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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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# Related GCSE Bad Tomatoes essays

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25 20 13 6 36 30 15 The nth term is: Part 2 Now I am looking at different sizes of trays and different positions in the tray. The first size I am going to look at is: 10 x 10 and the bad tomato will be positioned in the corner.

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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

4, 13 or 16 were the first tomatoes to go bad. It would take 6 hours. In the next example I will change the size of the tray, this might effect the time it take for the whole tray to go bad.

1. 2 * 10 - 3 = 17 Next I will investigate patterns in the trays by starting from different positions. I will use the same sizes trays for all of the different positions, (3*3, 4*4 and 5*5). The first trays will hold the bad tomatoes in the centre.

2. ## GCSE Maths Bad Tomato Investigation

be determined by the distance between the starting point and the furthest tomato from that point. If the starting point is changed then the previous explanation will no longer apply. I will now investigate the effect of placing the starting point in the centre of the tray. • Over 160,000 pieces
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