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<body lang=EN-US >

<div class=WordSection1>

<p class=MsoNormal><span class=PageNumberDAISY><span lang=EN-GB>1</span></span></p>

<h1>Math Sample Document</h1>

<p class=MsoNormal>This is a test of some example math equations. This document
can be used to test how different assistive technologies interact with math
content In addition, the document can be used for demonstrating how to convert
a MS Word document into other formats.</p>

<h2>Information</h2>

<p class=MsoNormal>The following math content was created using the MathType
plug-in for MS Word.</p>

<h3>Basic Math</h3>

<p class=MsoListNumberCxSpFirst >1.<span style='font:7.0pt "Times New Roman"'>      
</span><math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mfrac>
    <mn>7</mn>
    <mn>8</mn>
   </mfrac>
   <mo>+</mo><mfrac>
    <mn>3</mn>
    <mn>5</mn>
   </mfrac>
   <mo>=</mo><mi>x</mi></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeWaaSaaaeaacaaI3aaabaGaaGioaaaacqGHRaWkdaWcaaqa
  aiaaiodaaeaacaaI1aaaaiabg2da9iaadIhaaaa@3E92@
  </annotation>
 </semantics>
</math> </p>

<p class=MsoListNumberCxSpLast >2.<span style='font:7.0pt "Times New Roman"'>      
</span>Solve for x. </p>

<p class=MsoNormal style='text-indent:.25in'><math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mn>.75</mn><mo stretchy='false'>(</mo><mn>3</mn><mo>&#x2212;</mo><mn>6</mn><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mn>10</mn><mo>+</mo><mo stretchy='false'>(</mo><mn>8</mn><mi>x</mi><mo>&#x2212;</mo><mn>4</mn><mo stretchy='false'>)</mo></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaaiOlaiaaiEdacaaI1aGaaiikaiaaiodacqGHsislcaaI
  2aGaamiEaiaacMcacqGH9aqpcaaIXaGaaGimaiabgUcaRiaacIcaca
  aI4aGaamiEaiabgkHiTiaaisdacaGGPaaaaa@47A0@
  </annotation>
 </semantics>
</math></p>

<p class=MsoListNumber >3.<span style='font:7.0pt "Times New Roman"'>      
</span>An ant weighs <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mn>3</mn><mo>&#x00D7;</mo><msup>
    <mrow>
     <mn>10</mn></mrow>
    <mrow>
     <mo>&#x2212;</mo><mn>6</mn></mrow>
   </msup>
   </mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaaG4maiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacqGH
  sislcaaI2aaaaaaa@3EB1@
  </annotation>
 </semantics>
</math> grams, but can lift 16 grams. How many times
their body weight can an ant lift?</p>

<h3>Algebra</h3>

<p class=MsoListNumberCxSpFirst >1.<span style='font:7.0pt "Times New Roman"'>      
</span>Simplify the following expression: <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mo stretchy='false'>(</mo><mn>3</mn><msup>
    <mi>x</mi>
    <mn>5</mn>
   </msup>
   <mo>+</mo><mn>8</mn><msup>
    <mi>x</mi>
    <mn>3</mn>
   </msup>
   <mo stretchy='false'>)</mo><mo>&#x2212;</mo><mo stretchy='false'>(</mo><mn>7</mn><msup>
    <mi>x</mi>
    <mn>2</mn>
   </msup>
   <mo>&#x2212;</mo><mn>6</mn><msup>
    <mi>x</mi>
    <mn>3</mn>
   </msup>
   <mo stretchy='false'>)</mo></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaaiikaiaaiodacaWG4bWaaWbaaSqabeaacaaI1aaaaOGa
  ey4kaSIaaGioaiaadIhadaahaaWcbeqaaiaaiodaaaGccaGGPaGaey
  OeI0IaaiikaiaaiEdacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaeyOe
  I0IaaGOnaiaadIhadaahaaWcbeqaaiaaiodaaaGccaGGPaaaaa@48C1@
  </annotation>
 </semantics>
</math> </p>

<p class=MsoListNumberCxSpLast >2.<span style='font:7.0pt "Times New Roman"'>      
</span>Consider the function <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mo>&#x2212;</mo><mn>1</mn><mo>+</mo><mn>0.5</mn><mi>x</mi></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaamOzaiaacIcacaWG4bGaaiykaiabg2da9iabgkHiTiaa
  igdacqGHRaWkcaaIWaGaaiOlaiaaiwdacaWG4baaaa@4287@
  </annotation>
 </semantics>
</math> . For what value of x does <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mi>f</mi><mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo><mo>=</mo><mn>0</mn></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaamOzaiaacIcacaWG4bGaaiykaiabg2da9iaaicdaaaa@3D8F@
  </annotation>
 </semantics>
</math> ?</p>

