The relationships between the number of different spacers in an arrangement of square tiles and the dimensions of the tiles in the same arrangement.

Introduction We have been given the task of investigating the relationships between the number of different spacers in an arrangement of square tiles and the dimensions of the tiles in the same arrangement. I will begin my investigation by researching square arrangements of tiles, and then move onto rectangular arrangements. I will then investigate triangle arrangements. Stage 1 - Square arrangements The spacers that will be used in this investigation are - + Spacer T Spacer L Spacer I began by drawing 5 different arrangements of tiles, beginning with a 1x1 arrangement, and finishing with a 5x5 arrangement. I drew these on a separate piece of graph paper. (See sheet S1). The results gathered from these sketches are shown here: Pattern number Number of Squares + Spacers T Spacers L Spacers 0 0 4 2 4 4 4 3 9 4 8 4 4 6 9 2 4 5 25 6 6 4 The rule for the number of squares is xy. The pattern for the L spacers appears to be a rule, as L spacers only occur on the corners of the arrangements, and being a quadrilateral arrangement there will always be 4 corners. Therefore the rule for the L shaped spacers will be n = 4. For the + spacers the rule will be n = (n-1) . For the T Spacers the rule will be n = 4n - 4. I will now test these rules. I have now drawn the 10x10 arrangement and have written the actual properties as read from my sketch in this

  • Word count: 966
  • Level: GCSE
  • Subject: Maths
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Exposed cube sides

Introduction In this investigation I will be finding out how many labels are on an exposed side of a 3x3x3 cube when 27 small cubes are put together to make the large 3x3x3 cube. Method I will first start to count the number of small cubes out of the 27; have no labels, 1 label, 2 labels and 3 labels. Once I have done this I will the do the same for a 4x4x4 cube, 5x5x5 cube and finally a 6x6x6 cube and see if I can find a pattern. When I have found a pattern I will try to work out a formula and test if it works. 4x4x4 3x3x3 Key 3 labels 2 labels 1 label No labels 6x6x6 5x5x5 Results 3x3x3 4x4x4 5x5x5 6x6x6 3 labels 8 8 8 8 2 labels 2 24 36 48 labels 6 24 54 96 No labels 8 27 64 Formula The pattern for 3 labels is 8, 8, 8... U3 = 8 = 0x3+8 U4 = 8 = 0x4+8 U5 = 8 = 0x5+8 Un = 0n+8 The pattern for 2 labels is 12, 24, 36, 48... U3 = 12 = 12x3-24 U4 = 24 = 12x4-24 U5 = 36 = 12x5-24 Un = 12(n-2) The pattern for 1 label is 6, 24, 54, 96... U3 = 6 = 6x1 = 6x1² = 6(3-2) ² U4 = 24 = 6x4 = 6x2² = 6(4-2) ² U5 = 54 = 6x9 = 6x3² = 6(5-2) ² Un = 6(n-2)² The pattern for no labels is 1, 8, 27, 64... U3 = 1 = 1³ = (3-2) ³

  • Word count: 582
  • Level: GCSE
  • Subject: Maths
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The aim of this investigation is to find out what influences the price of used cars (second hand). Used cars usually cost less than brand new cars, but this can be affected by hypotheses' such as mileage, age, colour, how it has been used etc.

Cherry Robinson 10/79 01/05/2007 Maths Coursework: Strand one: Aim: The aim of this investigation is to find out what influences the price of used cars (second hand). Used cars usually cost less than brand new cars, but this can be affected by hypotheses' such as mileage, age, colour, how it has been used etc. My investigation is to find out how these hypotheses affect a used cars' price. Hypotheses: For my example I have chosen to use the hypotheses: 1: age, 2: mileage, 3: weather it was expensive when new and 4: make. I have chosen these because I think they are most likely to affect the price of used cars. Sample: Out of my database of 150 I need to randomly select at least 30 samples. Samples are used representatively. They represent the whole database. We use samples because it would take too long to investigate every piece of data on the database, so we only investigate the samples. This is acceptable because they are selected randomly. The samples are very poor because there was a database of 150 and only 30 samples. The probability of getting a common car (i.e. Ford) is higher than less common cars (i.e. Mercedes) Testing hypotheses one. I'd expect to find negative correlation. But vintage cars might be worth more as they get older. Good condition old cars might be worth more when older. New cars that are written off might be worth less than others of

  • Word count: 2135
  • Level: GCSE
  • Subject: Maths
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A comparison of literary styles in two newspapers.

