth factor</title><p>
<term>n</term>, the factor by which an initial value of a growing quantity is multiplied to obtain the final value.
</p></li>
<li><title>guidepoints</title><p>
<term>n</term>, individual points that are plotted to help draw a graph (by hand).
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>half-life</title><p>
<term>n</term>, (of exponential decay) the time required for a quantity to diminish to half its original size.
</p></li>
<li><title>half-plane</title><p>
<term>n</term>, either of the two regions of a plane that has been divided into two regions by a straight line
</p></li>
<li><title>height</title><p>
<em>see</em> altitude.
</p></li>
<li><title>htermisphere</title><p>
<term>n</term>, half a sphere (on one side or the other of a plane passing through the center).
</p></li>
<li><title>horizontal asymptote</title><p>
<term>n</term>, a line parallel to the <m>x</m>-axis toward which the graph of an equation tends as the value of <m>x</m> grows or diminishes without bound.
</p></li>
<li><title>horizontal axis</title><p>
<term>n</term>, the horizontal coordinate axis. Often called the <m>x</m>-<term>axis</term>.
</p></li>
<li><title>horizontal intercept</title><p>
<term>n</term>, where the graph meets the horizontal axis. Also called <m>x</m>-<term>intercept</term>.
</p></li>
<li><title>horizontal line test</title><p>
<term>n</term>, a test to determine if a function has an inverse function: If no horizontal line intersects the graph of a function more than once, then the inverse is also a function.
</p></li>
<li><title>horizontal translation (of a graph)</title><p>
<term>n</term>, the result of moving all points of the graph straight left (or all straight right) by the same distance.
</p></li>
<li><title>hypotenuse</title><p>
<term>n</term>, the longest side of a right triangle. (It is always the side opposite the right angle.)
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>identity</title><p>
<term>n</term>, an equation that is true for all permissible values of the variable(s).
</p></li>
<li><title>imaginary axis</title><p>
<term>n</term>, the vertical axis in the complex plane.
</p></li>
<li><title>imaginary number</title><p>
<term>n</term>, a complex number of the form <m>bi</m>, where <m>b</m> is a real number and <m>i^2 = -1</m>.
</p></li>
<li><title>imaginary part</title><p>
<term>n</term>, (of a complex number) the coefficient of <m>i</m> when the complex number is written in the form <m>a + bi</m>, where <m>a</m> and <m>b</m> are real numbers. For example, the imaginary part of <m>4 - 7i</m> is <m>- 7</m>.
</p></li>
<li><title>imaginary unit</title><p>
<term>n</term>, a nonreal number denoted by <m>i</m> and which satisfies <m>i^2= -1</m>, that is, <m>i</m> is defined to be a square root of <m>-1</m>.
</p></li>
<li><title>inconsistent</title><p>
<term>adj</term>, (of a system of equations) having no solution.
</p></li>
<li><title>increasing</title><p>
<term>adj</term>, (i) (of numbers) moving to the right on a number line: Positive numbers are increasing when moving farther from zero, and negative numbers are increasing when they move closer to <m>0</m>; (ii) (of a graph) having increasing values of y when moving along the graph from left to right; (iii) (of a function) having an increasing graph.
</p></li>
<li><title>independent</title><p>
<term>adj</term>, (i) (of a system of <m>2</m> linear equations in <m>2</m> variables) having different graphs for the two equations; (ii) (of a system of <m>n</m> linear equations in <m>n</m> variables) having no one equation equal to a linear combination of the others.
</p></li>
<li><title>independent variable</title><p>
<term>n</term>, a variable whose value determines the value of the dependent variable.
</p></li>
<li><title>index</title><p>
<term>n</term>, (of a radical) the number at the left of the radical symbol that indicates the type of root involved; for example, the index of <m>3</m> in the expression <m>\sqrt[3]{x}</m> indicates a cube root.
</p></li>
<li><title>inequality</title><p>
<term>n</term>, a mathematical statement of the form <m>a\lt b</m>, <m>a\le b</m>, <m>a\gt b</m>, <m>a\ge b</m>, or <m>a\ne b</m>.
</p></li>
<li><title>inflation</title><p>
<term>n</term>, a persistent increase over time of consumer prices.
