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  • Level: GCSE
  • Subject: Maths
  • Word count: 2758

T-Total Maths coursework

Extracts from this document...

Introduction

Daniel Smith                Maths Coursework

image03.png

Maths Coursework

T Total Introduction

In my maths casework I am investigating the relationship between the T-Number and the T-Total, throughout a range of different size grids. I am going to work out the rule for any size grid that is by 10, below is a 9 by 10 grid, the t is the coloured in bit and the red number is the T-Number.

                                                                So the T-Number is 50 in this 9X10 grid is 50. The T-Total for this T is all the numbers in the T added up 50+41+31+32+33=187image04.png

The T-Total would be 187 as this is all the coloured in squares added up.

So in my coursework I am going to use different grid sizes to translate the T-Shape to different positions .I will then investigate the relationship between the T-Number and the T-Total, and the grid size.

I am then going to use different size grids to try to work out Ts in all different ways. Like the grid below, I am going to work out rules for all the T-Numbers with the T standing different ways.

 This grid shows the ways in which I am going to work out the T- Number in different ways.image15.png

Looking for patterns and predicting the next T

9X10 Grids

image26.png

I am first going to work out the T-Total for 5 consecutive Ts, starting at 20 and going up to 24.

image37.png

T-Number = 20

T-Total = 37

image47.png

T-Number = 21

T-Total = 42

image48.png

T-Number = 22

T-Total = 47

image49.png

T-Number = 23

T-Total = 52

image50.png

T-Number = 24

T-Total = 57

T-Number

T-Total

20

37

21

42

22

47

23

52

24

57

...read more.

Middle

23

45

24

50

25

55

26

60

From this table I can see that each time I move the T one place to the right, this is because each digit increases by 1, making it 5 each time. From this I predict that for T-Number 27 the T-Total will be 65, I will now prove my theory.

image13.png

        T-Number - 27

        T-Total – 65

This shows that my prediction was correct, each time I move the T one place to the right that the T-Total increases by 5.  This is because each time the T moves one place to the right each number increase by 1, there are 5 numbers in the T, so the T-Total will increase by 5.

The formula for a T in the upright position in a 10X10 grid.

I am going to use the T with the numbers

image14.png

From this I can see that there is a rule for the way that the numbers in the T are arranged and I can see that it is

image16.png

From this I can see that on a 10 by 10 grid the formula equals

N + (N-10) + (N-20) + (N-21) + (N-19)

I can now simplify this by gathering up all the n terms and the numbers to make the formula 5N – 70

I will now prove this on a 10 by 10 grid using the numbers

image17.png

I will now use my formula to work out the T-Total

T-Total = 5N – 70

         = (57X5) – 70

         = 285 - 70

         = 215

This shows that my formula works as the numbers in my T added up = 36+37+38+47+57 = 215

...read more.

Conclusion

T-Total = 5N + 7image43.png

          = (5X59) + 7

          = 295 + 7

           = 302

By using the formula my T-Total is 302 I will now prove this by adding the numbers up manually

59 + 60 + 61 + 52 + 70 = 302.

This shows that my formula for a T on its side is 5N + 7. I am now going to work out the formula for a T on its other side.

image44.png

Using these numbers I am going to work out the difference between the each number in the T, I will then put it into a diagram below.

image45.png

This diagram shows me the difference between the numbers in any 9X10 grid that is on its side, now I have the differences I am going to gather them up to get my formula.

T-Total = N + (N - 1) + (N - 2) + (N + 7) + (N - 11)

Now I will gather it all up and it comes to 5N - 7.

To prove this works I am going to randomly select a T from a 9X10 grid then work out its T-Total by adding it up, and then using my formula.

image46.png

T-Total = 5N – 7

         = (5X62) – 7

          = 310 – 7

         = 303

By using the formula my T-Total is 303 I will now prove this by adding the numbers up manually

62 + 61 + 60 + 51 + 69 = 303.

This shows that my formula for a T on its side is 5N - 7.

I have now found out the formulas for Ts in a upright, upside down and on bots side positions I am now going to put them into a table below and try to work out a pattern.

Which way up

Rule

image02.png

5N - 63

5N + 7

5N - 7

5N + 63

2007                T-Total coursework

...read more.

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