Gleichungen bei Diophant

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Andreas Vohns

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Andreas Vohns 4 years, 5 months ago

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Question statement

Wir betrachten ein weiteres Problem der Form: Zwei Zahlen finden, deren Summe und deren Summe der Quadrate der Zahlen gegeben sind.

Summe sei $\var{sum}$ , Quadratsumme $\var{qsum}$ .

Wir bezeichnen die Differenz der beiden Zahlen mit $2\cdot x$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

sum	integer	70
a	rational	20
b	rational	50
qsum	rational	2900
x	integer	15

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(4..8)*10

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

→ Used by:

Statement
Advice
"Part a)" → "a" - Correct answer
"Part a)" → "b" - Correct answer

Parts

Part a) Gap-fill
1. Gap a Mathematical expression
  Add
2. Gap b Mathematical expression
  Add
Part b) Gap-fill
1. Gap a Number entry
  Add
2. Gap b Number entry
  Add
3. Gap x Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Dann ist die kleinere der beiden Zahlen $a=$ a und die größere der beiden Zahlen $b=$ b.

Jeweils einen Term in Abhängigkeit von $x$ eintragen!

Advice

a) Es ist $a=\frac{\var{sum}}{2}-x=\var{sum/2}-x$ , $b=\frac{\var{sum}}{2}+x=\var{sum/2}+x$ .

b) Es ergibt sich: $\var{qsum}=2\cdot\var{(sum/2)^2}+2x^2\Leftrightarrow x^2=\frac{\var{qsum}-\var{2*(sum/2)^2}}{2}=\frac{\var{(qsum-2*(sum/2)^2)}}{2}=\var{(qsum-2*(sum/2)^2)/2}\Leftrightarrow x=\var{x}$

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Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Andreas Vohns 4 years, 5 months ago

Andreas Vohns 4 years, 5 months ago

Andreas Vohns 4 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Gleichungen bei Diophant

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Andreas Vohns 4 years, 5 months ago

Andreas Vohns 4 years, 5 months ago

Andreas Vohns 4 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`