By Hugh Neill, Douglas Quadling, Julian Gilbey
Written to compare the contents of the Cambridge syllabus. natural arithmetic 2 corresponds to devices P2 and P3. It covers algebra, logarithmic and exponential services, trigonometry, differentiation, integration, numerical resolution of equations, vectors, differential equations and complicated numbers.
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Extra resources for Advanced Level Mathematics: Pure Mathematics 2 and 3
At what time will the culture exceed 4 million bacteria? 11 A dangerous radioactive substance has a half-life of 90 years. 05 of its initial value. How long will it be before it is deemed safe? 12 Finding log 3 10 is equivalent tq solving the equation x = log 3 10, which itself is equivalent to solving 3x = 10 . Find the following logarithms by forming and solving the appropriate equations. Give your answers correct to 3 significant figures. 8 Graphs of exponential growth The technique of taking logarithms is often useful when you are dealing with economic, social or scientific data which you think might exhibit exponential growth or decay.
Investigate how well these figures can be described by an exponential model. 1, calculate the values given by the equation E for the four animals, and compare these with the numbers given in the table. ) The table shows the mean relative distance, X, of some of the planets from the Earth and the time, T years; taken for one revolution round the sun. By drawing an appropriate graph show that there is an ~pproximate law of the form T = axn , stating the values of a and n . 5 6 Jack takes out a fixed rate savings bond.
6). Find the values of k and n. (b) Estimate how much wheat would be obtained from the use of 250 kg of fertiliser. (MEI, adapted) 14 An experiment was conducted to discover how a heavy beam sagged when a load was hung from it. The results are summarised in a table, where w is the load in tonnes and y is the sag in millimetres. w y 18 2 3 4 5 2} 39 56 82 (a) A suggested model for these data is given by y =a+ bw 2 , where a and b are constants. Use the results for w = 1 and w = 5 to find estimates of a and b, correct to one decimal place.
Advanced Level Mathematics: Pure Mathematics 2 and 3 by Hugh Neill, Douglas Quadling, Julian Gilbey