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12 Commits
7713a71342
...
7bc3520855
Author | SHA1 | Date | |
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7bc3520855 | |||
f89ec34a63 | |||
de13c46a18 | |||
db7ea36df9 | |||
8b796b36e8 | |||
65737c9da6 | |||
151d05ea3a | |||
eef1aa5c0e | |||
5cdd35ea72 | |||
8494666394 | |||
e8224846ab | |||
b9751385d1 |
@ -137,7 +137,11 @@
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}
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}
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#let notsolution(content) = {
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#let if_solutions(content) = {
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if show_solutions { content }
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}
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#let if_no_solutions(content) = {
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if not show_solutions { content }
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}
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@ -126,7 +126,7 @@ Fill the following tropical addition and multiplication tables
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#let col = 10mm
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#notsolution(
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#if_no_solutions(
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table(
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columns: (1fr, 1fr),
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align: center,
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@ -63,7 +63,7 @@ where all exponents represent repeated tropical multiplication.
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Draw a graph of the tropical polynomial $f(x) = x^2 #tp 1x #tp 4$. \
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#hint([$1x$ is not equal to $x$.])
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#notsolution(graphgrid(none))
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#if_no_solutions(graphgrid(none))
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#solution([
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$f(x) = min(2x , 1+x, 4)$, which looks like:
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@ -132,7 +132,7 @@ How can we use the graph to determine these roots?
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Graph $f(x) = -2x^2 #tp x #tp 8$. \
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#hint([Use half scale. 1 box = 2 units.])
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#notsolution(graphgrid(none))
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#if_no_solutions(graphgrid(none))
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#solution([
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#graphgrid({
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@ -210,7 +210,7 @@ and always produces $7$ for sufficiently large inputs.
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#problem()
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Graph $f(x) = 1x^2 #tp 3x #tp 5$.
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#notsolution(graphgrid(none))
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#if_no_solutions(graphgrid(none))
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#solution([
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The graphs of all three terms intersect at the same point:
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@ -261,7 +261,7 @@ How are the roots of $f$ related to its coefficients?
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#problem()
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Graph $f(x) = 2x^2 #tp 4x #tp 4$.
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#notsolution(graphgrid(none))
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#if_no_solutions(graphgrid(none))
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#solution(
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graphgrid({
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@ -10,7 +10,7 @@ Consider the polynomial $f(x) = x^3 #tp x^2 #tp 3x #tp 6$. \
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- use this graph to find the roots of $f$
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- write (and expand) a product of linear factors with the same graph as $f$.
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#notsolution(graphgrid(none))
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#if_no_solutions(graphgrid(none))
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#solution([
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- Roots are 1, 2, and 3.
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@ -48,7 +48,7 @@ Consider the polynomial $f(x) = x^3 #tp x^2 #tp 6x #tp 6$. \
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- use this graph to find the roots of $f$
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- write (and expand) a product of linear factors with the same graph as $f$.
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#notsolution(graphgrid(none))
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#if_no_solutions(graphgrid(none))
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#solution([
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- Roots are 1, 2.5, and 2.5.
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@ -82,7 +82,7 @@ Consider the polynomial $f(x) = x^3 #tp 6x^2 #tp 6x #tp 6$. \
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- use this graph to find the roots of $f$
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- write (and expand) a product of linear factors with the same graph as $f$.
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#notsolution(graphgrid(none))
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#if_no_solutions(graphgrid(none))
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#solution([
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- Roots are 2, 2, and 2.
