54 results found

#### In this piece of coursework I will investigate the gradient function.

• Word count: 2434
• Level: GCSE
• Subject: Maths

#### The Gradient Function - Aim: to investigate the gradient function for all kinds of curves.

• Word count: 1610
• Level: GCSE
• Subject: Maths

#### For this investigation, I have to find the relationship between a point of any non-linear graph and the gradient of the tangent, which is the gradient function.

• Word count: 1322
• Level: GCSE
• Subject: Maths

#### Algrebra:Gatwick airport temperatures

AS Use of Maths Working with algebraic and graphical techniques Assignment 2: Gatwick airport average temperatures Introduction Data: Graph: This is cyclical and will there for be modelled by a trigonometrical function of the form Y = A sin (?(t + ?)) + C where A is the amplitude ? is the frequency t is the time in days ? is the phase shift C is the central line Finding the model The central line is: (min + max)/2 = (3.8+16.5)/2 = 10.15 The amplitude is: (max - min)/2 = (16.5-3.8)/2 = 6.35 The frequency: 360/period(cycle length) = 360/365 = 0.986 This gives a first model of y = 6.35snin (0.986t) + 10.15 The initial estimate for the phase shift was 110 to the right, so by translation t --> (t - 110). This result was not on the original data, but further modifications gave rise to t --> ( t -113) which appeared closest. On checking the values for the average absolute error for the points given by the data, this also gave the smallest error. So y = 6.35snin (0.986(t - 113)) + 10.15 is the model for the data Checking the model works The data give (197, 16.5) When t = 197, the model gives y = 6.6 sin (0.986(197 - 113)) + 10.2 y = 6.6 sin (82.824)+10.2 = 6.6 x 0.992 + 10.2 = 16.75 is very close to the data value of 16.7, so the model works Applications of the model . Finding the rate of change of the temperature To find the approximate

• Word count: 585
• Level: GCSE
• Subject: Maths

The Gradient Function I am trying to find a formula that will work out the gradient of any line (the gradient function) I am going to start with the simplest cases, e.g. y=x² as they are probably going to be the easiest equations to solve as they are likely to be less complex and hopefully the formulas to the more complex equations will be easier to discover by looking at the previous formulas. I am going to look at the line y=x² first. y=x² X 2 3 4 y 4 9 6 One of the most obvious things I notice is that as the co-ordinates increase so does the gradient. Not only can you see that from the results below, but also on the graph you can that the line gets steeper and steeper. This makes sense as the higher the number x is the larger the difference between x² and x. Another thing that I have noticed is that the larger the co-ordinates the smaller the increase in gradient. Point Gradient (tangent) Gradient (Small Increment Method) (1,1) 2 2.01 (2,4) 3.3 3.01 (3,9) 6.36 (2dp) 6.01 (3.5,12.3) 6.4 7.001 As the table above shows there are two methods that I am using for calculating the gradient of line. The first being drawing a tangent at the point, working out the distances on the tangent using the scale on the graph and then using this formula: dy/dx However there is another way called small increment method. This method gives a more

• Word count: 863
• Level: GCSE
• Subject: Maths

• Word count: 3331
• Level: GCSE
• Subject: Maths

#### Investigate the elastic properties of a strip of metal (hacksaw blade) and use the results to determine the value of Young's Modulus of the metal.

Physics Coursework - Making sense of data Aim To investigate the elastic properties of a strip of metal (hacksaw blade) and use the results to determine the value of Young's Modulus of the metal from the following experiment: The Young's Modulus, E, is given by: a2 = Ebd3 Cos? b = width of blade 6Mg d = thickness of blade g = acceleration due to gravity: 9.81ms-2 Young's Modulus For the description of the elastic properties of linear objects like wires, rods, columns which are either stretched or compressed, a convenient parameter is the ratio of the stress to the strain, a parameter called the Young's modulus of the material. Young's modulus can be used to predict the elongation or compression of an object as long as the stress is less than the yield strength of the material. To obtain a suitable value for Young's Modulus, a graph needs to be plotted. We can see that the initial equation is in the form y = mx: y = a2 m = Ebd3 6Mg x = Cos? From this we can say that the graph that is to be plotted will be a2 against Cos?. On this graph, three lines will be drawn: a line of maximum gradient, a best fit line and a line with minimum gradient going through the points. The gradient (m) will equal the part of the equation above. This will be re-arranged to give the Young's Modulus as follows: E = 6Mgm bd3 Appearance of the graph - from the gradient we can say

• Word count: 1351
• Level: GCSE
• Subject: Maths

GRADIENT FUNCTION The aim of this assignment is to find the relationship between the gradient function. For this assignment I will use the height of drops and the number of drops needed to crack open nuts of different sizes; large, medium and small. The models are then compared in terms of the usefulness of the models. The table below shows the average number of drops it takes to break open large nuts from varying heights. Large nuts Height of drop (m) Number of drops 1.7 42.0 2.0 21.0 2.9 0.3 4.1 6.8 5.6 5.1 6.3 4.8 7.0 4.4 8.0 4.1 0.0 3.7 3.9 3.2 Let (h) metres be the height of drop and (n) be the number of drops. The graph below is of n against h From the graph above, the number of drops to crack open the nuts depends on the height of the drop. Therefore the independent variable is the height of the drop (h) while the dependent variable is the number of drops (n). The control variable is the size of the nuts which is large for the above specific graph. Parameters, the characteristic of the population: The coordinates of the graph form a smooth line. The number of drops is decreasing as the height increases. The height of a drop can never be negative or zero, therefore, h>0. The number of drops will never be negative or less than one, therefore, n?1. By estimating the values of parameter, we can infer that the domain and range is the set of

• Word count: 604
• Level: GCSE
• Subject: Maths

#### Graphical Maths Project

Year 11 Graphical Maths project The aim of this project is to be able to create a system for understanding the relationship between the gradients of tangents of curves. Unlike straight lines, curves cannot have a single gradient that applies to the whole curve, but there are an infinite number of straight lines that can touch the curve at one point. There is only one perfect tangent line for each point on a curve, and all of these tangent lines have different gradients. It is the relationship between these gradients that will be explored in the first part of this investigation. The first task to be carried out was to find several perfect tangents of the graph y=x2. This presented a challenge, as there is no easy way to discover lines that are perfect tangents of a curve. In my first attempt, I created a line in autograph and gradually changed the y intercept parameters in an attempt to "move" the line into position as a tangent of the graph y=x2. This proved time consuming and ineffective however, as the following screenshots show; Here the blue line appears to cross the red line at y=0.25, x=0.45, but this is unclear because of the distance from the point. Further zooming reinforces the possibility that the line could be an exact tangent. Further zooming still makes the possibility of a potential discovery significantly less likely; however, when even more zooming takes

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• Word count: 520
• Level: GCSE
• Subject: Maths