Oefeningen niveau 1

$\newenvironment {prompt}{}{} \newcommand {\accordion }[0]{} \newcommand {\ungraded }[0]{} \newcommand {\xmDefaultPreamble }[0]{xmPreamble.tex} \newcommand {\AfterLastShipout }[0]{\AddToHook {enddocument/afterlastpage}} \newcommand {\AtVeryEndDocument }[0]{\AddToHook {enddocument/afteraux}} \newcommand {\AtEndAfterFileList }[0]{\AddToHook {enddocument/info}} \newcommand {\AtVeryVeryEnd }[0]{\AddToHook {enddocument/end}} \newcommand {\multirowsetup }[0]{\raggedright } \newcommand {\tdplotsinandcos }[3]{\pgfmathsetmacro {#1}{sin(#3)}\pgfmathsetmacro {#2}{cos(#3)}} \newcommand {\tdplotdiv }[3]{\pgfmathsetmacro {#1}{#2/#3}} \newcommand {\tdplotcheckdiff }[5]{\par \par \pgfmathparse { abs(#2 - #1)<#3 } \par \ifthenelse {\equal {\pgfmathresult }{1}}{#4}{#5} } \newcommand {\tdplotsetmaincoords }[2]{\pgfmathsetmacro {\tdplotmaintheta }{#1} \pgfmathsetmacro {\tdplotmainphi }{#2} \tdplotcalctransformmainscreen \tikzset {tdplot_main_coords/.style={x={(\raarot cm,\rbarot cm)},y={(\rabrot cm, \rbbrot cm)},z={(\racrot cm, \rbcrot cm)}}}} \newcommand {\tdplotcalctransformmainscreen }[0]{\tdplotsinandcos {\sintheta }{\costheta }{\tdplotmaintheta }\tdplotsinandcos {\sinphi }{\cosphi }{\tdplotmainphi }\tdplotmult {\stsp }{\sintheta }{\sinphi }\tdplotmult {\stcp }{\sintheta }{\cosphi }\tdplotmult {\ctsp }{\costheta }{\sinphi }\tdplotmult {\ctcp }{\costheta }{\cosphi }\pgfmathsetmacro {\raarot }{\cosphi }\pgfmathsetmacro {\rabrot }{\sinphi }\pgfmathsetmacro {\racrot }{0}\pgfmathsetmacro {\rbarot }{-\ctsp }\pgfmathsetmacro {\rbbrot }{\ctcp }\pgfmathsetmacro {\rbcrot }{\sintheta }\pgfmathsetmacro {\rcarot }{\stsp }\pgfmathsetmacro {\rcbrot }{-\stcp }\pgfmathsetmacro {\rccrot }{\costheta }} \newcommand {\tdplotcalctransformrotmain }[0]{\tdplotsinandcos {\sinalpha }{\cosalpha }{\tdplotalpha } \tdplotsinandcos {\sinbeta }{\cosbeta }{\tdplotbeta } \tdplotsinandcos {\singamma }{\cosgamma }{\tdplotgamma } \tdplotmult {\sasb }{\sinalpha }{\sinbeta } \tdplotmult {\sbsg }{\sinbeta }{\singamma } \tdplotmult {\sasg }{\sinalpha }{\singamma } \tdplotmult {\sasbsg }{\sasb }{\singamma } \tdplotmult {\sacb }{\sinalpha }{\cosbeta } \tdplotmult {\sacg }{\sinalpha }{\cosgamma } \tdplotmult {\sbcg }{\sinbeta }{\cosgamma } \tdplotmult {\sacbsg }{\sacb }{\singamma } \tdplotmult {\sacbcg }{\sacb }{\cosgamma } \tdplotmult {\casb }{\cosalpha }{\sinbeta } \tdplotmult {\cacb }{\cosalpha }{\cosbeta } \tdplotmult {\cacg }{\cosalpha }{\cosgamma } \tdplotmult {\casg }{\cosalpha }{\singamma } \tdplotmult {\cacbsg }{\cacb }{\singamma } \tdplotmult {\cacbcg }{\cacb }{\cosgamma } \pgfmathsetmacro {\raaeul }{\cacbcg - \sasg } \pgfmathsetmacro {\rabeul }{-\cacbsg - \sacg } \pgfmathsetmacro {\raceul }{\casb } \pgfmathsetmacro {\rbaeul }{\sacbcg + \casg } \pgfmathsetmacro {\rbbeul }{-\sacbsg + \cacg } \pgfmathsetmacro {\rbceul }{\sasb } \pgfmathsetmacro {\rcaeul }{-\sbcg } \pgfmathsetmacro {\rcbeul }{\sbsg } \pgfmathsetmacro {\rcceul }{\cosbeta } } \newcommand {\tdplotcalctransformmainrot }[0]{\tdplotsinandcos {\sinalpha }{\cosalpha }{\tdplotalpha } \tdplotsinandcos {\sinbeta }{\cosbeta }{\tdplotbeta } \tdplotsinandcos {\singamma }{\cosgamma }{\tdplotgamma } \tdplotmult {\sasb }{\sinalpha }{\sinbeta } \tdplotmult {\sbsg }{\sinbeta }{\singamma } \tdplotmult {\sasg }{\sinalpha }{\singamma } \tdplotmult {\sasbsg }{\sasb }{\singamma } \tdplotmult {\sacb }{\sinalpha }{\cosbeta } \tdplotmult {\sacg }{\sinalpha }{\cosgamma } \tdplotmult {\sbcg }{\sinbeta }{\cosgamma } \tdplotmult {\sacbsg }{\sacb }{\singamma } \tdplotmult {\sacbcg }{\sacb }{\cosgamma } \tdplotmult {\casb }{\cosalpha }{\sinbeta } \tdplotmult {\cacb }{\cosalpha }{\cosbeta } \tdplotmult {\cacg }{\cosalpha }{\cosgamma } \tdplotmult {\casg }{\cosalpha }{\singamma } \tdplotmult {\cacbsg }{\cacb }{\singamma } \tdplotmult {\cacbcg }{\cacb }{\cosgamma } \pgfmathsetmacro {\raaeul }{\cacbcg - \sasg } \pgfmathsetmacro {\rabeul }{\sacbcg + \casg } \pgfmathsetmacro {\raceul }{-\sbcg } \pgfmathsetmacro {\rbaeul }{-\cacbsg - \sacg } \pgfmathsetmacro {\rbbeul }{-\sacbsg + \cacg } \pgfmathsetmacro {\rbceul }{\sbsg } \pgfmathsetmacro {\rcaeul }{\casb } \pgfmathsetmacro {\rcbeul }{\sasb } \pgfmathsetmacro {\rcceul }{\cosbeta } } \newcommand {\tdplotsetrotatedcoords }[3]{\pgfmathsetmacro {\tdplotalpha }{#1} \pgfmathsetmacro {\tdplotbeta }{#2} \pgfmathsetmacro {\tdplotgamma }{#3} \tdplotcalctransformrotmain \par \tdplotmult {\raaeaa }{\raarot }{\raaeul } \tdplotmult {\rabeba }{\rabrot }{\rbaeul } \tdplotmult {\raceca }{\racrot }{\rcaeul } \tdplotmult {\raaeab }{\raarot }{\rabeul } \tdplotmult {\rabebb }{\rabrot }{\rbbeul } \tdplotmult {\racecb }{\racrot }{\rcbeul } \tdplotmult {\raaeac }{\raarot }{\raceul } \tdplotmult {\rabebc }{\rabrot }{\rbceul } \tdplotmult {\racecc }{\racrot }{\rcceul } \tdplotmult {\rbaeaa }{\rbarot }{\raaeul } \tdplotmult {\rbbeba }{\rbbrot }{\rbaeul } \tdplotmult {\rbceca }{\rbcrot }{\rcaeul } \tdplotmult {\rbaeab }{\rbarot }{\rabeul } \tdplotmult {\rbbebb }{\rbbrot }{\rbbeul } \tdplotmult {\rbcecb }{\rbcrot }{\rcbeul } \tdplotmult {\rbaeac }{\rbarot }{\raceul } \tdplotmult {\rbbebc }{\rbbrot }{\rbceul } \tdplotmult {\rbcecc }{\rbcrot }{\rcceul } \pgfmathsetmacro {\raarc }{\raaeaa + \rabeba + \raceca } \pgfmathsetmacro {\rabrc }{\raaeab + \rabebb + \racecb } \pgfmathsetmacro {\racrc }{\raaeac + \rabebc + \racecc } \pgfmathsetmacro {\rbarc }{\rbaeaa + \rbbeba + \rbceca } \pgfmathsetmacro {\rbbrc }{\rbaeab + \rbbebb + \rbcecb } \pgfmathsetmacro {\rbcrc }{\rbaeac + \rbbebc + \rbcecc } \tikzset {tdplot_rotated_coords/.append style={x={(\raarc cm,\rbarc cm)},y={(\rabrc cm, \rbbrc cm)},z={(\racrc cm, \rbcrc cm)}}}} \newcommand {\tdplotsetrotatedcoordsorigin }[1]{\tikzset {tdplot_rotated_coords/.append style={shift=#1}}} \newcommand {\tdplotresetrotatedcoordsorigin }[0]{\tikzset {tdplot_rotated_coords/.append style={shift={(0,0,0)}}}} \newcommand {\tdplotsetthetaplanecoords }[1]{\tdplotresetrotatedcoordsorigin \tdplotsetrotatedcoords {270 + #1}{270}{0}} \newcommand {\tdplotsetrotatedthetaplanecoords }[1]{\tdplotsetrotatedcoords {\tdplotalpha }{\tdplotbeta }{\tdplotgamma + #1}\tikzset {tdplot_rotated_coords/.append style={y={(\raarc cm,\rbarc cm)},z={(\rabrc cm, \rbbrc cm)},x={(\racrc cm, \rbcrc cm)}}}} \newcommand {\tdplotsetpolarplotrange }[4]{\pgfmathsetmacro {\tdplotlowerphi }{#3} \pgfmathsetmacro {\tdplotupperphi }{#4} \pgfmathsetmacro {\tdplotlowertheta }{#1} \pgfmathsetmacro {\tdplotuppertheta }{#2} } \newcommand {\tdplotresetpolarplotrange }[0]{\pgfmathsetmacro {\tdplotlowerphi }{0} \pgfmathsetmacro {\tdplotupperphi }{360} \pgfmathsetmacro {\tdplotlowertheta }{0} \pgfmathsetmacro {\tdplotuppertheta }{180} } \newcommand {\tdplotgetpolarcoords }[3]{\pgfmathsetmacro {\vxcalc }{#1} \pgfmathsetmacro {\vycalc }{#2} \pgfmathsetmacro {\vzcalc }{#3} \pgfmathsetmacro {\vcalc }{ sqrt((\vxcalc )^2 + (\vycalc )^2 + (\vzcalc )^2) } \par \pgfmathsetmacro {\vxycalc }{ sqrt((\vxcalc )^2 + (\vycalc )^2) } \par \pgfmathsetmacro {\tdplotrestheta }{asin(\vxycalc /\vcalc )} \pgfmathparse {\vzcalc < 0} \ifthenelse {\equal {\pgfmathresult }{1}}{\pgfmathsetmacro {\tdplotrestheta }{180 - \tdplotrestheta } } {} \ifthenelse {\equal {\vxcalc }{0.0}}{\pgfmathparse {\vycalc < 0} \ifthenelse {\equal {\pgfmathresult }{1}}{\pgfmathsetmacro {\tdplotresphi }{270} } {\pgfmathparse {\vycalc > 0} \ifthenelse {\equal {\pgfmathresult }{1}}{\pgfmathsetmacro {\tdplotresphi }{90} } {\pgfmathsetmacro {\tdplotresphi }{0} } } } {\pgfmathsetmacro {\tdplotresphi }{atan(\vycalc /\vxcalc )} \pgfmathparse {\vxcalc < 0} \ifthenelse {\equal {\pgfmathresult }{1}}{\pgfmathsetmacro {\tdplotresphi }{\tdplotresphi +180} } { } \par \pgfmathparse {\tdplotresphi < 0} \ifthenelse {\equal {\pgfmathresult }{1}}{\pgfmathsetmacro {\tdplotresphi }{\tdplotresphi +360} } {} } } \newcommand {\textscale }[2]{\leavevmode \begingroup \relscale {#1}#2\endgroup } \newcommand {\officialeuro }[0]{{\fontencoding {U}\fontfamily {eurosym}\selectfont {}e}} \newcommand {\eurobars }[0]{{\fontencoding {U}\fontfamily {eurosym}\selectfont {}A}} \newcommand {\eurobarsnarrow }[0]{{\fontencoding {U}\fontfamily {eurosym}\selectfont {}B}} \newcommand {\eurobarswide }[0]{{\fontencoding {U}\fontfamily {eurosym}\selectfont {}C}} \newcommand {\p }[0]{} \newcommand {\captionnewline }[0]{\\\relax } \newcommand {\memcaptioninfo }[4]{} \newcommand {\captiongroup }[0]{\setcaptiontype } \newcommand {\LTcaptype }[0]{table} \newcommand {\showtodonotes }[0]{disable} \newcommand {\todo }[1]{\typeout {TODO #1}} \newcommand {\tcbpkgprefix }[0]{} \newcommand {\blue }[1]{{\color {blue}#1}} \newcommand {\red }[1]{{\color {red}#1}} \newcommand {\CancelColor }[0]{\color {xmaccent!50!black}} \newcommand {\important }[1]{\ensuremath {\fcolorbox {black}{white}{$#1$}}} \newcommand {\pdfnl }[0]{} \newcommand {\handoutnl }[0]{} \newcommand {\importantcell }[1]{\ensuremath {#1}} \newcommand {\xmPlotsColor }[0]{ \pgfplotsset { plot1/.style={darkgray,no marks,samples=100}, plot2/.style={lightgray,no marks,samples=100}, plotresult/.style={blue,no marks,samples=100}, plotblue/.style={blue,no marks,samples=100}, plotred/.style={red,no marks,samples=100}, plotgreen/.style={green,no marks,samples=100}, plotpurple/.style={purple,no marks,samples=100} } } \newcommand {\xmPlotsBlackWhite }[0]{ \pgfplotsset { plot1/.style={black,loosely dashed,no marks,samples=100}, plot2/.style={black,loosely dotted,no marks,samples=100}, plotresult/.style={black,no marks,samples=100}, plotblue/.style={black,no marks,samples=100}, plotred/.style={black,dotted,no marks,samples=100}, plotgreen/.style={black,dashed,no marks,samples=100}, plotpurple/.style={black,dashdotted,no marks,samples=100} } } \newcommand {\xmPlotsColorAndStyle }[0]{ \pgfplotsset { plot1/.style={darkgray,no marks,samples=100}, plot2/.style={lightgray,no marks,samples=100}, plotresult/.style={blue,no marks,samples=100}, plotblue/.style={xmblue,no marks,samples=100}, plotred/.style={xmred,dashed,thick,no marks,samples=100}, plotgreen/.style={xmgreen,dotted,very thick,no marks,samples=100}, plotpurple/.style={purple,no marks,samples=100} } } \newcommand {\geqnoslant }[0]{\geq } \newcommand {\geq }[0]{\geqslant } \newcommand {\leqnoslant }[0]{\leq } \newcommand {\leq }[0]{\leqslant } \newcommand {\emph }[1]{\textit {#1}} \newcommand {\ds }[0]{\displaystyle } \newcommand {\ts }[0]{\textstyle } \newcommand {\bron }[1]{\begin {scriptsize} \emph {#1} \end {scriptsize}} \newcommand {\R }[0]{\ensuremath {\mathbb {R}}} \newcommand {\Rnul }[0]{\ensuremath {\mathbb {R}_0}} \newcommand {\Reen }[0]{\ensuremath {\mathbb {R}\setminus \{1\}}} \newcommand {\Rnuleen }[0]{\ensuremath {\mathbb {R}\setminus \{0,1\}}} \newcommand {\Rplus }[0]{\ensuremath {\mathbb {R}^+}} \newcommand {\Rmin }[0]{\ensuremath {\mathbb {R}^-}} \newcommand {\Rnulplus }[0]{\ensuremath {\mathbb {R}_0^+}} \newcommand {\Rnulmin }[0]{\ensuremath {\mathbb {R}_0^-}} \newcommand {\Rnuleenplus }[0]{\ensuremath {\mathbb {R}^+\setminus \{0,1\}}} \newcommand {\N }[0]{\ensuremath {\mathbb {N}}} \newcommand {\Nnul }[0]{\ensuremath {\mathbb {N}_0}} \newcommand {\Z }[0]{\ensuremath {\mathbb {Z}}} \newcommand {\Znul }[0]{\ensuremath {\mathbb {Z}_0}} \newcommand {\Zplus }[0]{\ensuremath {\mathbb {Z}^+}} \newcommand {\Zmin }[0]{\ensuremath {\mathbb {Z}^-}} \newcommand {\Znulplus }[0]{\ensuremath {\mathbb {Z}_0^+}} \newcommand {\Znulmin }[0]{\ensuremath {\mathbb {Z}_0^-}} \newcommand {\C }[0]{\ensuremath {\mathbb {C}}} \newcommand {\Cnul }[0]{\ensuremath {\mathbb {C}_0}} \newcommand {\Cplus }[0]{\ensuremath {\mathbb {C}^+}} \newcommand {\Cmin }[0]{\ensuremath {\mathbb {C}^-}} \newcommand {\Cnulplus }[0]{\ensuremath {\mathbb {C}_0^+}} \newcommand {\Cnulmin }[0]{\ensuremath {\mathbb {C}_0^-}} \newcommand {\Q }[0]{\ensuremath {\mathbb {Q}}} \newcommand {\Qnul }[0]{\ensuremath {\mathbb {Q}_0}} \newcommand {\Qplus }[0]{\ensuremath {\mathbb {Q}^+}} \newcommand {\Qmin }[0]{\ensuremath {\mathbb {Q}^-}} \newcommand {\Qnulplus }[0]{\ensuremath {\mathbb {Q}_0^+}} \newcommand {\Qnulmin }[0]{\ensuremath {\mathbb {Q}_0^-}} \newcommand {\perdef }[0]{\overset {\mathrm {def}}{=}} \newcommand {\pernot }[0]{\overset {\mathrm {notatie}}{=}} \newcommand {\perinderdaad }[0]{\overset {!}{=}} \newcommand {\perhaps }[0]{\overset {?