The Open Box Problem
I had the task of making a box out of an A4 piece of paper with the largest possible volume. First of all I made a box out of an A4 piece of paper. To do this I had to cut squares out of each corner of the paper and fold up the sides. I used random measurements in this test to see the results. I found that the size of the squares I cut out of the corner changed the volume of the box I made, so, using a spreadsheet I tried to find the maximum volume. Box Made From A4 paper Corner Length Width Height Volume mms mms mms mms mm3 0 297 210 0 0 0 277 90 0 526300 20 257 70 20 873800 30 237 50 30 066500 40 217 30 40 128400 50 97 10 50 083500 60 77 90 60 955800 70 57 70 70 769300 80 37 50 80 548000 90 17 30 90 315900 00 97 0 00 97000 I first found out the box volumes for box corner sizes 0 - 100mm. I found out that 40mm corners made the largest volume. To find the measurements that gave the biggest volume possible I put more accurate numbers into my spreadsheet. Box Made From A4 Paper Corner Length Width Height Volume mms mms mms mms mm3 35 227 40 35 112300 36 225 38 36 117800 37 223 36 37 122136 38 221 34 38 125332 39 219 32 39 127412 40 217 30 40 128400 41 215 28 41 128320 42 213 26 42 127196 43 211 24 43 125052 44 209 22 44 121912 45 207
The Open Box Problem
The Open Box An open box is to be made from a sheet of card. Identical squares are cut off the Four Corners of the card as shown. 10 The card is then folded along the dotted lines to make the box. The main aim of this activity is to determine the size of the square cut which makes the volume of the box as large as possible for any given rectangular sheet of card. . For any sized square sheet of card investigate the size of the cut out square corner which makes an open box of the largest volume. 2. For any sized rectangular sheet of card investigate size of the cut out square corner which makes an open box of the largest volume. We will use a ten-cm square. We are using a square because it is easier to use one variable because a squares width and length are the same. Cut size (cm) Original length Original width Width Length Height Volume 0 0 8 8 64 2 0 0 6 6 2 72 3 0 0 4 4 3 48 4 0 0 2 2 4 6 Therefore we can see that the maximum box area is made from the cut size of 2cms. Now I will try between 1-2 cm's. Cut size Original length Original width Width Length Height Volume .1 0 0 7.8 7.8 .1 66.924 .2 0 0 7.6 7.6 .2 69.312 .3 0 0 7.4 7.4 .3 71.188 .4 0 0 7.2 7.2 .4 72.576 .5 0 0 7 7 .5 73.5 .6 0 0 6.8 6.8 .6 73.984 .7 0 0 6.6 6.6 .7 74.052 .8 0 0 6.4 6.4 .8 73.728 .9 0 0
The open box problem
The open box problem An open box is to be made from a sheet of card. Identical squares are cut off the four corners of the card as shown below. The card is then folded along the dotted lines to make the box. The aim of this project is to determine the size of the square cut out in any given size rectangle sheet of card with the largest volume. Task 1: For any sized square sheet of card, investigate the size of the cut out square which makes an open box of the largest volume. For this task I will use 20cm*20cm square sheet of card. The formula used to get a volume is V=length x Width x height But if were cutting out 4 small squares out of the 20cm square, will be using this formula= V=length-(2H) x width-(2H) x height {Height = H, volume = V} Example: L=20cm, W=20cm, H=1cm V= H x ((L-2H) x (W-2H)) V= 1 x ((20-2) x (20-2)) = 1 x (18x18) = 1 x 324 = 324cm3 This calculation would be used to make an investigation on different height. By using different height I will acquire the best size to cut out so that the box has a high volume. The investigation will be processed on excel to give a most accurate results. I will use a graph to differentiate the readings of 20cm2 . Length (cm) Width (cm) Height (cm) Volume (cm3) 20 20 324 20 20 2 512 20 20 3 588 20 20 4 576 20 20 5 500 20 20 6 384 20 20 7 252 20 20 8 28 20 20 9 36
The listeners
