Examples in the user manual 01. A first example: Determinant of a matrix Calculate the determinant of the matrix #m. Error!!! 1 0.1 0 0 0 #sol «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«mo»:=«/mo»«mi»random«/mi»«mfenced»«mrow»«mo»-«/mo»«mn»3«/mn»«mo»,«/mo»«mn»3«/mn»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sol«/mi»«mo»=«/mo»«mi»determinant«/mi»«mfenced»«mi»m«/mi»«/mfenced»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»2«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sol«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»14«/mn»«/math»«/output»«/command»«/group»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session» 02. The field Algorithm: Factorisation of an integer What is the factorisation of #n ? 1 0.1 0 1 truetrue abc #a #b #c «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«apply»«csymbol definitionURL=¨http://www.wiris.com/XML/csymbol¨»repeat«/csymbol»«mrow»«mi»n«/mi»«mo»=«/mo»«mi»random«/mi»«mo»(«/mo»«mn»1«/mn»«mo»,«/mo»«mn»100«/mn»«mo»)«/mo»«/mrow»«mrow»«mi»length«/mi»«mfenced»«mrow»«mi»factor«/mi»«mo»(«/mo»«mi»n«/mi»«mo»)«/mo»«/mrow»«/mfenced»«mo»§gt;«/mo»«mn»2«/mn»«/mrow»«/apply»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»=«/mo»«mi»factor«/mi»«mo»(«/mo»«mi»n«/mi»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«mo»=«/mo»«mi»factor«/mi»«mo»(«/mo»«mn»2«/mn»«mo»*«/mo»«mi»n«/mi»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«mo»=«/mo»«mi»factor«/mi»«mfenced»«mfrac»«mi»n«/mi»«msub»«mi»a«/mi»«mrow»«mn»2«/mn»«mo»,«/mo»«mn»1«/mn»«/mrow»«/msub»«/mfrac»«/mfenced»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»66«/mn»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo»*«/mo»«mn»3«/mn»«mo»*«/mo»«mn»11«/mn»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»2«/mn»«mn»2«/mn»«/msup»«mo»*«/mo»«mn»3«/mn»«mo»*«/mo»«mn»11«/mn»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo»*«/mo»«mn»11«/mn»«/math»«/output»«/command»«/group»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session»;;;;; 03. Randomness: Prime numbers Is #n a prime number? 1 1 0 0 true false«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#n«/mi»«mo»=«/mo»«mi»#f«/mi»«/math»]]> «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«mo»=«/mo»«mi»random«/mi»«mfenced»«mrow»«mn»1«/mn»«mo».«/mo»«mo».«/mo»«mn»100«/mn»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sol«/mi»«mo»=«/mo»«mi»prime«/mi»«mo»?«/mo»«mo»(«/mo»«mi»n«/mi»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»=«/mo»«mi»factor«/mi»«mfenced»«mi»n«/mi»«/mfenced»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»n«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»20«/mn»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sol«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»false«/mi»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mn»2«/mn»«mn»2«/mn»«/msup»«mo»*«/mo»«mn»5«/mn»«/math»«/output»«/command»«/group»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session»#sol 04. Graphical content: Graphical representation of a function «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»#h«/mi»«/math»?
#p
]]> 1 1 0 0 true false «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mo»)«/mo»«mo»:«/mo»«mo»=«/mo»«mi»random«/mi»«mfenced»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«msup»«exponentiale/»«mi»x«/mi»«/msup»«mo»,«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»,«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»,«/mo»«msup»«mi»x«/mi»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«mo»,«/mo»«msup»«mi»x«/mi»«mrow»«mo»-«/mo»«mn»2«/mn»«/mrow»«/msup»«mo»,«/mo»«mi»ln«/mi»«mo»§nbsp;«/mo»«mi»x«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»sin«/mi»«mo»§nbsp;«/mo»«mi»x«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»cos«/mi»«mo»§nbsp;«/mo»«mi»x«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»=«/mo»«mi»f«/mi»«mo»(«/mo»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»h«/mi»«mo»=«/mo»«mi»random«/mi»«mo»(«/mo»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»f«/mi»«mo»(«/mo»«mo»)«/mo»«mo»,«/mo»«mi»g«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»=«/mo»«mi»plot«/mi»«mo»(«/mo»«mi»g«/mi»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»:=«/mo»«mo»(«/mo»«mi»g«/mi»«mo»=«/mo»«mi»h«/mi»«mo»)«/mo»«mo»?«/mo»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»,«/mo»«mi»h«/mi»«mo»,«/mo»«mi»r«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»cos«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»,«/mo»«mi»cos«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»,«/mo»«mi»true«/mi»«/math»«/output»«/command»«/group»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»,«/mo»«mi»h«/mi»«mo»,«/mo»«mi»r«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«exponentiale/»«mi»x«/mi»«/msup»«mo»,«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»,«/mo»«mi»false«/mi»«/math»«/output»«/command»«/group»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session»#r 05. Feedback for the student: Degree of a polynomial ]]> 1 0.1 0 1 truetrue none #g Well done! You have chosen the right answer.]]> #c leading coefficient of the polynomial.]]> #i constant term of the polynomial.
]]> «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mo»)«/mo»«mo»:=«/mo»«mi»random«/mi»«mo»(«/mo»«mo»-«/mo»«mn»10«/mn»«mo»,«/mo»«mn»10«/mn»«mo»)«/mo»«mo»*«/mo»«msup»«mi»x«/mi»«mrow»«mi»random«/mi»«mo»(«/mo»«mn»0«/mn»«mo»,«/mo»«mn»5«/mn»«mo»)«/mo»«/mrow»«/msup»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»:=«/mo»«mi»degree«/mi»«mfenced»«mi»p«/mi»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«mo»:=«/mo»«msub»«mi»p«/mi»«mi»g«/mi»«/msub»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»i«/mi»«mo»:=«/mo»«msub»«mi»p«/mi»«mn»0«/mn»«/msub»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«apply»«csymbol definitionURL=¨http://www.wiris.com/XML/csymbol¨»repeat«/csymbol»«mrow»«mi»p«/mi»«mo»=«/mo»«mo»§nbsp;«/mo»«mi»f«/mi»«mo»(«/mo»«mo»)«/mo»«mo»+«/mo»«mi»f«/mi»«mo»(«/mo»«mo»)«/mo»«mo»+«/mo»«mi»f«/mi»«mo»(«/mo»«mo»)«/mo»«mo»+«/mo»«mi»f«/mi»«mo»(«/mo»«mo»)«/mo»«mo»+«/mo»«mi»f«/mi»«mo»(«/mo»«mo»)«/mo»«/mrow»«mrow»«mi»g«/mi»«mo»§ne;«/mo»«mi»c«/mi»«mo»§nbsp;«/mo»«mo»§and;«/mo»«mo»§nbsp;«/mo»«mi»g«/mi»«mo»§ne;«/mo»«mi»i«/mi»«mo»§nbsp;«/mo»«mo»§and;«/mo»«mo»§nbsp;«/mo»«mi»c«/mi»«mo»§ne;«/mo»«mi»i«/mi»«/mrow»«/apply»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»7«/mn»«mo»*«/mo»«msup»«mi»x«/mi»«mn»4«/mn»«/msup»«mo»-«/mo»«mn»3«/mn»«mo»*«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»-«/mo»«mn»6«/mn»«mo»*«/mo»«mi»x«/mi»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»7«/mn»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»i«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»0«/mn»«/math»«/output»«/command»«/group»«/session»;;;;; 06. True / False: Types of numbers «math xmlns="http://www.w3.org/1998/Math/MathML"»«mo»§#8712;«/mo»«/math» #c]]> More information on number types in the following chapter. 1 1 0 0 trueCongratulations! Try with another example. false«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi mathvariant="normal"»§#8469;«/mi»«/math» are the natural numbers, «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi mathvariant="normal"»§#8484;«/mi»«/math» are the integers and  «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi mathvariant="normal"»§#8474;«/mi»«/math» are the rational numbers.]]> «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«mo»:=«/mo»«mi»random«/mi»«mfenced»«mrow»«mo»-«/mo»«mn»100«/mn»«mo»,«/mo»«mn»100«/mn»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»z«/mi»«mo»=«/mo»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»q«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mrow»«mrow»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mrow»«/mfrac»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»=«/mo»«msqrt»«mfenced close=¨§verbar;¨ open=¨§verbar;¨»«mrow»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mrow»«/mfenced»«/msqrt»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»e«/mi»«mo»=«/mo»«mi»random«/mi»«mfenced»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»z«/mi»«mo»,«/mo»«mi»q«/mi»«mo»,«/mo»«mi»r«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«mo»=«/mo»«mi»random«/mi»«mfenced»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«naturalnumbers/»«mo»,«/mo»«integers/»«mo»,«/mo»«rationals/»«/mtd»«/mtr»«/mtable»«/mfenced»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sol«/mi»«mo»:«/mo»«mo»=«/mo»«mfenced»«mrow»«mi»e«/mi»«mo»§isin;«/mo»«mi»c«/mi»«/mrow»«/mfenced»«mo»?