}{=}} \newcommand {\degree }[0]{^\circ } \DeclareMathOperator {\dom }{dom} \DeclareMathOperator {\codom }{codom} \DeclareMathOperator {\bld }{bld} \DeclareMathOperator {\graf }{graf} \DeclareMathOperator {\rico }{rico} \DeclareMathOperator {\co }{co} \DeclareMathOperator {\gr }{gr} \DeclareMathOperator {\bgsin }{bgsin} \DeclareMathOperator {\bgcos }{bgcos} \DeclareMathOperator {\bgtan }{bgtan} \DeclareMathOperator {\bgcot }{bgcot} \DeclareMathOperator {\bgsinh }{bgsinh} \DeclareMathOperator {\bgcosh }{bgcosh} \DeclareMathOperator {\bgtanh }{bgtanh} \DeclareMathOperator {\bgcoth }{bgcoth} \newcommand {\d }[0]{\mathrm {d}} \newcommand {\dx }[0]{\d x} \newcommand {\dd }[1]{\frac {\mathrm {d}}{\mathrm {d}#1}} \newcommand {\ddx }[0]{\dd {x}} \newcommand {\afg }[1]{\frac {\mathrm {d}}{\mathrm {d}x} \left (#1\right ) } \newcommand {\xmshortabstract }[0]{} \newcommand {\theabstract }[0]{} \newcommand {\xmopje }[1]{\iftoggle {showxmopje}{#1}{}} \newcommand {\formulevb }[2]{ {\centering \par \begin {xmdiv}{xmformulevb} \begin {tabular}{lcl} \important {#1} & & {$#2$} \end {tabular} \end {xmdiv} } } \newcommand {\xmcolorbox }[2]{ \HCode {\Hnewline <div class="xmcolorbox">\Hnewline }#2\HCode {\Hnewline </div>\Hnewline } } \newcommand {\xmopmerking }[1]{ \HCode {\Hnewline <div class="xmopmerking">\Hnewline }#1\HCode {\Hnewline </div>\Hnewline } } \newcommand {\proofname }[0]{Bewijs} \newcommand {\xmonlineChoice }[1]{\pdfOnly {\wordchoicegiventrue }\wordChoice {#1}\pdfOnly {\wordchoicegivenfalse }} \newcommand {\onlineChoice }[1]{\pdfOnly {\wordchoicegiventrue }\wordChoice {#1}\pdfOnly {\wordchoicegivenfalse }} \newcommand {\TJa }[0]{\nlentext { Ja }{ Yes }} \newcommand {\TNee }[0]{\nlentext { Nee }{ No }} \newcommand {\TJuist }[0]{\nlentext { Juist }{ True }} \newcommand {\TFout }[0]{\nlentext { Fout }{ False }} \newcommand {\choiceTrue }[0]{{\wordChoice {\choice [correct]{\TJuist }\choice {\TFout }}}} \newcommand {\choiceFalse }[0]{{\wordChoice {\choice {\TJuist }\choice [correct]{\TFout }}}} \newcommand {\choiceYes }[0]{{\wordChoice {\choice [correct]{\TJa }\choice {\TNee }}}} \newcommand {\choiceNo }[0]{{\wordChoice {\choice {\TJa }\choice [correct]{\TNee }}}} \newcommand {\choiceEen }[0]{{\wordChoice {\choice [correct]{een }\choice {geen }}}} \newcommand {\choiceGeen }[0]{{\wordChoice {\choice {een }\choice [correct]{geen }}}} \newcommand {\choiceminimumverticalsize }[0]{\vphantom {$\tfrac {2}{2}$}} \newcommand {\setchoicedefanswer }[0]{ \ifdefined \HCode \else \let \inlinechoice \inlinechoicedefanswer \fi } \newcommand {\xmsection }[0]{\subsection } \newcommand {\xmsubsection }[0]{\subsubsection } \newcommand {\activitychapter }[1]{ \typeout {ACTIVITYCHAPTER #1} \chapterstyle \activity {#1} } \newcommand {\activitysection }[1]{ \typeout {ACTIVITYSECTION #1} \sectionstyle \activity {#1} } \newcommand {\practicesection }[1]{ \typeout {PRACTICESECTION #1} \sectionstyle \activity {#1} } \newcommand {\hypertarget }[1]{\HCode {<a class="ximera-label" id="#1"></a>}} \newcommand {\hyperlink }[2]{\HCode {<a class="reference reference-keeptext" href="\##1">}#2\HCode {</a>}} \newcommand {\figurename }[0]{Figuur} \newcommand {\tablename }[0]{Tabel} \newcommand {\printFull }[0]{ \hintstrue \handoutfalse \toggletrue {showonline} } \newcommand {\onlyOnline }[1]{\ifdefined \HCode #1\fi } \newcommand {\nl }[0]{\Hnewline } \newcommand {\basicOnly }[0]{} \newcommand {\basicSkip }[0]{} \newcommand {\tab }[0]{\quad } \newcommand {\instructorNotes }[0]{\setbox 0\vbox \bgroup } \newcommand {\nlen }[2]{#1} \newcommand {\nlentext }[2]{\text {#1}} \newcommand {\nlentextbf }[2]{\textbf {#1}} \newcommand {\TWaar }[0]{\nlentext { Waar }{ True }} \newcommand {\TOnwaar }[0]{\nlentext { Vals }{ False }} \newcommand {\Ten }[0]{\nlentext { en }{ and }} \newcommand {\Tof }[0]{\nlentext { of }{ or }} \newcommand {\Tdus }[0]{\nlentext { dus }{ so }} \newcommand {\Tendus }[0]{\nlentext { en dus }{ and thus }} \newcommand {\Tvooralle }[0]{\nlentext { voor alle }{ for all }} \newcommand {\Took }[0]{\nlentext { ook }{ also }} \newcommand {\Tals }[0]{\nlentext { als }{ when }} \newcommand {\Twant }[0]{\nlentext { want }{ as }} \newcommand {\Tmaal }[0]{\nlentext { maal }{ times }} \newcommand {\Toptellen }[0]{\nlentext { optellen }{ add }} \newcommand {\Tde }[0]{\nlentext { de }{ the }} \newcommand {\Thet }[0]{\nlentext { het }{ the }} \newcommand {\Tis }[0]{\nlentext { is }{ is }} \newcommand {\Tmet }[0]{\nlentext { met }{ where }} \newcommand {\Tnooit }[0]{\nlentext { nooit }{ never }} \newcommand {\Tmaar }[0]{\nlentext { maar }{ but }} \newcommand {\Tniet }[0]{\nlentext { niet }{ not }} \newcommand {\Tuit }[0]{\nlentext { uit }{ from }} \newcommand {\Ttov }[0]{\nlentext { t.o.v. }{ w.r.t. }} \newcommand {\Tzodat }[0]{\nlentext { zodat }{ such that }} \newcommand {\Tdeth }[0]{\nlentext {de }{th }} \newcommand {\Tomdat }[0]{\nlentext {omdat }{because }} \newcommand {\Im }[1]{\text {Im}#1} \newcommand {\Re }[1]{\text {Re}#1} \newcommand {\xmdivEnvironmentStart }[3]{\ifdefined \HCode \HCode {\Hnewline <div class="#2">}\fi \problemEnvironmentStart {#1}{#3}} \newcommand {\xmdivEnvironmentEnd }[0]{\problemEnvironmentEnd \ifdefined \HCode \HCode {\Hnewline </div>}\fi } \newcommand {\xmFixFormatLength }[0]{} \newcommand {\xmFixFormatPosition }[0]{l} \newcommand {\declaretranslationfallback }[0]{\declaretranslation {fallback}} \newcommand {\definetranslationfallback }[0]{\definetranslation {fallback}} \newcommand {\redefinetranslationfallback }[0]{\redefinetranslation {fallback}} \newcommand {\addtranslationfallback }[0]{\addtranslation {fallback}} \newcommand {\kader }[1]{\framebox {\begin {minipage}[t]{0.98\textwidth }#1\end {minipage}}} \newcommand {\cleartoleftpage }[0]{\clearpage \ifodd \value {page}\hbox {}\newpage \fi } \newcommand {\xmorganisatienaam }[0]{} \newcommand {\xmcursusnaam }[0]{} \newcommand {\xmafdelingsnaam }[0]{} \newcommand {\xmsource }[0]{ \ifonlineTF { \begin {xmdiv}{xmsource} Gebaseerd op cursus SPC 2021 \end {xmdiv} }{ \renewcommand {\xmorganisatienaam }{{\smaller Gebaseerd op cursus SPC 2021}} } } \newcommand {\fixmelogo }[0]{\textsf {FiXme}} \newcommand {\FXProvidesLayout }[1]{\ProvidesPackage {fxlayout#1}} \newcommand {\fixmeindexname }[0]{\fixmelogo } \newcommand {\FXProvidesEnvLayout }[1]{\ProvidesPackage {fxenvlayout#1}} \newcommand {\FXEnvLayoutPlainEnd }[2]{} \newcommand {\FXProvidesTargetLayout }[1]{\ProvidesPackage {fxtargetlayout#1}} \newcommand {\fxenglishnotename }[0]{Note} \newcommand {\fxenglishnotesname }[0]{Notes} \newcommand {\fxenglishwarningname }[0]{Warning} \newcommand {\fxenglishwarningsname }[0]{Warnings} \newcommand {\fxenglisherrorname }[0]{Error} \newcommand {\fxenglisherrorsname }[0]{Errors} \newcommand {\fxenglishfatalname }[0]{Fatal} \newcommand {\fxenglishfatalsname }[0]{Fatal errors} \newcommand {\englishlistfixmename }[0]{List of Corrections} \newcommand {\fxfrenchnotename }[0]{Note} \newcommand {\fxfrenchnotesname }[0]{Notes} \newcommand {\fxfrenchwarningname }[0]{Attention} \newcommand {\fxfrenchwarningsname }[0]{Avertissements} \newcommand {\fxfrencherrorname }[0]{Erreur} \newcommand {\fxfrencherrorsname }[0]{Erreurs} \newcommand {\fxfrenchfatalname }[0]{Fatal} \newcommand {\fxfrenchfatalsname }[0]{Erreurs fatales} \newcommand {\frenchlistfixmename }[0]{Liste des Corrections} \newcommand {\fxspanishnotename }[0]{Nota} \newcommand {\fxspanishnotesname }[0]{Notas} \newcommand {\fxspanishwarningname }[0]{Aviso} \newcommand {\fxspanishwarningsname }[0]{Avisos} \newcommand {\fxspanisherrorname }[0]{Error} \newcommand {\fxspanisherrorsname }[0]{Errores} \newcommand {\fxspanishfatalname }[0]{Fatal} \newcommand {\fxspanishfatalsname }[0]{Errores fatales} \newcommand {\spanishlistfixmename }[0]{Lista de Correcciones} \newcommand {\fxitaliannotename }[0]{Nota} \newcommand {\fxitaliannotesname }[0]{Note} \newcommand {\fxitalianwarningname }[0]{Avviso} \newcommand {\fxitalianwarningsname }[0]{Avvisi} \newcommand {\fxitalianerrorname }[0]{Errore} \newcommand {\fxitalianerrorsname }[0]{Errori} \newcommand {\fxitalianfatalname }[0]{Fatale} \newcommand {\fxitalianfatalsname }[0]{Errori fatali} \newcommand {\italianlistfixmename }[0]{Corrigenda} \newcommand {\fxgermannotename }[0]{Anm} \newcommand {\fxgermannotesname }[0]{Anmerkungen} \newcommand {\fxgermanwarningname }[0]{Warnung} \newcommand {\fxgermanwarningsname }[0]{Warnungen} \newcommand {\fxgermanerrorname }[0]{Fehler} \newcommand {\fxgermanerrorsname }[0]{Fehler} \newcommand {\fxgermanfatalname }[0]{Verh\"angnisvoll} \newcommand {\fxgermanfatalsname }[0]{Verh\"angnisvolle fehler} \newcommand {\germanlistfixmename }[0]{Verzeichnis der Korrekturen} \newcommand {\fxdanishnotename }[0]{Note} \newcommand {\fxdanishnotesname }[0]{Noter} \newcommand {\fxdanishwarningname }[0]{Advarsel} \newcommand {\fxdanishwarningsname }[0]{Advarsler} \newcommand {\fxdanisherrorname }[0]{Fejl} \newcommand {\fxdanisherrorsname }[0]{Fejl} \newcommand {\fxdanishfatalname }[0]{Fatal} \newcommand {\fxdanishfatalsname }[0]{Fatale fejl} \newcommand {\danishlistfixmename }[0]{Rettelser} \newcommand {\fxcroatiannotename }[0]{Poruka} \newcommand {\fxcroatiannotesname }[0]{Poruke} \newcommand {\fxcroatianwarningname }[0]{Upozorenja} \newcommand {\fxcroatianwarningsname }[0]{Upozorenje} \newcommand {\fxcroatianerrorname }[0]{Gre\v ska} \newcommand {\fxcroatianerrorsname }[0]{Greske} \newcommand {\fxcroatianfatalname }[0]{Fatalan} \newcommand {\fxcroatianfatalsname }[0]{Kobne gre\v ske} \newcommand {\croatianlistfixmename }[0]{Popis korekcija} \newcommand {\FXProvidesTheme }[1]{\ProvidesPackage {fxtheme#1}} \newcommand {\fxusetheme }[1]{\usepackage {fxtheme#1}} \newcommand {\FXEnvLayoutColorEnd }[2]{} \newcommand {\xmDefaultPrintstyle }[0]{xmPrintstyle.sty} \newcommand {\luastring }[1]{"\luatexluaescapestring {#1}"} \newcommand {\luastringO }[1]{\luastring {\unexpanded \expandafter {#1}}} \newcommand {\luastringN }[1]{\luastring {\unexpanded {#1}}} \newcommand {\RestoreMathJaxEnvironment }[1]{\expandafter \let \csname #1\expandafter \endcsname \csname mathjax-#1\endcsname \expandafter \let \csname end#1\expandafter \endcsname \csname mathjax-end#1\endcsname } \newcommand {\DeclareMicrotypeVariants }[1]{} \newcommand {\DeclareMicrotypeAlias }[2]{} \newcommand {\LoadMicrotypeFile }[1]{} \newcommand {\DeclareMicrotypeFilePrefix }[1]{} \newcommand {\DeclareMicrotypeBabelHook }[2]{} \newcommand {\microtypesetup }[1]{} \newcommand {\microtypecontext }[1]{} \newcommand {\textmicrotypecontext }[2]{#2} \newcommand {\leftprotrusion }[1]{#1} \newcommand {\rightprotrusion }[1]{#1} \newcommand {\noprotrusionifhmode }[0]{} \newcommand {\lsstyle }[0]{} \newcommand {\lslig }[1]{#1} \newcommand {\maketitle }[0]{} \newcommand {\problem }[0]{ } \newcommand {\exercise }[0]{ } \newcommand {\question }[0]{ } \newcommand {\exploration }[0]{ } \newcommand {\ConfigureTheoremEnv }[1]{\renewenvironment {#1}[1][]{\refstepcounter {problem}\ifthenelse {\equal {###1}{}}{}{\HCode {<span class="theorem-like-title">}###1\HCode {</span>}}}{} \ConfigureEnv {#1}{\stepcounter {identification}\ifvmode \IgnorePar \fi \EndP \HCode {<div class="theorem-like problem-environment #1" id="problem\arabic {identification}" titletext=" \GetTranslation {#1}">}}{\ifvmode \IgnorePar \fi \EndP \HCode {</div>}\IgnoreIndent }{}{}} \newcommand {\dialogue }[0]{\begin {description}} \newcommand {\foldable }[0]{\stepcounter {identification}\ifvmode \IgnorePar \fi \EndP \HCode {<div id="foldable\arabic {identification}" class="foldable">}} \newcommand {\unfoldable }[1]{\HCode {<span class="unfoldable">}#1\HCode {</span>}} \newcommand {\selectAll }[0]{\refstepcounter {problem}} \newcommand {\freeResponse }[0]{\refstepcounter {problem}} \newcommand {\javascript }[0]{\NoFonts } \newcommand {\sageCell }[0]{\NoFonts } \newcommand {\sageOutput }[0]{\NoFonts } \newcommand {\sagesilent }[0]{\NoFonts } \newcommand {\ungraded }[0]{\ifvmode \IgnorePar \fi \EndP \HCode {<div class="ungraded">}\IgnoreIndent } \newcommand {\accordion }[0]{\ifvmode \IgnorePar \fi \EndP \HCode {<div class="accordion">} } \newcommand {\expandable }[2]{\stepcounter {identification}\ifvmode \IgnorePar \fi \EndP \HCode {<div class="accordion">\Hnewline }\HCode {<h3 class="#1">}#2\HCode {</h3>\Hnewline }\HCode {<div id="accordion-item\arabic {identification}" class="accordion-item #1-content">\Hnewline } } \newcommand {\paragraph }[1]{\HCode {<span class="paragraphHead">}#1\HCode {</span>}\par \IgnorePar } \newcommand {\subparagraph }[1]{\HCode {<span class="subparagraphHead">}#1\HCode {</span>}\par \IgnorePar } \newcommand {\outcome }[1]{\HCode {<span class="learning-outcome">#1</span>} } \newcommand {\javascriptCode }[0]{\NoFonts } \newcommand {\ref }[1]{\HCode {<a class="reference" href="\##1">#1</a>}} \newcommand {\choicesom }[0]{{\wordChoice {\choice [correct]{som}\choice {product}}}} \newcommand {\choiceprod }[0]{{\wordChoice {\choice {som}\choice [correct]{product}}}} \newcommand {\choiceuit }[0]{{\wordChoice {\choice [correct]{uitwerken}\choice {ontbinden}\choice {geen van beide}}}} \newcommand {\choiceont }[0]{{\wordChoice {\choice {uitwerken}\choice [correct]{ontbinden}\choice {geen van beide}}}} \newcommand {\choiceand }[0]{{\wordChoice {\choice {uitwerken}\choice {ontbinden}\choice [correct]{geen van beide}}}} \newcommand {\xmFixFormatLength }[0]{31ex}$

