// Numbas version: exam_results_page_options {"name": "Examen Ajla", "metadata": {"description": "

Voorbeeldvragen examencommissie

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Hoogte, valtijd en gemiddelde snelheid berekenen.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Je laat een bal van een toren vallen. De hoogte $h$ van de bal ten opzichte van de grond (in meter) na $t$ seconden wordt beschreven door de functie met voorschrift $h(t)=-4,9t²+\\var{hoogte}$.

", "advice": "

De hoogte is de constante term uit de vergelijking (op $t=0$ bevindt de bal zich bovenaan de toren), dus {hoogte} m.

\n

De valtijd bedraagt $h = 0 <=> 0 = -4,9t² + \\var{hoogte} <=> t² = \\frac{\\var{hoogte}}{4,9} <=> t = \\sqrt{\\frac{\\var{hoogte}}{4,9}}=\\var{formatnumber(precround(grond,1),\"plain-eu\")}$ s.

\n

De gemiddelde snelheid is het differentiequotiënt over het interval $[0; \\var{tijd}]$.

\n

$\\frac{f(\\var{tijd})-f(0)}{\\var{tijd}-0}=\\frac{-4,9 \\cdot \\var{tijd}²+\\var{hoogte}-\\var{hoogte}}{\\var{tijd}}=-4,9 \\cdot \\var{tijd} = \\var{formatnumber(precround(snelheid,2),\"plain-eu\")}$$\\frac{m}{s}$

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Hoe hoog is de toren?

\n

[[0]] m

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Na hoeveel seconden raakt de steen de grond?

\n

[[0]] s

\n

Geef je antwoord op 1 decimaal nauwkeurig.

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Wat is de gemiddelde snelheid van de bal in de eerste {formatnumber(tijd,\"plain-eu\")} seconden van de val?

\n

Geef je antwoord op twee decimalen nauwkeurig.

\n

De gemiddelde snelheid van de bal in de eerste {formatnumber(tijd,\"plain-eu\")} seconden van de val bedraagt [[0]] $\\frac{m}{s}$.

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Multiple choice

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{geogebra_applet('tfg75cyr',[['b',b]],[])}

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Welk punt op de goniometrische cirkel levert het punt P op?

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Voorschrift dalende exponentiële functie.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Het aantal mensen dat zich een reclame op Instagram herinnert, neemt exponentieel af in de loop van de tijd.

\n

Je ziet in de tabel het aantal mensen (in %) dat zich de rickame herinnert $t$ dagen na bekijken.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$t$13
$N(t)${percentage1} %{formatnumber(percentage3,\"plain-eu\")} %
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Wat is het voorschrift $N(t)$ van de functie die het aantal mensen $N$ (in %) uitdrukt in functie van de tijd $t$ in dagen, met $t=0$ de dag van bekijken?

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Schopafstand berekenen en controleren of de bal in het doel belandt.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

{naam} is {afstand} m verwijderd van het doel en ziet dat de keeper te ver uit hun doel staat. {die} probeert de bal door een lob over de keeper te krijgen. 
De grafiek van de functie met voorschrift $h(x)=\\simplify{-{b}/200*x²}+\\simplify{({afstand}+1)/20*x}$ stelt de baan van de bal voor, met $x$ de afstand (in m) tot {naam} en $h$ de hoogte (in m) van de bal ten opzichte van de grond.

", "advice": "

Om de schopafstand te bepalen, zoek de nulwaarde van de functie.

\n

De positie van {naam} is $x=0$. De andere nulwaarde is $x=\\simplify{({afstand}+1)/20}*\\simplify{200/{b}}=\\simplify{({afstand}+1)/20*200/{b}}=\\var{formatnumber(precround(schopafstand,1),\"plain-eu\")}$

\n

Om te bepalen of de bal in de goal belandt, bereken je de hoogte op een afstand {afstand} m.

\n

Dus $h(\\var{afstand})=\\simplify{-{b}/200*{afstand}²}+\\simplify{({afstand}+1)/20*{afstand}}=\\var{formatnumber(hoogte,\"plain-eu\")}$.

\n

Het is dus {welofniet} goal.

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Wat is de afstand tussen {naam} en het punt waar de bal de grond weer raakt.

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Het doel is 2,54 m hoog.
Belandt de bal in het doel?

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Antwoord in °C. Hoogte moet omgezet worden in km.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Water kookt bij een temperatuur van 100°C op zeeniveau. Op de Mount Everest (hoogte 8848 m) kookt water echter al bij een temperatuur van 69°C. Dit komt doordat de luchtdruk afneemt naarmate de hoogte stijgt. 
Benaderend kunnen we het verband tussen de kooktemperatuur van water en de hoogte voorstellen door het voorschrift $T(h) = -3,5036h+100$
met $T$ de kooktemperatuur (in °C) en $h$ de hoogte (in km).

