## Sample Quiz Questions

\begin{document} \maketitle \textbf{ $\C$ 2011, Prof. George K. Francis, Mathematics Department, University of Illinois} \section{Introduction} What follows is intended to show the reader the sort of questions to expect on an exam in the course. All tests come with a set of instructions whose purpose is to optimize both taking and grading the work. This includes \begin{itemize} \item Read over the entire exam, and work on the "easy" ones first. \item Because every problem is worth the same number of points, and each part of a problem receives the same amount of partial credig. \item Start each problem on a new side/page/piece of paper. \item Because problems that start in the middle of text are apt to be overlooked, and scoring is additive, not subtractive. \item Write your name on the upper right corner of each page. \item Because papers get shuffled sometimes. \item Start writing 1 inch below the top of each page. \item Because stapling the sheets top left hides anything written there. \item Draw and label your figures accurately. \item Because a figure simplified your exposition and sometimes covers for omitted hypotheses. \item When in doubt what is asked, state what you are proving. \item Because you may be answering the "wrong" question, one not asked. Or you must substitute, and tell the grader what you're doing. \item Return the cover sheet with your exam. \item Because it has the score-box on it, and items you might not have repeated in you work. The grader receives a self-contained paper. \item Cross out rather than erasing large sections of work. \item Return any scratch paper you used with the exam. \item Because about 1 out of 10 papers has correct work crossed out or on the scratch paper, but was presented incorrectly. \item Read and follow the instructions. \item Because there may be addtional instructions, such as "do 3 out ot 4". and points may be subtracted for sloppy work. \end{itemize} On some tests you may use your class Journal for reference. Read the Advice on how to keep your Journal. On a test it is important that you can find items quickly. Never refer to theorem numbers, pages in the the textbook, or blindly copy items from your journal. You will loose points for a soltution on a test that gives no evidence of your thinking through your answers. \subsection{Axiomatic systems} A problem on system of axioms could read like this one. Expect a different set of axioms, and similar questions about them arranged in a similar way. Note the capitalization convention we follow in this section of the course. \begin{itemize} \item \textbf{Problem} Consider this system of axioms: \begin{itemize} \item \textbf{A1} There are exactly four Lines. \\ \item \textbf{A2} Every pair of Lines has exactly one Point in common.\\ \item \textbf{A3} Every Point lies on exactly two Lines.\\ \end{itemize} \item \textbf{(a)} Is this axiomatic system consistent? Why or why not? \item \textbf{(b)} Show that the third axiom is independent of the other two.\\ \item \textbf{(c)} Prove that every Line has exactly three Points on it.\\ \end{itemize} \subsection{Greek geometry} There are exemplary theorems and proofs that were introduced at the beginning of the course. Their knowledge is tested by questions like the following. Keep a list of such theorem in your journal. Know the difference between being asked to \textit{name, state, prove} a theorem. You name it in a justification step, you state it together with the most relevant definitions, and you prove the best you can. See the Advice sections for more detail. \begin{itemize} \item \textbf{Problem} \item \textbf{(a)} State Thales' Theorem. \\ \item \textbf{(b)} Draw and label a figure relevant for a proof.\\ \item \textbf{(c)} Prove Thales' Theorem \\ \end{itemize} \end{document}