Literary Styles: A comparison of literary styles in two newspapers. Julia Hodgson Maths Division 1 November 2001 Introduction I have chosen to compare two national newspapers. The Times is an older, more historical and hopefully more traditional newspaper. The Independent is newer, more modern and up to date. Research on the Internet has shown that The Times sells more copies than The Independent, but The Times reader has an average age of 49 whilst the Independent is bought by slightly younger people on average 40. This information shows that although they aim for similar target audiences, they each represent a different section of this market. The data will be collected from these two newspapers that are printed on the same day and are on the same topic. Newspaper A: The Times, October 30th 2001, New York Prayer Service. Newspaper B: The Independent, October 30th 2001, New York Prayer Service. The aim of this Coursework is to obtain data from each article that will help provide a conclusion to several hypotheses. Each hypothesis will have several objectives to be completed before a conclusion will be drawn. Hypotheses . 'The Times will have more syllables per word than The Independent' Objectives Choose a sampling method to allow fair and random data to be measured. Count the number of syllables in each selected word and record the

  • Word count: 3169
  • Level: GCSE
  • Subject: Maths
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Maths Project : Cubes and Hidden Faces

Maths Project : Cubes and Hidden Faces I am finding out if there is a pattern to the ratio of cubes to the number of hidden faces and finding the nth term. With 1 Cube = 1 hidden face With 2 Cubes = 4 hidden faces With 3 Cubes = 7 hidden faces With 4 Cubes = 10 hidden faces With 5 Cubes = 13 hidden faces With 6 Cubes = 16 hidden faces Already I can see a pattern, which is that with each cube, added there are 3 more hidden faces. Now I will try to find the nth term. 1st 2nd 3rd 4th 5th 6th 1 4 7 10 13 16 3 3 3 3 3 3X1=3 and I need 1 3X2=6 and I need 4 3X3=9 and I need 7 3X4=12 and I need 10 It looks like that I have to-2 to get the numbers I want so the nth term is 3n-2. To find the 100 you time 3 by 100 and-4 which = 296 Using this nth term I have made a table with out having to draw all of the pictures. Number of cubes Number of hidden faces 2 4 3 7 4 0 5 3 6 6 7 9 8 22 9 25 0 28 1 31 2 34 3 37 4 40 5 43 6 46 7 49 8 52 9 55 20 58 Hidden Faces Part 2 I am still looking for the pattern but this time using different shapes. 2 cubes = 4 hidden faces. 4 cubes = 12 hidden faces 6 cubes = 20 hidden Faces 8 cubes = 28 hidden faces This time the pattern goes up in 8 and I will now find the nth term. st 2nd 3rd 4th 4 12 20 28 8 8 8 8X1= 8 and I need 4 8X2= 16

  • Word count: 615
  • Level: GCSE
  • Subject: Maths
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Look at 3 different newspapers and analyse differences in content and style.

Newspaper Comparison By Chris Wood 6/10/2002 Aim: Look at 3 different newspapers and analyse differences in content and style. I'm going to look at a Tabloid, a Broadsheet and a Quality. The newspapers I am going to use are: Newspaper Type Date of issue Daily Mirror Tabloid Mon 14th October 02 Daily Mail Quality Mon 14th October 02 The Guardian Broadsheet Mon 14th October 02 I made sure I got the newspapers on the same day, as weekend papers differ to weekday papers. Hypothesis: I think that The Guardian will have the longest sentences, because it is a broadsheet and it was the most expensive. I think that The Daily Mirror will have the shortest sentences as it was the cheapest, it is also a Tabloid which are full of pictures and don't have many sentences. Preliminary Test: I did a small investigation to give me an idea of what length the sentences are. I have chosen to look at the first 10 sentences in the Sport sections of each paper. My preliminary test shows that there are differences in sentence length. Daily Mirror: Daily Mail: The Guardian: I made a few rules that I will use throughout this investigation: Rule 1: a number counts as 1 word (e.g. 123) Rule 2: slang words count as 1 word (e.g. don't) Rule 3: double barrel words count as 1 word (e.g. cross-section) By keeping to this my

  • Word count: 2133
  • Level: GCSE
  • Subject: Maths
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Is there maths behind M.C. Escher’s work? If so, what elements are there?

