Test Set for MathML Cloud

Last updated: September 18, 2014

Source: Carnegie Learning Math Series Level 2

$Equation negative 5 and one-fifth minus 6 and two-thirds equals$
$Equation negative 7 and three-fourths minus left-parenthesis negative 4 and seven-eighths right-parenthesis equals$
$Equation negative 24.15 minus left-parenthesis 13.7 right-parenthesis equals$
$Equation left-parenthesis negative 4 right-parenthesis times 3 equals negative 12$
$Equation negative 12 division-sign 3 equals negative 4$
$Equation negative 12 division-sign left-parenthesis negative 4 right-parenthesis equals 3$
$Equation 6 times 5$
$Equation 6 times left-parenthesis negative 5 right-parenthesis$
$Equation negative 6 times 5$
$Equation negative 6 times left-parenthesis negative 5 right-parenthesis$
$Equation negative 8 times 7$
$Equation negative 8 times left-parenthesis negative 7 right-parenthesis$
$Equation 8 times left-parenthesis negative 7 right-parenthesis$
$Equation 8 times 7$

Source: Glencoe/McGraw-Hill Mathematics: Applications and Concepts Course 1

$Equation m angle 1 equals 30 degree-sign$ , $Equation m angle 2 equals 60 degree-sign$ , $Equation m angle 1 plus m angle 2 equals 90 degree-sign$
$Equation m angle upper M plus m angle upper N equals 180 degree-sign$ .
$Equation upper A equals one-half b h$
$Equation StartFraction area of triangle Over area of square EndFraction equals StartFraction 1 unit Superscript 2 Baseline Over 16 units Superscript 2 EndFraction$
$Equation 0.6 squared$
$Equation 1.5 squared$

Source: Teacher Created

$Equation 4 left-parenthesis 2 x plus 3 x right-parenthesis$
$Equation 36 plus 4 y minus 1 y squared plus 5 y squared minus 2$
$Equation left-parenthesis 5 plus 9 right-parenthesis minus 4 plus 3 equals$

Source: Holt McDougal Mathematics

Line BC, or $Equation times times BC left right-arrow$
$Equation times times PQ right-arrow$
$Equation times times GH spacing-macron$
$Equation times times WX spacing-macron approximately-equals times times YZ spacing-macron$
Some angles are contained within other, larger angles. For instance, $Equation prefix angle upper B upper E upper F$ includes $Equation prefix angle upper B upper E upper D$ and $Equation prefix angle upper D upper E upper F$ .

Source: Say It With Symbols: Making Sense of Symbols (Pearson)

$Equation x equals StartFraction negative b plus-or-minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction$
$Equation y equals x squared plus 8 x plus 16$
$Equation y equals one-third left-parenthesis 3 Superscript x Baseline right-parenthesis$
$Equation y equals 10 minus 2 x$
$Equation y equals 2 x cubed plus 5$
$Equation y equals left-parenthesis prefix x squared plus 1 right-parenthesis left-parenthesis x squared plus 3 right-parenthesis$
$Equation y equals 0.5 Superscript x$
$Equation y equals 22 minus 2 x$
$Equation y equals StartFraction 3 Over x EndFraction$
$Equation y equals left-parenthesis x plus 4 right-parenthesis left-parenthesis x plus 4 right-parenthesis$
$Equation y equals left-parenthesis 4 x minus 3 right-parenthesis left-parenthesis x plus 1 right-parenthesis$
$Equation y equals 20 x minus 4 x squared$
$Equation y equals x squared$
$Equation y equals 3 Superscript x minus 1$
$Equation y equals 16 minus 2 left-parenthesis x plus 3 right-parenthesis$
$Equation y equals 4 x squared minus x minus 3$
$Equation y equals x plus StartFraction 1 Over x EndFraction$
$Equation y equals 4 x left-parenthesis 5 minus x right-parenthesis$
$Equation y equals 2 left-parenthesis x minus 3 right-parenthesis plus 6 left-parenthesis 1 minus x right-parenthesis$

