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@BillFoster
Created January 15, 2012 18:45
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list as an answer in a jme gapfill
{ notes: ""
name: MAS3214 20122013 CBA1_4
percentPass: 50
shuffleQuestions: false
rulesets:{
std:[all,fractionNumbers, !collectNumbers,!noLeadingMinus]
}
navigation: {
allowregen: true
showfrontpage: false
reverse: true
browse: true
}
feedback: {
showtotalmark: true
}
questions: [
{
name: MAS3214 20122013 CBA1_4
variables: {
n: "p*q"
p: "random(5,7,11)"
q: "switch(p=7,random(2,3,5),random(2,3))"
a: "random(2..n-1)"
m: "random(1..3)"
b: "if(a+p-m*q>=0,mod(a+p-m*q,n),n+mod(a+p-m*q,n))"
a1: "mod(a+p,n)"
b1: "if(a-m*q>=0,mod(a-m*q,n),n+mod(a-m*q,n))"
c: "mod(a+b,n)"
d: "mod(a*b,n)"
ans: "sort([b,a1,b1])"
}
parts: [
{
type: gapfill
prompt: """
Show that $x=\var{a}$ is a solution of the quadratic equation in $\mathbb{Z}_{\var{n}}$ :
\[\simplify[std]{x^2 -{c}x+{d} = 0}\]
There are four solutions in $\mathbb{Z}_{\var{n}}$ of this quadratic equation.
Enter the other 3 roots apart from $x=\var{a}$ in a list below as elements in $\mathbb{Z}_{\var{n}}$ i.e. in the form $[a,b,c]$ with $0\le a \lt b \lt c \le \var{n-1}$
Other three roots are: [[0]]
"""
gaps: [
{type: jme, answer: "{ans}", marks: 4}
]
}
]
advice: """
"""
}
]
}
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