In this piece of coursework I will investigate the gradient function.
Victoria Jennings- 11SEG GCSE Mathematics Coursework 2003 The Gradient Function In this piece of coursework I will investigate the gradient function. The "steepness" of a curve is measured by its gradient. The gradient of a curve at a particular point is defined as the gradient of the tangent drawn to the curve at that point. The gradient at a point on any curve is defined as the gradient function. I will carry out this investigation using the equation: y = axn I am trying to find a formula that will work out the gradient of any line. ...................................................................................................... We can use the "tangent method" to obtain the gradients of graphs of different functions. I am going to look at y=x1 first because it is the easiest. See graph A y -4 -3 -2 -1 0 2 3 4 x -4 -3 -2 -1 0 2 3 4 As we see, the gradients of y=x is very simple, g=1. We even do not need to draw any tangents to obtain the gradients. So the relationship between g and x can be shown in the table below: x g (gradient) -4 -3 -2 -1 0 2 3 4 So it is obvious that in the graph of y=x, whatever x is, the gradient, g stays 1. ...................................................................................................... I will now look at the graph of y=x2. See graph B By drawing the tangents of each point, we can
Glasgow Sonnets by Edwin Morgan
Glasgow Sonnets by Edwin Morgan ____________________________________________________________________ Critical Essay Q: Structure is an important feature in poetry. Choose a poem which has very deliberate structure (rhyme, rhythm, form etc) and write about it in such a way as to explain the contribution made by its structure to your appreciation of the poem. ____________________________________________________________________ Glasgow Sonnets by Edwin Morgan is a great example of the importance of structure in poetry. The poem consists of fourteen lines of equal length, which is split into an eight line octet and a six line sestet. The first eight lines - octet - are describing the area which the poem is based on, the focus is on a bleak looking building and everything that surrounds it. The opening line has great significance as it describes the wind as 'mean' this instantly gives me an insight to the tone of the poem, which is one of sadness, poverty and deprivation. By the use of the word 'mean' it personifies the wind which is being described, making me visualise deprivation and poverty. Also in the first line Morgan uses alliteration in the words 'wind wanders' I do not usually associate the word 'wander' with the wind, this in turn portrays to me a wind that is aimless and has no specific place to blow. The last word in the first line 'trash' has a
Compare three different newspapers by using readability, the amount of space devoted to various sections, and the number of pages.
Mathematics Coursework - Statistics My objective is to compare three different newspapers by using the following information: > The readability in terms of standard of language evidenced in different newspapers. > The amount of space devoted to various sections such as Sport, news and business. > The number of pages, size and the cost of each of the three newspapers. > Another thing that I will look at is the average newspaper in terms of size and cost. The three newspapers that I will compare are: - > The Sunday Times, which is a Broadsheet newspaper sold right throughout the UK containing news from right across the UK. It is mostly read by a person with a high standard of language such as a businessman. People may also wish to read the advertisements for housing, recruitment and classified advertisements. There are pages in this newspaper. > The Western Mail, which is a Tabloid newspaper, containing national news. This is one of the most popular tabloid newspapers currently being sold. It contains news on a variety of current events with a focus on features and leisure. It is considered an interesting paper for the reader. There are 90 pages in this newspaper. > The Telegraph is a Broadsheet newspaper with news from all over the world. It is known for its well-written articles and opinions and its readership tends to be members of the professional and business
Is there a connection between the size (surface area) of a leaf and the between the trunk to the road?
