test-9d-mate-sincai-Algebra - W - Collection-20130516-1959 Argumentul unui nr. complex Aflati argumentul redus al numarului z = #z .

Sa se determine numarul submultimilor cu trei elemente, ale multimii A, care contin elementul #e.

Numarul submultimilor cu cate doua elemente, ale multimii cu #j elemente este si numarul submultimilor cu cate trei elmente ale multimii A, care contin elementul #e .

]]> Combinatorica - Probabilitati Sa se determine probabilitatea ca , alegand un numar din multimea numerelor naturale nenule, mai mici sau egale decat #a, acesta sa fie patrat perfect.

]]> 1.0000000 0.3333333 0 0 #p <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>1000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">while</csymbol><mrow><msup><mi>i</mi><mn>2</mn></msup><mo>⩽</mo><mi>a</mi></mrow><mrow><mi>i</mi><mo>=</mo><mi>i</mi><mo>+</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mrow><mi>i</mi><mo>-</mo><mn>1</mn></mrow><mi>a</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#p</correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Determinant - 3 Se da matricea M = #M.

Sa se determine x «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8712;«/mo»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#8450;«/mi»«/math» astfel incat rangul matricei M sa fie cel mult egal cu 2.

]]> 1.0000000 0.3333333 0 0 #a Determinantul matricei #M este #d .

Sa se determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#8474;«/mi»«/math» astfel incat rangul matricei M sa fie cel mult egal cu 2.

]]> 1.0000000 0.3333333 0 0 #a Determinantul matricei #M este #d .

]]> 1.0000000 0.3333333 0 true Coeficientul termenului liber al ecuatiei det#M = 0, este

]]> #c Coeficientul termenului ce il contine pe x in ecuatia det#M = 0, este

]]> #b Determinantul matricei #M este :

]]> #d #e Multimea solutiilor reale aleecuatiei det #M = 0 este

]]> #v #u #z <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>x</mi></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>x</mi></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>determinant</mi><mo>(</mo><mi>N</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>determinant</mi><mo>(</mo><mi>M</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><msub><mi>d</mi><mn>0</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msub><mi>d</mi><mn>1</mn></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>solve</mi><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd/></mtr></mtable></mfenced></mrow><mrow><mo>"</mo><mi>vida</mi><mo>"</mo></mrow><mrow><mo>"</mo><mi>nevida</mi><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v</mi><mo>=</mo><mo>"</mo><mi>vida</mi><mo>"</mo></mrow><mi>nevida</mi><mrow><mo>"</mo><mi>vida</mi><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>z</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mn>10</mn><mo>)</mo></mrow><mrow><mo>(</mo><mi>z</mi><mo>≠</mo><mi>b</mi><mo>)</mo><mo>∧</mo><mo>(</mo><mi>z</mi><mo>≠</mo><mi>c</mi><mo>)</mo></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> Se dau matricele A= #A si B =#B.

]]> 1.0000000 0.3333333 0 true Produsul dintre matricele A=#A si B=#B este

]]> #P #Q Det(A)=

]]> #a Valoarea lui x pentru care det(A) = det(B) este

]]> #r #u #b #c <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>x</mi></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>x</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>A</mi><mo>*</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mi>A</mi><mo>*</mo><mi>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>determinant</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>determinant</mi><mo>(</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>determinant</mi><mo>(</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msub><mi>s</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><msub><mi>t</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>22</mn></mtd><mtd><mn>3</mn></mtd><mtd><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn></mtd></mtr><mtr><mtd><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></mtd><mtd><mo>-</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn></mtd><mtd><mn>8</mn></mtd></mtr><mtr><mtd><mn>28</mn></mtd><mtd><mn>3</mn></mtd><mtd><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>10</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>70</mn><mn>19</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Discriminant -1 Ecuatia #a x² + #b x + #c = 0 are discriminantul egal cu :

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>d</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>44</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>44</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ecuatie - progresii arittmetice Sa se determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#8469;«/mi»«/math», astfel incat 1 + 5 + 9 + . . . + x = #s

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>13</mn><mo>,</mo><mn>63</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mo>(</mo><mn>1</mn><mo>+</mo><mi>x</mi><mo>)</mo><mo>*</mo><mo>(</mo><mi>k</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Ecuatie-calcul algebric 1.0000000 0.3333333 0 true Multimea valorilor reale ale lui x, pentru care ecuatia «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»3«/mn»«/math», nu are sens, este :

