Difference between revisions of "008A Sample Final A"

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<span class = "biglink">[[8A_F11_Q3|&nbsp;Question 3&nbsp;]]</span> a) Find the vertex, standard graphing form, and X-intercept for <math>x = -3y^2-6y+2</math>
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<span class = "biglink">[[008A Sample Final A, Question 3|&nbsp;Question 3&nbsp;]]</span> a) Find the vertex, standard graphing form, and X-intercept for <math>x = -3y^2-6y+2</math>
  
 
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<span class = "biglink">[[8A_F11_Q4|&nbsp;Question 4&nbsp;]]</span> Solve. Provide your solution in interval notation. <math>(x-4)(2x+1)(x-1)<0</math>
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<span class = "biglink">[[008A Sample Final A, Question 4|&nbsp;Question 4&nbsp;]]</span> Solve. Provide your solution in interval notation. <math>(x-4)(2x+1)(x-1)<0</math>
  
  
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<span class = "biglink">[[8A_F11_Q5|&nbsp;Question 5&nbsp;]]</span> Graph the system of inequalities <math>y < \vert x\vert +1 </math> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math>x^2 + y^2 \le 9</math>
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<span class = "biglink">[[008A Sample Final A, Question 5|&nbsp;Question 5&nbsp;]]</span> Graph the system of inequalities <math>y < \vert x\vert +1 </math> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math>x^2 + y^2 \le 9</math>
  
  
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<span class = "biglink">[[8A_F11_Q6|&nbsp;Question 6&nbsp;]]</span>  Sketch <math>4x^2 + 9(y + 1)^2 = 36</math>. Give coordinates of each of the 4 vertices of the graph.
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<span class = "biglink">[[008A Sample Final A, Question 6|&nbsp;Question 6&nbsp;]]</span>  Sketch <math>4x^2 + 9(y + 1)^2 = 36</math>. Give coordinates of each of the 4 vertices of the graph.
  
  
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<span class = "biglink">[[8A_F11_Q7|&nbsp;Question 7&nbsp;]]</span> Solve <math>2\vert 3x-4\vert -7 = 7</math>
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<span class = "biglink">[[008A Sample Final A, Question 7|&nbsp;Question 7&nbsp;]]</span> Solve <math>2\vert 3x-4\vert -7 = 7</math>
  
  
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<span class = "biglink">[[8A_F11_Q8|&nbsp;Question 8&nbsp;]]</span> Given a sequence <math> 27, 23, 19, 15, \ldots </math> use formulae to compute <math>S_{10}</math> and <math>A_{15}</math>.
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<span class = "biglink">[[008A Sample Final A, Question 8|&nbsp;Question 8&nbsp;]]</span> Given a sequence <math> 27, 23, 19, 15, \ldots </math> use formulae to compute <math>S_{10}</math> and <math>A_{15}</math>.
  
  
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<span class = "biglink">[[8A_F11_Q9|&nbsp;Question 9&nbsp;]]</span> a) List all the possible rational zeros of the function <math>f(x) = x^4 + 5x^3 - 27x^2 +31x -10</math><br>
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<span class = "biglink">[[008A Sample Final A, Question 9|&nbsp;Question 9&nbsp;]]</span> a) List all the possible rational zeros of the function <math>f(x) = x^4 + 5x^3 - 27x^2 +31x -10</math><br>
 
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b) Find all the zeros, that is, solve f(x) = 0
 
b) Find all the zeros, that is, solve f(x) = 0
  
  
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<span class = "biglink">[[8A_F11_Q10|&nbsp;Question 10&nbsp;]]</span> Graph the function. Give equations of any asymptotes, and list any intercepts <math>y = \frac{x-1}{2x+2}</math>
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<span class = "biglink">[[008A Sample Final A, Question 10|&nbsp;Question 10&nbsp;]]</span> Graph the function. Give equations of any asymptotes, and list any intercepts <math>y = \frac{x-1}{2x+2}</math>
  
  
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<span class = "biglink">[[8A_F11_Q11|&nbsp;Question 11&nbsp;]]</span> Decompose into separate partial fractions <math>\frac{3x^2+6x+7}{(x+3)^2(x-1)}</math>
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<span class = "biglink">[[008A Sample Final A, Question 11|&nbsp;Question 11&nbsp;]]</span> Decompose into separate partial fractions <math>\frac{3x^2+6x+7}{(x+3)^2(x-1)}</math>
  
  
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<span class = "biglink">[[8A_F11_Q12|&nbsp;Question 12&nbsp;]]</span> Find and simplify the difference quotient <math>\frac{f(x+h)-f(x)}{h}</math> for f(x) = <math>\frac{2}{3x+1}</math>
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<span class = "biglink">[[008A Sample Final A, Question 12|&nbsp;Question 12&nbsp;]]</span> Find and simplify the difference quotient <math>\frac{f(x+h)-f(x)}{h}</math> for f(x) = <math>\frac{2}{3x+1}</math>
  
  
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<span class = "biglink">[[8A_F11_Q13|&nbsp;Question 13&nbsp;]]</span> Set up, but do not solve, the following word problem. <br>One evening 1500 concert tickets were sold for the Riverside Jazz Festival. Tickets cost $25 for a covered pavilion seat and $15 for a lawn seat. Total receipts were $28,500. How many of each type of ticket were sold?
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<span class = "biglink">[[008A Sample Final A, Question 13|&nbsp;Question 13&nbsp;]]</span> Set up, but do not solve, the following word problem. <br>One evening 1500 concert tickets were sold for the Riverside Jazz Festival. Tickets cost $25 for a covered pavilion seat and $15 for a lawn seat. Total receipts were $28,500. How many of each type of ticket were sold?
  
