• date post

18-Dec-2015
• Category

## Documents

• view

216

2

Embed Size (px)

### Transcript of Click to Start Higher Maths Unit 3 Chapter 3 Logarithms Experiment & Theory

• Slide 1
• Slide 2
• Click to Start
• Slide 3
• Higher Maths Unit 3 Chapter 3 Logarithms Experiment & Theory
• Slide 4
• In experimental work Introduction data can often be modelled by equations of the form: we often want to create a mathematical model Polynomial function Exponential function
• Slide 5
• Polynomial function Exponential function Often it is difficult to know which model to choose
• Slide 6
• A useful way is to take logarithms (i)For This is like or rearranging
• Slide 7
• A useful way is to take logarithms (ii)For This is like or rearranging
• Slide 8
• Plotting log y against log x gives us a straight line In the case of a simple polynomial In the case of An exponential Plotting log y against x gives us a straight line
• Slide 9
• By drawing the straight line graph The constants for the gradient m the y-intercept c can be found cm c m
• Slide 10
• 1.01.6 2.0 2.3 x y 2.1 2.2 1.11.21.31.41.5 Example The table shows the result of an experiment x1.11.21.31.41.51.6 y2.062.112.162.212.262.30 How are x and y related ? A quick sketch x x x x x x suggests
• Slide 11
• Now take logarithms of x and y 0.040.080.110.150.180.20 0.310.320.330.340.350.36 We can now draw the best fitting straight line Take 2 points on the line (0.04, 0.31) and (0.18, 0.35) To find c, use:
• Slide 12
• Recall our initial suggestion Taking logs of both sides n = 0.29 a = 2 (1 dp) Our model is approximately
• Slide 13
• Putting it into practice 1.From the Graph find the gradient 2.From the Graph find or calculate the y-intercept Make sure the graph shows the origin, if reading it directly 3.Take logs of both sides of suggested function 4.Arrange into form of a straight line 5.Compare gradients and y-intercept
• Slide 14
• Qu. 1 AssumeExpress equation in logarithmic form From the graph: m = 0.7 c = 0.2 Relation between x and y is: Find the relation between x and y n = 0.7
• Slide 15
• Qu. 2 AssumeExpress equation in logarithmic form From the graph: m = -0.7 c = 0.4 Relation between x and y is: Find the relation between x and y n = -0.7
• Slide 16
• Qu. 3 When log 10 y is plotted against log 10 x, a best fitting straight line Given m = 2 c = -0.8 Relation between x and y is: has gradient 2 and passes through the point (0.6, 0.4) n = 2 Fit this data to the model Using
• Slide 17
• Qu. 4 When log 10 y is plotted against log 10 x, a best fitting straight line Given m = -1 c = 1.1 Relation between x and y is: has gradient -1 and passes through the point (0.9, 0.2) n = -1 Fit this data to the model Using
• Slide 18
• Qu. 5 AssumeExpress equation in logarithmic form From the graph: m = 0.0025 c = 0.15 Relation between x and y is: Find the relation between x and y
• Slide 19
• Qu. 6 AssumeExpress equation in logarithmic form From the graph: m = -0.015 c = 0.6 Relation between x and y is: Find the relation between x and y
• Slide 20
• 2002 Paper I 11.The graph illustrates the law If the straight line passes through A(0.5, 0) and B(0, 1). Find the values of k and n. ( 4 )
• Slide 21
• 2000 Paper II B11. The results of an experiment give rise to the graph shown. a) Write down the equation of the line in terms of P and Q. ( 2 ) It is given that and b)Show that p and q satisfy a relationship of the form stating the values of a and b. ( 4 )
• Slide 22
• THE END