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# GCSE Math Coursework: Triminoes

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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) =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.

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                6     +1        +1        +1                +1        +1

Linear Equation FORMULA

f (n) =an + b

f (n) = 1n + 0

Sum of all numbers

6        30        90         210                     420              756     +24           +60                +120               +210             +336    +36           +60                +90                 +126   +24                      +30                +36  +6                   +6

Quartic Equation

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

n=1  a + b + c + d + e = 6 n=2 16a + 8b + 4c + 2d + e = 30 n=3 81a + 27b + 9c + 3d + e = 90 n=4 256a + 64b + 16c +4d + e = 210 n=5 625a + 125b + 25c + 5d + e = 420

Equation 5 – 4  369a + 61b + 9c + d = 210  Equation 4 – 3 175a + 37b + 7c + d = 120 Equation 3 – 2 65a + 19b + 5c + d = 60 Equation 2 – 1 15a+ 7b + 3c + d = 24

Equation 6 – 7   194a + 24b + 2c = 90 Equation 7 – 8 110a + 18b + 2c = 60 Equation 8 – 9 50a + 12b + 2c =36 Equation 10 – 11

84a + 6b = 30  Equation 11 – 12 60a + 6b = 24

Equation 13 – 14  24a = 6

= 6÷24

= 0.25

a = 0.25

Equation 13 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 n -2 -1 0 1 2 fn 0 0 0 6 30

AHSAN AHMED   Candidate Number 9065

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