«/mo»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»e«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»19«/mn»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«rationals/»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sol«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»true«/mi»«/math»«/output»«/command»«/group»«/session»#sol 07. Multiple choice: Range of a matrix What is the range of the following matrix? #m 1 0.1 0 1 truetrue none #sol Correct answer! #a You did not get it right. Try again. #b You did not get it right. Try again.]]> #c You did not get it right. Try again.]]> «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«mo»:=«/mo»«mi»random«/mi»«mfenced»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«mo»,«/mo»«mn»1«/mn»«mo»,«/mo»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«mo»,«/mo»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»a«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sol«/mi»«mo»=«/mo»«mi»rank«/mi»«mfenced»«mi»m«/mi»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«mo»=«/mo»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mn»0«/mn»«mo»,«/mo»«mn»1«/mn»«mo»,«/mo»«mn»2«/mn»«mo»,«/mo»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§nbsp;«/mo»«mo»/«/mo»«mo»§nbsp;«/mo»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»sol«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»=«/mo»«msub»«mi»L«/mi»«mn»1«/mn»«/msub»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«mo»=«/mo»«msub»«mi»L«/mi»«mn»2«/mn»«/msub»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«mo»=«/mo»«msub»«mi»L«/mi»«mn»3«/mn»«/msub»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mtable»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»sol«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mn»0«/mn»«mo»,«/mo»«mn»1«/mn»«mo»,«/mo»«mn»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»«/output»«/command»«/group»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session»;;;;;; 08. Matching: Functions and their graphical representations Match each function with its graphical representation. 1 0.1 0 1 #g1 exp(x) #g2 #f2 #g3 #f3 #f4 «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s1«/mi»«mo»=«/mo»«mi»plotter«/mi»«mo»(«/mo»«mo»)«/mo»«mo»;«/mo»«mi»s2«/mi»«mo»=«/mo»«mi»plotter«/mi»«mo»(«/mo»«mo»)«/mo»«mo»;«/mo»«mi»s3«/mi»«mo»=«/mo»«mi»plotter«/mi»«mo»(«/mo»«mo»)«/mo»«mo»;«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f1«/mi»«mo»=«/mo»«msup»«exponentiale/»«mi»x«/mi»«/msup»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g1«/mi»«mo»=«/mo»«mi»plot«/mi»«mo»(«/mo»«mi»s1«/mi»«mo»,«/mo»«mi»f1«/mi»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f2«/mi»«mo»=«/mo»«mi»log«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g2«/mi»«mo»=«/mo»«mi»plot«/mi»«mo»(«/mo»«mi»s2«/mi»«mo»,«/mo»«mi»f2«/mi»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f3«/mi»«mo»=«/mo»«mi»random«/mi»«mfenced»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»sin«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»,«/mo»«mi»cos«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mtd»«/mtr»«/mtable»«/mfenced»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f4«/mi»«mo»=«/mo»«msub»«mfenced»«mrow»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»sin«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»,«/mo»«mi»cos«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§nbsp;«/mo»«mo»/«/mo»«mo»§nbsp;«/mo»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»f3«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mfenced»«mn»1«/mn»«/msub»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g3«/mi»«mo»=«/mo»«mi»plot«/mi»«mo»(«/mo»«mi»s3«/mi»«mo»,«/mo»«mi»f3«/mi»«mo»)«/mo»«/math»«/input»«/command»«/group»«/library»«/session» 09. Simple short answer: Tangent line to a function at a point Find the expression of the tangent line to «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«/math»#f at the point of abscissa  «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»x«/mi»«mo»=«/mo»«mi»#p«/mi»«/math» . #d
]]> 1 0.1 0 0 0 #r #f «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math»! Try it again...]]> «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»random«/mi»«mfenced»«mrow»«mn»1«/mn»«mo»,«/mo»«mn»5«/mn»«/mrow»«/mfenced»«mo»*«/mo»«mi»random«/mi»«mfenced»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»sin«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»cos«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/mtd»«/mtr»«/mtable»«/mfenced»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»=«/mo»«mi»g«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«mo»=«/mo»«pi/»«mo»*«/mo»«mfrac»«mrow»«mi»random«/mi»«mo»(«/mo»«mo»-«/mo»«mn»4«/mn»«mo»,«/mo»«mn»4«/mn»«mo»)«/mo»«/mrow»«mrow»«mi»random«/mi»«mo»(«/mo»«mn»1«/mn»«mo»,«/mo»«mn»4«/mn»«mo»)«/mo»«/mrow»«/mfrac»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»q«/mi»«mo»=«/mo»«mi»point«/mi»«mfenced»«mrow»«mi»p«/mi»«mo»,«/mo»«mi»g«/mi»«mo»(«/mo»«mi»p«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»=«/mo»«mi»line«/mi»«mfenced»«mrow»«mi»q«/mi»«mo»,«/mo»«mi»g«/mi»«mo»§apos;«/mo»«mo»(«/mo»«mi»p«/mi»«mo»)«/mo»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»d«/mi»«mo»=«/mo»«mi»plot«/mi»«mfenced»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»f«/mi»«mo»,«/mo»«mi»q«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»d«/mi»«mo»=«/mo»«mi»plot«/mi»«mfenced»«mrow»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»r«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»,«/mo»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»color«/mi»«mo»=«/mo»«mi»red«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mfenced»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»4«/mn»«mo»*«/mo»«mi»sin«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mo»-«/mo»«mn»2«/mn»«mo»*«/mo»«msqrt»«mn»2«/mn»«/msqrt»«mo»*«/mo»«mi»x«/mi»«mo»+«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»*«/mo»«pi/»«mo»*«/mo»«msqrt»«mn»2«/mn»«/msqrt»«/mrow»«mn»2«/mn»«/mfrac»«mo»+«/mo»«mn»2«/mn»«mo»*«/mo»«msqrt»«mn»2«/mn»«/msqrt»«/math»«/output»«/command»«/group»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session»editor=true 10. Grading function for simple short answer: A prime number Introduce a prime number larger than 50. 1 0.1 0 0 0 #a «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»=«/mo»«mn»53«/mn»«/math»«/input»«/command»«maction actiontype=¨comment¨»«comment»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»test«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»:=«/mo»«mfenced»«mrow»«mi»x«/mi»«mo»§gt;«/mo»«mn»50«/mn»«mo»§nbsp;«/mo»«mo»§and;«/mo»«mo»§nbsp;«/mo»«mi»prime«/mi»«mo»?«/mo»«mfenced»«mi»x«/mi»«/mfenced»«/mrow»«/mfenced»«mo»?«/mo»«/math»«/comment»«/maction»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»test«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»:=«/mo»«apply»«csymbol definitionURL=¨http://www.wiris.com/XML/csymbol¨»begin«/csymbol»«mtable»«mtr»«mtd»«mi»sol«/mi»«mo»:«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfenced»«mrow»«mo»(«/mo»«mi»x«/mi»«mo»§gt;«/mo»«mn»50«/mn»«mo»)«/mo»«mo»§nbsp;«/mo»«mo»§and;«/mo»«mo»§nbsp;«/mo»«mo»(«/mo»«mi»prime«/mi»«mo»?«/mo»«mfenced»«mi»x«/mi»«/mfenced»«mo»)«/mo»«/mrow»«/mfenced»«mo»?«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»return«/mi»«mo»§nbsp;«/mo»«mi»sol«/mi»«/mtd»«/mtr»«/mtable»«/apply»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»test«/mi»«mo»(«/mo»«mn»52«/mn»«mo»)«/mo»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»false«/mi»«/math»«/output»«/command»«/group»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session»testFunctionName%5B0%5D=test&testFunction%5B1423%5D=0 11. Compound short answer: Linear system
«math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»#M«/mi»«mo»·«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»x«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»z«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»#b1«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#b2«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»#b3«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