]]> { #c1, #c2 } Multimea solutiilor ecuatiei : «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»3«/mn»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«mrow»«mn»2«/mn»«mi»x«/mi»«mo»-«/mo»«mo»#«/mo»«mi»a«/mi»«mn»1«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mn»3«/mn»«/math» , este :

]]> { #s1, #s2 } { #sf1, #s2 } { #c1, #cf2 } <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>simplify</mi><mo>(</mo><mfrac><mrow><mn>3</mn><mi>x</mi><mo>-</mo><mi>a1</mi></mrow><mrow><mi>x</mi><mo>+</mo><mi>a1</mi></mrow></mfrac><mo>+</mo><mfrac><mrow><mi>x</mi><mo>+</mo><mi>a1</mi></mrow><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfrac><mo>-</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>num</mi><mo>(</mo><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>den</mi><mo>(</mo><mi>a</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>S</mi><mo>∩</mo><mi>C</mi><mo>=</mo><mo>{</mo><mo> </mo><mo>}</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mi>S</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mo>"</mo><mi>atn</mi><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><msub><mi>S</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><msub><mi>S</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msub><mi>C</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><msub><mi>C</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sf1</mi><mo>=</mo><mi>s1</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cf2</mi><mo>=</mo><mi>c2</mi><mo>-</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>35</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mn>7</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ecuatii logaritmice O solutie a ecuatiei log₂(x - #b) + log₂ ( 2x - #c ) = #a, este :

]]> 1.0000000 0.3333333 0 0 #s1 <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>solve</mi><mfenced><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo><mo>=</mo><msup><mn>2</mn><mi>a</mi></msup></mrow></mfenced></mtd></mtr><mtr><mtd><mi>s1</mi><mo>=</mo><msub><mi>s</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>s2</mi><mo>=</mo><msub><mi>s</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>max</mi><mo>(</mo><mi>b</mi><mo>,</mo><mfrac><mi>c</mi><mn>2</mn></mfrac><mo>)</mo></mtd></mtr></mtable><mrow><mi>s1</mi><mo>∈</mo><rationals/><mo>∧</mo><mi>s1</mi><mo>></mo><mi>m</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>9</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s1</correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Formule trigonometrice Sa se calculeze cos(#a)

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>{</mo><pi/><mo>/</mo><mn>5</mn><mo>,</mo><mn>2</mn><mo>*</mo><pi/><mo>/</mo><mn>5</mn><mo>,</mo><pi/><mo>/</mo><mn>8</mn><mo>,</mo><pi/><mo>/</mo><mn>12</mn><mo>,</mo><mn>5</mn><mo>*</mo><pi/><mo>/</mo><mn>12</mn><mo>,</mo><mn>5</mn><mo>*</mo><pi/><mo>/</mo><mn>8</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>2</mn><pi/><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>cos</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>5</mn></msqrt><mn>4</mn></mfrac><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Formule utile : cos(x) = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#177;«/mo»«msqrt»«mfrac»«mrow»«mn»1«/mn»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mi»cos«/mi»«mo»(«/mo»«mn»2«/mn»«mi»x«/mi»«mo»)«/mo»«/mrow»«mn»2«/mn»«/mfrac»«/msqrt»«/math»

]]> Formule trigonometrice II «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»r«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»r«/mi»«mi»i«/mi»«mi»c«/mi»«mi»e«/mi»«mo»§#160;«/mo»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mo»§#160;«/mo»«mi»R«/mi»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mo»{«/mo»«mo»§#160;«/mo»«mi»k«/mi»«mo»*«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»/«/mo»«mi mathvariant=¨normal¨»k«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»Z«/mi»«mo»§#160;«/mo»«mo»}«/mo»«mspace linebreak=¨newline¨/»«/math», #t * cos2x *cos4x = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»sin«/mi»«mo»(«/mo»«mn»8«/mn»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mn»8«/mn»«mo»*«/mo»«mi»sin«/mi»«mi»x«/mi»«/mrow»«/mfrac»«/math»

]]> Graficul functiei f :

]]> 1.0000000 0.3333333 0 true Varful parabolei asociate functiei f este de coordonate :

]]> (#xv, #yv) Valoarea minima a functiei f este :

