Binome & Verwandtes

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Question statement

Binome und Verwandtes

Verwenden Sie * als Multiplikationszeichen und ^ für Exponenten.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	6
b	integer	5
a2	integer	-6
b2	integer	-3
c	integer	4
d	integer	5

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(2,4,6)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

Parts

Part a) Gap-fill
1. Gap binom1 Mathematical expression
  Add
Part b) Gap-fill
1. Gap binom2 Mathematical expression
  Add
Part c) Gap-fill
1. Gap binom3 Mathematical expression
  Add
Part d) Gap-fill
1. Gap binom4 Mathematical expression
  Add

Gap-fill

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

Multiplizieren Sie aus!

$\left(\var{a}\cdot x+\var{b}\right)^2=$ binom1

Advice

Lösung zu a):

$\left(\var{a}\cdot x+\var{b}\right)^2=\left(\var{a}\cdot x+\var{b}\right)\cdot\left(\var{a}\cdot x+\var{b}\right)$

$\quad=\var{a}\cdot x\cdot\var{a}\cdot x+\var{a}\cdot x\cdot\var{b}+\var{b}\cdot\var{a}\cdot x+\var{b}\cdot\var{b}=\var{a^2}x^2+\var{2*a*b}\cdot x+\var{b^2}$

Lösung zu b):

$\left(\simplify{{a2}*y+{b2}}\right)^2=\left((\var{a2})\cdot y \var{if(b2>0,latex('+{b2}'),b2)}\right)\cdot\left((\var{a2})\cdot y\var{if(b2>0,latex('+{b2}'),b2)}\right)$

$\quad=(\var{a2})\cdot y\cdot(\var{a2})\cdot y+(\var{a2})\cdot y\cdot\var{if(b2>0,b2,latex('({b2})'))}+\var{if(b2>0,b2,latex('({b2})'))}\cdot(\var{a2})\cdot y+\var{if(b2>0,b2,latex('({b2})'))}\cdot\var{if(b2>0,b2,latex('({b2})'))}$

Lösung zu c):

$\var{d^2}-\var{c^2}\cdot z^2=\var{d}^2-\left(\var{c}\cdot z\right)^2$ wofür wir die dritte binomische Formel $a^2-b^2=(a+b)\cdot(a-b)$ mit $a=\var{d},b=\var{c}\cdot z$ anwenden können und somit erhalten:

$\var{d}^2-\left(\var{c}\cdot z\right)^2=(\var{d}+\var{c}\cdot z)\cdot(\var{d}-\var{c}\cdot z)$

Lösung zu d):

Wir benötigen die Summenregel $f(x)=g(x)+h(x) \rightarrow f'(x)=g'(x)+h'(x)$ und die Potenzregel $f(x)=a\cdot x^n\rightarrow f'(x)=n\cdot a\cdot x^{n-1}$ und erhalten:

$f'(x)=3\cdot\var[fractionNumbers]{b^2/3}x^2+2\cdot\var{a*b}x^2+\var{a^2}=\var{if(b^2=1,"",b^2)}x^2+\var{2*a*b}x^2+\var{a^2}=(\var{if(b^2=1,"",b^2)} x+\var{a})^2$

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Taxonomy: mathcentre

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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

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Generated value: `integer`

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Gap-fill

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Binome & Verwandtes

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`