Insert your answer using fractions and one line per variable. For example:
«math xmlns="http://www.w3.org/1998/Math/MathML"»«mtable columnalign="left" rowspacing="0"»«mtr»«mtd»«mi»x«/mi»«mo»=«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi»z«/mi»«mo»=«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«/mtd»«/mtr»«/mtable»«/math»
]]> 1 0.1 0 0 0 #x (50%) #y (25%) #z (25%) «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«mo»:«/mo»«mo»=«/mo»«mi»random«/mi»«mo»(«/mo»«mo»-«/mo»«mn»4«/mn»«mo»,«/mo»«mn»4«/mn»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«apply»«csymbol definitionURL=¨http://www.wiris.com/XML/csymbol¨»repeat«/csymbol»«mrow»«mi»M«/mi»«mo»=«/mo»«mfenced»«mtable»«mtr»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«/mtr»«mtr»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«mtd»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«mi»rank«/mi»«mfenced»«mi»M«/mi»«/mfenced»«mo»=«/mo»«mn»3«/mn»«/mrow»«/mfenced»«mo»?«/mo»«/mrow»«/apply»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«mo»=«/mo»«mfenced close=¨]¨ open=¨[¨»«mrow»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«mo»,«/mo»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«mo»,«/mo»«mi»r«/mi»«mo»(«/mo»«mo»)«/mo»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mi»x«/mi»«mo»,«/mo»«mi»y«/mi»«mo»,«/mo»«mi»z«/mi»«mo»]«/mo»«mo»=«/mo»«mi»solve«/mi»«mo»(«/mo»«mi»M«/mi»«mo»,«/mo»«mi»b«/mi»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»[«/mo»«mi»b1«/mi»«mo»,«/mo»«mi»b2«/mi»«mo»,«/mo»«mi»b3«/mi»«mo»]«/mo»«mo»=«/mo»«mi»b«/mi»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session»editor=true&multipleAnswers=true 12. Cloze I: A simple example How many sides has a pentagon? {1:MC:3~4~=5~6~7~8} 
How many sides has a triangle? {2:SA:=3#Congratulations! A triangle has three sides and three angles.}.
]]> 0 13. Cloze II: Graphical representation and derivative of a polynomial Given a polynomial function «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«/math»#f, introduce its derivative  {#1} and choose the graphical representation of the function «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math» {#2}.]]> 2 0.1 0 0 Given a polynomial function «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«mo»=«/mo»«/math»#f, introduce its derivative  {:SA:\#f~=\#g~*#It is incorrect. Try again.} and choose the graphical representation of the function «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»f«/mi»«mfenced»«mi»x«/mi»«/mfenced»«/math» {:MCV:\#p1~=\#p2~\#p3}.]]> «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b1«/mi»«mo»=«/mo»«mi»plotter«/mi»«mfenced»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»height«/mi»«mo»=«/mo»«mn»12«/mn»«mo»,«/mo»«mi»width«/mi»«mo»=«/mo»«mn»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b2«/mi»«mo»=«/mo»«mi»plotter«/mi»«mfenced»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»height«/mi»«mo»=«/mo»«mn»12«/mn»«mo»,«/mo»«mi»width«/mi»«mo»=«/mo»«mn»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b3«/mi»«mo»=«/mo»«mi»plotter«/mi»«mfenced»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd»«mi»height«/mi»«mo»=«/mo»«mn»12«/mn»«mo»,«/mo»«mi»width«/mi»«mo»=«/mo»«mn»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»m«/mi»«mo»(«/mo»«mo»)«/mo»«mo»:=«/mo»«mi»random«/mi»«mfenced»«mrow»«mo»-«/mo»«mn»2«/mn»«mo»,«/mo»«mn»2«/mn»«/mrow»«/mfenced»«mo»*«/mo»«msup»«mi»x«/mi»«mrow»«mi»random«/mi»«mfenced»«mrow»«mn»1«/mn»«mo»,«/mo»«mn»4«/mn»«/mrow»«/mfenced»«/mrow»«/msup»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«apply»«csymbol definitionURL=¨http://www.wiris.com/XML/csymbol¨»repeat«/csymbol»«mrow»«mi»f«/mi»«mo»:=«/mo»«mi»m«/mi»«mo»(«/mo»«mo»)«/mo»«mo»+«/mo»«mi»m«/mi»«mo»(«/mo»«mo»)«/mo»«mo»+«/mo»«mi»m«/mi»«mo»(«/mo»«mo»)«/mo»«mo»+«/mo»«mi»m«/mi»«mo»(«/mo»«mo»)«/mo»«/mrow»«mrow»«mi»degree«/mi»«mfenced»«mi»f«/mi»«/mfenced»«mo»§gt;«/mo»«mn»2«/mn»«/mrow»«/apply»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«mo»=«/mo»«mi»f«/mi»«mo»§apos;«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p1«/mi»«mo»=«/mo»«mi»plot«/mi»«mfenced»«mrow»«mi»b1«/mi»«mo»,«/mo»«mi»f«/mi»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p2«/mi»«mo»=«/mo»«mi»plot«/mi»«mfenced»«mrow»«mi»b2«/mi»«mo»,«/mo»«mi»g«/mi»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p3«/mi»«mo»=«/mo»«mi»plot«/mi»«mfenced»«mrow»«mi»b3«/mi»«mo»,«/mo»«mi»g«/mi»«mo»§apos;«/mo»«/mrow»«/mfenced»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p1«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»plotter1«/mi»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p2«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»plotter2«/mi»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p3«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»plotter3«/mi»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mo»*«/mo»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»g«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»6«/mn»«mo»*«/mo»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math»«/output»«/command»«/group»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session» 14. WIRIS CAS for the student: Orthogonal line to another line throught a point What is the orthogonal line to #r through the point «math xmlns="http://www.w3.org/1998/Math/MathML"»«mi»p«/mi»«mo»=«/mo»«mi»#p«/mi»«/math» ? #q

