Difference between revisions of "008A Sample Final A"
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<div class="noautonum">__TOC__</div> | <div class="noautonum">__TOC__</div> | ||
<span class="exam"> | <span class="exam"> | ||
| − | ==[[008A_Sample Final_A, Question 1|<span class = "biglink"> Question 1 </span>]]== | + | ==[[008A_Sample Final_A, Question 1|<span class = "biglink" style="font-size:80%"> Question 1 </span>]]== |
<span class = "exam">Find <math>f^{-1}(x)</math> for <math>f(x) = \log_3(x+3)-1</math> | <span class = "exam">Find <math>f^{-1}(x)</math> for <math>f(x) = \log_3(x+3)-1</math> | ||
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| − | ==[[008A Sample Final A, Question 2|<span class = "biglink"> Question 2 </span>]]== | + | ==[[008A Sample Final A, Question 2|<span class = "biglink" style="font-size:80%"> Question 2 </span>]]== |
<span class="exam">Find f(5) for f(x) given in problem 1. | <span class="exam">Find f(5) for f(x) given in problem 1. | ||
| − | ==[[008A Sample Final A, Question 3|<span class = "biglink"> Question 3 </span>]]== | + | ==[[008A Sample Final A, Question 3|<span class = "biglink" style="font-size:80%"> Question 3 </span>]]== |
<span class="exam">a) Find the vertex, standard graphing form, and X-intercept for <math>x = -3y^2-6y+2</math> | <span class="exam">a) Find the vertex, standard graphing form, and X-intercept for <math>x = -3y^2-6y+2</math> | ||
<span class="exam">b) Sketch the graph. Provide the focus and directrix. | <span class="exam">b) Sketch the graph. Provide the focus and directrix. | ||
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<span class="exam"> | <span class="exam"> | ||
| − | ==[[008A Sample Final A, Question 4|<span class = "biglink"> Question 4 </span>]]== | + | ==[[008A Sample Final A, Question 4|<span class = "biglink" style="font-size:80%"> Question 4 </span>]]== |
<span class = "exam">Solve. Provide your solution in interval notation. <math>(x-4)(2x+1)(x-1)<0</math> | <span class = "exam">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 5|<span class = "biglink"> Question 5 </span>]]== | + | ==[[008A Sample Final A, Question 5|<span class = "biglink" style="font-size:80%"> Question 5 </span>]]== |
<span class="exam">Graph the system of inequalities <math>y < \vert x\vert +1 </math> <math>x^2 + y^2 \le 9</math> | <span class="exam">Graph the system of inequalities <math>y < \vert x\vert +1 </math> <math>x^2 + y^2 \le 9</math> | ||
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| − | ==[[008A Sample Final A, Question 6|<span class = "biglink"> Question 6 </span>]]== | + | ==[[008A Sample Final A, Question 6|<span class = "biglink" style="font-size:80%"> Question 6 </span>]]== |
<span class="exam">Sketch <math>4x^2 + 9(y + 1)^2 = 36</math>. Give coordinates of each of the 4 vertices of the graph. | <span class="exam">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 7|<span class = "biglink"> Question 7 </span>]]== | + | ==[[008A Sample Final A, Question 7|<span class = "biglink" style="font-size:80%"> Question 7 </span>]]== |
<span class="exam">Solve <math>2\vert 3x-4\vert -7 = 7</math> | <span class="exam">Solve <math>2\vert 3x-4\vert -7 = 7</math> | ||
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| − | ==[[008A Sample Final A, Question 8|<span class = "biglink"> Question 8 </span>]]== | + | ==[[008A Sample Final A, Question 8|<span class = "biglink" style="font-size:80%"> Question 8 </span>]]== |
<span class="exam">Given a sequence <math> 27, 23, 19, 15, \ldots </math> use formulae to compute <math>S_{10}</math> and <math>A_{15}</math>. | <span class="exam">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"> Question 9 </span>]]== | + | ==[[008A Sample Final A, Question 9|<span class = "biglink" style="font-size:80%"> Question 9 </span>]]== |
<span class="exam">a) List all the possible rational zeros of the function <math>f(x) = x^4 + 5x^3 - 27x^2 +31x -10</math><br> | <span class="exam">a) List all the possible rational zeros of the function <math>f(x) = x^4 + 5x^3 - 27x^2 +31x -10</math><br> | ||
<span class="exam">b) Find all the zeros, that is, solve f(x) = 0 | <span class="exam">b) Find all the zeros, that is, solve f(x) = 0 | ||
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| − | ==[[008A Sample Final A, Question 10|<span class = "biglink"> Question 10 </span>]]== | + | ==[[008A Sample Final A, Question 10|<span class = "biglink" style="font-size:80%"> Question 10 </span>]]== |