Surface Area of leaves Research question: Is there a connection between the size (surface area) of a leaf and the between the trunk to the road? Aim: To find a connection between the size(surface area) of the leaf and the distance between the trunk and the road. Hypothesis: Yes, I believe that the surface area of the leaves will increase the further away from the road they are. I believe that there are many reasons all due to different pollutions, caused by the cars driving on the road. I'm sure that it affects the leaves in other ways such as premature leaf drop, delayed maturity, plant growth, reproduction....but also the size will get affected. Cars are responsible for a tremendous amount of air pollution and wasted energy that affect humans and our environment. Acid rain, which is caused by air pollution, poisons our water as well as plants. The smoke and fumes from burning fossil fuels rise into the atmosphere and combine with the moisture in the air to form acids rain. The main chemicals here are sulphur dioxide and nitrogen oxides. The tree's roots absorb water from the ground, as a life source and when the acid rain, rains around that tree its life source is poisoned. The acid rain also harm the leaves as fog, acid fog, which the leaves will bath in, and that will make their protective waxy coating can, wear away. Which could lead to water loss, which makes the
Investigating Number Stairs
Maths Coursework(c) - Investigating Number Stairs Part 1 46 36 37 26 27 28 To investigate the relationship of other 3-step stairs, their stair total and their position on the grid, we can move it one space to the right. We then get the following in the 10x10grid: 26+27+28+36+37+46=200 Therefore total = 200 If we continue moving the shape to the right, and continue this for each row on the grid, we get a pattern like this: 2 3 4 5 94 200 206 212 218 S+20 S+10 S+11 S S+1 S+2 We can say that it increases in a linear fashion (the increase is constant). To use a formula to find out the stair total every time, we can make use of the bottom left had corner of the stair and change it to S. Every other number can be changed so that it is related to S So the total for any 3-step stair on the 10x10 grid= 6S+44 We can test this formula for the very first grid we did: (6x25) + (44) = 194 So OK! Part 2 To investigate the relationship of the 3-step stair on a 11x11 and a 12x12 we have to modify the step stair: S+21 S+11 S+12 S S+1 S+2 S+22 S+12 S+13 S S+1 S+2 So we get 6S+ 47 for 11x11 and 6S+49 for 12x12 Since we have the formulae for 10x10, 11x11 and 12x12, we can make a general formula for finding the stair total for a 3-step stair for any grid size. We can do this since it increases in a linear fashion (+2 every time). We get the formulae:
Investigating three step stairs.
Aim I am set the task of investigating three step stairs (which I will go into some more detail on later on) and how their position on the number grid and the step total corresponds to the step number. Prediction My basic prediction is that... Definitions Step total - the total of all the numbers in the stair added up Stair number - this is the lowest number in the stair and is found in the bottom left hand corner of them Number grid - this is a ten by ten square with the numbers from one to one hundred in it as ten time ten is 100. The ten by ten grid is the grid we will be using in the first part of the investigation but in the second stage of the investigation other smaller and larger number grids will be tested. Step number - this is the number of steps the stair is comprised of. As I have stated the step number I will be using for the main part for this investigation will be a three step stair, with a three step number there will be six numbers within the stair. Establishing a connection In order to establish a link between n (n=stair number) and the st (st=step total) I must conduct a series of tests on various different three step stairs in different positions on the ten by ten grid. I will, whilst examining the results I gain from different stairs, attempt to find a formula that can be used to predict the st of any
Symmetry in Nature
Khan Salinder Snowflake . A snowflake is an example of rotational symmetry. When you rotate it 60 degrees you will find that the snowflake will still look the same as it did before it was rotated. Or you can say that it has six lines of symmetry. It can be folded in half in six different ways and both halves look the same. Snowflakes can have either hexagonal or triangular symmetry although the hexagonal snowflake is most common. Beehive A beehive has translational symmetry meaning that it has a repeating pattern of hexagons. Individual cells of a honeycomb have rotational symmetry they can be rotated one sixth of a turn and still look like the same as before the rotation. A honey comb is built slanted so that honey doesn't fall over. The hexagonal shape of a cell gives strong construction and also uses less building material. Seashell A seashell has reflectional or bilateral symmetry. A seashell only has one line of symmetry. It can be split in half so that one side is like a mirror reflection of the other side. The lines on a seashell are arranged in such a way that you see perfect symmetry. Animal Most animals are symmetrical in at least one way. For animals, symmetry is related to fitness. Symmetrical horses can run faster than non-symmetrical horses. There are two types of animals; radiata and bilateria. Radiata has radial symmetry. Bilateria