]]> #yv (#xf, #yf) #yf <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo> </mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xv</mi><mo>=</mo><mo>-</mo><mfrac><mi>b</mi><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yv</mi><mo>=</mo><mi>f</mi><mo>(</mo><mo>-</mo><mfrac><mi>b</mi><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xf</mi><mo>=</mo><mfrac><mi>b</mi><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yf</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>xf</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> Functie de gradul I - identificare diferenta coeficienti «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»D«/mi»«mi»a«/mi»«mi»c«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»m«/mi»«mi»a«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»j«/mi»«mi»o«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mi»v«/mi»«mi»e«/mi»«mi»m«/mi»«mo»§#160;«/mo»«mi»r«/mi»«mi»e«/mi»«mi»p«/mi»«mi»r«/mi»«mi»e«/mi»«mi»z«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»g«/mi»«mi»r«/mi»«mi»a«/mi»«mi»f«/mi»«mi»i«/mi»«mi»c«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»f«/mi»«mi»u«/mi»«mi»n«/mi»«mi»c«/mi»«mi»t«/mi»«mi»i«/mi»«mi»e«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»f«/mi»«mo»§#160;«/mo»«mo»:«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#8594;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mi»a«/mi»«mi»x«/mi»«mo»+«/mo»«mi»b«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mi»t«/mi»«mi»u«/mi»«mi»n«/mi»«mi»c«/mi»«mi»i«/mi»«/math»

a - b =

]]> 1.0000000 0.3333333 0 0 #s <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>plotter</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>center</mi><mo>=</mo><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>width</mi><mo>=</mo><mn>5</mn><mo>,</mo><mo> </mo><mi>height</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced></mfenced></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plotter1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plotter1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>a</mi><mo>-</mo><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"/><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data></localData></question> O solutie simpla ar fi : a -b = - f(-1) !

]]> Grafic Graficul functiei f : R → R, f(x) = #a*«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«/math» +#b*x + #c , este situat in intregime deasupra axei Ox.

]]> Graficul functiei date :

]]> 1.0000000 1.0000000 0 Adevărat Fals <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>a</mi><mo>></mo><mn>0</mn><mo>∧</mo><mi>d</mi><mo><</mo><mn>0</mn><mo>)</mo></mrow><mrow><mi>s</mi><mo>=</mo><mi>true</mi></mrow><mrow><mi>s</mi><mo>=</mo><mi>false</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>f</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>128</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>false</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Identificare functii 2 Care din graficele de mai jos este al functiei liniare «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»§#160;«/mo»«mo»:«/mo»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«mo»§#160;«/mo»«mo»§#8594;«/mo»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» , «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»=«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#183;«/mo»«mi»x«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mo»?«/mo»«/math»

]]> 1.0000000 0.3333333 0 true true abc #f

]]> #g

]]> #h

]]> #k

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>random</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>random</mi><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>plotter</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>center</mi><mo>=</mo><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>width</mi><mo>=</mo><mn>10</mn><mo>,</mo><mo> </mo><mi>height</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>plotter</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>center</mi><mo>=</mo><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>width</mi><mo>=</mo><mn>10</mn><mo>,</mo><mo> </mo><mi>height</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mi>plotter</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>center</mi><mo>=</mo><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>width</mi><mo>=</mo><mn>10</mn><mo>,</mo><mo> </mo><mi>height</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mi>plotter</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>center</mi><mo>=</mo><mi>point</mi><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>width</mi><mo>=</mo><mn>10</mn><mo>,</mo><mo> </mo><mi>height</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>s1</mi><mo>,</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>black</mi><mo>,</mo><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>s2</mi><mo>,</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>-</mo><mn>1</mn><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>black</mi><mo>,</mo><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>s3</mi><mo>,</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>black</mi><mo>,</mo><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>s4</mi><mo>,</mo><mo>(</mo><mi>a</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>+</mo><mn>1</mn><mo>,</mo><mo>{</mo><mi>color</mi><mo>=</mo><mi>black</mi><mo>,</mo><mi>line_width</mi><mo>=</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> Imaginea unei functii Pentru functia f(x) = #a*x²+#b*x + #c, Imf = [#v, ∞)

