• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11
12. 12
12
13. 13
13
14. 14
14
• Level: GCSE
• Subject: Maths
• Word count: 1497

# Borders - find out the differences in the patterns of the colored squares.

Extracts from this document...

Introduction

George Eghator 11

Middle

Table of Results

Num.          num black                   num white                             total

1.        0        1        1

2.        1        4        5

3.        5        8        13

4.        13        12        25

5.        25        16        41

6.        41        20        61

7.        61        24        85

8.        85        28        113

9.        113        32        145

N                      Total                                       Structure

1        1        (1+1)2+1²

2        5        (2+1)2+2²

3        13        (3+1)2+3²

4        25        (4+1)2+4²

5        41        (5+1)2+5²

6        61        (6+1)2+6²

7        85        (7+1)2+7²

8        113        (8+1)2+8²

9        145        (9+1)2+9²

Order of the squares

1 + 3 + 1 = 5

1 + 3 + 5 + 3 + 1 = 13

In each of these cases, 2 have been added.

1 + 3 +5 7 + 5 + 3 + 1 = 25

As seen in the other pattern, there are additions with 2 being added on.

For the next pattern, I think that the total number of squares will be 41, using the following pattern:

1 + 3 + 5 + 7 + 9 + 7 + 5 + 3 + 1 = 41

Now I am going to test my prediction.

Number of squares = 25 + 16 = 41

 Pattern Dark squares White squares 1 1 4 1 + 4 = 5 2 5 8 5 + 8 = 13 3 13 12 13 + 12 = 25 4 25 16 25 + 16 = 41

This result is made because we are just adding onto it.

Differences

 Total 5     13      25      41     61      85      113     145   181    221 1st difference 8      12      16      20      24      28      32      36      40 2nd difference 4         4      4         4         4         4        4       4

From the quadratic sequence, we see that the main difference is 4. The first formula I will try to find is the formula for the surrounding white squares.

Conclusion

1. There will be an nth term for the number of white squares

2. There will be an nth term for the number of black squares

3. There will also be an nth term for the amount of colored squares

These are my theories which will be shown throughout the investigation as evidence.

C.  Plan of action

My plan of action will be to give indication to the methods and formulas that I will use. Algebraic expressions such as nth term will be used because it will be reliable towards my investigation.

Here are some of the expressions that will be used:

Quadratic formula- an2 + bn + c

Cubic formula- an3+ bn2+ cn + d

Using 3D formulas to find invisible patterns.

I will predict the variable sequences and compare results to analyze and explain them. Formulas for the patterns will be involved such as cubic and quadratic. Having this will help me to understand the concepts of my geometric investigation.

-  -

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

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related GCSE Miscellaneous essays

1. ## Maths Statistics Coursework

is closer to the lower quartile (-6.16). This means most of the estimates are between -4.76 and -6.16 and fewer above -4.76, extremely far off zero compared with Key Stage 4, and therefore the estimates are much less accurate. Of course, Key Stage 3 complied with the hypothesis, with a

2. ## Statistics coursework

I have also noticed that there is missing information in the data that I am given in the field "minor mistakes". These drivers have no data entered for their minor mistakes, these blanks in the data may affect the overall outcome of my graphs which could affect my hypotheses and

1. ## Maths Coursework

I discovered, by finding out about other bands, that in 2006 high street CD sales slumped by 20%. I believe this is because of Internet downloads as they can be obtained cheaper or even free. On the other hand, the album One Hot Minute experienced a fall in sales, but

2. ## Mathematics Handling Data Coursework: How well can you estimate length?

= 0.26 Year 11 S.D. = 123.965 78.1 � 50 50 = 0.19863... = 0.20 My results are as expected. Year Seven's standard deviation was 0.26 - larger than Year Eleven's 0.20. This shows that Year Seven has a more spread out set of data, and so Year Eleven's estimates were more accurate, proving my hypothesis correct.

1. ## maths estimation coursework

8: 111/226 x 120 = 59 Year 12: 115/226 x 120 = 61 The gender ratio of year 8 is 58 males to 53 females Male: 58 / 111 x 59 = 31 Female: 53 / 111 x 59 = 28 The gender ratio of year 12 is 50 males

2. ## Data Handling

BMI condition BMI Mode Median Mean Underweight Less than 18.5 54 / 60 / 61 / 62 64 61.3 = 61 Normal 18.5 - 25 77 74 71.1 = 71 Overweight 25 - 30 83 82 80.9 = 81 Obese 30 - 40 70 / 76 / 78 / 87

1. ## GCSE STATISTICS/Data Handling Coursework 2008

In order to study the second hypothesis I shall use box plots. I will be able to compare difference as the children grow older easily the median averages and how data is spread, i.e. inter quartile range. I will group the data by year, then create box plots using autograph which will show lower quartile, median, upper quartile, and outliers.

2. ## Statistics coursework. My first hypothesis is that people with a smaller hand span ...

Females have a bigger range. This graph does not seem to be accurate enough to obtain the lower quartile, the median and the upper quartile from. So instead of reading the graph to obtain these values, I worked them out by putting all the average reaction times in order.

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to
improve your own work