Is de gegeven uitdrukking te beschouwen als een product of als een som?

$ a \cdot b \cdot c + 1 $ is een somproduct

$ a \cdot b \cdot c + 1 $ is de som van de termen $ a \cdot b \cdot c $ en $ 1 $

$ (x + y)^2 $ is een somproduct

$ (x + y)^2 $ is een macht, en dus het product van $x+y$ met zichzelf.

$ a \cdot (4b + c) $ is een somproduct

$ x \cdot y + x \cdot z $ is een somproduct

$ a \cdot b \cdot (c + 1) $ is een somproduct

Onderzoek telkens of je van links naar rechts ontbindt, uitwerkt, of geen van beide.

$(3a+b)^2 = 9a^2 + 6ab + b^2 $ uitwerkenontbindengeen van beide

$9a^2 + 6ab + b^2 = (3a+b)^2 $ uitwerkenontbindengeen van beide

$4(x^2 - y^2) = 4x^2 - 4y^2 $ uitwerkenontbindengeen van beide

$4(x^2 - y^2) = 4(x - y)(x + y) $ uitwerkenontbindengeen van beide

$3x^3 - 3x + 1 = 3x(x^2 - 1) + 1 = 3x(x - 1)(x + 1) + 1 $ uitwerkenontbindengeen van beide

$27a^3 - 27a^2 b + 9ab^2 - b^3 = (3a - b)^3 $ uitwerkenontbindengeen van beide

Ontbind in factoren door af te zonderen.

