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<h1>
Analysis of errors in definitions 
</h1>
This page shows the results of analysis of error distribution over definitions used in four performed tasks. You see the total number of errors per definition. The recommended methodical exercise aim trains an ability to lay down definitions.
<hr  align="center" width="100%" size="1" ></hr>
<div align="center"><h1>Analysis: definitions - All performed tasks</h1></div>
<b>Contents</b>
<table width="100%"><tr><td></td><td>
<a href="#pont0">Table</a>
</td></tr><tr><td></td><td>
<a href="#tont0">Plot</a>
</td></tr><tr><td></td><td>
<a href="#font0">Methodical recommendations:</a>
</td></tr>
</table>
<a name="font0"></a><a href="#cont0"><b>Methodical recommendations:</b></a><br></br>
<br></br>
<b>Perform the task</b>
<br></br>
Rational equations<br></br>
Quadratic equations<br></br>
Equations. Method of substitution. Grouping method<br></br>
Solve the equation<br></br>
<table width="100%">
<tr>
<td>
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<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msup><mfenced><mrow><mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>40 </mi><msup><mi>y</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>26 </mi><mi>y</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>3 </mi></mrow></mrow></mrow></mfenced><mrow><mrow><mrow><mi>2 </mi></mrow></mrow></mrow></msup><mo>+</mo><msup><mfenced><mrow><mrow><mrow><mi>20 </mi><msup><mi>y</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>13 </mi><mi>y</mi></mrow><mrow><mo>+</mo><mi>6 </mi></mrow></mrow></mrow></mfenced><mrow><mrow><mrow><mi>2 </mi></mrow></mrow></mrow></msup><mo>=</mo><msup><mfenced><mrow><mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>20 </mi><msup><mi>y</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>13 </mi><mi>y</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>2 </mi></mrow></mrow></mrow></mfenced><mrow><mrow><mrow><mi>2 </mi></mrow></mrow></mrow></msup><mo>+</mo><mrow><mrow><mi>2 </mi></mrow></mrow><mo>&#x00B7;</mo><mrow><mo maxsize="2">(</mo><mrow><mrow><mrow><mi>20 </mi><msup><mi>y</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>13 </mi><mi>y</mi></mrow><mrow><mo>+</mo><mi>6 </mi></mrow></mrow></mrow><mo maxsize="2">)</mo></mrow><mo>&#x00B7;</mo><mrow><mo maxsize="2">(</mo><mrow><mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>40 </mi><msup><mi>y</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>26 </mi><mi>y</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>3 </mi></mrow></mrow></mrow><mo maxsize="2">)</mo></mrow></mrow></mrow></math>
</td>
</tr>
</table>
<b>Solve the problem with any of the following techniques </b>
<table width="100%">
<tr>
<td>
</td>
<td width="95%">
Scheme "To view 3"
</td>
</tr>
<tr>
<td>
</td>
<td width="95%">
Scheme "To relate the step with category 2"
</td>
</tr>
<tr>
<td>
</td>
<td width="95%">
Scheme "To learn categories 2"
</td>
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<tr>
<td>
</td>
<td width="95%">
Scheme "To view and learn categories 2"
</td>
</tr>
<tr>
<td>
</td>
<td width="95%">
Scheme "To relate categories with the step 2"
</td>
</tr>
<tr>
<td>
</td>
<td width="95%">
Scheme "To select for transformation 2"
</td>
</tr>
</table>
<a name="pont0"></a><a href="#cont0"><b>Table</b></a>
<br></br>
<br></br>
<table width="100%" border="1" cellspacing="1" cellpadding="1" bordercolor="#3399CC">
<tr bgcolor="#336699" class="tableh1">
<td width="3%">
<b>N</b>
</td>
<td><div align="center">
Formulation
</div></td>
<td width="5%">
Errors:
</td>
<td width="5%">
Hints:
</td>
<td width="5%">
Total:
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>0</b>
</td>
<td >
A binary operation on a set is referred to as an operation relating (transforming) two elements of the set to the third element of this set: "aTb=c", where a, b, c are the elements of the set, and T is a binary operation
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>5</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>6</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>1</b>
</td>
<td >
Monomial is referred to as an algebraic expression consisting of numerals, variables to different natural powers and operation of multiplication
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>2</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>3</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>2</b>
</td>
<td >
The addition principle of equivalence of equations: The same expression may be added to and subtracted from both sides of equation
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>2</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>2</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>3</b>
</td>
<td >
A region of formula definition is referred to as all values of argument and parameters entering the formula, at which the formula's relation is defined
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>2</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>4</b>
</td>
<td >
A solution of an inequality is referred to as a range of unknown under which an inequality is valid
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>5</b>
</td>
<td >
A product equals to zero when at least one multiplier equals to zero and the other multipliers do not lose their numeric sense
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>6</b>
</td>
<td >
A substitution is referred to as a replacement of argument by a function of new argument according to the rule: x=f(t) (where x is the old argument, t - the new argument, f - the function of substitution), supplemented with indication of the region of substitution definition
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>7</b>
</td>
<td >
An operation of addition is referred to as a binary operation on a set, satisfying the associative and commutative laws with the existing neutral (zero point) element and inverse elements
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>8</b>
</td>
<td >
A root of equation is referred to as a value of the unknown converting the equation into identity
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
<tr>
<td bgcolor="#CCCCCC">
<b>9</b>
</td>
<td >
The binomial coefficients are referred to as factors entering the binomial formula; they depend on power exponent. These factors are calculated using the combinatorial relations
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>0</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
<td bgcolor="#CCCCCC">
<div align="center"><b>1</b></div>
</td>
</tr>
</table>
<br></br>
<a name="tont0"></a><a href="#cont0"><b>Plot</b></a>
<div align="center"><table>
<tr>
<td>
<img src="8.jpg"  border="0" align="bottom" alt="detail" width="726" height="520"></img>
</td>
</tr>
</table></div>
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<div>EMTeachline &#x00A9; 2003-2005</div>
<div>Utrecht, The Netherlands </div></span></div>
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