]]> 1.0000000 1.0000000 0 Adevărat Fals <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>-</mo><mfrac><mi>d</mi><mrow><mn>4</mn><mo>*</mo><mi>a</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mi>v</mi><mo>,</mo><mo> </mo><mi>v</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>u</mi><mo>=</mo><mo>-</mo><mfrac><mi>d</mi><mrow><mn>4</mn><mo>*</mo><mi>a</mi></mrow></mfrac><mo>∧</mo><mi>a</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>s</mi><mo>=</mo><mi>true</mi></mrow><mrow><mi>s</mi><mo>=</mo><mi>false</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>true</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> Inecuatie de grad 2 In multimea numerelor reale, multimea solutiilor inecuatiei #a X² + #b X + #c «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8804;«/mo»«/math» 0 :

]]> Rezolvarea inecuatiei de gr. II, se bazeaza pe propozitia privind semnul functiei de gr. II.

]]> 1.0000000 0.3333333 0 false true abc este un interval nemarginit

]]> este un interval marginit si inchis

]]> este intervalul [ #u, #v ]

]]> este un interval de lungime #f

]]> este multimea vida

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»,«/mo»«mo»§#160;«/mo»«msqrt»«mn»5«/mn»«/msqrt»«mo»,«/mo»«mo»§#160;«/mo»«mfrac»«msqrt»«mn»10«/mn»«/msqrt»«mn»2«/mn»«/mfrac»«mo»,«/mo»«mo»§#160;«/mo»«msqrt»«mn»7«/mn»«/msqrt»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»8«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»§#160;«/mo»«mi»s«/mi»«mi»u«/mi»«mi»n«/mi»«mi»t«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»a«/mi»«mi»t«/mi»«mi»e«/mi»«mi»v«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»e«/mi»«mi»x«/mi»«mi»a«/mi»«mi»m«/mi»«mi»p«/mi»«mi»l«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»d«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»e«/mi»«mi»r«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»r«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mo»!«/mo»«/math»

Def. Valoarea absoluta a unui numar real, este distanta pe o axa a numerelor reale, de la origine la imaginea pe axa a numarului.

]]> 1.0000000 0.3333333 0 0 #sol «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»,«/mo»«mo»§#160;«/mo»«msqrt»«mn»5«/mn»«/msqrt»«mo»,«/mo»«mo»§#160;«/mo»«mfrac»«msqrt»«mn»10«/mn»«/msqrt»«mn»2«/mn»«/mfrac»«mo»,«/mo»«mo»§#160;«/mo»«msqrt»«mn»7«/mn»«/msqrt»«mo»§#160;«/mo»«mo»-«/mo»«mo»§#160;«/mo»«mn»8«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo».«/mo»«mo».«/mo»«mo».«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mi»r«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»o«/mi»«mi»m«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»e«/mi»«mi»x«/mi»«mi»a«/mi»«mi»m«/mi»«mi»p«/mi»«mi»l«/mi»«mi»e«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mi»o«/mi»«mi»f«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»r«/mi»«mi»a«/mi»«mi»t«/mi»«mi»i«/mi»«mi»o«/mi»«mi»n«/mi»«mi»a«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»b«/mi»«mi»e«/mi»«mi»r«/mi»«mi»s«/mi»«mo»§#160;«/mo»«mo»!«/mo»«/math»

The absolute value of a real number is the distance from the origin to the image point of number (on a number line )

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Irational</mi><mo> </mo><mo>-</mo><mo> </mo><mi>grading</mi><mo> </mo><mi>function</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>-</mo><msqrt><mn>2</mn></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><mi>sol</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>x</mi><mo>∉</mo><rationals/><mo>∧</mo><mi>x</mi><mo><</mo><mn>0</mn><mo>∧</mo><mi>absolute</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>></mo><mi>a</mi><mo>)</mo><mo>?</mo></mtd></mtr><mtr><mtd><mi>return</mi><mo> </mo><mi>sol</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mo>-</mo><pi/><mo>-</mo><mn>2</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>true</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>test</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>false</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">test</param></assertion><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_symbolic" correctAnswer="1"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"/><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data></localData></question> Numere complexe - 1 Daca n = #n, calculati argumentul redus al numarului «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»z«/mi»«mo»§#160;«/mo»«mo»=«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mi»n«/mi»«/munderover»«msup»«mi»i«/mi»«mi»k«/mi»«/msup»«/math»

