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GCSE Math Coursework: Triminoes

Extracts from this document...

Introduction

        -  -

GCSE Math Coursework

INTRODUCTION

Triminoes is a game similar to dominoes. The game is played using triangular pieces of card. Each card has three numbers on it. Instead of drawing the triangles I will write the three numbers in brackets below.

E.g.

(000)                (001)                (002)                (011)                (012)

(022)                (111)                (112)                (122)                (222)

The aim of this investigation will be to:

  1. Investigate the relationship between the number of Triminoe cards in a set and the largest number used in a set.
  2. Investigate the relationship between the sum of all numbers on a set of Triminoe cards and the largest number used on the cards.

PLANNING

These are some of the formulas I will be using in order to complete the tasks:

f (n) =an+b                                 (Linear equation)

f (n) =an2+bn+c                         (Quadratic equation)

f (n) =an3+bn2+cn+d                 (Cubic equation)

f (n) =an4+bn3+cn2+dn+e         (Quartic equation)

METHOD

  1. First I am going to the number 0 and find out how much different possibilities I can make with the one number, this is obviously one.
  2. I will then try two numbers 0 and 1 and find out how much different possibilities I can make with the two numbers.
...read more.

Middle

01

1

6

4

012

2

30

10

0123

3

90

20

01234

4

210

35

012345

5

420

56

0123456

6

756

84

Largest Number

1                2                3                4                5                6image02.pngimage02.pngimage02.pngimage02.pngimage02.png

        +1        +1        +1                +1        +1

Linear Equationimage03.png

FORMULA

f (n) =an + b

f (n) = 1n + 0

Sum of all numbers

6        30        90         210                     420              756image04.pngimage04.pngimage04.pngimage04.pngimage04.png

       +24           +60                +120               +210             +336image04.pngimage04.pngimage04.pngimage04.png

                +36           +60                +90                 +126image04.pngimage04.pngimage04.png

                          +24                      +30                +36image04.pngimage04.png

                   +6                   +6

Quartic Equation

f (n) =an4+bn3+cn2+dn+e

n=1image06.pngimage07.png

        a + b + c + d + e = 6image08.png

n=2image10.png

        16a + 8b + 4c + 2d + e = 30image08.png

n=3image11.png

        81a + 27b + 9c + 3d + e = 90image08.png

n=4image12.png

        256a + 64b + 16c +4d + e = 210image08.png

n=5image13.png

        625a + 125b + 25c + 5d + e = 420

Equation 5 – 4
image08.pngimage14.png

        369a + 61b + 9c + d = 210image15.pngimage08.png

Equation 4 – 3image17.png

        175a + 37b + 7c + d = 120image08.png

Equation 3 – 2image18.png

        65a + 19b + 5c + d = 60image08.png

Equation 2 – 1image19.png

        15a+ 7b + 3c + d = 24

Equation 6 – 7
image08.pngimage21.pngimage20.png

        194a + 24b + 2c = 90image08.png

Equation 7 – 8image23.png

        110a + 18b + 2c = 60image08.png

Equation 8 – 9image24.png

        50a + 12b + 2c =36image08.png

Equation 10 – 11

        84a + 6b = 30image25.pngimage08.png

Equation 11 – 12image26.png

        60a + 6b = 24

Equation 13 – 14
image08.pngimage27.png

        24a = 6

                  = 6÷24

          = 0.25

               a = 0.25

Equation 13image28.png

...read more.

Conclusion


CONCLUSION
The main aim of the investigation was to find the relationship between the cubic formula and the quartic formula, I have found a few difference between the two formulas I done this by factorizing both formulas then looking for the differences. I was able to solve the patterns in the equations. I was also able to find the connection between the sum of cards, the largest number and the number of cards. I was also able to draw graphs of the equations; sadly the graphs are not complete as you could see if I had continued to draw the graph another curve would have appeared. If I were to do this investigation again I would perhaps use different numbers.


n

-2

-1

0

1

2

fn

0

0

0

1

4

image37.png
























n

-2

-1

0

1

2

fn

0

0

0

6

30
























AHSAN AHMED   Candidate Number 9065                                          

...read more.

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