</p></li>
<li><title>inflection point</title><p>
<term>n</term>, a point where a graph changes concavity.
</p></li>
<li><title>initial value</title><p>
<term>n</term>, the starting value of a variable, often when <m>t = 0</m>.
</p></li>
<li><title>input</title><p>
<term>n</term>, value of the independent variable.
</p></li>
<li><title>integer</title><p>
<term>n</term>, a whole number or the negative of a whole number.
</p></li>
<li><title>intercept</title><p>
<term>n</term>, a point where a graph meets a coordinate axis.
</p></li>
<li><title>intercept method</title><p>
<term>n</term>, a method for graphing a line by finding its horizontal and vertical intercepts.
</p></li>
<li><title>interest</title><p>
<term>n</term>, money paid for the use of money. For example, after borrowing money, the borrower must pay the lender not only the original amount of money borrowed (known as the <term>principal</term>) but also the interest on the principal.
</p></li>
<li><title>interest rate</title><p>
<term>n</term>, the fraction of the principal that is paid as interest for one year. For example, an interest rate of <m>10\%</m> means that the interest for one year will be <m>10\%</m> of the principal.
</p></li>
<li><title>interpolate</title><p>
<term>v</term>, to estimate the value of a dependent variable based on data that include both larger and smaller values of the independent variable.
</p></li>
<li><title>intersection point</title><p>
<term>n</term>, a point in common to two graphs.
</p></li>
<li><title>interval</title><p>
<term>n</term>, a set of numbers that includes all the numbers between <m>a</m> and <m>b</m> (possibly but not necessarily including <m>a</m> and/or <m>b</m>), where <m>a</m> and <m>b</m> are real numbers. Or the set of all numbers less than <m>b</m> (and possibly including <m>b</m>), or the set all numbers greater than <m>a</m> (and possibly including <m>a</m>).
</p></li>
<li><title>interval notation</title><p>
<term>n</term>, notation used to designate an interval. For example, <m>[2, 3]</m> is the interval notation to designate all the real numbers from <m>2</m> to <m>3</m>, including both <m>2</m> and <m>3</m>.
</p></li>
<li><title>inverse function</title><p>
<term>n</term>, a function whose inputs are outputs of a given function <m>f</m>, and whose outputs are the corresponding inputs of <m>f</m>.
</p></li>
<li><title>inverse square law</title><p>
<term>n</term>, a physical law that states that the magnitude of some quantity is inversely proportional to the square of the distance to the source of that quantity.
</p></li>
<li><title>inverse variation</title><p>
<term>n</term>, a relation between two variables in which one is a constant divided by the other (so that the product of the two variables is the constant), or in which one is a constant divided by a positive exponent power of the other.
</p></li>
<li><title>inversely proportional</title><p>
<term>adj</term>, describing variables related by inverse variation.
</p></li>
<li><title>irrational number</title><p>
<term>n</term>, a number that is not rational but does correspond to a point on the number line.
</p></li>
<li><title>isolate</title><p>
<term>v</term>, (a variable or expression) to create an equivalent equation (or inequality) in which the variable or expression is by itself on one side of the equation (or inequality).
</p></li>
<li><title>isosceles triangle</title><p>
<term>n</term>, a triangle with two sides of equal length.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>joint variation</title><p>
<term>n</term>, a relationship among three or more variables in which whenever all but two variables are held constant, those remaining two variables vary directly or inversely with each other.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>law of exponents</title><p>
<term>n</term>, a basic property about powers and exponents.
</p></li>
<li><title>lead coefficient</title><p>
<term>n</term>, (of a polynomial) the coefficient of term with highest degree.
</p></li>
<li><title>leading entry</title><p>
<term>n</term>, (of a row in a matrix) the first nonzero entry of the row, when read from left to right.
</p></li>
<li><title>leg</title><p>
<term>n</term>, one of the two shorter sides of a right triangle, or the length of that side.
</p></li>
<li><title>like fractions</title><p>
<term>n</term>, fractions with equivalent denominators.
</p></li>
<li><title>like terms</title><p>
<term>n</term>, terms with equivalent variable parts.
</p></li>
<li><title>line segment</title><p>
<term>n</term>, the points on a single line that join two specified points (the <term>endpoints</term>) on that line.
