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Introduction

Identical good tomatoes are placed in a 4 by 4 tray:

Each tomato is a circle.

Each tomato just touches all the tomatoes next to it as shown in the diagram.

One hour later, all the tomatoes it touches go bad.

After another hour, the bad tomatoes make all the good tomatoes they touch go bad.

This continues until all the tomatoes in the tray go bad.

The first part of this project is to investigate how tomatoes in the tray go bad.

The second part of this project is to investigate how tomatoes in other trays go bad.

## Part 1

There are 3 different positions for the tomatoes to start going bad.

The first position is anywhere in the middle of any side:

Middle

16

As you can see, the number gone bad are symmetrical. I worked out the total number gone bad using the ‘cumulative frequency method’-: 1; 1+3=4; 4+4=8; 8+4=12; 12+3=15; 15+1=16

A graph can be drawn for both the number gone bad and the total number gone bad:

As you can see from the graph, the relationship between x and z seems to resemble a cumulative frequency curve. This is interesting because the total number gone bad was calculated using the ‘cumulative frequency method’. But there is a relationship between x and y. This can be modelled by a quadratic equation since it is a quadratic curve:

The second position is any corner of the tray:

A table can be drawn from this for analysis and to generate a formula:

 Number of hours (  ) 0 1 2 3 4 5 6

Conclusion

0  x  3 and the other is from 3  x  6.

So therefore there’ll be 2 equations – one for each part. These can be modelled by a linear equation since it is a linear graph:

The third and final position is anywhere in the middle:

A table can be drawn from this for analysis and to generate a formula:

 Number of hours (  ) 0 1 2 3 4 Number gone bad (  ) 1 4 6 4 1 Total number gone bad (  ) 1 5 11 15 16

As you can see, the number gone bad are symmetrical. I worked out the total number gone bad using the ‘cumulative frequency method’-: 1; 1+4=5; 5+6=11; 11+4=15; 15+1=16

A graph can be drawn for both the number gone bad and the total number gone bad:

This student written piece of work is one of many that can be found in our GCSE Bad Tomatoes section.

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1. ## GCSE Maths Bad Tomato Investigation

If the original bad tomato's postion is changed, the above expression will not apply anymore. Now I'll change the bad tomato to being in the middle of a tray. There are now two possibilities as to where the bad tomato will be.

2. ## GCSE Mathematics - Bad tomatoes

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