- Level: AS and A Level
- Subject: Maths
- Word count: 1654
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:
- Investigate the relationship between the number of Triminoe cards in a set and the largest number used in a set.
- 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
- 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.
- I will then try two numbers 0 and 1 and find out how much different possibilities I can make with the two numbers.
Middle
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
This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.
Found what you're looking for?
- Start learning 29% faster today
- 150,000+ documents available
- Just £6.99 a month