]]> 1.0000000 1.0000000 0 Adevărat Fals <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>33</mn><mo>,</mo><mn>1700</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mo>(</mo><mfrac><mrow><mn>1</mn><mo>+</mo><imaginaryi/></mrow><mrow><mn>1</mn><mo>-</mo><imaginaryi/></mrow></mfrac><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>rem</mi><mo>(</mo><mi>n</mi><mo>,</mo><mn>4</mn><mo>)</mo><mo>∈</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo></mrow><mrow><mi>s</mi><mo>=</mo><mi>true</mi></mrow><mrow><mi>s</mi><mo>=</mo><mi>false</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>166</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>true</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Numere Complexe - 6 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»r«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mo»=«/mo»«mo»#«/mo»«mi»n«/mi»«mo»,«/mo»«mo»§#160;«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mi»n«/mi»«/munderover»«mo»(«/mo»«mfrac»«mrow»«mn»1«/mn»«mo»+«/mo»«mi»i«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»-«/mo»«mi»i«/mi»«/mrow»«/mfrac»«msup»«mo»)«/mo»«mi»k«/mi»«/msup»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math»

]]> Numere complexe - modul (interpretare geometrica) Fie z = #a + #b*i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8450;«/mi»«/math» , si P(z) imaginea numarului z intr-un reper cartezian XOY.

Lungimea segmentului [OP] este mai mica decat 7.

]]> 1.0000000 1.0000000 0 Adevărat Fals <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>10</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo><</mo><mn>7</mn></mrow><mrow><mi>s</mi><mo>=</mo><mi>true</mi></mrow><mrow><mi>s</mi><mo>=</mo><mi>false</mi></mrow></apply></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>true</mi></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options></question> Numere complexe - modulul unui cat «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»a«/mi»«mi»l«/mi»«mi»c«/mi»«mi»u«/mi»«mi»l«/mi»«mi»e«/mi»«mi»z«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»m«/mi»«mi»o«/mi»«mi»d«/mi»«mi»u«/mi»«mi»l«/mi»«mi»u«/mi»«mi»l«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»a«/mi»«mi»r«/mi»«mi»u«/mi»«mi»l«/mi»«mi»u«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»o«/mi»«mi»m«/mi»«mi»p«/mi»«mi»l«/mi»«mi»e«/mi»«mi»x«/mi»«mo»§#160;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»i«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«mo»+«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#183;«/mo»«mi»i«/mi»«mo»§#160;«/mo»«/mrow»«/mfrac»«/math»

]]> Modulul unui cat de numere complexe este egal cu catul modulelor !

]]> Re(a+bi) = a

Im(a+bi) = b

(paranteza din "suma" este la puterea k )

]]> 1.0000000 1.0000000 0 Adevărat Fals <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>33</mn><mo>,</mo><mn>1700</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mo>(</mo><mfrac><mrow><mn>1</mn><mo>+</mo><imaginaryi/></mrow><mrow><mn>1</mn><mo>-</mo><imaginaryi/></mrow></mfrac><msup><mo>)</mo><mi>k</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>rem</mi><mo>(</mo><mi>n</mi><mo>,</mo><mn>4</mn><mo>)</mo><mo>=</mo><mn>1</mn></mrow><mrow><mi>s</mi><mo>=</mo><mi>true</mi></mrow><mrow><mi>s</mi><mo>=</mo><mi>false</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>986</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>false</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options></question> Operatii cu numere complexe «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»a«/mi»«mi»l«/mi»«mi»c«/mi»«mi»u«/mi»«mi»l«/mi»«mi»e«/mi»«mi»z«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»a«/mi»«mi»r«/mi»«mi»t«/mi»«mi»e«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»r«/mi»«mi»e«/mi»«mi»a«/mi»«mi»l«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»a«/mi»«mi»r«/mi»«mi»u«/mi»«mi»l«/mi»«mi»u«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»o«/mi»«mi»m«/mi»«mi»p«/mi»«mi»l«/mi»«mi»e«/mi»«mi»x«/mi»«mo»§#160;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»i«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«mo»+«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#183;«/mo»«mi»i«/mi»«mo»§#160;«/mo»«/mrow»«/mfrac»«/math»*( i+1 )