<span class="exam">Graph the function. Give equations of any asymptotes, and list any intercepts <math>y = \frac{x-1}{2x+2}</math> | <span class="exam">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 11|<span class = "biglink"> Question 11 </span>]]== | + | ==[[008A Sample Final A, Question 11|<span class = "biglink" style="font-size:80%"> Question 11 </span>]]== |
<span class="exam">Decompose into separate partial fractions <math>\frac{3x^2+6x+7}{(x+3)^2(x-1)}</math> | <span class="exam">Decompose into separate partial fractions <math>\frac{3x^2+6x+7}{(x+3)^2(x-1)}</math> | ||
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| − | ==[[008A Sample Final A, Question 12|<span class = "biglink"> Question 12 </span>]]== | + | ==[[008A Sample Final A, Question 12|<span class = "biglink" style="font-size:80%"> Question 12 </span>]]== |
<span class="exam">Find and simplify the difference quotient <math>\frac{f(x+h)-f(x)}{h}</math> for f(x) = <math>\frac{2}{3x+1}</math> | <span class="exam">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 13|<span class = "biglink"> Question 13 </span>]]== | + | ==[[008A Sample Final A, Question 13|<span class = "biglink" style="font-size:80%"> Question 13 </span>]]== |
| − | <span class="exam">Set up, but do not solve, the following word problem. <br> | + | <span class="exam">Set up, but do not solve, the following word problem. <br></span> |
| − | <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 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> |
| − | ==[[008A Sample Final A, Question 14|<span class = "biglink"> Question 14 </span>]]== | + | ==[[008A Sample Final A, Question 14|<span class = "biglink" style="font-size:80%"> Question 14 </span>]]== |
<span class="exam">Compute <math> \displaystyle{\sum_{n=1}^\infty 5\left(\frac{3}{5}\right)^n}</math> | <span class="exam">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"> Question 15 </span>]]== | + | ==[[008A Sample Final A, Question 15|<span class = "biglink" style="font-size:80%"> Question 15 </span>]]== |
<span class="exam">a) Find the equation of the line passing through (3, -2) and (5, 6).<br> | <span class="exam">a) Find the equation of the line passing through (3, -2) and (5, 6).<br> | ||
<span class="exam">b) Find the slope of any line perpendicular to your answer from a). | <span class="exam">b) Find the slope of any line perpendicular to your answer from a). | ||
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| − | ==[[008A Sample Final A, Question 16|<span class = "biglink"> Question 16 </span>]]== | + | ==[[008A Sample Final A, Question 16|<span class = "biglink" style="font-size:80%"> Question 16 </span>]]== |
<span class="exam">Solve. <math> \log_6(x+2)+\log_6(x-3) = 1 </math> | <span class="exam">Solve. <math> \log_6(x+2)+\log_6(x-3) = 1 </math> | ||
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| − | ==[[008A Sample Final A, Question 17|<span class = "biglink"> Question 17 </span>]]== | + | ==[[008A Sample Final A, Question 17|<span class = "biglink" style="font-size:80%"> Question 17 </span>]]== |
<span class="exam">Compute the following trig ratios: a) <math> \sec \frac{3\pi}{4}</math> b) <math> \tan \frac{11\pi}{6}</math> c) <math>\sin(-120)</math> | <span class="exam">Compute the following trig ratios: a) <math> \sec \frac{3\pi}{4}</math> b) <math> \tan \frac{11\pi}{6}</math> c) <math>\sin(-120)</math> | ||
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| − | ==[[008A Sample Final A, Question 18|<span class = "biglink"> Question 18 </span>]]== | + | ==[[008A Sample Final A, Question 18|<span class = "biglink" style="font-size:80%"> Question 18 </span>]]== |
<span class="exam">Compute <math>\cos(\arctan\frac{5}{3})</math> | <span class="exam">Compute <math>\cos(\arctan\frac{5}{3})</math> | ||
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| − | ==[[008A Sample Final A, Question 19|<span class = "biglink"> Question 19 </span>]]== | + | ==[[008A Sample Final A, Question 19|<span class = "biglink" style="font-size:80%"> Question 19 </span>]]== |
<span class="exam">Compute <math>\arcsin -\frac{\sqrt{3}}{2}</math>. Provide your answer in radians. | <span class="exam">Compute <math>\arcsin -\frac{\sqrt{3}}{2}</math>. Provide your answer in radians. | ||
Revision as of 22:43, 25 May 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.