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@ -1,150 +0,0 @@
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\documentclass[
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solutions,
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singlenumbering,
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nopagenumber
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]{../../../lib/tex/ormc_handout}
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\usepackage{../../../lib/tex/macros}
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\makeatletter
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\newcommand{\thisone}{
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\if@solutions
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{\color{red} $\Leftarrow$ \texttt{this one}}
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\else\fi
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}
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\title{Zeno's Furniture}
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\uptitlel{Warm Ups}
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\uptitler{\smallurl{}}
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\subtitle{Prepared by Mark on \today}
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\begin{document}
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\maketitle
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Zeno Furniture sells exactly five types of furniture:
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\begin{itemize}
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\item Footstools
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\item Hutches
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\item Sideboards
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\item Tables
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\item Vanities
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\end{itemize}
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Irene buys four items, each of a different type,
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and each made of exactly one kind of wood:
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\begin{itemize}
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\item Maple
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\item Oak
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\item Pine
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\item Rosewood
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\end{itemize}
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The following conditions govern Irene's purchases:
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\begin{itemize}
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\item Any vanity she buys is Maple.
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\item Any rosewood item she buys is a sideboard.
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\item If she buys a vanity, she does not buy a footstool.
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\item If she buys a footstool, she also buys a table made of the same material.
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\item Irene does not buy an oak table.
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\item Exactly two of the items she buys are made of the same kind of wood.
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\end{itemize}
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\problem{}
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Which one of the following could be an accurate
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list of the items Irene buys? \par
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\begin{itemize}
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\item maple footstool, maple hutch, rosewood sideboard, maple table
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\item oak hutch, rosewood sideboard, pine table, oak vanity
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\item rosewood hutch, maple sideboard, oak table, maple vanity
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\item pine footstool, rosewood sideboard, pine table, maple vanity
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\item maple footstool, pine hutch, oak sideboard, maple table \thisone{}
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\end{itemize}
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\vfill
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\problem{}
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If Irene buys one item made of rosewood and two items made
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of maple, then which one of the following pairs could be two
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of the items she buys?
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\begin{itemize}
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\item a rosewood sideboard and an oak footstool
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\item an oak hutch and a pine sideboard
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\item an oak hutch and a maple table \thisone{}
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\item a maple sideboard and a maple vanity
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\item a maple hutch and a maple table
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\end{itemize}
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\vfill
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\pagebreak
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\problem{}
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Which one of the following is a complete and accurate list
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of all the woods any footstool that Irene buys could be made of?
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\begin{itemize}
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\item maple, oak
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\item maple, pine \thisone{}
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\item maple, rosewood
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\item maple, oak, pine
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\item maple, oak, pine, rosewood
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\end{itemize}
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\vfill
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\problem{}
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Suppose Irene buys a footstool. Then which one of the following
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is a complete and accurate list of items and any one of which she
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could buy in maple?
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\begin{itemize}
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\item footstool, hutch, sideboard, table, vanity
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\item footstool, hutch, sideboard, table \thisone{}
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\item footstool, hutch, sideboard
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\item footstool, hutch
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\item footstool
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\end{itemize}
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\vfill
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\problem{}
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Which one of the following cannot be the two items Irene
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buys that are made of the same wood as each other?
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\begin{itemize}
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\item footstool, hutch \thisone{}
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\item hutch, sideboard
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\item hutch, table
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\item sideboard, vanity
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\item table, vanity
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\end{itemize}
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\vfill
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\pagebreak
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\problem{}
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If Irene does not buy an item made of maple, then each of the
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following must be true except...
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\begin{itemize}
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\item Irene buys a footstool
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\item Irene buys a pine hutch \thisone{}
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\item Irene buys a rosewood sideboard
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\item Irene buys exactly one item made of oak
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\item Irene buys exactly two items made of pine
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\end{itemize}
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\vfill
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\problem{}
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Suppose the condition that Irene does not buy an oak table is
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replaced with the condition that she does not buy a pine table.
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If all the other conditions hold as originally given, which of the
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following cannot be true?
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\begin{itemize}
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\item Irene buys an oak footstool.
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\item Irene buys a hutch and a table made of the same wood.
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\item Irene buys a vanity, but she does not buy an oak table.
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\item Irene buys a maple table and an oak hutch.