</p></li>
<li><title>linear combination</title><p>
<term>n</term>, (i) the sum of a nonzero constant multiple of one equation and a nonzero constant multiple of a second equation; (ii) the sum of constant multiples of quantities.
</p></li>
<li><title>linear combinations</title><p>
<term>n</term>, a procedure for solving a linear system of equations which requires taking one or more linear combination of equations.
</p></li>
<li><title>linear equation</title><p>
<term>n</term>, an equation such as <m>2x + 3y = 4</m> or <m>x - 3y = 7</m> in which each term has degree <m>0</m> or <m>1</m>.
</p></li>
<li><title>linear programming</title><p>
<term>n</term>, the study of optimizing functions with constraint equations and/or constraint inequalities.
</p></li>
<li><title>linear regression</title><p>
<term>n</term>, the process of using a line to predict values of a (dependent) variable.
</p></li>
<li><title>linear system</title><p>
<term>n</term>, a set of linear equations.
</p></li>
<li><title>linear term</title><p>
<term>n</term>, a term that consists of a constant times a variable.
</p></li>
<li><title>log</title><p>
<em>see</em> <term>logarithm</term>.
</p></li>
<li><title>log scale</title><p>
<term>n</term>, a scale of measurement that uses the logarithm of a physical quantity rather than the quantity itself.
</p></li>
<li><title>log-log paper</title><p>
<term>n</term>, a type of graph paper in which both horizontal and vertical axes use log scales.
</p></li>
<li><title>logarithm</title><p>
<term>n</term>, (i) an exponent; (ii) a function whose outputs are exponents associated with a given base.
</p></li>
<li><title>logarithmic equation</title><p>
<term>n</term>, an equation involving the logarithm of a variable expression.
</p></li>
<li><title>logarithmic function</title><p>
<term>n</term>, a function of the form <m>f (x) = \log_b(x)</m>, where <m>b</m> is a positive constant different from <m>1</m>.
</p></li>
<li><title>lowest common denominator (LCD)</title><p>
<term>n</term>, (of two or more fractions) the smallest denominator that is a multiple of the denominators in the given fractions.
</p></li>
<li><title>lowest common multiple (LCM)</title><p>
<term>n</term>, (of two or more counting numbers) the smallest counting number that the given numbers divide into evenly.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>mathematical model</title><p>
<term>n</term>, a representation of relationships among quantities using equations, tables, and/or graphs.
</p></li>
<li><title>matrix</title><p>
<term>n</term>, a rectangular array of numbers.
</p></li>
<li><title>maximum</title><p>
<term>adj</term>, largest or greatest.
</p></li>
<li><title>maximum</title><p>
<term>n</term>, largest value.
</p></li>
<li><title>maximum value</title><p>
<term>n</term>, (of a variable expression) the largest value that the expression can equal when the variable is allowed to assume all possible values.
</p></li>
<li><title>mean</title><p>
<term>n</term>, the average of a set of numbers, computed by adding the numbers and dividing by how many are in the set. For example, the mean of <m>5</m>, <m>2</m>, and <m>11</m> is <m>\frac{5+2+11}{3}= 6</m>.
</p></li>
<li><title>mechanistic model</title><p>
<term>n</term>, an equation whose graph (approximately) fits a given set of data and whose parameters are estimates about the physical properties involved.
</p></li>
<li><title>median</title><p>
<term>n</term>, the middle number in a set of numbers when written in increasing order. For example, the median of <m>5</m>, <m>2</m>, and <m>11</m> is <m>5</m>. If the set has two numbers in the middle when written in order, then the median of the set is the mean of those middle numbers. For example, the median of <m>6</m>, <m>1</m>, <m>9</m>, and <m>27</m> is <m>\frac{6+9}{2}= 7.5</m>.
</p></li>
<li><title>minimum</title><p>
<term>adj</term>, least or smallest.
</p></li>
<li><title>minimum</title><p>
<term>n</term>, smallest value.
</p></li>
<li><title>minimum value</title><p>
<term>n</term>, (of a variable expression) the smallest value that the expression can equal when the variable is allowed to assume all possible values.
</p></li>
<li><title>mode</title><p>
<term>n</term>, the number that occurs most frequently in a set of numbers. For example, the mode of <m>1</m>, <m>1</m>, <m>2</m>, and <m>3</m> is <m>1</m>.