]]> Re(a+bi) = a

Im(a+bi) = b

]]> 1.0000000 0.3333333 0 0 #s #S <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>absolute</mi><mo>(</mo><mi>c</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>real_part</mi><mo>(</mo><mo>(</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></mrow><mrow><mi>c</mi><mo>+</mo><mi>d</mi><mo>*</mo><imaginaryi/></mrow></mfrac><mo>)</mo><mo>*</mo><mo>(</mo><imaginaryi/><mo>+</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>23</mn><mn>17</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi></math>]]></correctAnswer><correctAnswer id="1">#S</correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"/><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data></localData></question> Oronata - varf parabola Daca f : «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»R«/mi»«mo»§#160;«/mo»«mo»§#8594;«/mo»«mo»§#160;«/mo»«mi»R«/mi»«/math», f(x) = #a*x² + #b*x + #c, atunci ordonata varfului parabolei ce reprezinta graficul lui f , este :

]]> 1.0000000 0.3333333 0 0 #s «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi»x«/mi»«mi»V«/mi»«/msub»«mo»=«/mo»«mo»-«/mo»«mfrac»«mi»b«/mi»«mrow»«mn»2«/mn»«mi»a«/mi»«/mrow»«/mfrac»«/math»

Valoarea nenula a lui m pentru care graficul functiei f este tangent axei Ox, este :

]]> 1.0000000 0.3333333 0 0 #ok <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>{</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>(</mo><mi>m</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mo>-</mo><mfrac><mi>m</mi><mn>2</mn></mfrac><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo> </mo><mi>solve</mi><mfenced><mrow><mi>e</mi><mo>(</mo><mi>m</mi><mo>)</mo><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ok</mi><mo>=</mo><msub><mi>sol</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>o</mi><mi>k</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Parte intreaga Partea intreaga a numarului #a este #c .

]]> 1.0000000 1.0000000 0 Adevărat Fals <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>+</mo><msqrt><mrow><mi>random</mi><mo>{</mo><mn>8</mn><mo>,</mo><mn>18</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>20</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>90</mn><mo>}</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>round</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>floor</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>{</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>d</mi><mo>=</mo><mi>c</mi></mrow><mrow><mi>s</mi><mo>=</mo><mi>true</mi></mrow><mrow><mi>s</mi><mo>=</mo><mi>false</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>7</mn></msqrt><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>true</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options></question> Partea imaginara a unui nr. complex «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»S«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»a«/mi»«mi»l«/mi»«mi»c«/mi»«mi»u«/mi»«mi»l«/mi»«mi»e«/mi»«mi»z«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»p«/mi»«mi»a«/mi»«mi»r«/mi»«mi»t«/mi»«mi»e«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»i«/mi»«mi»m«/mi»«mi»a«/mi»«mi»g«/mi»«mi»i«/mi»«mi»n«/mi»«mi»a«/mi»«mi»r«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»n«/mi»«mi»u«/mi»«mi»m«/mi»«mi»a«/mi»«mi»r«/mi»«mi»u«/mi»«mi»l«/mi»«mi»u«/mi»«mi»i«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»o«/mi»«mi»m«/mi»«mi»p«/mi»«mi»l«/mi»«mi»e«/mi»«mi»x«/mi»«mo»§#160;«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»+«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#183;«/mo»«mi»i«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»c«/mi»«mo»+«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#183;«/mo»«mi»i«/mi»«mo»§#160;«/mo»«/mrow»«/mfrac»«/math»

]]> Re(a+bi) = a

Im(a+bi) = b

]]> 1.0000000 0.3333333 0 0 #m <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>≠</mo><mi>absolute</mi><mo>(</mo><mi>c</mi><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>imaginary_part</mi><mo>(</mo><mfrac><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>*</mo><imaginaryi/></mrow><mrow><mi>c</mi><mo>+</mo><mi>d</mi><mo>*</mo><imaginaryi/></mrow></mfrac><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>25</mn><mn>34</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>m</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="1"/><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"/><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data></localData></question> Progresii Daca intr-o progresie aritmetica a_#x = #a si a_#y=#b, atunci a_#z=]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>{</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>p</mi><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>y</mi><mo>+</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>s</mi><mo>*</mo><mi>r</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo> </mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>29</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"></data></localData></question> Progresii aritmetice Sa se rezolve ecuatia : #a + #b + #c +#d + . . . + x = #s