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\item Irene buys a rosewood sideboard and exactly two items made of pine. \thisone{}
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\end{itemize}
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\vfill
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\pagebreak
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\end{document}
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131
src/Warm-Ups/Zeno's Furniture/main.typ
Normal file
131
src/Warm-Ups/Zeno's Furniture/main.typ
Normal file
@ -0,0 +1,131 @@
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#import "@local/handout:0.1.0": *
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#show: doc => handout(
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doc,
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quarter: link(
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"https://betalupi.com/handouts",
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"betalupi.com/handouts",
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),
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title: [Warm-Up: Zeno's Furniture],
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by: "Mark",
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)
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#let thisone = if_solutions(
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text(fill: ored, [#sym.arrow.l.double.long `this one`]),
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)
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Zeno's Furniture sells exactly five types of furniture: \
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Footstools, Hutches, Sideboards, Tables, and Vanities.
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#v(3mm)
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Each can be made of exactly one kind of wood: \
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Maple, Oak, Pine, or Rosewood
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#v(3mm)
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Irene buys four items, each of a different type. \
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The following conditions govern Irene's purchases:
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- Any vanity she buys is Maple.
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- Any rosewood item she buys is a sideboard.
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- If she buys a vanity, she does not buy a footstool.
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- If she buys a footstool, she also buys a table made of the same material.
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- Irene does not buy an oak table.
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- Exactly two of the items she buys are made of the same kind of wood.
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#v(5mm)
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#problem()
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Which one of the following could be an accurate
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list of the items Irene buys? \
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- maple footstool, maple hutch, rosewood sideboard, maple table
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- oak hutch, rosewood sideboard, pine table, oak vanity
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- rosewood hutch, maple sideboard, oak table, maple vanity
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- pine footstool, rosewood sideboard, pine table, maple vanity
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- maple footstool, pine hutch, oak sideboard, maple table #thisone
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#v(1fr)
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#problem()
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If Irene buys one item made of rosewood and two items made
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of maple, then which one of the following pairs could be two
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of the items she buys?
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- a rosewood sideboard and an oak footstool
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- an oak hutch and a pine sideboard
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- an oak hutch and a maple table #thisone
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- a maple sideboard and a maple vanity
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- a maple hutch and a maple table
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#v(1fr)
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#pagebreak()
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#problem()
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Which one of the following is a complete and accurate list
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of all the woods any footstool that Irene buys could be made of?
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- maple, oak
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- maple, pine #thisone
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- maple, rosewood
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- maple, oak, pine
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- maple, oak, pine, rosewood
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#v(1fr)
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#problem()
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Suppose Irene buys a footstool. Then which one of the following
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is a complete and accurate list of items and any one of which she
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could buy in maple?
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- footstool, hutch, sideboard, table, vanity
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- footstool, hutch, sideboard, table #thisone
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- footstool, hutch, sideboard
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- footstool, hutch
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- footstool
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#v(1fr)
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#problem()
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Which one of the following cannot be the two items Irene
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buys that are made of the same wood as each other?
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- footstool, hutch #thisone
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- hutch, sideboard
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- hutch, table
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- sideboard, vanity
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- table, vanity
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#v(1fr)
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#pagebreak()
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#problem()
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If Irene does not buy an item made of maple, then each of the
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following must be true except...
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- Irene buys a footstool
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- Irene buys a pine hutch #thisone
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- Irene buys a rosewood sideboard
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- Irene buys exactly one item made of oak
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- Irene buys exactly two items made of pine
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#v(1fr)
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#problem()
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Suppose the condition that Irene does not buy an oak table is
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replaced with the condition that she does not buy a pine table.
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If all the other conditions hold as originally given, which of the
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following cannot be true?
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- Irene buys an oak footstool.
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- Irene buys a hutch and a table made of the same wood.
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- Irene buys a vanity, but she does not buy an oak table.
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- Irene buys a maple table and an oak hutch.
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- Irene buys a rosewood sideboard and exactly two items made of pine. #thisone
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#v(1fr)
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