Difference between revisions of "008A Sample Final A"

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<span class = "biglink">[[8A_F11_Q1|&nbsp;Question 1&nbsp;]]</span> Find <math>f^{-1}(x)</math> for <math>f(x) = \log_3(x+3)-1</math>
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'''This is a sample final, and is meant to represent the material usually covered in Math 8A.  Moreover, it contains enough questions to represent a three hour test.  An actual test may or may not be similar.  Click on the <span class="biglink" style="color:darkblue;">&nbsp;boxed problem numbers&nbsp;</span> to go to a solution.'''
  
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<div class="noautonum">__TOC__</div>
  
<span class = "biglink">[[8A_F11_Q2|&nbsp;Question 2&nbsp;]]</span> Find f(5) for f(x) given in problem 1.
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==[[008A_Sample Final_A, Question 1|<span class = "biglink" style="font-size:80%">&nbsp;Question 1&nbsp;</span>]]==
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<span class = "exam">Find <math style="vertical-align: -15%">f^{-1}(x)</math> for <math style="vertical-align: -15%">f(x) = \log_3(x+3)-1</math>
  
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==[[008A Sample Final A, Question 2|<span class = "biglink" style="font-size:80%">&nbsp;Question 2&nbsp;</span>]]==
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<span class="exam">Find f(5) for f(x) given in problem 1.
  
<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>
 
  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 
b) Sketch the graph. Provide the focus and directrix.
 
  
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==[[008A Sample Final A, Question 3|<span class = "biglink" style="font-size:80%">&nbsp;Question 3&nbsp;</span>]]==
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<span class="exam">a) Find the vertex, standard graphing form, and X-intercept for <math style="vertical-align: -15%">x = -3y^2-6y+2</math><br></span>
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<span class="exam">b) Sketch the graph. Provide the focus and directrix.
  
<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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==[[008A Sample Final A, Question 4|<span class = "biglink" style="font-size:80%">&nbsp;Question 4&nbsp;</span>]]==
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<span class = "exam">Solve. Provide your solution in interval notation. <math>(x-4)(2x+1)(x-1)<0</math>
  
  
<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>
 
  
  
<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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==[[008A Sample Final A, Question 5|<span class = "biglink" style="font-size:80%">&nbsp;Question 5&nbsp;</span>]]==
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<span class="exam">Graph the system of inequalities <math style="vertical-align: -10%">y < \vert x\vert +1 </math> &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math style="vertical-align: -10%">x^2 + y^2 \le 9</math>
  
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==[[008A Sample Final A, Question 6|<span class = "biglink" style="font-size:80%">&nbsp;Question 6&nbsp;</span>]]==
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<span class="exam">Sketch <math style="vertical-align: -10%">4x^2 + 9(y + 1)^2 = 36</math>. Give coordinates of each of the 4 vertices of the graph.
  
<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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==[[008A Sample Final A, Question 7|<span class = "biglink" style="font-size:80%">&nbsp;Question 7&nbsp;</span>]]==
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<span class="exam">Solve <math style="vertical-align: -10%">2\vert 3x-4\vert -7 = 7</math>
  
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==[[008A Sample Final A, Question 8|<span class = "biglink" style="font-size:80%">&nbsp;Question 8&nbsp;</span>]]==
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<span class="exam">Given a sequence <math style="vertical-align: -12%"> 27, 23, 19, 15, \ldots </math> use formulae to compute <math style="vertical-align: -10%">S_{10}</math> and <math style="vertical-align: -10%">A_{15}</math>.
  
<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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==[[008A Sample Final A, Question 9|<span class = "biglink" style="font-size:80%">&nbsp;Question 9&nbsp;</span>]]==
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<span class="exam">a) List all the possible rational zeros of the function <math style="vertical-align: -12%">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
  
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==[[008A Sample Final A, Question 10|<span class = "biglink" style="font-size:80%">&nbsp;Question 10&nbsp;</span>]]==
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<span class="exam">Graph the function. Give equations of any asymptotes, and list any intercepts <math style="vertical-align: -50%">y = \frac{x-1}{2x+2}</math>
  
<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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==[[008A Sample Final A, Question 11|<span class = "biglink" style="font-size:80%">&nbsp;Question 11&nbsp;</span>]]==
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
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<span class="exam">Decompose into separate partial fractions <math style="vertical-align: -80%">\frac{3x^2+6x+7}{(x+3)^2(x-1)}</math>
b) Find all the zeros, that is, solve f(x) = 0
 