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Bereken de kooktemperatuur van water op de Kilimanjaro in Tanzania (hoogte {hoogte} m).

\n

Bereken de kooktemperatuur van water in Kathmandu in Nepal (hoogte {hoogte} m).

\n

Antwoord op 1 °C nauwkeurig.

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Korting en nieuwe prijs berekenen op basis van oude prijs.

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Stel dat je {procent} % korting krijgt op een nieuwe jeansbroek.

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Welke van onderstaande voorschriften geeft de korting $y$ in functie van de oude prijs $x$?

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Welke van onderstaande voorschriften geeft de nieuwe prijs $y$ in functie van de oude prijs $x$?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$y = ${formatnumber(groeifactor,\"plain-eu\")}$x $", "$y = x - ${formatnumber(groeifactor,\"plain-eu\")}", "$y = ${formatnumber(kortingfactor,\"plain-eu\")}$x $", "$y = x-${formatnumber(kortingfactor,\"plain-eu\")}"], "matrix": ["1", 0, "0", 0], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vraagstuk notaris bijkomende kosten", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Hans Denayer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18121/"}], "tags": [], "metadata": {"description": "

Voorschrift opstellen en aankoopprijs berekenen uit totale prijs.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Bij de aankoopprijs van een woning met men nog ongeveer {formatnumber(kosten,\"plain-eu\")} % bijkomende kosten rekenen (registratie- en notariskosten).

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Als $x$ de aankoopprijs is, stel dan een functievoorschrift op voor de bijkomende kosten.

\n

Vul de formule in die je gebruikt om het voorschrift te bepalen, of direct de uitkomst.

\n

Gebruik een punt als komma.

", "answer": "({kosten}/100)*x", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Als $x$ de aankoopprijs is, stel dan een functievoorschrift op voor de totale kosten.

\n

Vul de formule in die je gebruikt om het voorschrift te bepalen, of direct de uitkomst.

\n

Gebruik een punt als komma.

", "answer": "(1+{kosten}/100)*x", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": [{"name": "x", "value": ""}]}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Als je in totaal € {kostprijs} moet betalen, wat was dan de aankoopprijs?

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Tijd bepalen in uur en minuten.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Het aantal bezoekers dat zich op een zomerse dag in een pretpark bevindt, kan je voorstellen met de functie:

\n

$n(t)=-\\var{a}t³+\\var{b}t²+\\var{c}t$ voor $0\\le t \\le10$ 

\n

met n het aantal bezoekers en t de tijd in uren vanaf 10 uur 's ochtends.

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Wanneer waren er {bezoekers} bezoekers die avond?

\n

Rond je resultaat af op de minuut.

\n

Om [[0]]h [[1]] waren er {bezoekers} bezoekers in het pretpark.

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Vul de x-waarden van de extrema in.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Bekijk volgende grafische voorstelling van de reële functie $f$.

\n

{{geogebra_applet('zxvx7aks',defs,[])}}

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Voor welke $x$-waarden vind je de extrema van de functie $f$?

\n

$x=$[[0]] en $x=$[[1]]

\n

Vul eerst de kleinste waarde in en dan de grootste waarde.

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Zoek het voorschrift van de even functies.

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Bepaal welke van onderstaande functies even zijn. Er zijn meerdere antwoorden mogelijk.

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Parameters bepalen van y=b*a^x + c

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

{geogebra_applet('e3gkrhkp',defs,[])}

\n

Zoek het voorschrift van de vorm {latex('y=b \\\\cdot a^x +c')}

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a=[[0]]

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b=[[0]]

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b", "maxValue": "b", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": true, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

c=[[0]]

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "c", "maxValue": "c", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en", "plain-eu"], "correctAnswerStyle": "plain-eu"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vraagstuk exponenti\u00eble functie", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Hans Denayer", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18121/"}], "tags": [], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "

Je plaatst een kapitaal van € {startkapitaal} op een spaarrekening met een rente van {formatnumber(rente,\"plain-eu\")} % per maand.

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Hoeveel bedraagt de rentevoet op jaarbasis (in procent)?

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Hoeveel staat er op de spaarrekening na 5 jaar?

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Na hoeveel jaar is het kapitaal verdubbeld? Rond af op 1 cijfer na de komma.

\n

Maak gebruik van GeoGebra om deze vraag op te lossen: https://www.geogebra.org/calculator

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Op basis van de grafiek even of oneven beoordelen.

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Bekijk onderstaande grafieken. Antwoord of de functies even of oneven, even en oneven of geen van beide zijn.

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