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Gør beregning af indekstal nemt – se her og lær hvordan!

I denne artikel kigger vi nærmere på beregning af indekstal. Vi vil med denne artikel gøre den studerende i stand til at beregne indekstal i eksamens øjemed. Til den skriftlige matematik eksamen kan der komme tre varianter af emnet indekstal. Den ene variant er selve beregningen af et indekstal. Den anden variant er, at bestemme en pris, antal etc. ud fra et indekstal, og sidste variant går på en sammenligning mellem tal beregnet ud fra indekstal (eller direkte sammenligning af indekstal). Vi vil i de efterfølgende afsnit gennemgå de tre varianter ved hjælp af opgaver som kunne have været eksamensopgaver.

Eksempel på en eksamensopgave, når man skal beregne et indekstal

Tabellen herunder viser den månedlig leasing ydelse på en BMW 320 i år 2000, år 2005 og år 2010

Indekstal 1

Bestem indekstallene når det oplyses, at basisåret er år 2000.

Et indekstal beregnes ud fra følgende formel:

Indekstal 2

Da det oplyses at basisåret er år 2000 betyder det, at indekstallet er 100. Indekstallet er altid 100 i basisåret. Da vi nu ved at indekstallet i basisåret er 100 beregner vi indekstallet for år 2005 herunder:

Indekstal 3

Nu har vi indekstallene for år 2000 og år 2005. Vi beregner indekstallet for år 2010.

Indekstal 4

Vi har nu indekstallene for alle årene. Vi kan nu opstille en tabel som viser indekstallene for den månedlig ydelse i år 2000, år 2005 og år 2010.

Indekstal 5

 

Træn endnu flere opgaver i indekstal og bliv endnu bedre. Skamrost matematik træner. 9 ud af 10 får en bedre karakter. Prøv systemet gratis allerede idag!

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Eksempel på en enksamensopgave, når man skal beregne en pris ud fra et indekstal

Tabellen herunder viser prisindekset for bilforsikringer i år 2000, 2005 og 2010 (basisår 2000).

Indekstal 6

Det oplyses at en bilforsikring hos et bestemt forsikringsselskab kostede 4.500 kr. i år 2000.

Bestem hvad den samme bilforsikring hos det samme forsikringsselskab kostede i år 2010.

For at kunne bestemme hvad bilforsikringen kostede i år 2010 skal man først finde fremskrivningsfaktoren. Fremskrivningsfaktoren findes ved følgende formel:

Indekstal 7

Når fremskrivningsfaktoren er fundet ganges den med den oplyste pris i basisåret, og man finder dermed hvad bilforsikringen kostede i år 2010. Vi finder først fremskrivningsfaktoren.

Indekstal 8

Fremskrivningsfaktoren ganges med prisen i basisåret for at finde ud af hvad bilforsikringen kostede i år 2010.

Indekstal 9

Prisen for den samme bilforsikring hos det samme forsikringsselskab kostede i år 2010 6.291 kr.

 

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Eksempel på en eksamensopgave, hvor der skal sammenlignes indekstal

Tabellen viser indekstallene for den månedlige leasingydelse for leje af en BMW 320 i år 2000, år 2005 og år 2010.

Indekstal 10

I nedenstående tabel er oplyst prisindekset for bilforsikringer (basisår 2000)

Indekstal 11

Undersøg om den månedlig leasingydelse eller om prisindekset for bilforsikringer er vokset mest fra år 2000 til år 2010.

For at kunne besvare spørgsmålet skal man finde den procentvise stigning for den månedlig leasingydelse og den procentvise stigning i prisindekset for bilforsikringer. Det gøres ved hjælp af fremskrivningsfaktorformlen. Først beregnes den procentvise stigning for den månedlig leasingydelse.

Indekstal 12

 

Hernæst findes den procentvise stigning i prisindeks for bilforsikringer.

Indekstal 13

Vi har nu beregnet den procentvise stigning for den månedlig leasingydelse og i prisindekset for bilforsikringer. Når der foretages sammenligning, så er den procentvise stigning for den månedlig leasingydelse 43,4% mod 39,8% i procentvis stigning i prisindekset for bilforsikringer, hvilket betyder at den månedlig leasingydelse er vokset mest i perioden år 2000 til år 2010.


Aktuel eksamensopgave i indekstal på matematik HF niveau C

Nedenstående tabel viser en opgørelse over antallet af dømte for butikstyveri.

indekstal-opgave

Spørgsmål 1 –
 Beregn indekstallet for 2006.

Først beregnes indekstallet for år 2006 ved hjælp af formlen for indekstal:

indekstal-formel

Vi indsætter i formlen:

indekstal-beregning

Det vil sige at indekstallet for år 2006 er 76

Spørgsmål 2 – Beregn antallet af dømte i 2012.

Antallet af dømte i 2012 beregnes ved hjælp af fremskrivningsfaktoren:

fremskrivningsfaktor-formel

Vi indsætter i formlen for, at finde fremskrivningsfaktoren:

fremskrivningsfaktor-beregning

Da vi nu har fundet ”fremskrivningsfaktoren” ganges den, med antallet af dømte i basisåret (basisår = 2000).

indekstal-beregning1

Antallet af dømte i 2012 er derfor 8121,55

Har du nu lært at beregne indekstal?

Vi anbefaler dig at træne flere opgaver i indekstal via vores matematik træner. Opret en gratis bruger og prøv systemet. Så kan du nemt og enkelt score topkarakter til din matematik eksamen. Gør som andre studerende landet over. Kom igang nu og se merkante resultater!

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