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 features, 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
301... This type of equation arises in various applications. h gives . 1 Iodine--131 is a radioactive isotope used in treatment of the thyroid gland. 9174 1 units. 1 units? 1. 1. Now beware! 708 .... 7 days. 01 3 + ... must be taken to give a sum greater than 1 million? Oln >IO 001. 01>logIO001. 6 .... 01 The smallest integer n satisfying this inequality is 926 . 6 was solved using logarithms to base 10, but the steps leading to x = logb 3 logb 2 could have been made with any base b. For example, you could choose base e_, using the [LN] key on your calculator to give .
8 Fig. 7 If the graph is drawn with the price shown on a logarithmic scale, you get Fig. 8. If the claim were true, this graph would be a straight line. This seems approximately true for the first three years, but more recently the graph has begun to bend downwards, suggesting that the early promise of exponential growth has not been sustained. The ideas of the last two examples can be combined, not just to investigate whether there is an exponential relationship, but also to find the numerical constants in the equation.
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. This means he makes one payment and leaves his money for a fixed number of years.
Advanced Level Mathematics: Pure Mathematics 2 and 3 by Hugh Neill, Douglas Quadling, Julian Gilbey