Source: Kentucky KCCT Practice Test

$Equation 0.25 greater-than five-sixteenths$
$Equation 32 dot-operator left-parenthesis 5 dot-operator 7 right-parenthesis$

Source: Pearson Filling and Wrapping Three-Dimensional Measurement

$Equation left-parenthesis one-half times one-half times pi times 2 right-parenthesis plus left-parenthesis 2 times one-half times pi times 5 right-parenthesis$

Source: Examples and Problems in Mathematical Statistics (Wiley)

$Equation liminf right-arrow right-arrow n infinity upper E Subscript n Baseline equals n-ary-union over n greater-than-or-equals 1 n-ary-intersection over k greater-than-or-equals n upper E Subscript k Baseline comma limsup right-arrow right-arrow n infinity upper E Subscript n Baseline equals n-ary-intersection over n greater-than-or-equals 1 n-ary-union over k greater-than-or-equals n upper E Subscript k Baseline period$
$Equation multiline equation row 1 left-parenthesis i right-parenthesis script s element-of script a semicolon row 2 left-parenthesis ii right-parenthesis if upper E element-of script a then upper E spacing-overscore element-of script a semicolon row 3 left-parenthesis iii right-parenthesis if upper E 1 comma upper E 2 element-of script a then upper E 1 union upper E 2 element-of script a period$
$Equation multiline equation row 1 left-parenthesis upper A period 1 right-parenthesis If upper A element-of script upper F then Baseline 0 less-than-or-equals upper P StartSet upper A EndSet less-than-or-equals 1 period left-parenthesis 1 right-parenthesis row 2 left-parenthesis upper A period 2 right-parenthesis upper P StartSet script s EndSet equals 1 period left-parenthesis 2 right-parenthesis row 3 left-parenthesis upper A period 3 right-parenthesis If StartSet upper E Subscript n Baseline comma n greater-than-or-equals 1 EndSet element-of script upper F is a sequence of disjoint left-parenthesis 3 right-parenthesis$
Theorem
(Bayes)
$Equation upper P StartSet upper B Subscript j Baseline vertical-bar upper A EndSet equals StartFraction upper P StartSet upper B Subscript j Baseline EndSet upper P StartSet upper A vertical-bar upper B Subscript j Baseline EndSet Over sigma-summation over j prime prefix element-of upper J upper P StartSet upper B Subscript j prime Baseline EndSet upper P StartSet upper A vertical-bar upper B Subscript j prime Baseline EndSet EndFraction period$
$Equation mu 1 left-parenthesis upper B right-parenthesis equals integral over upper B f left-parenthesis x right-parenthesis d mu 2 left-parenthesis x right-parenthesis$
$Equation lim right-arrow right-arrow n infinity upper E StartSet StartAbsoluteValue upper X Subscript n Baseline minus upper X EndAbsoluteValue EndSet equals upper E StartSet lim right-arrow right-arrow n infinity StartAbsoluteValue upper X Subscript n Baseline minus upper X EndAbsoluteValue EndSet equals 0 period$
$Equation multiline equation row 1 upper P Subscript mu comma sigma Baseline StartSet upper Y greater-than-or-equals l Subscript beta Baseline left-parenthesis upper Y spacing-overscore Subscript n Baseline comma upper S Subscript n Baseline right-parenthesis EndSet equals upper P Subscript mu comma sigma Baseline StartSet left-parenthesis upper Y minus upper Y spacing-overscore Subscript n Baseline right-parenthesis full-stop left-parenthesis upper S dot left-parenthesis 1 plus StartFraction 1 Over n EndFraction right-parenthesis Superscript 1 full-stop 2 Baseline right-parenthesis greater-than-or-equals minus t Subscript beta Baseline left-bracket n minus 1 right-bracket EndSet equals beta comma row 2 left-parenthesis 1 right-parenthesis$
$Equation upper L equals matrix row 1column 1 1 minus minus 1 row 2column 1 1 minus minus 10 row 3column 1 0 row 4column 1 1 minus minus 1 period$
$Equation StartRoot n EndRoot left-bracket upper Y spacing-overscore Subscript n Baseline minus left-parenthesis mu plus z Subscript beta Baseline sigma right-parenthesis right-bracket full-stop upper S Subscript n Baseline tilde StartFraction upper U plus StartRoot n EndRoot z Subscript 1 minus beta Baseline Over left-parenthesis chi squared left-bracket n minus 1 right-bracket full-stop left-parenthesis n minus 1 right-parenthesis right-parenthesis Superscript 1 full-stop 2 Baseline EndFraction tilde t left-bracket n minus 1 semicolon StartRoot n EndRoot z Subscript 1 minus beta Baseline right-bracket comma$
$Equation multiline equation row 1 gamma equals upper P left-brace upper E Subscript p comma q Baseline subset-of left-parenthesis upper X Subscript left-parenthesis r right-parenthesis Baseline comma upper X Subscript left-parenthesis s right-parenthesis Baseline right-brace row 2 equals StartFraction n exclamation-mark Over left-parenthesis r minus 1 right-parenthesis exclamation-mark EndFraction sigma-summation Underscript j equals 0 Overscript s minus r minus 1 Endscripts left-parenthesis negative 1 right-parenthesis Superscript j Baseline StartFraction p Superscript r plus j Baseline Over left-parenthesis n minus r minus j right-parenthesis exclamation-mark j exclamation-mark EndFraction upper I Subscript 1 minus q Baseline left-parenthesis n minus s plus 1 comma s minus r minus j right-parenthesis period$

