update practice exams

diff --git a/methods/methods-collated.tex b/methods/methods-collated.tex
index 4a0403a6248f93e03ae0378cc2e6c106cda9b30e..c4d21f10e356277e211572b0c50915794d520009 100644 (file)
--- a/methods/methods-collated.tex
+++ b/methods/methods-collated.tex
@@ -7,9 +7,10 @@
 \usepackage{dblfloatfix}
 \usepackage{enumitem}
 \usepackage{fancyhdr}
-\usepackage[a4paper,margin=2cm]{geometry}
+\usepackage[a4paper,margin=1.8cm]{geometry}
 \usepackage{graphicx}
 \usepackage{harpoon}
+\usepackage{keystroke}
 \usepackage{listings}
 \usepackage{makecell}
 \usepackage{mathtools}
@@ -96,8 +97,8 @@
 \definecolor{peach}{HTML}{e6beb2}
 \definecolor{lblue}{HTML}{e5e9f0}
 
-\newtcolorbox{cas}{colframe=cas!75!black, title=On CAS, left*=3mm}
-\newtcolorbox{warning}{colback=white!90!black, leftrule=3mm, colframe=important, coltext=important, fontupper=\sffamily\bfseries}
+\newtcolorbox{cas}{colframe=cas!75!black, fonttitle=\sffamily\bfseries, title=On CAS, left*=3mm}
+\newtcolorbox{warning}{colback=white!90!black, leftrule=3mm, colframe=important, coltext=darkgray, fontupper=\sffamily\bfseries}
 \newtcolorbox{theorembox}[1]{colback=green!10!white, colframe=blue!20!white, coltitle=black, fontupper=\sffamily, fonttitle=\sffamily, #1}
 
 
@@ -121,15 +122,11 @@
 \subsection*{One to one functions}
 
 \begin{itemize} \tightlist
-  \item
-    \(f(x)\) is \emph{one to one} if \(f(a) \ne f(b)\) if
-    \(a, b \in \operatorname{dom}(f)\) and \(a \ne b\)\\
-    \(\implies\) unique \(y\) for each \(x\) (\(\sin x\) is not 1:1,
-    \(x^3\) is)
-  \item
-    horizontal line test
-  \item
-    if not one to one, it is many to one
+  \item \(f(x)\) is 1:1 if \(f(a) \ne f(b) \> \forall \>\{a,b\} \in \operatorname{dom}(f)\) \\
+        \(\implies\) unique \(y\) for each \(x\)
+  \item e.g. \(\sin x\) is not 1:1, \(x^3\) is
+  \item horizontal line test
+  \item if not one to one, it is many to one
 \end{itemize}
 
 \subsection*{Odd and even functions}
@@ -219,6 +216,22 @@ For \(x^n\), parity of \(n \equiv\) parity of function
       \textbf{Open circle:} point included\\
       \textbf{Closed circle:} point not included
 
+\begin{cas}
+  Define piecewise functions: \\
+  \-\hspace{1em}Math3 \(\rightarrow\)
+  \begin{tikzpicture}%
+    \draw rectangle (0.5,0.5); 
+    \node at (0.08,0.25) {\(\{\)};
+    \filldraw [black] (0.15, 0.4) rectangle(0.25, 0.3);
+    \draw (0.35, 0.4) rectangle(0.45, 0.3);
+    \node [font=\footnotesize] at (0.3,0.3) {\verb;,;};
+    \draw (0.15, 0.2) rectangle(0.25, 0.1);
+    \node [font=\footnotesize] at (0.3,0.1) {\verb;,;};
+    \draw (0.35, 0.2) rectangle(0.45, 0.1);
+  \end{tikzpicture}
+  % TODO: finish this section
+\end{cas}
+
       \subsection*{Operations on functions}
 
       For \(f \pm g\) and \(f \times g\):
@@ -258,8 +271,10 @@ For \(x^n\), parity of \(n \equiv\) parity of function
       \begin{figure*}[ht]
         \centering
 
-        \begin{tabularx}{\textwidth}{r|Y|Y}
+        \begin{tabularx}{\textwidth}{|r|Y|Y|}
 
+          \hline
+          \rowcolor{lblue}
           & \(n\) is even & \(n\) is odd \\ \hline
 
           \centering \(x^n, n \in \mathbb{Z}^+\) &