]]> 1 0.1 0 0 0 #s «session lang=¨en¨ version=¨2.0¨»«library closed=¨false¨»«mtext style=¨color:#ffc800¨ xml:lang=¨es¨»variables«/mtext»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«apply»«csymbol definitionURL=¨http://www.wiris.com/XML/csymbol¨»repeat«/csymbol»«mtable»«mtr»«mtd»«mi»a«/mi»«mo»=«/mo»«mi»random«/mi»«mfenced»«mrow»«mo»-«/mo»«mn»7«/mn»«mo»,«/mo»«mn»7«/mn»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mi»b«/mi»«mo»=«/mo»«mi»random«/mi»«mfenced»«mrow»«mo»-«/mo»«mn»7«/mn»«mo»,«/mo»«mn»7«/mn»«/mrow»«/mfenced»«/mtd»«/mtr»«/mtable»«mrow»«mi»a«/mi»«mo»§ne;«/mo»«mn»0«/mn»«mo»§nbsp;«/mo»«mo»§and;«/mo»«mo»§nbsp;«/mo»«mi»b«/mi»«mo»§ne;«/mo»«mn»0«/mn»«/mrow»«/apply»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»c«/mi»«mo»=«/mo»«mi»random«/mi»«mfenced»«mrow»«mo»-«/mo»«mn»7«/mn»«mo»,«/mo»«mn»7«/mn»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«mo»=«/mo»«mi»line«/mi»«mfenced»«mrow»«mi»a«/mi»«mo»*«/mo»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«mo»*«/mo»«mi»y«/mi»«mo»+«/mo»«mi»c«/mi»«mo»=«/mo»«mn»0«/mn»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«apply»«csymbol definitionURL=¨http://www.wiris.com/XML/csymbol¨»repeat«/csymbol»«mrow»«mi»p«/mi»«mo»=«/mo»«mi»point«/mi»«mfenced»«mrow»«mi»random«/mi»«mfenced»«mrow»«mo»-«/mo»«mn»7«/mn»«mo»,«/mo»«mn»7«/mn»«/mrow»«/mfenced»«mo»,«/mo»«mi»random«/mi»«mfenced»«mrow»«mo»-«/mo»«mn»7«/mn»«mo»,«/mo»«mn»7«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mrow»«mrow»«mi»p«/mi»«mo»§cap;«/mo»«mi»r«/mi»«mo»==«/mo»«mfenced close=¨}¨ open=¨{¨»«mtable align=¨center¨»«mtr»«mtd/»«/mtr»«/mtable»«/mfenced»«/mrow»«/apply»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«mo»=«/mo»«mi»perpendicular«/mi»«mfenced»«mrow»«mi»r«/mi»«mo»,«/mo»«mi»p«/mi»«/mrow»«/mfenced»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»q«/mi»«mo»=«/mo»«mi»plot«/mi»«mo»(«/mo»«mi»r«/mi»«mo»)«/mo»«/math»«/input»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»q«/mi»«mo»=«/mo»«mi»plot«/mi»«mo»(«/mo»«mi»p«/mi»«mo»,«/mo»«mo»{«/mo»«mi»label«/mi»«mo»=«/mo»«mi»p«/mi»«mo»,«/mo»«mo»§nbsp;«/mo»«mi»show_label«/mi»«mo»=«/mo»«mi»true«/mi»«mo»}«/mo»«mo»)«/mo»«/math»«/input»«/command»«/group»«/library»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»p«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced»«mrow»«mn»2«/mn»«mo»,«/mo»«mo»-«/mo»«mn»5«/mn»«/mrow»«/mfenced»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»r«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mn»3«/mn»«mo»*«/mo»«mi»x«/mi»«mo»+«/mo»«mfrac»«mn»1«/mn»«mn»2«/mn»«/mfrac»«/math»«/output»«/command»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»s«/mi»«/math»«/input»«output»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»y«/mi»«mo»=«/mo»«mo»-«/mo»«mfrac»«mn»1«/mn»«mn»3«/mn»«/mfrac»«mo»*«/mo»«mi»x«/mi»«mo»-«/mo»«mfrac»«mn»13«/mn»«mn»3«/mn»«/mfrac»«/math»«/output»«/command»«/group»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session»editor=true1«session lang=¨en¨ version=¨2.0¨»«group»«command»«input»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨/»«/input»«/command»«/group»«/session» 15. Repeating decimals Write down this fraction as a decimal number with repeating decimals:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»10«/mn»«mn»9«/mn»«/mfrac»«/math»