<p class=MsoNormal><span class=PageNumberDAISY><span lang=EN-GB>2</span></span></p>

<p class=MsoListNumber >3.<span style='font:7.0pt "Times New Roman"'>      
</span>Given the Quadratic Formula, <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mi>x</mi><mo>=</mo><mfrac>
    <mrow>
     <mo>&#x2212;</mo><mi>b</mi><mo>&#x00B1;</mo><msqrt>
      <mrow>
       <msup>
        <mi>b</mi>
        <mn>2</mn>
       </msup>
       <mo>&#x2212;</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow>
     </msqrt>
     </mrow>
    <mrow>
     <mn>2</mn><mi>a</mi></mrow>
   </mfrac>
   </mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaamiEaiabg2da9maalaaabaGaeyOeI0IaamOyaiabggla
  XoaakaaabaGaamOyamaaCaaaleqabaGaaGOmaaaakiabgkHiTiaais
  dacaWGHbGaam4yaaWcbeaaaOqaaiaaikdacaWGHbaaaaaa@457D@
  </annotation>
 </semantics>
</math> , please solve the following equation <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mn>3</mn><msup>
    <mi>x</mi>
    <mn>2</mn>
   </msup>
   <mo>+</mo><mn>2</mn><mi>x</mi><mo>&#x2212;</mo><mn>5</mn><mo>=</mo><mn>0</mn></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaaG4maiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHRaWk
  caaIYaGaamiEaiabgkHiTiaaiwdacqGH9aqpcaaIWaaaaa@4142@
  </annotation>
 </semantics>
</math> </p>

<h3>Algebra 2</h3>

<p class=MsoListNumberCxSpFirst >1.<span style='font:7.0pt "Times New Roman"'>      
</span>Please solve the following equation: <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mo>&#x2212;</mo><msqrt>
    <mrow>
     <mi>y</mi><mo>+</mo><mn>15</mn></mrow>
   </msqrt>
   <mo>=</mo><mo>&#x2212;</mo><mn>4</mn></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaeyOeI0YaaOaaaeaacaWG5bGaey4kaSIaaGymaiaaiwda
  aSqabaGccqGH9aqpcqGHsislcaaI0aaaaa@3FAB@
  </annotation>
 </semantics>
</math> </p>

<p class=MsoListNumberCxSpMiddle >2.<span style='font:7.0pt "Times New Roman"'>      
</span>Simplify your answer: <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mfrac>
    <mrow>
     <mn>16</mn><msup>
      <mi>x</mi>
      <mn>2</mn>
     </msup>
     <msup>
      <mi>y</mi>
      <mn>2</mn>
     </msup>
     </mrow>
    <mrow>
     <mn>14</mn><mi>x</mi><mi>y</mi></mrow>
   </mfrac>
   <mo>&#x22C5;</mo><mn>19</mn><msup>
    <mi>x</mi>
    <mn>2</mn>
   </msup>
   <mi>y</mi></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeWaaSaaaeaacaaIXaGaaGOnaiaadIhadaahaaWcbeqaaiaa
  ikdaaaGccaWG5bWaaWbaaSqabeaacaaIYaaaaaGcbaGaaGymaiaais
  dacaWG4bGaamyEaaaacqGHflY1caaIXaGaaGyoaiaadIhadaahaaWc
  beqaaiaaikdaaaGccaWG5baaaa@4824@
  </annotation>
 </semantics>
</math> </p>

<p class=MsoListNumberCxSpLast >3.<span style='font:7.0pt "Times New Roman"'>      
</span>Simplify the following: <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mn>3</mn><mo stretchy='false'>(</mo><mo>&#x2212;</mo><mn>5</mn><mi>i</mi><mo stretchy='false'>)</mo></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaaG4maiaacIcacqGHsislcaaI1aGaamyAaiaacMcaaaa@3D3E@
  </annotation>
 </semantics>
</math>.
Please write your answer as <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mi>a</mi><mo>+</mo><mi>b</mi><mi>i</mi></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaamyyaiabgUcaRiaadkgacaWGPbaaaa@3C2B@
  </annotation>
 </semantics>
</math> </p>

<h3>Calculus</h3>

<p class=MsoListNumber >1.<span style='font:7.0pt "Times New Roman"'>      
</span>Find the following limits.</p>