"THE TABLOID VERSUS THE BROADSHEET"AN INVESTIGATION INTO THE EDITORIAL AND PICTORIAL CONTENT OF THE DAILY MAIL AND THE GUARDIAN NEWSPAPERS
"THE TABLOID VERSUS THE BROADSHEET" AN INVESTIGATION INTO THE EDITORIAL AND PICTORIAL CONTENT OF THE DAILY MAIL AND THE GUARDIAN NEWSPAPERS . INTRODUCTION British newspapers fall loosely into two categories the tabloid (which is half the size of a broadsheet) and the broadsheet itself, with tabloid newspapers tending to be quite different from broadsheets in style and content as well as in size. The so-called intelligent media represented by the Independent and the Guardian seem to present problems to their readers and say 'here is an article, judge for yourself from the information and the informed journalists that we offer.' Commentators such as the art critic Brian Sewell stated, "Opinion, as expressed by a rag is worthless" with Mark Thompson the Director of BBC Television, commenting, "I think people use the media in quite sophisticated ways. They might read a tabloid newspaper for fun but it doesn't mean they believe everything in it is true." If you look on a news-stand, the British national newspapers can be roughly divided as follows:- Broadsheet Tabloid The Guardian The Daily Mail The Independent The Express The Financial Times The Star The Telegraph The Sun The Times The Mirror The table shown above illustrates an example of a stratified sample. This type of sample is made up of different layers of the population (individuals or items) that
GCSE Math's Statistics Coursework Introduction: I have been given a database which contains information about one hundred different used cars
GCSE Math's Statistics Coursework Introduction: I have been given a database which contains information about one hundred different used cars. We are investigating what is the most influential factor when buying a second hand car. The factors which I will be using are the age and mileage of the cars to see how they affect the price. Hypothesis: Cars which are older and have got more mileage are generally cheaper, but if I have a vintage (antique) car it will change my graph so it would skew my data as an outlier. Also some cars will depreciate quicker than others in their first year. Plan: Using the data which has been given to me I will compare age to mileage on a scatter graph with price. If I did the investigation by hand I would have chosen a sample of 100 cars of about 20 being picked at random using every 5th car as a sample and picking where to start counting at random by putting the numbers lets say the numbers 1-5 in a hat and pulling one out at random, But however I have been given the data on excel. By doing the charts on excel I will be able to plot all the data on the scatter graph and then draw a line of best fit (trendline) more easily and then compare between age and mileage because the computer can generate a graph much quicker than if done by hand. This will show me what sort of correlation the graph has, whether positive or negative and how strong it
CAR SALES MATHS COURSEWORK
CAR SALES MATHS COURSEWORK For my maths/statistics coursework I am to analyse a set of data given to me. The purpose of this investigation is to distinguish any possible correlation between certain variables. Furthermore, I must determine what factors affect the price of a car. From my data I am looking at particular variables as I feel these variables will the most subsequent to the price. The variables I am going to investigate are as follows: * The age of the cars. * The mileage of cars. * The engine size. * The makes. * The cost of the car when new * The second price. Initially, I am going to find any obvious links between the above variables. Moreover after finding the link's I will develop the data in an attempt to locate the influential links that affect the price of the car. To assist me in doing this I am going to draw graphs and obtain conclusions that will lead me on to finding a general formula. Out of the data given to me I have used the random function on my calculator to generate random number with which I was able to collect the cars I hope to analyse. Out of 100 cars I have chosen 36. I feel that 36 are a sufficient number to get the best possible conclusion. These are the following cars I am going to analyse: Car no. Make Price when new Second hand price Age Mileage Engine size Peugeot 8300 2000 7 65000 .4 2 Vauxhall 8700 500 9