</p></li>
<li><title>model</title><p>
<term>n</term>, a mathematical equation or graph or table used to represent a situation in the world or a situation described in words. For example, the equation <m>P = R - C</m> is a model for the relationship among the variables of profit, revenue, and cost.
</p></li>
<li><title>model</title><p>
<term>v</term>, to create a model.
</p></li>
<li><title>monomial</title><p>
<term>n</term>, an algebraic expression with only one term.
</p></li>
<li><title>monotonic</title><p>
<term>adj</term>, (of a function or graph) either never increasing or never decreasing.
</p></li>
<li><title>multiplicative property (of absolute values)</title><p>
<term>n</term>, the property that <m>\abs{a\cdot b} = \abs{a}\cdot\abs{b}</m> for any real numbers <m>a</m> and <m>b</m>.
</p></li>
<li><title>multiplicity</title><p>
<term>n</term>, (i) (of a zero of a polynomial) the number of times the corresponding linear factor appears as a factor of the polynomial. For example, <m>-9</m> is a zero of multiplicity one and <m>7</m> is a zero of multiplicity two for the polynomial <m>p(x) =x^3 - 5x^2 - 77x + 441</m> because <m>p(x)</m> factors as <m>p(x) =(x + 9) (x - 7)^2</m>; (ii) (of a solution to a polynomial equation) the multiplicity of the zero of the corresponding polynomial. For example, <m>-9</m> is a solution of multiplicity one and <m>7</m> is a solution of multiplicity two for the polynomial equation <m>x^3 = 5x^2 + 77x - 441</m> because the equation can be written in the standard form <m>p(x) = 0</m>, where <m>p(x)</m> factors as <m>p(x) =(x + 9)(x - 7)^2</m>.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>natural base</title><p>
<term>n</term>, the irrational number <m>e\approx 2.71828182846</m>, which is useful in calculus, statistics, and other mathematical topics.
</p></li>
<li><title>natural exponential function</title><p>
<term>n</term>, the function <m>f(x) = e^x</m>, where <m>e</m> is the natural base.
</p></li>
<li><title>natural log or natural logarithm</title><p>
<term>n</term>, the logarithm with base <m>e</m>, where <m>e</m> is the natural base.
</p></li>
<li><title>natural number</title><p>
<term>n</term>, a counting number.
</p></li>
<li><title>negative number</title><p>
<term>n</term>, a number that is less than zero.
</p></li>
<li><title>negative of</title><p>
<term>n</term>, the opposite of.
</p></li>
<li><title>net change</title><p>
<term>n</term>, the final value of a variable minus the initial value. For example, if an object's weight decreases from <m>15</m> pounds to <m>13</m> pounds, the net change in weight is <m>-2</m> pounds.
</p></li>
<li><title>nonstrict inequality</title><p>
<term>n</term>, a mathematical statement of the form <m>a \le b</m> or <m>a \ge b</m>.
</p></li>
<li><title>normal</title><p>
<term>adj</term>, perpendicular.
</p></li>
<li><title><m>n</m>th root</title><p>
<term>n</term>, a number which when raised to the power <m>n</m> gives a desired value. When <m>b^n = a</m>, then <m>b</m> is an <m>n</m>th root of <m>a</m>.
</p></li>
<li><title>number line</title><p>
<term>n</term>, a line with coordinates marked on it representing the real numbers.
</p></li>
<li><title>numerator</title><p>
<term>n</term>, the expression in a fraction that is above the fraction bar.
</p></li>
<li><title>numerical solution</title><p>
<term>n</term>, a method for solving equations by reading values from an appropriate table of values. Compare with <term>algebraic solution</term> and <term>graphical solution</term>.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>objective function</title><p>
<term>n</term>, (in linear programming) the function that is to be optimized.
</p></li>
<li><title>one-to-one</title><p>
<term>adj</term>, (pertaining to a function) having the property that every output comes from one and only one input.