<p class=MsoListNumber3CxSpFirst >1.<span style='font:7.0pt "Times New Roman"'>      
</span><math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <munder>
    <mrow>
     <mi>lim</mi></mrow>
    <mrow>
     <mi>x</mi><mo>&#x2192;</mo><mn>1</mn></mrow>
   </munder>
   <mfrac>
    <mrow>
     <msup>
      <mi>x</mi>
      <mn>3</mn>
     </msup>
     <mo>&#x2212;</mo><msup>
      <mi>x</mi>
      <mn>2</mn>
     </msup>
     <mo>+</mo><mn>1</mn></mrow>
    <mrow>
     <msup>
      <mi>x</mi>
      <mn>2</mn>
     </msup>
     <mo>&#x2212;</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow>
   </mfrac>
   </mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeWaaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadIhacqGH
  sgIRcaaIXaaabeaakmaalaaabaGaamiEamaaCaaaleqabaGaaG4maa
  aakiabgkHiTiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaaI
  XaaabaGaamiEamaaCaaaleqabaGaaGOmaaaakiabgkHiTiaaikdaca
  WG4bGaey4kaSIaaGymaaaaaaa@4BF4@
  </annotation>
 </semantics>
</math> </p>

<p class=MsoListNumber3CxSpLast >2.<span style='font:7.0pt "Times New Roman"'>      
</span><math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <munder>
    <mrow>
     <mi>lim</mi></mrow>
    <mrow>
     <mi>x</mi><mo>&#x2192;</mo><mi>&#x221E;</mi></mrow>
   </munder>
   <mfrac>
    <mrow>
     <mo>&#x2212;</mo><msup>
      <mi>x</mi>
      <mn>2</mn>
     </msup>
     <mo>+</mo><mn>1</mn></mrow>
    <mrow>
     <mi>x</mi><mo>+</mo><mn>2</mn></mrow>
   </mfrac>
   </mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeWaaCbeaeaaciGGSbGaaiyAaiaac2gaaSqaaiaadIhacqGH
  sgIRcqGHEisPaeqaaOWaaSaaaeaacqGHsislcaWG4bWaaWbaaSqabe
  aacaaIYaaaaOGaey4kaSIaaGymaaqaaiaadIhacqGHRaWkcaaIYaaa
  aaaa@4721@
  </annotation>
 </semantics>
</math> </p>

<p class=MsoListNumber >2.<span style='font:7.0pt "Times New Roman"'>      
</span>Compute the following: <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mstyle displaystyle='true'>
    <mrow>
     <msubsup>
      <mo>&#x222B;</mo>
      <mn>1</mn>
      <mn>2</mn>
     </msubsup>
     <mrow>
      <mi>sin</mi></mrow>
    </mrow>
    
   </mstyle><mo stretchy='false'>(</mo><mi>&#x03C0;</mi><mi>x</mi><mo>+</mo><mn>1</mn><mo stretchy='false'>)</mo><mi>d</mi><mi>x</mi></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeWaa8qmaeaaciGGZbGaaiyAaiaac6gaaSqaaiaaigdaaeaa
  caaIYaaaniabgUIiYdGccaGGOaGaeqiWdaNaamiEaiabgUcaRiaaig
  dacaGGPaGaamizaiaadIhaaaa@46A6@
  </annotation>
 </semantics>
</math> </p>

<p class=MsoNormal><span class=PageNumberDAISY><span lang=EN-GB>3</span></span></p>

<p class=MsoListNumber >3.<span style='font:7.0pt "Times New Roman"'>      
</span>Find the average value of <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <msup>
    <mrow>
     <mi>sin</mi></mrow>
    <mn>2</mn>
   </msup>
   <mo stretchy='false'>(</mo><mi>x</mi><mo stretchy='false'>)</mo></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaci4CaiaacMgacaGGUbWaaWbaaSqabeaacaaIYaaaaOGa
  aiikaiaadIhacaGGPaaaaa@3EAF@
  </annotation>
 </semantics>
</math> on <math xmlns='http://www.w3.org/1998/Math/MathML' style='background-color:#'>
 <semantics>
  <mrow>
   <mn>0</mn><mo>&#x2264;</mo><mi>x</mi><mo>&#x2264;</mo><mi>&#x03C0;</mi></mrow>
  <annotation encoding='MathType-MTEF'>MathType@MTEF@5@5@+=
  feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn
  hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr
  4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9
  vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x
  fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeeaaaaaa6di
  eB1vgapeGaaGimaiabgsMiJkaadIhacqGHKjYOcqaHapaCaaa@3F6C@
  </annotation>
 </semantics>
</math> . </p>

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