]]> 1.0000000 0.3333333 0 0 #f <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>c</mi><mo>+</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>9</mn><mo>,</mo><mn>28</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>a</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>f</mi><mo>)</mo><mo>*</mo><mi>n</mi><mo>/</mo><mn>2</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#f</correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"></data></localData></question> Progresii geometrice Sa se calculeze «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»0«/mn»«/mrow»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/munderover»«/math»(#a)^k

]]> 1.0000000 0.3333333 0 true true abc #s

]]> #a

]]> #b

]]> #c

]]> Radacini cubice ale unitatii Daca z_{1 ,}z₂ radacini ale ecuatiei z² + z + 1= 0, calculati z₁^#n + z₂^#n .

]]> Radacini reale

Ecuatia «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mi»b«/mi»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«mo»=«/mo»«mn»0«/mn»«/math» nu are radacini reale.

a=#a ; b=#b ; c=#c

]]> 1.0000000 1.0000000 0 Adevărat Raspuns corect !

]]> Fals Gresit !

1)Pentru «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#916;«/mi»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8805;«/mo»«mn»0«/mn»«/math», ecuatia are radacini reale.

2)Pentru «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#916;«/mi»«/math» < 0, ecuatia nu are radacini reale.

Valorile lui x «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8712;«/mo»«mo»§#160;«/mo»«mi mathvariant=¨normal¨»§#8450;«/mi»«/math», pentru care rangM este cel mult egal cu 2, sunt :

]]> Rangul unei matrice patratice de ordin 3 este cel mult 2, daca determinantul matricei este nul !

]]> 1.0000000 0.3333333 0 false true abc Foarte bine , Felicitari !

]]> Raspuns corect, dar incomplet !

]]> #a

]]> #b

]]> #u

]]> #v

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>x</mi></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>r</mi><mo>(</mo><mo>)</mo></mtd><mtd><mi>x</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>determinant</mi><mo>(</mo><mi>M</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>s</mi><mo>=</mo><mi>solve</mi><mo>(</mo><mi>d</mi><mo>=</mo><mn>0</mn><mo>,</mo><complexes/><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>degree</mi><mo>(</mo><mi>d</mi><mo>)</mo><mo>=</mo><mn>2</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>s</mi><mn>1</mn></msub><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msub><mi>s</mi><mn>2</mn></msub><mfenced><mi>x</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>a</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>b</mi><mo>+</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Ratie progresii aritmetice Daca intr-o progresie aritmetica a_#x = #a si S_#n = #s atunci ratia progresiei este :]]> 1.0000000 0.3333333 0 0 #r <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>{</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>-</mo><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>sol</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mo>(</mo><mi>sol</mi><mo>+</mo><mi>an</mi><mo>)</mo><mo>*</mo><mi>n</mi><mo>/</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>385</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo> </mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"></data></localData></question> Relatiile lui Viete I

Sa se determine «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»b«/mi»«mo»§#160;«/mo»«mo»§#8712;«/mo»«mo»§#160;«/mo»«mo»(«/mo»«mn»0«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»§#8734;«/mo»«mo»)«/mo»«mo»§#160;«/mo»«/math»astfel incat suma cuburilor radacinilor ecuatiei

#a*x² + b*x + #c = 0 , sa fie egala cu zero .

]]> 1.0000000 0.3333333 0 0 #sol E nevoie de relatiile lui F. Viete !

]]> Relatiile lui Viete II

Sa se determine c«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» , astfel incat suma cuburilor radacinilor ecuatiei

#a*x² + #b*x + c = 0 , sa fie egala cu zero .

]]> 1.0000000 0.3333333 0 0 #sol E nevoie de relatiile lui F. Viete !

]]> Relatiile lui Viete III

Sa se determine a«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8712;«/mo»«mi mathvariant=¨normal¨»§#8477;«/mi»«/math» , astfel incat suma cuburilor radacinilor ecuatiei

a*x² + #b*x + #c = 0 , sa fie egala cu zero .

]]> 1.0000000 0.3333333 0 0 #sol E nevoie de relatiile lui F. Viete !

]]> Semn radacini Daca a=#a, b=#b si c=#c, atunci ecuatia ax² + bx + c = 0 are radacinile reale si de semne contrare.

