I denne artikel vil jeg fokusere på matematikprogrammet Geogebra. Hvis man er interesseret i matematikprogrammet kan man med fordel downloade det via følgende side:
https://geogebra.da.softonic.com/
Geogebra er et stærkt visuelt matematikprogram, og så er det tilmed gratis! For studerende kan Geogebra med fordel anvendes til den skriftlige matematikeksamen med hjælpemidler uanset, hvilket niveau man er på. Det eneste det kræver er, at man sætter sig en i de basale funktioner som programmet kan. Det er lidt ligesom at lære at bruge en lommeregner eller et CAS værktøj. Her kræver det også at man sætter sig ind i hvad programmet eller for den sags skyld hvad lommeregneren kan. Men har du først tilegnet dig de basale funktioner i Geogebra, så står du stærkt!
Geogebra er er rigtigt godt værktøj til eksempelvis at kontrollere at man har regnet rigtigt, og at gøre sin skriftlige eksamensbesvarelse grafisk ”outstanding”. Formålet med denne artikel, er at vise nogle af de basale funktioner i Geogebra, og forhåbentlig hjælpe på den matematiske forståelse.
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Anvendelse af Geogebra til en eksamensopgave med geometri/trigonometri
Herunder vil jeg vise to eksempler på, hvad man kan bruge Geogebra til, såfremt man får en opgave i emnet.
Eksempel 1 er et eksempel på en eksamensopgave, hvor følgende opgavetekst lyder:
Herover ses en trekant ABC med 2 vinkler og en side angivet.
Bestem vinkel B, siden BC og arealet af trekant ABC (standard eksamensopgave på STX niveau)
Vi kan bestemme vinkel B i trekanten. Vinkel B kan beregnes som 180 grader – Vinkel A – Vinkel C. Vinkel B = 59,9 grader. Da vi nu kender alle tre vinkler og en side kan vi tegne trekanten i Geogebra. Det har jeg gjort i nedenstående video. Det smarte er at når først vi har tegnet trekanten i Geogebra, så bliver alle trekantens oplysninger tilgængelige :o) På den måde kan man efterprøve/sammenligne sine beregninger/resultater for at se om de er korrekte. Kan det være bedre og nemmere? Det eneste det kræver er, at man sætter sig ind i de basale funktioner i Geogebra.
Et andet eksempel kunne være en trekant ABC, hvor man kender alle sidelængderne, hvor AB = 10, AC = 8 og BC = 7. I videoen herunder har jeg vist, hvordan man kan tegne trekanten ABC med de givne sidelængder.
Jeg håber ovenstående videoer har givet inspiration til, hvorledes man kan anvende Geogebra når man har en opgave i geometri/trigonometri, og hvordan man relativt hurtigt kan finde sidelængder, vinkler og beregne arealer.
Træn eksamensopgaver i matematik og få en højere karakter. Opret dig med Facebook på 2 sekunder! Kom igang gratis!
Anvendelse af Geogebra til regression
Geogebra er også et rigtigt stærkt værktøj, hvis man gerne vil lave lineær, eksponentiel eller potens regression. Igen vil jeg tage udgangspunkt i et eksempel fra en eksamensopgave i eksponentiel regression:
Eksempel på en eksamensopgave på STX niveau
Nordisk Film har i 2014 udgivet spillefilmen ”Kartellet”. Tabellen herunder viser omsætningen for denne spillefilm efter udgivelsen i de danske biografer.
Denne sammenhæng kan med god tilnærmelse beskrives ved funktionen:
f(x) = b . ax
hvor x er antal uger efter udgivelsen, og f(x) er indtjeningen pr. uge i millioner kr.
I nedenstående video har jeg vist, hvorledes man ud fra eksemplet kan lave eksponentiel regression på baggrund af opgavetekstens oplysninger. Se videoen herunder:
I videoen har jeg vist, hvor hurtigt man kan lave lineær, eksponentiel eller potens regression. Når først man har indtastet sine punkter, så får man ”serveret” funktionsforskriften, hvilket er genialt hvis man vil efterprøve sine beregninger.
Anvendelse af Geogebra til polynomier/ligninger og integral beregning
I dette afsnit vil jeg gerne vise, at Geogebra også kan anvendes til polynomier/ligninger. Man kan hvis man indsætter et polynomium i Geogebra få en grafisk illustration af polynomiet på en pæn og overskuelig måde. I næste video, skal vi se nærmere på følgende polynomier:
f(x) = x2 – 4
g(x) = 2x3 + 3x2 + 2
t(x) = 2x – 1
Jeg vil vise hvordan man tegner funktionerne i Geogebra samt hvorledes man kan lave integral beregninger ved simple kommandoer.
Vi har i videoen vist hvorledes man kan tegne funktioner og hvordan man ved hjælp af Geogebra kan lave integral beregninger.
Jeg håber denne artikel har fanget din opmærksomhed, og givet dig lidt inspiration til hvordan Geogebra kan anvendes, og hvordan du kan lave gode grafiske illustrationer til eksempelvis en skriftlig matematikaflevering eller til den skriftlige matematikeksamen.
Det vi har vist her, er kun en mikroskopisk brøkdel af hvad Geogebra kan, og det er stort set kun fantasien der sætter grænser. Jeg har et godt råd, kom i gang med at anvende Geogebra nu!
Det var alt for nu – vi håber i har fået tips og tricks til, hvordan i bliver bedre til GeoGebra. Kom gerne med kommentare 🙂
Vil du læse flere artikler, så har vi herunder samlet en del som kunne være interessante for dig 🙂
Læs hvordan Sam fik 10 til matematik eksamen, Alt hvad du skal vide om vektorregning, Bliv bedre til potensfunktioner
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