The listeners Standing in the misty distance was a shadowy forest; trees swaying, rough leaves softly whispering in the wind. White moon-beams shone brightly upon the woodland that lay below. In the sky, dancing beams of light caught sight of a neglected tower. The ancient turret stood covered in gloomy climbing ivy in a clearing of the forest floor. An extremely weary traveller came out through the damp vegetation. He emerged from his drained stead. Swooping above him, birds flew into the hazy night. With the sound of jiggling spurs smashed the moon-lit beams. Yet he proceeded towards the fortress. The explorer painstakingly walked to the mount. He knocked gently upon the ramshackle ingress. With a cry "Is anybody there?" Echoing around the shadowy woodland was sounds of 'Tap', 'Tap', 'Tap'. Reverberated echoes, shaking wildlife form their winter beds. The tower replied with a sudden silence. Tried and incredibly hungry, the elderly gentleman again knocked ferociously onto the ingress. However with a massive roar he yelled "Is anybody there?" Once again his cry was met by zilch. The tall perplexed vagabond stood unease, eavesdropping into the magical surroundings around him. The drowsy explorer found a small window under the climbing ivy. He slowly bent down to only find a shadowy staircase lied in front of him. Suddenly the trekker rose up. His awareness had sense
Maths Coursework
Maths Coursework Introduction In this investigation I am going to find out the readability of three different types of newspapers: tabloid, broadsheet and quality. To do this I will take the average sentence length and compare them with each other. In my opinion, the shorter the average sentence length of the newspaper, the easier the newspaper will be to read. Plan This investigation will find the readability of the newspapers by comparing sentence length. Four different categories will be used: news, entertainment, business and sport. These were chosen because all three different newspapers had a number of pages on these categories. At the moment by looking at the newspapers a number of problems have been found. Firstly, all the different categories are not placed in order or together within the newspaper so to get completely random pages will be difficult. To resolve this problem the pages in the same category that are not together in the newspaper will be numbered. Then a random number chosen by using the calculator's random button will find which page to use. If the random number chosen by the calculator is bigger than the amount of pages, that number will be left out and another random number chosen. The next problem that will be encountered when starting the investigation will be how to chose random sentences of a page. This will also be resolved by
Maths CourseWork
Aims, Design and Strategy ? A familiar problem but thoroughly and clearly laid out. ? Score 3 Selection and Collection of Data ? Relevant data from more than one source ? Detailed and clear description of methods ? Justification and rejection in context of several recognised sampling methods ? Score 6 Presentation of Data ? Data recorded in tables ? Bar charts / multiple charts / cumulative step polygons / box plots all used highly effectively ? Reasons always given for method chosen ? Each time more is found out about the data ? Score 9 Calculations ? mean, mode, median, LQ, UQ, IQR, s.d., outliers, Spearman's ? strong justification given for all methods used ? Score 11 Interpretations and Conclusions ? very strong running commentary ? brought in external methods to compare the findings ? score 8 Total 3 + 6 + 9 + 11 + 8 =
maths coursework
Contents . Introduction 2. Hypotheses 3. Method 4. Statistical Analysis of 4 hypotheses 5. Limitations of 4 methods used 6. Evaluation of 4 hypotheses 7. Conclusion Introduction * Compare a broadsheet and tabloid newspaper * Investigate word length, sentence length, readability and article area in both papers. * Randomly select a story in the broadsheet (put the broadsheet page numbers in a 'hat' then randomly pick out, use the same story in the tabloid) This reduces bias. * Bought papers on the same day so that articles should be the same in terms of context and content. Hypotheses My hypotheses: . I expect to find that the broadsheet has longer words. 2. I expect to find that the broadsheet has longer sentences. 3. I expect to find that the broadsheet will have an older average reading age. 4. I expect the broadsheet to devote more of its page area to an article. Word Length Results Daily Telegraph Number of letters per word Tally Frequency, f Frequency x Number of Letters, fx 6 6 6 2 21 21 42 3 7 7 54 4 6 6 64 5 9 9 45 6 9 9 54 7 2 2 84 8 3 3 24 9 3 3 27 0 3 3 30 1 1 The Sun Number of letters per word Tally Frequency, f Frequency x Number of letters, fx 6 6 6 2 7 7 34 3 24 24 72 4 21 21 84 5 1 1 55 6 9 9 54 7 3 3 21 8 2 2 6 9 5 5 45 0 0 1 0 0 0 2 2 Word
