AS and A Level: Core & Pure Mathematics
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 Marked by Teachers essays 3

C3 Coursework  different methods of solving equations.
5 star(s)I repeat this until I get down to increments the size of 0.00001 x F(x) 3.1 8.429 3.2 6.712 3.3 4.843 3.4 2.816 3.5 0.625 3.6 1.736 3.7 4.273 3.8 6.992 3.9 9.899 4.0 13 x F(x) 3.51 0.396649 3.52 0.166592 3.53 0.06518 3.54 0.29866 3.55 0.53387 3.56 0.77082 3.57 1.00949 3.58 1.24991 3.59 1.49208 3.60 1.736 x F(x) 3.521 0.143492 3.522 0.120375 3.523 0.097241 3.524 0.07409 3.525 0.050922 3.526 0.027736 3.527 0.004534 3.528 0.01869 3.529 0.04192 3.530 0.06518 x F(x) 3.5271 0.002213 3.5272 0.00011 3.5273 0.00243 3.5274 0.00475 3.5275 0.00707 3.5276 0.0094 3.5277 0.01172 3.5278 0.01404 3.5279 0.01636 3.5280 0.01869 x F(x)
 Word count: 3460

The Gradient Function
5 star(s)This is the formula used for this method: Gradient = Vertical (change in y axis) Horizontal (change in x axis) Therefore the gradient of the curve equals  Gradient = 124/42 = 8/2=4 This is most likely wrong and most certainly not accurate  it is only estimation. The second method, the increment method is far more accurate. Increment method  This is where you plot two points, represented by the letters P and Q, on the curve, and draw a line to join them.
 Word count: 6489

Estimate a consumption function for the UK economy explaining the economic theory and statistical techniques you have used.
3 star(s)That is...dC/dY is positive and less than unity."(Keynes, 1936,p.96) From this statement can be derived the Keynesian consumption function (Absolute income) which is usually expressed in the following way: Ct=c0+c1Yt Where Ct is consumption, c0 is autonomous consumption, Yt is income and c1 is the marginal propensity to consume. The Keynesian view is that when income rises, consumption will rises as well, but less than income. This indicates that c1, the marginal propensity of consume, is lees than l. Keynes believed that the main influence on consumption is consumers' disposable income. When their disposable income fluctuates, the consumption would follow.
 Word count: 4377