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Get Advanced Level Mathematics: Pure Mathematics 2 and 3 PDF

By Hugh Neill, Douglas Quadling, Julian Gilbey

ISBN-10: 0521530121

ISBN-13: 9780521530125

ISBN-10: 0521696356

ISBN-13: 9780521696357

Written to check 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 answer of equations, vectors, differential equations and intricate numbers.

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Extra resources for Advanced Level Mathematics: Pure Mathematics 2 and 3

Example text

It is useful to introduce the symbol <=> for 'is equivalent to'. Ix I= Ia I <=> x2 =a2' \xl>lal <=> x2 >a2; 2 2 if a-:F-0, lxl x x 2 - 4x + 4 2 2 = 4x 2 - ¢::> 3x ¢::> 3{x + l){x -1) = 0 x=-1 or x=l. 2) Solve the inequality / x - 2 /;;;o / 2x - 3 /.

Cb) I x -1 I=I x I+ 1 , (c) Ix-1 I+ Ixi= 1. Volve the equations ca) Ix I= 11- x I+ 1, 5 Are the following statements true or false? Give a counterexample where appropriate. (a) The graph of y =I f(x) I never has negative values for y. ;·:~~3;·:7I~~:~ ~ 1 Solve the inequality r> y. Miscellaneous exercise 2 Ix+ l I< Ix - 21. (OCR) 2 Find the greatest and least values of x satisfying the inequality I2x -1 I~ 5. 3 Sketch, on a single diagram, the graphs of x I I otherwise, solve the inequality x + 2 < 4 Solve the equation and y =Ix+ 21.

006 If you plot these values for yourself, you will see that they aIJpear to fit an exponential decay graph; but to show this conclusively it is necessary to rewrite the equation so that it can be represented by a straight line. Now if p = e -kt as suggested in the question, In p = -kt, so ~ graph of In p against t would be a straight line through the origin with gradient -k . 12 These val,ues are plotted in Fig. 11. 3 in that you know that the graph must pass through the origin. So draw the best line that you can through the origin to fit the plotted points.

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Advanced Level Mathematics: Pure Mathematics 2 and 3 by Hugh Neill, Douglas Quadling, Julian Gilbey

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