Statistics Coursework
Statistics Coursework - Pulse Rates Aim ~ The aim of my investigation is to compare pulse rates, body temperature and hours of exercise, from pupils in my school. "The normal pulse rate for 11 - 16 year olds is 70 - 100 beats per minute." Hypothesis: ~ Females have faster pulse rates than males because when I researched this, I found that a female's heart does generally beat faster than males. ~ The older you are, the lower your pulse rate, because according to research, an increased age means decreasing resting pulse rate and a decreased exercising pulse rate. ~ The more hours of exercise you do, the slower the pulse rate because research says regular exercise keeps you fit, therefore your heart doesn't need to work twice as hard. ~ The year 7's have slower pulse rates because they are forced to stay healthy and eat healthy. Youngsters are also a lot more active. ~ The higher the body temperature, the higher the pulse rates, because my research explains that the pulse generally increases 7 - 10 beats for each degree of temperature elevation. (Hypothesis for Primary Data.) I am doing this investigation because it is interesting and important to understand the heart. Strategy ~ The data I am going to collect are: * Gender (Qualitative) * Age (Quantitative) * Year Group (Quantitative) * Number of hours of exercise per week
REad all About it
Plan: My Statistics coursework! Introduction In my coursework I am trying to prove and disprove my hypotheses that I have mentioned below. I am using two newspapers, which are "The Metro" and "The Daily Mail." Students, who use the train or the bus, in the morning, to get to university or school, mainly read the metro. Also, men and women who use the same transport to get to work would also read the paper. These are the papers target audience. So therefore, to the benefit of the students the newspaper would use smaller words or not too complicated long words. Typically, the paper would have smaller words and fewer words in a sentence. We also expect there to be bigger pictures with less text than the Daily Mail. Older people, educated people and conservative minded tend to read "The Daily Mail." These are typically the target audience of the newspaper. So everyone would expect that the newspaper would use long complicated words and typically the paper would have longer words and more words in sentences. We also expect there to be more information and less picture (and smaller). Hypotheses . "The Daily Mail" has longer words than "The Metro" 2. "The Metro" has fewer words in a sentence than in "The Daily Mail" 3. "The Metro" has bigger pictures (area) than in "The Daily Mail" Planning of hypothesis 1 "The Daily Mail" has longer words than "The Metro" I will
Read All About It
st Hypothesis HYPOTHESIS: Broadsheets have longer words than tabloids and are therefore harder to read. I have chosen a hypothesis, which I will use to compare 2 different newspapers, one Tabloid, one Broadsheet (both from the same day, so as to avoid bias), and I will use a stratified sample of articles from different sections of the newspapers. Tabloid newspapers are aimed towards young adults and older teenagers, whereas broadsheets are aimed generally towards older people (40's or older). I chose this hypothesis because I asked 50 of my friends whether they like reading Tabloids or Broadsheets more. 41 people said they preferred reading Tabloids, while the other 9 stated they like reading Broadsheets. Then I chose this hypothesis to expand further on it and to see whether longer words were the reason why less people read broadsheets - because they are harder to read. Plan To select the words, I will use stratified sampling. I am using stratified sampling as it shows an overall representation of the whole population - i.e. if "Section A" is bigger than Section B, and I am taking data from both, I will take more data from Section A, so that I get an overall representation of the population, where the data taken is proportional to the size of each section. Stratified sampling is a fair way of representing the whole population. I will choose articles to use from each