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**Extra resources for Numerische Mathematic Bd. 67 - 84**

**Example text**

18 Solve the system of linear equations y = – x + 7 and y = 2x + 1 . S o We sketch both lines on the same set of axes: l u t i o n y Reading off the grid we can see that the straight lines meet at the point with coordinates (2, 5). So, the solution to the given system of equations is x = 2 and y = 5. 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 x The graphical approach has a disadvantage. Sometimes it can only provide an approximate answer. This depends on the accuracy of the sketch or simply on the equations, for example, sketching the pair of straight lines with equations y = result in an approximate solution.

1977). A. H. Freeman & Co. 6 THE EXTENDED ESSAY We would like to encourage students to consider Mathematics as a choice of subject for their extended essay. Whilst there is a requirement that these have solid academic content, it is not necessary to record an original discovery to produce an excellent essay! That said, many of the great original discoveries of mathematics are the work of comparatively young individuals with a modest level of ‘experience’. An excellent example is Evariste Galois who struggled to enter university and whose life was cut short by a duel in 1832 at age 21.

The set of all sets of type 2 cannot be properly deﬁned without reaching a contradiction. The most commonly accepted result of Russell’s paradox is the conclusion that we have to be very careful when we talk about sets of everything. The most usual way out is to work within a carefully deﬁned universal set, chosen to be appropriate to the mathematics that we are undertaking. If we are doing normal arithmetic, the universal set is the set of real numbers. 5 MATHEMATICS AND OTHER DISCIPLINES When writing Theory of Knowledge essays, students are required to develop their arguments in a cross disciplinary way.