]]> 1.0000000 0.3333333 0 0 1.1⏜]]> Ok!

]]> 10/9]]> The answer is Mathematically equal to the solution, but it has not the desired form. 

]]> * Wrong!

]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mover><mn>1</mn><mo>&#9180;</mo></mover></math>]]></correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>/</mo><mn>9</mn></math>]]></correctAnswer><correctAnswer id="2">*</correctAnswer></correctAnswers><assertions><assertion name="equivalent_literal"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic" correctAnswer="1"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> 16. Any answer You buy 60 cantaloupes at #p each one. How does it all cost?

]]> 1.0000000 0.3333333 0 0 #a Perfect!

 * Only in math problems you can buy 60 cantaloupes and nobody asks what the hell is wrong with you!

]]> 60*#n]]> Ok, but don't forget to always write the units (€).

]]> *]]> Hummm...

Each cantaloupe costs #p, so we have to add #p+#p+#p+... up to 60 times.

So the answer is 60 * #p, that is #a.

Please study Lesson 3 page 14, before trying again this question.

 

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>euro</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>60</mn><mo>*</mo><mi>p</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer><correctAnswer id="1" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>*</mo><mo>#</mo><mi>n</mi></math>]]></correctAnswer><correctAnswer id="2" type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>*</mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic"/><assertion name="equivalent_all" correctAnswer="2"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic" correctAnswer="1"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 17. Currencies A "Krabby Patty" burger costs $1.99,

and a "Krusty Dog" is $3.99.

How do they cost together?

 

]]> 1.0000000 0.3333333 0 0 $1.99+$3.99]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>$</mo><mn>1</mn><mo>.</mo><mn>99</mn><mo>+</mo><mo>$</mo><mn>3</mn><mo>.</mo><mn>99</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 18. Intervals What's the domain of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»f«/mi»«/math»?

]]> You can answer in both formats:

  • #i
  • #e

 

]]> 1.0000000 0.3333333 0 0 #i]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mfrac><msqrt><mfenced><mrow><mi>x</mi><mo>-</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfenced></msqrt><mfenced><mrow><mi>x</mi><mo>-</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mo>+</mo><mn>5</mn></mrow></mfenced></mrow></mfenced></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>domain</mi><mfenced><mi>f</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>expression_to_set</mi><mfenced><mrow><mi>e</mi><mo>,</mo><mi>x</mi></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">i</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"><param name="intervals">true</param></assertion><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 19. Percentages What's the probability to get an odd number from a die roll?

]]> 1.0000000 0.3333333 0 0 3/6]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>/</mo><mn>6</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param><param name="decimalseparators">', �, ., \,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 20. Separators How much is 220?

]]> 1.0000000 0.3333333 0 0 1048576 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>2</mn><mn>20</mn></msup></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1048576</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>1048576</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param><param name="decimalseparators">', �, .</param><param name="digitgroupseparators">\,</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 21. Text - triangles Classify this triangle according to its sides:

#p

]]> 1.0000000 0.3333333 0 0 #a <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>plotter</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>window_width</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>window_height</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>show_axis</mi><mo>=</mo><mi>false</mi><mo>,</mo><mi>show_grid</mi><mo>=</mo><mi>false</mi><mo>,</mo><mi>center</mi><mo>=</mo><mi>point</mi><mfenced><mrow><mn>8</mn><mo>,</mo><mn>6</mn></mrow></mfenced></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>type</mi><mo>=</mo><mi>random</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>name_list</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>&quot;</mo><mi>scalene</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mo>&quot;</mo><mi>isosceles</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mo>&quot;</mo><mi>equilateral</mi><mo>&quot;</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tri_list</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>triangle</mi><mfenced><mrow><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mfenced><mrow><mn>16</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>6</mn></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>triangle</mi><mfenced><mrow><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mfenced><mrow><mn>16</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mfenced><mrow><mn>8</mn><mo>,</mo><mn>4</mn></mrow></mfenced></mrow></mfenced></mtd></mtr><mtr><mtd><mi>triangle</mi><mfenced><mrow><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mfenced><mrow><mn>16</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>point</mi><mfenced><mrow><mn>8</mn><mo>,</mo><mn>13</mn><mo>.</mo><mn>856</mn></mrow></mfenced></mrow></mfenced></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mfenced><msub><mi>tri_list</mi><mi>type</mi></msub></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>name_list</mi><mi>type</mi></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_string"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 22. Text - hexadecimal Convert #d to hexadecimal.

Give the answer with exactly 8 digits.

]]> 1.0000000 0.3333333 0 0 #h <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mfenced><mrow><msup><mn>2</mn><mn>4</mn></msup><mo>,</mo><msup><mn>2</mn><mn>32</mn></msup><mo>-</mo><mn>1</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>hexadecimal</mi><mfenced><mi>d</mi></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>padding</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mo>&quot;</mo><mn>00000000</mn><mo>&quot;</mo><mo>|</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>length</mi><mfenced><mi>h</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><msub><mi>h</mi><mrow><mi>l</mi><mo>-</mo><mn>7</mn><mo>.</mo><mo>.</mo><mi>l</mi></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#h</correctAnswer></correctAnswers><assertions><assertion name="syntax_string"/><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 23. Sets Find the roots of the polynomial #p.

Hint: they are all integers.

Write each one in its own line.

]]> 1.0000000 0.3333333 0 0 #r <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mo>+</mo><mn>5</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mo>+</mo><mn>5</mn></mrow></mfenced><mo>,</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mo>+</mo><mn>5</mn></mrow></mfenced></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfenced><mrow><mi>x</mi><mo>-</mo><msub><mi>r</mi><mn>1</mn></msub></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><msub><mi>r</mi><mn>2</mn></msub></mrow></mfenced><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><msub><mi>r</mi><mn>3</mn></msub></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><assertion name="equivalent_symbolic"><param name="ordermatters">false</param><param name="repetitionmatters">false</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 24. Lists Sort in ascending order these integers:

#u

Put commas between them.

]]> 1.0000000 0.3333333 0 0 #o <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mfenced><mrow/></mfenced><mo>:</mo><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>r</mi><mfenced><mrow/></mfenced><mo>&nbsp;</mo><mi>with</mi><mo>&nbsp;</mo><mi>i</mi><mo>&nbsp;</mo><mi>in</mi><mo>&nbsp;</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o</mi><mo>=</mo><mi>sort</mi><mfenced><mi>u</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#o</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"><param name="nobracketslist">true</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 25. Different data ¿Which function is this?