Source: Fractal Geometry

$Equation upper S Subscript i Baseline vector element 1 t element 2 x equals matrix row 1column 1 full-stop full-stop 1 m 0 row 2column 1 airi vector element 1 t element 2 x plus vector element 1 left-parenthesis i minus 1 right-parenthesis full-stop m element 2 b Subscript i Baseline comma$
$Equation c 1 h Superscript 4 minus 2 s less-than-or-equals StartFraction 1 Over 2 upper T EndFraction integral Subscript negative upper T Superscript upper T Baseline left-parenthesis f left-parenthesis t plus h right-parenthesis minus f left-parenthesis t right-parenthesis right-parenthesis squared d t less-than-or-equals c 2 h Superscript 4 minus 2 s$
$Equation upper C left-parenthesis 0 right-parenthesis minus upper C left-parenthesis h right-parenthesis asymptotically-equals c h Superscript 4 minus 2 s$
$Equation upper S left-parenthesis omega right-parenthesis equals lim over upper T right-arrow infinity StartFraction 1 Over 2 upper T EndFraction StartAbsoluteValue integral Subscript negative upper T Superscript upper T Baseline comma f comma left-parenthesis comma t comma right-parenthesis comma e Super Superscript italic it omega Superscript comma d comma t EndAbsoluteValue squared period$
$Equation integral Subscript 0 Superscript 1 Baseline integral Subscript 0 Superscript 1 Baseline left-bracket StartAbsoluteValue f left-parenthesis t right-parenthesis minus f left-parenthesis u right-parenthesis vertical-bar squared postfix plus EndAbsoluteValue t minus u vertical-bar squared right-bracket Superscript negative s full-stop 2 Baseline d t d u less-than infinity$
$Equation sans-serif upper E left-parenthesis sigma-summation over upper I element-of upper E Subscript k plus 1 Baseline vertical-bar upper I vertical-bar Superscript s Baseline right-parenthesis equals sans-serif upper E left-parenthesis sigma-summation over upper I element-of upper E Subscript k Baseline vertical-bar upper I vertical-bar Superscript s Baseline right-parenthesis sans-serif upper E left-parenthesis upper R 1 Superscript s Baseline plus upper R 2 Superscript s Baseline right-parenthesis period$

Source: Miscellaneous Demostration Examples

The Distance Formula: The distance between points $Equation left-parenthesis x 1 comma y 1 right-parenthesis$ and $Equation left-parenthesis x 2 comma y 2 right-parenthesis$ is given by the formula:

$Equation d equals StartRoot left-parenthesis x 2 minus x 1 right-parenthesis squared plus left-parenthesis y 2 minus y 1 right-parenthesis squared EndRoot$
$Equation double-struck upper R$ is the set of all real numbers: $Equation double-struck upper R equals left-parenthesis negative infinity comma infinity right-parenthesis$
If S is the set $Equation StartSet 1 comma 2 comma 3 EndSet$ then all of the following statements are true: $Equation 1 element-of upper S$ , $Equation 3 element-of upper S$ and $Equation 4 not-an-element-of upper S$ .
$Equation a equals StartRoot 3 x minus 1 EndRoot plus left-parenthesis 1 plus x right-parenthesis squared$
$Equation a equals StartFraction left-parenthesis b plus c right-parenthesis squared Over d EndFraction plus StartFraction left-parenthesis e plus f right-parenthesis squared Over g EndFraction$
$Equation x equals left-bracket left-parenthesis a plus b right-parenthesis squared left-parenthesis c minus b right-parenthesis squared right-bracket plus left-bracket left-parenthesis d plus e right-parenthesis squared left-parenthesis f minus e right-parenthesis squared right-bracket$
$Equation x equals left-bracket left-parenthesis a plus b right-parenthesis squared right-bracket plus left-bracket left-parenthesis f minus e right-parenthesis squared right-bracket$
$Equation x equals left-bracket left-parenthesis a plus b right-parenthesis squared right-bracket$
$Equation x equals left-parenthesis a plus b right-parenthesis squared$
$Equation x equals a plus b squared$
$Equation StartFraction one-half Over three-fourths EndFraction equals two-thirds$
$Equation 2 left-parenthesis left-parenthesis x plus 1 right-parenthesis left-parenthesis x plus 3 right-parenthesis minus 4 left-parenthesis left-parenthesis x minus 1 right-parenthesis left-parenthesis x plus 2 right-parenthesis minus 3 right-parenthesis right-parenthesis equals y$
$Equation cosine x equals 1 minus StartFraction x squared Over 2 exclamation-mark EndFraction plus StartFraction x Superscript 4 Baseline Over 4 exclamation-mark EndFraction minus ellipsis$
$Equation x equals StartFraction negative b plus-or-minus StartRoot b squared minus 4 a c EndRoot Over 2 a EndFraction$
$Equation x plus y Superscript StartFraction 2 Over k plus 1 EndFraction$
$Equation lim over x right-arrow 0 StartFraction sine x Over x EndFraction equals 1$
$Equation d equals StartRoot left-parenthesis x 2 minus x 1 right-parenthesis squared plus left-parenthesis y 2 minus y 1 right-parenthesis squared EndRoot$
$Equation upper F Subscript n Baseline equals upper F Subscript n minus 1 Baseline plus upper F Subscript n minus 2$

Source: Silicon and Related Materials (Elsevier)

$Equation bold upper Pi equals matrix row 1column 1 pi 11 pi 12 pi 12000 row 2column 1 pi 12 pi 11 pi 12000 row 3column 1 pi 12 pi 12 pi 11000 row 4column 1 000 pi 4400 row 5column 1 0000 pi 440 row 6column 1 00000 pi 44$
$Equation s 11 equals StartFraction c 11 plus c 12 Over left-parenthesis c 11 minus c 12 right-parenthesis left-parenthesis c 11 plus 2 c 12 right-parenthesis EndFraction$
$Equation Si upper O 2 plus 6 upper H upper F right-arrow upper H 2 Si upper F 6 plus 2 upper H 2 upper O$

Source: Systematic Synthesis Methods (Elsevier)

$Equation StartFraction d Over d x EndFraction left-parenthesis upper E left-parenthesis x right-parenthesis upper A left-parenthesis x right-parenthesis StartFraction d w left-parenthesis x right-parenthesis Over d x EndFraction right-parenthesis plus p left-parenthesis x right-parenthesis equals 0$