  
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<span class = "biglink">[[8A_F11_Q14|&nbsp;Question 14&nbsp;]]</span> Compute <math> \displaystyle{\sum_{n=1}^\infty 5\left(\frac{3}{5}\right)^n}</math>
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<span class = "biglink">[[008A Sample Final A, Question 14|&nbsp;Question 14&nbsp;]]</span> Compute <math> \displaystyle{\sum_{n=1}^\infty 5\left(\frac{3}{5}\right)^n}</math>
  
  
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<span class = "biglink">[[8A_F11_Q15|&nbsp;Question 15&nbsp;]]</span> a) Find the equation of the line passing through (3, -2) and (5, 6).<br>
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<span class = "biglink">[[008A Sample Final A, Question 15|&nbsp;Question 15&nbsp;]]</span> a) Find the equation of the line passing through (3, -2) and (5, 6).<br>
 
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b) Find the slope of any line perpendicular to your answer from a)
 
b) Find the slope of any line perpendicular to your answer from a)
  
  
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<span class = "biglink">[[8A_F11_Q16|&nbsp;Question 16&nbsp;]]</span> Solve. <math> \log_6(x+2)+\log_6(x-3) = 1 </math>
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<span class = "biglink">[[008A Sample Final A, Question 16|&nbsp;Question 16&nbsp;]]</span> Solve. <math> \log_6(x+2)+\log_6(x-3) = 1 </math>
  
  
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<span class = "biglink">[[8A_F11_Q17|&nbsp;Question 17&nbsp;]]</span> Compute the following trig ratios: a) <math> \sec \frac{3\pi}{4}</math> &nbsp; &nbsp; &nbsp; b) <math> \tan \frac{11\pi}{6}</math> &nbsp; &nbsp; &nbsp; c) <math>\sin(-120)</math>
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<span class = "biglink">[[008A Sample Final A, Question 17|&nbsp;Question 17&nbsp;]]</span> Compute the following trig ratios: a) <math> \sec \frac{3\pi}{4}</math> &nbsp; &nbsp; &nbsp; b) <math> \tan \frac{11\pi}{6}</math> &nbsp; &nbsp; &nbsp; c) <math>\sin(-120)</math>
  
  
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<span class = "biglink">[[8A_F11_Q18|&nbsp;Question 18&nbsp;]]</span> Compute <math>\cos(\arctan\frac{5}{3})</math>
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<span class = "biglink">[[008A Sample Final A, Question 18|&nbsp;Question 18&nbsp;]]</span> Compute <math>\cos(\arctan\frac{5}{3})</math>
  
  
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<span class = "biglink">[[8A_F11_Q19|&nbsp;Question 19&nbsp;]]</span> Compute <math>\arcsin -\frac{\sqrt{3}}{2}</math>. Provide your answer in radians.
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<span class = "biglink">[[008A Sample Final A, Question 19|&nbsp;Question 19&nbsp;]]</span> Compute <math>\arcsin -\frac{\sqrt{3}}{2}</math>. Provide your answer in radians.

Revision as of 13:01, 28 April 2015

 Question 1  Find for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = \log_3(x+3)-1}


 Question 2  Find f(5) for f(x) given in problem 1.


 Question 3  a) Find the vertex, standard graphing form, and X-intercept for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x = -3y^2-6y+2}

                  b) Sketch the graph. Provide the focus and directrix.


 Question 4  Solve. Provide your solution in interval notation. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x-4)(2x+1)(x-1)<0}


 Question 5  Graph the system of inequalities Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y < \vert x\vert +1 }           Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 + y^2 \le 9}


 Question 6  Sketch Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 4x^2 + 9(y + 1)^2 = 36} . Give coordinates of each of the 4 vertices of the graph.


 Question 7  Solve Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2\vert 3x-4\vert -7 = 7}


 Question 8  Given a sequence Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 27, 23, 19, 15, \ldots } use formulae to compute Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S_{10}} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A_{15}} .


 Question 9  a) List all the possible rational zeros of the function Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = x^4 + 5x^3 - 27x^2 +31x -10}
                  b) Find all the zeros, that is, solve f(x) = 0


 Question 10  Graph the function. Give equations of any asymptotes, and list any intercepts Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = \frac{x-1}{2x+2}}


 Question 11  Decompose into separate partial fractions Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{3x^2+6x+7}{(x+3)^2(x-1)}}


 Question 12  Find and simplify the difference quotient Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{f(x+h)-f(x)}{h}} for f(x) = Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{2}{3x+1}}


 Question 13  Set up, but do not solve, the following word problem.
One evening 1500 concert tickets were sold for the Riverside Jazz Festival. Tickets cost $25 for a covered pavilion seat and $15 for a lawn seat. Total receipts were $28,500. How many of each type of ticket were sold?


 Question 14  Compute Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \displaystyle{\sum_{n=1}^\infty 5\left(\frac{3}{5}\right)^n}}


 Question 15  a) Find the equation of the line passing through (3, -2) and (5, 6).
                    b) Find the slope of any line perpendicular to your answer from a)


 Question 16  Solve. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \log_6(x+2)+\log_6(x-3) = 1 }


 Question 17  Compute the following trig ratios: a) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sec \frac{3\pi}{4}}       b) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tan \frac{11\pi}{6}}       c) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sin(-120)}


 Question 18  Compute Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cos(\arctan\frac{5}{3})}


 Question 19  Compute Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \arcsin -\frac{\sqrt{3}}{2}} . Provide your answer in radians.

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