Is there maths behind M.C. Escher's work? If so, what elements are there? In this essay, before I start anything, I must first clarify that I deeply consider mathematics as a subject that has had a great influence on the artist and his masterpieces, therefore I already alarm you that throughout my essay I will talk about Escher's work and try to persuade you that there has been a considerable integration of the subject matter with his very artworks. In order to make you understand my objective, I have gathered some of his work, then selected a few, which I found had more mathematical elements, then with a decreased amount of drawings to work with, I would be able to study all components and show you that there has been a great influence of maths on him. I believe these images without the existence of any mathematical aspect would not be able to be fully accomplished. Elements like: symmetry (reflection also included), pattern/tessellation (repetition), transformation, crystallography, "impossible shapes", proportion and the 'Fibonacci Sequence' or the 'Golden Ratio'. Are suggested to be present in M.C. Escher's artworks, these I believe have been responsible to create the effect they create on the viewer, which is wonder and marvellous of the impressive art that cannot belong to the real world. Later on I will mention and try to explain these components, so that a random

  • Word count: 1523
  • Level: GCSE
  • Subject: Maths
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Read all About It - The Length of Words in Newspapers and Magazines

Read all About It - The Length of Words in Newspapers and Magazines Introduction In general terms, newspapers and magazines fall into two main broad categories, Quality and popular publications. It creates two kinds of influence: societal influence, which is not for sale, and commercial influence, which is for sale. Magazines and the national press are separated into three markets; quality press, popular press and mid-market newspapers. The consumption of each market is in relation to Social Grade, which is a classification system that separates people according to their career and income; A (upper professional); B (lower professional); C1 (routine clerical); C2 (skilled manual); D (unskilled manual); E (economically inactive). Using this system the broadsheet titles (or quality press) have most of their readers in the A and B categories with hardly any of the others consuming their newspapers. C1, C2, D and E are more consumers of popular press, proving that readership of quality press belongs to upper and middle classes whereas the working class prefer popular press. The consequence of this social division is that both Newspapers and Magazines categories operate very differently in order to maximise profit. The popular press are very much sales orientated and are not interested in who buys their newspapers. As a result, the structure, style, language and wordings are

  • Word count: 2210
  • Level: GCSE
  • Subject: Maths
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Rolling and annealing of copper block.

Title: Rolling and annealing of copper block. Abstract: The hardness of a soft copper block was tested at City University, of increasing lengths and decreasing thickness after undergoing cold rolling. After the maximum length was obtained the copper a cut section was annealed to different temperatures. From the experiment it was found that as the block got thinner and longer the hardness increased. The experiment also shows that when the long copper section was annealed as the temperature was increased the breaking or tensile stress decreased. Introduction: The purpose of this Lab exercise is to investigate the effects of cold working and of annealing on the crystal structure and the hardness of a sample of copper (dimensioned at 50x25x5mm). The experiment is designed to allow us to see first hand the changes that take place in the material as it is subjected to varying degrees of work (deformation) and heat treatment. Cold working uses the concept of "strain hardening", to "temper" the metal, which is based on increasing the dislocation density within the material. These dislocations are misalignments of atoms in the crystal lattice and interrupt the regular order of the slip planes along which the material will deform, since dislocations tend to be repulsive in the presence of other dislocations. Prior to cold working, the crystal grains in copper will have

  • Word count: 1646
  • Level: GCSE
  • Subject: Maths
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Number Stairs Investigation

Number Stairs Investigation 91 92 93 94 95 96 97 98 99 00 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51 52 53 54 55 56 57 58 59 60 41 42 43 44 45 46 47 48 49 50 31 32 33 34 35 36 37 38 39 40 21 22 23 24 25 26 27 28 29 30 1 2 3 4 5 6 7 8 9 20 2 3 4 5 6 7 8 9 0 lowest number (n) Long operation Total (t) st Difference (D0) + 2 + 3 + 11 + 12 + 21 50 6 2 2 + 3 + 4 + 12 + 13 + 22 56 6 3 3 + 4 + 5 + 13 + 14 + 23 62 6 4 4 + 5 + 6 + 14 + 15 + 24 68 6 5 5 + 6 + 7 + 15 + 16 + 25 74 6 Judging by this, the first part of the overall equation for a 3 step stair is 6n +? n 6n T D0 6 50 44 2 2 56 44 3 8 62 44 4 24 68 44 5 30 74 44 This shows the difference between 6n and T as + 44 Therefore the equation for a 3 step stair on a 10x10 grid is 6n + 44 The same sequence can be used for a 4 step stair lowest number (n) Long operation Total (t) st Difference (D0) + 2 + 3 + 4 + 11 + 12 + 13 + 21 + 22 + 31 20 0 2 2 + 3 + 4 + 5 + 12 + 13 + 14 + 22 + 23 + 32 30 0 3 3 + 4 + 5 + 6 + 13 + 14 + 15 + 23 + 24 + 33 40 0 4 4 + 5 + 6 + 7 + 14 + 15 + 16 + 24 + 25 + 34 50 0 5 5 + 6 + 7 + 8 + 15 + 16 + 17 + 25 + 26 + 35 60 0 n 0n T D0 0 20 10 2 20 30 10 3 30 40 10 4 40 50 10 5

  • Word count: 442
  • Level: GCSE
  • Subject: Maths
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