#p

]]> 1.0000000 0.3333333 0 true true none #r1

]]> #r2

]]> #r3

]]> #r4

]]> #r5

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Generate</mi><mo>&nbsp;</mo><mi>one</mi><mo>&nbsp;</mo><mi>data</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>data</mi><mfenced><mrow/></mfenced><mo>&nbsp;</mo><mo>:</mo><mo>=</mo><mo>&nbsp;</mo></mtd></mtr><mtr><mtd><mo>&nbsp;</mo><mo>&nbsp;</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></mtd></mtr><mtr><mtd><mi>return</mi><mo>&nbsp;</mo><mi>d</mi></mtd></mtr></mtable></apply><mo>;</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>correct</mi><mo>=</mo><mi>data</mi><mfenced><mrow/></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Here</mi><mo>&nbsp;</mo><mi>we</mi><mo>&nbsp;</mo><mi>must</mi><mo>&nbsp;</mo><mi>make</mi><mo>&nbsp;</mo><mi>the</mi><mo>&nbsp;</mo><mi>wording</mi><mo>,</mo><mo>&nbsp;</mo><mi>using</mi><mo>&nbsp;</mo><mi>the</mi><mo>&nbsp;</mo><mi>correct</mi><mo>&nbsp;</mo><mi>answer</mi><mo>.</mo><mo>.</mo><mo>.</mo></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>For</mi><mo>&nbsp;</mo><mi>instance</mi><mo>,</mo><mo>&nbsp;</mo><mi>we</mi><mo>&nbsp;</mo><mi>plot</mi><mo>&nbsp;</mo><mi>it</mi><mo>:</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>plot</mi><mfenced><mi>correct</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Generate</mi><mo>&nbsp;</mo><mi>a</mi><mo>&nbsp;</mo><mi>list</mi><mo>&nbsp;</mo><mi>of</mi><mo>&nbsp;</mo><mn>5</mn><mo>&nbsp;</mo><mi>different</mi><mo>&nbsp;</mo><mi>data</mi></math></comment></maction><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>The</mi><mo>&nbsp;</mo><mi>first</mi><mo>&nbsp;</mo><mi>one</mi><mo>&nbsp;</mo><mi>is</mi><mo>&nbsp;</mo><mi>the</mi><mo>&nbsp;</mo><mi>correct</mi><mo>&nbsp;</mo><mi>answer</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>correct</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>i</mi><mo>&nbsp;</mo><mi>in</mi><mo>&nbsp;</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">local</csymbol><mtable align="top"><mtr><mtd><mi>a</mi></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>a</mi><mo>=</mo><mi>data</mi><mfenced><mrow/></mfenced></mrow><mrow><mi>a</mi><mo>∉</mo><mi>L</mi></mrow></apply></mtd></mtr><mtr><mtd><mi>L</mi><mo>&nbsp;</mo><mo>|</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></apply><mo>;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>L</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>We</mi><mo>&nbsp;</mo><mi>insert</mi><mo>&nbsp;</mo><mi>an</mi><mo>&nbsp;</mo><mi>open</mi><mo>&nbsp;</mo><mi>option</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mrow><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn></mrow></mfenced></mrow></msub><mo>=</mo><mo>&quot;</mo><mo>[</mo><mi>none</mi><mo>&nbsp;</mo><mi>of</mi><mo>&nbsp;</mo><mi>the</mi><mo>&nbsp;</mo><mi>others</mi><mo>]</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>We</mi><mo>&nbsp;</mo><mi>assign</mi><mo>&nbsp;</mo><mi>the</mi><mo>&nbsp;</mo><mi>list</mi><mo>&nbsp;</mo><mi>to</mi><mo>&nbsp;</mo><mi>the</mi><mo>&nbsp;</mo><mi>answers</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mi>r3</mi><mo>,</mo><mi>r4</mi><mo>,</mo><mi>r5</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mi>L</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 26. Equivalent equations Give the equation of the line that passes through point «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mo»#«/mo»«mi»p«/mi»«mi»x«/mi»«mo»,«/mo»«mo»#«/mo»«mi»p«/mi»«mi»y«/mi»«mo»)«/mo»«/math» with slope #m.

]]> 1.0000000 0.3333333 0 0 #e]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>px</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>py</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mi>py</mi></mrow><mrow><mi>x</mi><mo>-</mo><mi>px</mi></mrow></mfrac><mo>=</mo><mi>m</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 27. Equivalent equations Solve:

#eq

]]> 1.0000000 0.3333333 0 0 #sol Great, that's the solution!

]]> #sol This looks like a step in the correct direction, but it's not the solution.

]]> * Uh? this is far from correct...

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>x</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>random</mi><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>sol1</mi><mo>=</mo><mi>sol2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>random</mi><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></mrow></mfenced><mo>*</mo><mi>x</mi><mo>+</mo><mi>random</mi><mfenced><mrow><mfenced><mrow><mo>-</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>10</mn></mrow></mfenced><mo>/</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>s</mi><mo>+</mo><mi>sol1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>s</mi><mo>+</mo><mi>sol2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eq</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn><mo>=</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>16</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1">#sol</correctAnswer><correctAnswer id="2">*</correctAnswer></correctAnswers><assertions><assertion name="equivalent_equations" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> 28. Equivalent equations Give the equation of this line:

#p

 

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mi>y</mi><mo>&nbsp;</mo><mo>=</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn></mrow></mfenced><mo>*</mo><mi>x</mi><mo>+</mo><mi>random</mi><mfenced><mrow><mn>1</mn><mo>.</mo><mo>.</mo><mn>3</mn></mrow></mfenced><mo>&nbsp;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>plotter</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>width</mi><mo>=</mo><mn>11</mn><mo>,</mo><mi>height</mi><mo>=</mo><mn>11</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mfenced><mrow><mi>sol</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>line_width</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 29. Discrete probability Let «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»X«/mi»«/math» be a discrete random variable whose distribution is given by the table below.

 
#ω #p


(the probability that «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»X«/mi»«/math» equals a number outside of the left column is zero)

Calculate:

  1. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»E«/mi»«mfenced»«mi»X«/mi»«/mfenced»«/math»
  2. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»V«/mi»«mi»a«/mi»«mi»r«/mi»«mfenced»«mi»X«/mi»«/mfenced»«/math»
  3. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mfenced»«mrow»«mi»X«/mi»«mo»§#60;«/mo»«mn»4«/mn»«/mrow»«/mfenced»«/math»
]]> 1.0000000 0.3333333 0 0 EX=#expectancyVarX=#varPX<4=#solution3]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ω</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>random</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>10</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>&nbsp;</mo><mi>with</mi><mo>&nbsp;</mo><mi>i</mi><mo>&nbsp;</mo><mi>in</mi><mo>&nbsp;</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>7</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>random</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mfrac><mn>1</mn><mn>6</mn></mfrac></mrow></mfenced><mo>&nbsp;</mo><mi>with</mi><mo>&nbsp;</mo><mi>i</mi><mo>&nbsp;</mo><mi>in</mi><mo>&nbsp;</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>6</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>1</mn><mo>-</mo><mi>sum</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mtable align="center"><mtr><mtd><msub><mi>p</mi><mn>1</mn></msub><mo>,</mo><msub><mi>p</mi><mn>2</mn></msub><mo>,</mo><msub><mi>p</mi><mn>3</mn></msub><mo>,</mo><msub><mi>p</mi><mn>4</mn></msub><mo>,</mo><msub><mi>p</mi><mn>5</mn></msub><mo>,</mo><msub><mi>p</mi><mn>6</mn></msub><mo>,</mo><mi>q</mi></mtd></mtr></mtable></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>expectancy</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>7</mn></munderover><msub><mi>ω</mi><mi>i</mi></msub><mo>*</mo><msub><mi>p</mi><mi>i</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>var</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mn>7</mn></munderover><msup><mfenced><msub><mi>ω</mi><mi>i</mi></msub></mfenced><mn>2</mn></msup><mo>*</mo><msub><mi>p</mi><mi>i</mi></msub><mo>&nbsp;</mo><mo>-</mo><mo>&nbsp;</mo><msup><mi>expectancy</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solution3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">for</csymbol><mrow><mi>k</mi><mo>&nbsp;</mo><mi>in</mi><mo>&nbsp;</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>7</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><msub><mi>ω</mi><mi>k</mi></msub><mo>&lt;</mo><mn>4</mn></mrow><mrow><mi>solution3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>solution3</mi><mo>+</mo><msub><mi>p</mi><mi>k</mi></msub></mrow></apply></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mfenced><mi>X</mi></mfenced><mo>=</mo><mo>#</mo><mi>exp</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>tan</mi><mi>c</mi><mi>y</mi><mspace linebreak="newline"/><mi>V</mi><mi>a</mi><mi>r</mi><mfenced><mi>X</mi></mfenced><mo>=</mo><mo>#</mo><mi>v</mi><mi>a</mi><mi>r</mi><mspace linebreak="newline"/><mi>P</mi><mfenced><mrow><mi>X</mi><mo>&lt;</mo><mn>4</mn></mrow></mfenced><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">3</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">33.33 33.33 33.33</data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 30. Pattern guessing with tables #M]]> 1.0000000 0.3333333 0 0 X = 9Y = 256Z = 125]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo> </mo><mo>=</mo><mfenced><mtable><mtr><mtd><mn>2</mn></mtd><mtd><mn>4</mn></mtd><mtd><mn>8</mn></mtd><mtd><mn>16</mn></mtd></mtr><mtr><mtd><mn>3</mn></mtd><mtd><mi>X</mi></mtd><mtd><mn>27</mn></mtd><mtd><mn>81</mn></mtd></mtr><mtr><mtd><mn>4</mn></mtd><mtd><mn>16</mn></mtd><mtd><mn>64</mn></mtd><mtd><mi>Y</mi></mtd></mtr><mtr><mtd><mn>5</mn></mtd><mtd><mn>25</mn></mtd><mtd><mi>Z</mi></mtd><mtd><mn>625</mn></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mn>9</mn><mspace linebreak="newline"/><mi>Y</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#x2009;</mo><mn>256</mn><mspace linebreak="newline"/><mi>Z</mi><mo>&#xA0;</mo><mo>=</mo><mo>&#xA0;</mo><mn>125</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 31. Basic arithmetic M is a number whose remainder when divided by 7 is 2. It is also divisible by 2, but not by 4.

 

Give a possible value of M.

]]> 1.0000000 0.3333333 0 0 30 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>decrease_mark</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn><mo>.</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>&nbsp;</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>remainder</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>7</mn><mo>)</mo><mo>=</mo><mn>2</mn><mo>&nbsp;</mo><mo>∨</mo><mo>&nbsp;</mo><mi>remainder</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>7</mn><mo>)</mo><mo>=</mo><mo>-</mo><mn>5</mn><mo>)</mo></mrow><mtable><mtr><mtd><mi>credit1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn><mo>.</mo><mn>4</mn></mtd></mtr><mtr><mtd><mi>decrease_mark</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>1</mn></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>remainder</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>2</mn><mo>)</mo><mo>=</mo><mn>0</mn><mo>)</mo></mrow><mrow><mi>credit2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo>*</mo><mi>decrease_mark</mi></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>remainder</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>2</mn><mo>)</mo><mo>=</mo><mn>0</mn><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mi>remainder</mi><mo>(</mo><mi>x</mi><mo>,</mo><mn>4</mn><mo>)</mo><mo>≠</mo><mn>0</mn><mo>)</mo></mrow><mrow><mi>credit3</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn><mo>.</mo><mn>3</mn><mo>*</mo><mi>decrease_mark</mi></mrow></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo>&nbsp;</mo><mi>credit1</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>credit2</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>credit3</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>30</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 32. Linear system of equations Give a solution «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»v«/mi»«/math» to the following equation:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mi»v«/mi»«mo»=«/mo»«mi»b«/mi»«/math»

where

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»A«/mi»«mo»=«/mo»«mfenced open=¨[¨ close=¨]¨»«mtable»«mtr»«mtd»«mn»6«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»2«/mn»«/mtd»«mtd»«mn»0«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo»-«/mo»«mn»4«/mn»«/mtd»«mtd»«mo»-«/mo»«mn»3«/mn»«/mtd»«mtd»«mn»6«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mi»b«/mi»«mo»=«/mo»«mfenced open=¨[¨ close=¨]¨»«mtable»«mtr»«mtd»«mn»30«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»6«/mn»«/mtd»«/mtr»«mtr»«mtd»«mn»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

 

]]> 1.0000000 0.3333333 0 0 3,-4,0]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mn>6</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>1</mn></mtd></mtr><mtr><mtd><mn>2</mn></mtd><mtd><mn>0</mn></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>4</mn></mtd><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mn>6</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>30</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gf</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>n_columns</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>v</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msup><mi>v</mi><mo>T</mo></msup></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mo>(</mo><mi>A</mi><mo>*</mo><msub><mi>v</mi><mn>1</mn></msub><mo>=</mo><mi>b</mi><mo>)</mo><mo>?</mo></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="[" close="]"><mrow><mn>3</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 33. Local maxima Give the «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» coordinates of two distinct local maximums of

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#8201;«/mo»«mn»5«/mn»«mi»sin«/mi»«mfenced»«mrow»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»4«/mn»«/mfrac»«mfenced»«mrow»«mi»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mn»8«/mn»«/math».