</p></li>
<li><title>open interval</title><p>
<term>n</term>, a set of numbers denoted by <m>(a, b)</m>, which includes all the numbers between <m>a</m> and <m>b</m> but not the numbers <m>a</m> and <m>b</m> themselves, where <m>a</m> and <m>b</m> are real numbers and <m>a \ne b</m>. Or the set of numbers denoted by <m>(-\infty b)</m>, which includes all numbers less than <m>b</m>, or the set of numbers denoted by <m>(a, \infty)</m>, which includes all numbers greater than <m>a</m>.
</p></li>
<li><title>operation</title><p>
<term>n</term>, addition, subtraction, multiplication, or division (or raising to a power or taking a root).
</p></li>
<li><title>opposite</title><p>
<term>n</term>, the number on the number line that is on the other side of <m>0</m> and at the same distance. For example, <m>5</m> and <m>-5</m> are opposites.
</p></li>
<li><title>order</title><p>
<term>n</term>, (of a matrix) the numbers of rows and columns respectively of the matrix, also called the <term>dimension</term> of the matrix. For example, a matrix with order <m>2</m> by <m>3</m> (or <m>2 \times 3</m>) has two rows and three columns.
</p></li>
<li><title>order of operations</title><p>
<term>n</term>, rules that prescribe the order in which to carry out the operations in an expression.
</p></li>
<li><title>order symbol</title><p>
<term>n</term>, one of the four symbols <m>\lt</m>, or <m>\le</m>, or <m>\gt</m>, or <m>\ge</m>.
</p></li>
<li><title>ordered pair</title><p>
<term>n</term>, a pair of numbers enclosed in parentheses, like this: <m>(x, y )</m>. Often used to specify a point or a location on the coordinate plane.
</p></li>
<li><title>ordered triple</title><p>
<term>n</term>, three numbers enclosed in parentheses, like this: <m>(x, y, z)</m>. Often used to specify a solution to a system of equations in three variables or a point in three-dimensional space.
</p></li>
<li><title>origin</title><p>
<term>n</term>, the point where the coordinate axes meet. It has coordinates (0, 0).
</p></li>
<li><title>output</title><p>
<term>n</term>, value of the dependent variable.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>parabola</title><p>
<term>n</term>, a curve with the shape of the graph of <m>y = ax^2</m>, where <m>a\ne 0</m>.
</p></li>
<li><title>parallel lines</title><p>
<term>n</term>, lines that lie in the same plane but do not intersect, even if extended indefinitely.
</p></li>
<li><title>parameter</title><p>
<term>n</term>, a constant in an equation that varies in other equations of the same form. For example, in the slope-intercept formula <m>y = b + mx</m>, the constants <m>b</m> and <m>m</m> are parameters.
</p></li>
<li><title>percent</title><p>
<term>n</term>, a fraction with (an understood) denominator of <m>100</m>. For example, to express the fraction <m>\frac{51}{100}</m> as a percent, we write <m>51\%</m> or say "<m>51</m> percent."
</p></li>
<li><title>percent increase</title><p>
<term>n</term>, the change in some quantity, expressed as a percentage of the starting amount.
</p></li>
<li><title>perfect square</title><p>
<term>n</term>, the square of an integer. For example, <m>9</m> is a perfect square because <m>9 = 3^2</m>.
</p></li>
<li><title>perimeter</title><p>
<term>n</term>, the distance around the edge or boundary of a two-dimensional figure.
</p></li>
<li><title>perpendicular lines</title><p>
<term>n</term>, lines that meet and form right angles with each other.
</p></li>
<li><title>piecewise defined function</title><p>
<term>n</term>, a function defined by multiple expressions, one expression for each specified interval of the independent variable.
</p></li>
<li><title>point-slope form</title><p>
<term>n</term>, one way of writing the equation for a line: <m>y-y_1=m(x-x_1)</m> or <m>\frac{y-y_1}{x-x_1}= m</m>.
</p></li>
<li><title>polygon</title><p>
<term>n</term>, a simple closed geometric figure in the plane consisting of line segments (called sides) that meet only at their endpoints. For example, triangles are polygons with three sides.
</p></li>
<li><title>polynomial</title><p>
<term>n</term>, a sum of terms, where each term is either a constant or a constant times a power of a variable, and the exponent is a positive integer.