 
 
  
<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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==[[008A Sample Final A, Question 12|<span class = "biglink" style="font-size:80%">&nbsp;Question 12&nbsp;</span>]]==
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<span class="exam">Find and simplify the difference quotient <math style="vertical-align: -70%">\frac{f(x+h)-f(x)}{h}</math> for f(x) = <math style="vertical-align: -60%">\frac{2}{3x+1}</math>
  
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==[[008A Sample Final A, Question 13|<span class = "biglink" style="font-size:80%">&nbsp;Question 13&nbsp;</span>]]==
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<span class="exam">Set up, but do not solve, the following word problem. <br></span>
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<span class="exam">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?</span>
  
<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>
 
  
  
<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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==[[008A Sample Final A, Question 14|<span class = "biglink" style="font-size:80%">&nbsp;Question 14&nbsp;</span>]]==
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<span class="exam">Compute <math> \displaystyle{\sum_{n=1}^\infty 5\left(\frac{3}{5}\right)^n}</math>
  
<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?
 
  
  
<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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==[[008A Sample Final A, Question 15|<span class = "biglink" style="font-size:80%">&nbsp;Question 15&nbsp;</span>]]==
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<span class="exam">a) Find the equation of the line passing through (3, -2) and (5, 6).<br></span>
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<span class="exam">b) Find the slope of any line perpendicular to your answer from a).
  
<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>
 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
 
b) Find the slope of any line perpendicular to your answer from a)
 
  
  
<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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==[[008A Sample Final A, Question 16|<span class = "biglink" style="font-size:80%">&nbsp;Question 16&nbsp;</span>]]==
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<span class="exam">Solve. <math style="vertical-align: -15%"> \log_6(x+2)+\log_6(x-3) = 1 </math>
  
<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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==[[008A Sample Final A, Question 17|<span class = "biglink" style="font-size:80%">&nbsp;Question 17&nbsp;</span>]]==
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<span class="exam">Compute the following trig ratios: a) <math style="vertical-align: -45%"> \sec \frac{3\pi}{4}</math> &nbsp; &nbsp; &nbsp; b) <math style="vertical-align: -50%"> \tan \frac{11\pi}{6}</math> &nbsp; &nbsp; &nbsp; c) <math style="vertical-align: -10%">\sin(-120)</math>
  
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==[[008A Sample Final A, Question 18|<span class = "biglink" style="font-size:80%">&nbsp;Question 18&nbsp;</span>]]==
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<span class="exam">Compute <math style="vertical-align: -40%">\cos(\arctan\frac{5}{3})</math>
  
<span class = "biglink">[[8A_F11_Q18|&nbsp;Question 18&nbsp;]]</span> Compute <math>\cos(\arctan\frac{5}{3})</math>
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==[[008A Sample Final A, Question 19|<span class = "biglink" style="font-size:80%">&nbsp;Question 19&nbsp;</span>]]==
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<span class="exam">Compute <math style="vertical-align: -40%">\arcsin -\frac{\sqrt{3}}{2}</math>. Provide your answer in radians.
  
  
<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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'''Contributions to this page were made by [[Contributors|Matthew Lee]]'''

Latest revision as of 11:42, 28 July 2015

This is a sample final, and is meant to represent the material usually covered in Math 8A. Moreover, it contains enough questions to represent a three hour test. An actual test may or may not be similar. Click on the  boxed problem numbers  to go to a solution.

 Question 1 

Find for

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

 Question 4 

Solve. Provide your solution in interval notation.



 Question 5 

Graph the system of inequalities          

 Question 6 

Sketch . Give coordinates of each of the 4 vertices of the graph.

 Question 7 

Solve

 Question 8 

Given a sequence use formulae to compute and .

 Question 9 

a) List all the possible rational zeros of the function
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

 Question 11 

Decompose into separate partial fractions

 Question 12 

Find and simplify the difference quotient for f(x) =

 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



 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.

 Question 17 

Compute the following trig ratios: a)       b)       c)

 Question 18 

Compute

 Question 19 

Compute . Provide your answer in radians.


Contributions to this page were made by Matthew Lee