In this investigation I am trying to find a rule for the difference between any consecutive numbers in a sequence. I am going to use a series of algebraic expressions to try and come up with a successful rule that works for every consecutive number I try.

Math's Investigation Consecutive Numbers Introduction In this investigation I am trying to find a rule for the difference between any consecutive numbers in a sequence. I am going to use a series of algebraic expressions to try and come up with a successful rule that works for every consecutive number I try. 2 Consecutive Numbers ,2 = 3 2,3 = 5 3,4 = 7 4,5 = 9 3 Consecutive Numbers ,2,3 = 6 2,3,4 = 9 3,4,5 = 12 4,5,6 = 15 4 Consecutive Numbers ,2,3,4 = 10 2,3,4,5 = 14 3,4,5,6 = 18 4,5,6,7 = 22 As you can see from these results if I carry on the difference goes up by 4 each time. 5 Consecutive Numbers ,2,3,4,5 = 15 2,3,4,5,6 = 20 3,4,5,6,7 = 25 4,5,6,7,8 = 30 Difference goes up by 5 each time. 6 Consecutive Numbers ,2,3,4,5,6 = 21 2,3,4,5,6,7 = 27 3,4,5,6,7,8 = 33 4,5,6,7,8,9 = 39 Difference goes up by 6 each time. I have chosen to display results from 2-6 consecutive numbers. I have done this because I think it is an adequate amount of data to find and predict patterns in the sequences. There is also no need to go any further than 6 because I have noticed a pattern, the pattern is: how ever many numbers there are in the sequence it equals the difference between each answer in that sequence every time... As you can see above, for 5 Consecutive numbers the difference goes up in 5's every time, 6 consecutive numbers the difference goes up in

  • Word count: 1971
  • Level: GCSE
  • Subject: Maths
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I am investigating how many regions can be created when n circles overlap. After I have looked at circles I will look at other shape and try to find if they have a general formula.

I am investigating how many regions can be created when n circles overlap. After I have looked at circles I will look at other shape and try to find if they have a general formula. When 2 Circles overlap When 3 Circles overlap When 4 circles overlap A maximum of 3 regions a maximum of 7 regions a maximum of 13 regions Can be created. Can be created. Can be created. Term U 1 2 3 4 Sequence 1 3 7 13 st difference 2 4 6 2nd difference 2 2 2 After looking at my results so far I can see that the 1st difference is changing but the 2nd difference is constant. This tells me my equation is quadratic, and there's a formula which applies to all quadratic equations. It is: Un = an*+ bn+c First of all to find out what a is I must half the 2nd difference so A = 1, So my formula now is: Un = n*+bn+c, to find b I have to make a new sequence. Term 1 2 3 4 5 Sequence 1 3 7 13 21 n* 1 4 9 16 25 New 0 -1 -2 -3 -4 Sequence st difference -1 -1 -1 -1 -1 And B Is the difference of the new sequence so b= -1 our formula now is Un = n*- n + c Now I have to find c we will have to put the formula into action: If n = 1 U1 = 1* - 1 + c and because u = 1 c must be +1 so the formula must be Un = n* - n + 1 My predicted formulae is n = n* - n + 1 This is the formula for the maximum number of regions Here is a table of results to show if

  • Word count: 1011
  • Level: GCSE
  • Subject: Maths
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Nth Term Investigation

Introduction In this bit of coursework I will draw shapes that tessellate and work on the parts in between them, I will look for patterns and will try to find the nth term, write a table of my results and draw line graphs as another way of showing my results. Squares I will firstly be looking at squares. Here is a table showing my results: n x n + x 1 4 0 0 2 x 2 4 4 3 x 3 4 8 4 4 x 4 4 2 9 For the second column ( ) each square has 4 because the symbol represents the corners and all squares have 4 corners. The nth term is n= 4 For the third column ( ) the amount goes up in 4's because an extra symbol is needed 1 more time on each of the sides and there is 4 sides. The nth term for this is (n-1) x4. For the fourth column the numbers are square numbers because in the middle where these (+) are found they are in a formation of a square 2 by 2, 3 by 3 etc so you times them and they are square numbers. The nth for this one is (n-1)2. Here are my predictions for other squares with different lengths. n x n + 0 x 10 4 36 81 25 x 25 4 96 576 50 x 50 4 96 2401 00 x 100 4 396 9801 Rectangles No.1 I will now move on to rectangles, as there are so many ways of doing rectangles I will start with one side going up by one each time (x) and the other side always being the same (t) which will be 2. Here is a table showing my results: n x

  • Word count: 2191
  • Level: GCSE
  • Subject: Maths
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2D & 3D Sequences.

2D & 3D Sequences Plan of Investigation In this experiment I am going to require the following: A calculator A pencil A pen Variety of sources of information Paper Ruler In this investigation I have been asked to find out how many squares would be needed to make up a certain pattern according to its sequence. The pattern is shown on the front page. In this investigation I hope to find a formula which could be used to find out the number of squares needed to build the pattern at any sequencial position. Firstly I will break the problem down into simple steps to begin with and go into more detail to explain my solutions. I will illustrate fully any methods I should use and explain how I applied them to this certain problem. I will firstly carry out this experiment on a 2D pattern and then extend my investigation to 3D. The Number of Squares in Each Sequence I have achieved the following information by drawing out the pattern and extending upon it. Seq. no. 1 2 3 4 5 6 7 8 No. Of cubes 1 5 13 25 41 61 85 113 I am going to use this next method to see if I can work out some sort of pattern: Sequence Calculations Answer =1 1 2 2(1)+3 5 3 2(1+3)+5 13 4 2(1+3+5)+7 25 5 2(1+3+5+7)+9 41 6 2(1+3+5+7+9)+11 61 7 2(1+3+5+7+9+11)+13 85 8 2(1+3+5+7+9+11+13)+15 113 9 2(1+3+5+7+9+11+13+15) +17 145 What I am doing above is shown with the aid of a

  • Word count: 924
  • Level: GCSE
  • Subject: Maths
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Dehumanisation and the Holocaust.

Dehumanisation and the Holocaust All the Jews had to wear all the same clothing so that they could be recognised as Jews. Gentiles who saw these people in these clothes knew that they were Jews and they could treat them how they liked not as humans as to the Gentiles the Jews were not humans. This is dehumanisation because they are not being treated as humans by wearing those clothes they are labelled as Jews, and not humans. This made such atrocities 'easier' to commit as they were being labelled as non - human and Jews so a picture is put into their heads that they are not human so it doesn't matter how they feel. The Viennese anti- Semitic picture paper depicts the Jew as a world-devouring vampire. They are dehumanising the Jews by describing the as "world- devouring vampires" whereas they are completely human and are not at all vampires. They have never done anything wrong to any Gentiles and aren't doing anything wrong, just believing something different to everyone but this does not mean they are world- devouring vampires. This made such atrocities 'easier' to commit as an image of a world- devouring vampire is being put into their heads, instead of normal human beings. The picture of a railway straight track going directly through the arch of a building represents a factory, mechanical, going straight in and straight out, they don't have a choice of where they are

  • Word count: 693
  • Level: GCSE
  • Subject: Maths
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