$\sqrt {5} a - 3\sqrt {5} b =\answer [onlineshowanswerbutton]{\sqrt {5} (a - 3b) } $

$\sqrt {7} x^2 + 2\sqrt {7} =\answer [onlineshowanswerbutton]{\sqrt {7} (x^2 + 2)} $

$15a^2 b + 12ab - 9ab^3 =\answer [onlineshowanswerbutton]{3ab(5a + 4 - 3b^2)} $

$x(x+4) - 2(x+4) =\answer [onlineshowanswerbutton]{(x + 4)(x - 2) } $

$2a(3a+1) + 5b(3a+1) =\answer [onlineshowanswerbutton]{(3a + 1)(2a + 5b) } $

$(x-1)(x+3) - 5(x+3) =\answer [onlineshowanswerbutton]{(x + 3)(x - 6) } $

$(y^2+3)(y-2) + y-2 =\answer [onlineshowanswerbutton]{(y - 2)(y^2 + 4) } $

$(a+4)(3a+2) - 3a - 2 =\answer [onlineshowanswerbutton]{(3a + 2)(a + 3) } $

$(x-3)(2x+3) - (4x+1)(2x+3) =\answer [onlineshowanswerbutton]{(2x + 3)(-3x - 4) } $

$3(x-1) + (x-1)^2 =\answer [onlineshowanswerbutton]{(x - 1)(x + 2) } $

Vul aan tot een merkwaardig product, indien mogelijk, en ontbind in dat geval.

$9x^2 + {\answer {24}} x + 16 $ $= \answer [onlineshowanswerbutton]{(3x+4)^2}$

$a^2 - 6ab + {\answer {9b^2 }} $ $= \answer [onlineshowanswerbutton]{(a-3b)^2}$

$ {\answer {49}} y^4 - 42y^2 + 9 $ $= \answer [onlineshowanswerbutton]{(7y^2+3)^2}$

$121x^2 - {\answer {0}} x - 4 $ $= \answer [onlineshowanswerbutton]{(11x-2)(11x+2)}$

$-81 - 4x^2 + {\answer {36x }} $ $= \answer [onlineshowanswerbutton]{-(2x-9)^2}$

Ontbind de tweetermen in factoren

$ x^2 - 121 =\answer [onlineshowanswerbutton]{(x - 11)(x + 11) } $

$ 9x^2 + 16 =\answer [onlineshowanswerbutton]{\text {geen oplossing} } $

$ 16x^2 - 25 =\answer [onlineshowanswerbutton]{(4x - 5)(4x + 5) } $

$ 4 - 9y^2 =\answer [onlineshowanswerbutton]{(2 - 3y)(2 + 3y) } $

$ 36a^2 - 5 =\answer [onlineshowanswerbutton]{(6a - \sqrt {5})(6a + \sqrt {5}) } $

$ 4a^2 - 81b^2 =\answer [onlineshowanswerbutton]{(2a - 9b)(2a + 9b) } $

$ 144x^2 - 49y^4 =\answer [onlineshowanswerbutton]{(12x - 7y^2)(12x + 7y^2) } $

$ 5x^2 - 3 =\answer [onlineshowanswerbutton]{(\sqrt {5}x - \sqrt {3})(\sqrt {5}x + \sqrt {3})} $

$ -4x^2 + 25y^2 =\answer [onlineshowanswerbutton]{(5y - 2x)(5y + 2x) } $

$ -1 + 7x^2 =\answer [onlineshowanswerbutton]{(\sqrt {7}x - 1)(\sqrt {7}x + 1) } $

Ontbind de drietermen in factoren

$ 25x^2 - 20x + 4 =\answer [onlineshowanswerbutton]{(5x - 2)^2 } $

$ x^4 + 6x^2 + 9 =\answer [onlineshowanswerbutton]{(x^2 + 3)^2 } $

$ 25a^2 - 30ab + 9b^2 =\answer [onlineshowanswerbutton]{(5a - 3b)^2 } $

$ 81 + 126t + 49t^2 =\answer [onlineshowanswerbutton]{(9 + 7t)^2 } $

$ 121x^2 + 66xy^2 + 9y^4 =\answer [onlineshowanswerbutton]{(11x + 3y^2)^2 } $

Ontbind de viertermen in factoren door termen samen te nemen.

$ 4x + 4y + ax + ay =\answer [onlineshowanswerbutton]{(x + y)(4 + a) } $

$ 3x + 5y + 6xy + 10y^2 =\answer [onlineshowanswerbutton]{(3x + 5y)(1 + 2y) } $

$ 2ax + 3a - 2bx - 3b =\answer [onlineshowanswerbutton]{(2x + 3)(a - b) } $

$ 7ab + 14a + b + 2 =\answer [onlineshowanswerbutton]{(b + 2)(7a + 1) } $

$ 1 - a - b + ab =\answer [onlineshowanswerbutton]{(1 - a)(1 - b) } $

$ 5x^3 - x^2 + 35x - 7 =\answer [onlineshowanswerbutton]{(5x - 1)(x^2 + 7) } $

$ x^3 + x^2 + x + 1 =\answer [onlineshowanswerbutton]{(x + 1)(x^2 + 1) } $

$ 2x^6 + 3x^4 + 6x^2 + 9 =\answer [onlineshowanswerbutton]{(2x^2 + 3)(x^4 + 3)} $

$ a^2 - 6b - 2ab + 3a =\answer [onlineshowanswerbutton]{(a - 2b)(a + 3) } $

$ 12ab^2 - 1 - 4b^2 + 3a =\answer [onlineshowanswerbutton]{(3a - 1)(4b^2 + 1) } $