Source: Pressure Sensors (Elsevier)

$Equation TCS Subscript gas Baseline equals minus one-half left-parenthesis StartFraction upper P Subscript seal Baseline Over upper P Subscript max Baseline EndFraction right-parenthesis left-parenthesis StartFraction 1 Over upper T Subscript seal Baseline EndFraction right-parenthesis$
$Equation upper B Subscript p Baseline equals StartStartFraction StartFraction 7 minus v squared Over 3 EndFraction left-parenthesis 1 plus StartFraction c squared Over a squared EndFraction plus StartFraction c Superscript 4 Baseline Over a Superscript 4 Baseline EndFraction right-parenthesis plus StartFraction left-parenthesis 3 minus v right-parenthesis squared c squared Over left-parenthesis 1 plus v right-parenthesis a squared EndFraction OverOver left-parenthesis 1 minus v right-parenthesis left-parenthesis 1 minus StartFraction c Superscript 4 Baseline Over a Superscript 4 Baseline EndFraction right-parenthesis left-parenthesis 1 minus StartFraction c squared Over a squared EndFraction right-parenthesis EndEndFraction$
$Equation upper Q Super Subscript tank Superscript Superscript series Baseline equals StartFraction 1 Over upper R Subscript s EndFraction StartRoot StartFraction upper L Subscript s Baseline Over upper C Subscript s Baseline EndFraction EndRoot$
$Equation upper Delta phi Subscript peak Baseline equals tangent Superscript negative 1 Baseline left-parenthesis k squared upper Q Super Subscript tank Superscript Superscript series Baseline right-parenthesis$

Source: Resonators, Oscillators, and Frequency References (Elsevier)

$Equation f equals 1.013 StartFraction upper W Over upper L squared EndFraction StartRoot StartFraction upper E Over rho EndFraction EndRoot StartRoot left-parenthesis 1 plus 0.293 StartFraction upper L squared Over EW Superscript 2 Baseline EndFraction sigma right-parenthesis EndRoot$
$Equation u Subscript n Baseline left-parenthesis x right-parenthesis equals gamma Subscript n Baseline left-parenthesis hyperbolic cosine k Subscript n Baseline x minus cosine k Subscript n Baseline x right-parenthesis plus left-parenthesis hyperbolic sine k Subscript n Baseline x minus sine k Subscript n Baseline x right-parenthesis$
$Equation multiline equation row 1 upper B equals StartStartFraction StartFraction upper F 0 Over m EndFraction OverOver StartRoot left-parenthesis left-parenthesis omega 0 squared minus omega squared right-parenthesis squared plus 4 n squared omega squared EndRoot EndEndFraction row 2 equals StartStartFraction StartFraction upper F 0 Over k EndFraction OverOver StartRoot left-parenthesis 1 postfix minus left-parenthesis omega full-stop omega 0 squared right-parenthesis squared right-parenthesis squared plus 4 left-parenthesis n full-stop omega 0 right-parenthesis squared left-parenthesis omega full-stop omega 0 right-parenthesis squared EndRoot EndEndFraction$

Source: Doing Data Science (O'Reilly)

$Equation p left-parenthesis upper A and upper B right-parenthesis equals p left-parenthesis upper A right-parenthesis p left-parenthesis upper B vertical-bar upper A right-parenthesis$
$Equation PMF left-parenthesis x right-parenthesis proportional-to left-parenthesis StartFraction 1 Over x EndFraction right-parenthesis Superscript alpha$
$Equation f left-parenthesis x right-parenthesis equals StartFraction 1 Over StartRoot 2 pi EndRoot EndFraction exp left-parenthesis left-parenthesis minus x squared postfix full-stop 2 right-parenthesis$
$Equation StartFraction d x Over d theta EndFraction equals StartFraction beta Over cosine squared theta EndFraction$
$Equation s full-stop StartRoot 2 left-parenthesis n minus 1 right-parenthesis EndRoot$