]]> 1.0000000 0.3333333 0 0 x1=9x2=-7]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>credit2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>gf</mi><mo>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo></mtd></mtr><mtr><mtd><mo>&nbsp;</mo><mo>&nbsp;</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mfenced><mrow><mi>remainder</mi><mo>(</mo><mi>u</mi><mo>,</mo><mn>8</mn><mo>)</mo><mo>=</mo><mn>1</mn><mo>&nbsp;</mo><mo>∨</mo><mo>&nbsp;</mo><mi>remainder</mi><mo>(</mo><mi>u</mi><mo>,</mo><mn>8</mn><mo>)</mo><mo>=</mo><mo>-</mo><mn>7</mn></mrow></mfenced><mrow><mi>credit1</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mfenced><mrow><mi>u</mi><mo>≠</mo><mi>v</mi><mo>&nbsp;</mo><mo>∧</mo><mo>&nbsp;</mo><mfenced><mrow><mi>remainder</mi><mo>(</mo><mi>v</mi><mo>,</mo><mn>8</mn><mo>)</mo><mo>=</mo><mn>1</mn><mo>&nbsp;</mo><mo>∨</mo><mo>&nbsp;</mo><mi>remainder</mi><mo>(</mo><mi>u</mi><mo>,</mo><mn>8</mn><mo>)</mo><mo>=</mo><mo>-</mo><mn>7</mn></mrow></mfenced></mrow></mfenced><mrow><mi>credit2</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo>&nbsp;</mo><mi>credit1</mi><mo>&nbsp;</mo><mo>+</mo><mo>&nbsp;</mo><mi>credit2</mi></mtd></mtr></mtable></apply></mtd></mtr></mtable></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>x</mi><mn>1</mn></msub><mo>=</mo><mn>9</mn><mspace linebreak="newline"/><msub><mi>x</mi><mn>2</mn></msub><mo>=</mo><mo>-</mo><mn>7</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 34. Tangent lines to a circle «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«/math» is a line tangent to the circumference «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»C«/mi»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»C«/mi»«mo»:«/mo»«mo»§#8201;«/mo»«msup»«mfenced»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«msup»«mfenced»«mrow»«mi»y«/mi»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mfenced»«mn»2«/mn»«/msup»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#160;«/mo»«mn»1«/mn»«/math»

and the slope of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«/math» is «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac bevelled=¨true¨»«mrow»«mo»-«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»6«/mn»«/mfrac»«/math». Give a point on «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»L«/mi»«/math» that isn't the point of tangency.
]]> 1.0000000 0.3333333 0 0 3+33,0]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mark</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>gf</mi><mo>(</mo><mi>P</mi><mo>)</mo><mo>:</mo><mo>=</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><mi>P</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><msub><mi>P</mi><mn>1</mn></msub></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mfenced><mrow><mi>belongs</mi><mo>?</mo><mfenced><mrow><mi>point</mi><mo>(</mo><mi>P</mi><mo>)</mo><mo>,</mo><mi>x</mi><mo>+</mo><msqrt><mn>3</mn></msqrt><mi>y</mi><mo>=</mo><mn>3</mn><mo>+</mo><mn>3</mn><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow></mfenced><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mfenced><mrow><mi>P</mi><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac><mo>+</mo><mn>3</mn></mrow></mfenced></mrow></mfenced><mrow><mi>mark</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn></mrow><mrow><mi>mark</mi><mo>=</mo><mn>1</mn></mrow></apply></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mfenced><mrow><mi>belongs</mi><mo>?</mo><mfenced><mrow><mi>point</mi><mo>(</mo><mi>P</mi><mo>)</mo><mo>,</mo><mi>x</mi><mo>+</mo><msqrt><mn>3</mn></msqrt><mi>y</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>+</mo><mn>3</mn><msqrt><mn>3</mn></msqrt></mrow></mfenced></mrow></mfenced><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mfenced><mrow><mi>P</mi><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mo>-</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><mo>+</mo><mn>3</mn></mrow></mfenced></mrow></mfenced><mrow><mi>mark</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn></mrow><mrow><mi>mark</mi><mo>=</mo><mn>1</mn></mrow></apply></apply></mtd></mtr><mtr><mtd><mi>return</mi><mo>&nbsp;</mo><mi>mark</mi></mtd></mtr></mtable></apply></mtd></mtr></mtable></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>+</mo><mn>3</mn><msqrt><mn>3</mn></msqrt><mo>,</mo><mn>0</mn></mrow></mfenced></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">gf</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 35. Student answer


]]> 1.0000000 0.3333333 0 0 #x 0 That isn't correct, because if the value of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«/math» were #answer, then we would have

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«mo»=«/mo»«mi»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi»cm«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mi»n«/mi»«mi»s«/mi»«mi»w«/mi»«mi»e«/mi»«mi»r«/mi»«mo»+«/mo»«mn»2«/mn»«mo»§#160;«/mo»«mi»cm«/mi»«mo»§#160;«/mo»«mo»=«/mo»«mo»§#8201;«/mo»«mo»#«/mo»«mi»s«/mi»«mi»t«/mi»«mi»u«/mi»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»_«/mi»«mi»b«/mi»«mi»a«/mi»«mi»s«/mi»«mi»e«/mi»«mspace linebreak=¨newline¨/»«mi»h«/mi»«mo»=«/mo»«mo»#«/mo»«mi»h«/mi»«mspace linebreak=¨newline¨/»«mspace linebreak=¨newline¨/»«mi»A«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»b«/mi»«mo»§#183;«/mo»«mi»h«/mi»«/mrow»«mn»2«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»s«/mi»«mi»t«/mi»«mi»u«/mi»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»_«/mi»«mi»b«/mi»«mi»a«/mi»«mi»s«/mi»«mi»e«/mi»«mo»§#183;«/mo»«mo»#«/mo»«mi»h«/mi»«/mrow»«mn»2«/mn»«/mfrac»«mo»=«/mo»«mo»#«/mo»«mi»s«/mi»«mi»t«/mi»«mi»u«/mi»«mi»d«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»_«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»a«/mi»«/math»


which is not equal to the given area of #A.

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mi>random</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>15</mn></mrow></mfenced><csymbol definitionURL="http://.../units/meter#c">cm</csymbol></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mfenced><mrow><mi>random</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>15</mn></mrow></mfenced><csymbol definitionURL="http://.../units/meter#c">cm</csymbol></mrow></mfenced><mo>*</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>A</mi></mrow><mi>h</mi></mfrac><mo>-</mo><mn>2</mn><csymbol definitionURL="http://.../units/meter#c">cm</csymbol></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>parameter</mi><mo>&nbsp;</mo><mi>answer</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>student_base</mi><mo>=</mo><mi>answer</mi><mo>+</mo><mn>2</mn><csymbol definitionURL="http://.../units/meter#c">cm</csymbol></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>student_area</mi><mo>&nbsp;</mo><mo>=</mo><mo>&nbsp;</mo><mfrac><mrow><mi>student_base</mi><mo>*</mo><mi>h</mi></mrow><mn>2</mn></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#x</correctAnswer><correctAnswer id="1">0</correctAnswer></correctAnswers><assertions><assertion name="equivalent_all" correctAnswer="1"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question>