]]> Vezi si interpretarea grafica pentru raspunsul tau ! (f : R $$ \rightarrow $$ R, f(x)=ax² +bx +c )

]]> 1.0000000 1.0000000 0 Adevărat Ai raspuns corect !

]]> Fals Pentru raspunsul corect conditiile sunt : 1) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#916;«/mi»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#10878;«/mo»«/math»0 si p <0 !

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo><mo>*</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><mi>c</mi><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>d</mi><mo>&ges;</mo><mn>0</mn><mo>)</mo><mo>&and;</mo><mo>(</mo><mi>p</mi><mo><</mo><mn>0</mn><mo>)</mo></mrow><mi>true</mi><mi>false</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>f</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>false</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>&map;</mo><mi>a</mi><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>c</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plot</mi><mo>(</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plotter1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mi>plot</mi><mo>(</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>plotter1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options></question> Suma de numere complexe I «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»r«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mo»=«/mo»«mo»#«/mo»«mi»n«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»s«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»a«/mi»«mi»l«/mi»«mi»c«/mi»«mi»u«/mi»«mi»l«/mi»«mi»e«/mi»«mi»z«/mi»«mi»e«/mi»«mo»§#160;«/mo»«munderover»«mo»§#8721;«/mo»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mi»n«/mi»«/munderover»«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mi»i«/mi»«msup»«mo»)«/mo»«mi»k«/mi»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #s <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mo>(</mo><mn>1</mn><mo>+</mo><imaginaryi/><msup><mo>)</mo><mi>k</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mn>3</mn><mo>*</mo><imaginaryi/></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s</correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"></data></localData></question> Sume - progresii aritmetice Daca intr-o progresie aritmetica a_#x = #a si a_#y=#b, atunci suma primilor #n termeni ai progresiei este :]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>{</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>p</mi><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>y</mi><mo>+</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a</mi><mo>-</mo><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mo>(</mo><mi>a1</mi><mo>+</mo><mi>an</mi><mo>)</mo><mo>*</mo><mi>n</mi><mo>/</mo><mn>2</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>38</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo> </mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>324</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"></data></localData></question> Sume de numere complexe «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»P«/mi»«mi»e«/mi»«mi»n«/mi»«mi»t«/mi»«mi»r«/mi»«mi»u«/mi»«mo»§#160;«/mo»«mi»n«/mi»«mo»=«/mo»«mo»#«/mo»«mi»n«/mi»«mo»,«/mo»«mo»§#160;«/mo»«mi»s«/mi»«mi»a«/mi»«mo»§#160;«/mo»«mi»s«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mi»c«/mi»«mi»a«/mi»«mi»l«/mi»«mi»c«/mi»«mi»u«/mi»«mi»l«/mi»«mi»e«/mi»«mi»z«/mi»«mi»e«/mi»«mo»§#160;«/mo»«mo»§#160;«/mo»«mi»s«/mi»«mi»u«/mi»«mi»m«/mi»«mi»a«/mi»«mo»§#160;«/mo»«munderover»«mrow»«mo»§#8721;«/mo»«mo»(«/mo»«/mrow»«mrow»«mi»k«/mi»«mo»=«/mo»«mn»1«/mn»«/mrow»«mi»n«/mi»«/munderover»«mn»1«/mn»«mo»-«/mo»«mi»i«/mi»«msup»«mo»)«/mo»«mi»k«/mi»«/msup»«mo»§#160;«/mo»«mo».«/mo»«/math»

]]> 1.0000000 0.3333333 0 0 #s <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mo>(</mo><mn>1</mn><mo>-</mo><imaginaryi/><msup><mo>)</mo><mi>k</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>+</mo><mn>15</mn><mo>*</mo><imaginaryi/></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>s</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"/><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data></localData></question> Termeni progresii aritmetice Daca intr-o progresie aritmetica a_#x = #a si a_#y=#b, atunci a₁=]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>{</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mi>p</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>p</mi><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi><mo>=</mo><mi>y</mi><mo>+</mo><mi>s</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>-</mo><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>r</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo> </mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>29</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="casSession"></data></localData></question> Varf parabola Daca f : «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»R«/mi»«mo»§#160;«/mo»«mo»§#8594;«/mo»«mo»§#160;«/mo»«mi»R«/mi»«/math», f(x) = #a*x² + #b*x + #c, atunci abscisa varfului parabolei ce reprezinta graficul lui f , este :