</p></li>
<li><title>polynomial function</title><p>
<term>n</term>, a function that can be written in the form <m>f (x) = a_nx^n + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} +\cdots + a_2x_2 + a_1x + a_0</m> where <m>a_0, a_1, a_2, \ldots a_n</m> are constants.
</p></li>
<li><title>positive number</title><p>
<term>n</term>, a number greater than zero.
</p></li>
<li><title>power</title><p>
<term>n</term>, an expression that consists of a base and an exponent.
</p></li>
<li><title>power function</title><p>
<term>n</term>, a function of the form <m>f(x) = ax^p</m>, where <m>a</m> and <m>p</m> are constants.
</p></li>
<li><title>prime (or prime number)</title><p>
<term>n</term>, an integer greater than <m>1</m> whose only whole number factors are itself and <m>1</m>.
</p></li>
<li><title>principal</title><p>
<term>n</term>, the original amount of money deposited in an account or borrowed from a lender. (Compare with <term>interest</term>.)
</p></li>
<li><title>principal root</title><p>
<em>see</em> <term>principal square root</term>.
</p></li>
<li><title>principal square root</title><p>
<term>n</term>, the nonnegative square root.
</p></li>
<li><title>product</title><p>
<term>n</term>, the result of a multiplication. For example, the expression <m>a\cdot b</m> represents the product of <m>a</m> and <m>b</m>.
</p></li>
<li><title>profit</title><p>
<term>n</term>, the money left after counting all the revenue that came in and subtracting the costs that had to be paid out.
</p></li>
<li><title>proportion</title><p>
<term>n</term>, an equation in which each side is a ratio.
</p></li>
<li><title>proportional</title><p>
<em>see</em> <term>directly proportional</term>, <term>inversely proportional</term>.
</p></li>
<li><title>pyramid</title><p>
<term>n</term>, a three-dimensional object like a cone except that the base is a polygon instead of a circle.
</p></li>
<li><title>Pythagorean theorem:</title><p>
If the legs of a right triangle are <m>a</m> and <m>b</m> and the hypotenuse is <m>c</m>, then <m>a^2 + b^2 = c^2</m>.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>
<p>
<dl>
<li><title>quadrant</title><p>
<term>n</term>, any of the four regions into which the coordinate axes divide the plane. The <term>first quadrant</term> consists of the points where both coordinates are positive; the <term>second quadrant</term> where the first coordinate is negative and the second coordinate positive; the <term>third quadrant</term> consists of points where both coordinates are negative; and the <term>fourth quadrant</term> contains the points where the first coordinate is positive and the second coordinate is negative.
</p></li>
<li><title>quadratic</title><p>
<term>adj</term>, relating to the square of a variable (or of an expression).
</p></li>
<li><title>quadratic equation</title><p>
<term>n</term>, an equation that equates zero to a polynomial of degree <m>2</m> (or an equivalent equation).
</p></li>
<li><title>quadratic formula</title><p>
<term>n</term>, the formula that gives the solutions of the quadratic equation <m>ax^2 + bx + c = 0</m>, namely <m>x = \frac{-b±\sqrt{b^2-4ac}}{2a}</m>.
</p></li>
<li><title>quadratic function</title><p>
<term>n</term>, a function of the form <m>f (x) = ax^2 + bx + c</m>.
</p></li>
<li><title>quadratic polynomial</title><p>
<term>n</term>, a polynomial whose degree is <m>2</m>.
</p></li>
<li><title>quadratic regression</title><p>
<term>n</term>, the process of using a quadratic function to predict values of a (dependent) variable.
</p></li>
<li><title>quadratic term</title><p>
<term>n</term>, a term whose degree is <m>2</m>.
</p></li>
<li><title>quadratic trinomial</title><p>
<term>n</term>, a polynomial of degree <m>2</m> and having exactly <m>3</m> terms.
</p></li>
<li><title>quadrilateral</title><p>
<term>n</term>, a polygon with exactly <m>4</m> sides.
</p></li>
<li><title>quartic</title><p>
<term>adj</term>, (pertaining to a polynomial) having degree <m>4</m>.
</p></li>
<li><title>quotient</title><p>
<term>n</term>, the result of a division. For example, the expression <m>a \div b</m> represents the quotient of <m>a</m> and <m>b</m>.
</p></li>
</dl>
</p>
</paragraphs>
<paragraphs>