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Non-mathematical Skills.tex
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PDF
\documentclass[10pt]{article} \usepackage{amssymb,amsmath} \usepackage[hmargin=1cm,vmargin=1cm]{geometry} \usepackage{setspace} \begin{document} %\singlespacing \onehalfspacing %\doublespacing %\setstretch{1.1} \noindent\large Non-mathematical Skills\normalsize\\ \\ \begin{tabular}{r l} \bf Hand Writing:\rm\quad 1.1&Neat and clear\\ 1.2&No possible alternative interpretations of writing\\ 1.3&Proper spacing between lines, especially lines with complex fractions\\ \\ \bf Presentation:\rm\quad 2.1&Answer the question\quad(Check what is being asked before writing the final answer.)\\ 2.2&Declare symbols before using them\quad(e.g. ``Let $\alpha=\angle ABC$'')\\ 2.3&Use the same 3-point angle or 2-point line representation through out a question whenever possible\\ 2.4&$\because$ and $\therefore$ must be followed by a statement\quad(e.g. ``$\therefore f(x)$ is an even function.'', not ``$\therefore$ even'')\\ 2.5&Degree indicators ($^{\circ}$) are compulsory\quad(e.g. $30^{\circ}$, not $30$)\\ 2.6&Write $\tfrac{\:a\:}{b}$, not $a/b$\\ 2.7&Write constant before symbols\quad(e.g. $2ab$, not $ab2$)\\ 2.8&Use proper terminology\quad(e.g. ``local minimum'', not just ``minimum'')\\ 2.9&State the answers at the end (instead of scattering them through out the question)\\ 2.10&State LHS=RHS or QED at the end of a proof\\ \\ \bf Organisation:\rm\quad 3.1&Plan the plot (or at least several steps ahead) before writing\\ 3.2&Consider alternative paths and take the shortest one\\ 3.3&Arrange steps in a logical order\\ 3.4&No missing links \--- Each step must be derivable from the previous step or some previous steps.\\ 3.5&Cross out unnecessary, unwanted or wrong steps \--- No liquid paper\\ \\ \bf Speed:\rm\quad 4.1&Simplify first before calculating or answering\\ 4.2&Always consider better or faster alternatives\\ 4.3&Use $f''(x)$ in concavity testing only if it is asked or easier than using value testing\\ 4.4&Geometric calculations can be brief (while proofs need to be detailed)\\ 4.5&More focused towards the end of an exam (as you grow tired while questions become harder)\\ \\ \bf Accuracy:\rm\quad 5.1&Check missing brackets and multilevel nested brackets\\ 5.2&Consider both $+$ and $-$ alternatives\\ 5.3&Use radians unless the question is in degrees or asks to do it in degrees\\ 5.4&Always test in case of maximum, minimum and point of inflection (table with $+$ and $-$ values)\\ 5.5&Check precision (number of significant digits or decimal places)\\ 5.6&Hand sketch a simple graph; this helps thinking \it a lot\rm.\\ 5.7&Solve absolute value inequalities on graph; use algebra only if required (still check on a graph)\\ 5.8&Always check validity of answers for questions with square roots or absolute values\\ \\ \bf Graphing:\rm\quad 6.1&Label all critical points: intercepts, stationary points, intersections, axes, curves, etc\\ 6.2&Plan the scale (domain and range) before sketching\\ 6.3&Avoid non-existing relationships\quad(e.g. No parallel, perpendicular, collinear, bisection, \ldots unless so)\\ 6.4&Check derived points on the graph against the \it original \rm equation (e.g. points derived from the shape).\\ \end{tabular} \begin{align*} \end{align*} \end{document}