diff --git a/amc-templates/amc_template_en/extra_section.tex b/amc-templates/amc_template_en/extra_section.tex index e510db0..e78a444 100644 --- a/amc-templates/amc_template_en/extra_section.tex +++ b/amc-templates/amc_template_en/extra_section.tex @@ -1,82 +1,83 @@ \setlength{\parindent}{0pt}% \newpage %*******************************************************************% % Suppress begin-question texts \renewcommand{\AMCbeginQuestion}[2]{\QuestionText{#1}} \def\QuestionText{\TEXT} \def\TEXT#1{} \def\NOTEXT#1{} \setlength{\parindent}{0pt}% +\addtocounter{AMCquestionaff}{1} %*******************************************************************% \subsection*{Third part, open questions} \noindent Answer in the empty space below. Your answer should be carefully justified, and all the steps of your argument should be discussed in details. Leave the check-boxes empty, they are used for the grading. \bigskip %% Leave at least 2 empty lines after the \bigskip %*************************** % Question A - 6points %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{description} \item[Question~\theAMCquestionaff :] \textit{This question is worth 6 points.} \end{description} \correctorSix{OPEN-A}{~} \correctorStop Let $\alpha\in \C$. \begin{itemize} \item [1.] Find the explicit formula for the elements of the matrix $A_n = \begin{pmatrix}\alpha &1\\ 0 &\alpha\end{pmatrix}^{n}$, where $n \geq 1$ is an integer. Show the formula by reccurance. \item [2.] Let $\alpha = 1+\textrm{i}$. Calculate $\alpha^{99}$ and $\alpha^{100}$. \item [3.] Calculate $\begin{pmatrix} 1+\textrm{i} &1\\ 0 &1+\textrm{i}\end{pmatrix}^{100}$. \end{itemize} \OpenGrid{16cm} % Question B - 10points %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{description} \item[Question~\theAMCquestionaff :] \textit{This question is worth 10 points.} \end{description} \correctorTenHalf{OPEN-B}{~} \correctorStop Let $\alpha\in \C$. \begin{itemize} \item [1.] Find the explicit formula for the elements of the matrix $A_n = \begin{pmatrix}\alpha &1\\ 0 &\alpha\end{pmatrix}^{n}$, where $n \geq 1$ is an integer. Show the formula by reccurance. \item [2.] Let $\alpha = 1+\textrm{i}$. Calculate $\alpha^{99}$ and $\alpha^{100}$. \item [3.] Calculate $\begin{pmatrix} 1+\textrm{i} &1\\ 0 &1+\textrm{i}\end{pmatrix}^{100}$. \end{itemize} \OpenGrid{17cm} \FullPageOpenGrid % Question C - 15points %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{description} \item[Question~\theAMCquestionaff :] \textit{This question is worth 20 points.} \end{description} \correctorTwenty{OPEN-C}{~} \correctorStop Let $\alpha\in \C$. \begin{itemize} \item [1.] Find the explicit formula for the elements of the matrix $A_n = \begin{pmatrix}\alpha &1\\ 0 &\alpha\end{pmatrix}^{n}$, where $n \geq 1$ is an integer. Show the formula by reccurance. \item [2.] Let $\alpha = 1+\textrm{i}$. Calculate $\alpha^{99}$ and $\alpha^{100}$. \item [3.] Calculate $\begin{pmatrix} 1+\textrm{i} &1\\ 0 &1+\textrm{i}\end{pmatrix}^{100}$. \end{itemize} \vskip 5pt \OpenBox{16.5cm}