005 Sample Final A - Revision history

MathAdmin at 21:43, 24 September 2015

2015-09-24T21:43:47Z

MathAdmin at 18:44, 28 July 2015

2015-07-28T18:44:10Z

MathAdmin at 18:42, 28 July 2015

2015-07-28T18:42:59Z

MathAdmin at 23:55, 5 June 2015

2015-06-05T23:55:41Z

MathAdmin: /* Question 3 */

2015-06-05T23:53:53Z

Question 3

MathAdmin at 23:53, 5 June 2015

2015-06-05T23:53:18Z

MathAdmin at 01:05, 1 June 2015

2015-06-01T01:05:41Z

MathAdmin at 01:03, 1 June 2015

2015-06-01T01:03:42Z

MathAdmin: /* Question 18 */

2015-06-01T01:03:14Z

Question 18

MathAdmin: /* Question 17 */

2015-06-01T01:02:54Z

Question 17

← Older revision		Revision as of 21:43, 24 September 2015
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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;"> boxed problem numbers </span> to go to a solution.'''	+	'''This is a sample final, and is meant to represent the material usually covered in Math 5. 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;"> boxed problem numbers </span> to go to a solution.'''

	<div class="noautonum">__TOC__</div>		<div class="noautonum">__TOC__</div>

← Older revision		Revision as of 18:44, 28 July 2015
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−	'''Contributions to this page were made by [[Contributors\|~~Kayla Murray~~]]'''	+	'''Contributions to this page were made by [[Contributors\|Matthew Lee]]'''

← Older revision		Revision as of 18:42, 28 July 2015
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	b. Find the sum <math> \displaystyle{\sum_{k=1}^\infty a_k}</math>		b. Find the sum <math> \displaystyle{\sum_{k=1}^\infty a_k}</math>
	</span>		</span>
		+
		+
		+	'''Contributions to this page were made by [[Contributors\|Kayla Murray]]'''

@@ Line 14: / Line 14: @@
 <span class = "exam">Find the domain of the following function. Your answer should be in interval notation <math> f(x) = \frac{1}{\sqrt{x^2-x-2}}</math> <br>
-==[[005 Sample Final A, Question 3|<span class = "biglink">&nbsp;Question 3&nbsp;</span>]]==
+==[[005 Sample Final A, Question 3|<span class = "biglink" style="font-size:80%">&nbsp;Question 3&nbsp;</span>]]==
 <span class = "exam">Find f <math>\circ</math> g and its domain if <math>f(x) = x^2+1 \qquad g(x)=\sqrt{x-1}</math>
-==[[005 Sample Final A, Question 4|<span class = "biglink"style="font-size:80%">&nbsp;Question 4&nbsp;</span>]]==
+==[[005 Sample Final A, Question 4|<span class = "biglink" style="font-size:80%">&nbsp;Question 4&nbsp;</span>]]==
 <span class = "exam">Find the inverse of the following function <math> f(x) = \frac{3x}{2x-1}</math>
-==[[005 Sample Final A, Question 5|<span class = "biglink"style="font-size:80%">&nbsp;Question 5&nbsp;</span>]]==
+==[[005 Sample Final A, Question 5|<span class = "biglink" style="font-size:80%">&nbsp;Question 5&nbsp;</span>]]==
 <span class = "exam">Solve the following inequality. Your answer should be in interval notation. <math>\frac{3x+5}{x+2}\ge 2</math>
-==[[005 Sample Final A, Question 6|<span class = "biglink"style="font-size:80%">&nbsp;Question 6&nbsp;</span>]] ==
+==[[005 Sample Final A, Question 6|<span class = "biglink" style="font-size:80%">&nbsp;Question 6&nbsp;</span>]] ==
 <span class = "exam"> Factor the following polynomial completely, &nbsp;&nbsp;&nbsp;&nbsp;<math>p(x) = x^4 + x^3 + 2x-4 </math>
-==[[005 Sample Final A, Question 7|<span class = "biglink"style="font-size:80%">&nbsp;Question 7&nbsp;</span>]] ==
+==[[005 Sample Final A, Question 7|<span class = "biglink" style="font-size:80%">&nbsp;Question 7&nbsp;</span>]] ==
 <span class="exam"> Solve the following equation, &nbsp;&nbsp;&nbsp;&nbsp; <math> 2\log_5(x) = 3\log_5(4)</math>
-==[[005 Sample Final A, Question 8|<span class = "biglink"style="font-size:80%">&nbsp;Question 8&nbsp;</span>]] ==
+==[[005 Sample Final A, Question 8|<span class = "biglink" style="font-size:80%">&nbsp;Question 8&nbsp;</span>]] ==
 <span class="exam"> Solve the following equation, &nbsp;&nbsp;&nbsp;&nbsp; <math> 3^{2x} + 3^x -2 = 0 </math>
-==[[005 Sample Final A, Question 9|<span class = "biglink"style="font-size:80%">&nbsp;Question 9&nbsp;</span>]]==
+==[[005 Sample Final A, Question 9|<span class = "biglink" style="font-size:80%">&nbsp;Question 9&nbsp;</span>]]==
 <span class = "exam"> Solve the following system of equations <br>
 <center><math>  \begin{align} 2x + 3y  &= & 1\\ -x + y & = & -3\end{align}</math></center>
-==[[005 Sample Final A, Question 10|<span class = "biglink"style="font-size:80%">&nbsp;Question 10&nbsp;</span>]]==
+==[[005 Sample Final A, Question 10|<span class = "biglink" style="font-size:80%">&nbsp;Question 10&nbsp;</span>]]==
 <span class="exam"> Write the partial fraction decomposition of the following, <center> <math> \frac{x+2}{x^3-2x^2+x}</math></center></span>
-==[[005 Sample Final A, Question 11|<span class = "biglink"style="font-size:80%">&nbsp;Question 11&nbsp;</span>]] ==
+==[[005 Sample Final A, Question 11|<span class = "biglink" style="font-size:80%">&nbsp;Question 11&nbsp;</span>]] ==
 <span class="exam">Solve the following equation in the interval <math> [0, 2\pi)</math> <br>
 <center><math> \sin^2(\theta) - \cos^2(\theta)=1+\cos(\theta)</math></center></span>
-==[[005 Sample Final A, Question 12|<span class = "biglink"style="font-size:80%">&nbsp;Question 12&nbsp;</span>]]==
+==[[005 Sample Final A, Question 12|<span class = "biglink" style="font-size:80%">&nbsp;Question 12&nbsp;</span>]]==
 <span class="exam"> Given that <math>\sec(\theta) = -2</math> and <math>\tan(\theta) > 0 </math>, find the exact values of the remaining trig functions.
-==[[005 Sample Final A, Question 13|<span class = "biglink"style="font-size:80%">&nbsp;Question 13&nbsp;</span>]]==
+==[[005 Sample Final A, Question 13|<span class = "biglink" style="font-size:80%">&nbsp;Question 13&nbsp;</span>]]==
 <span class="exam"> Give the exact value of the following if its defined, otherwise, write undefined. <br>
 <math>(a) \sin^{-1}(2) \qquad \qquad (b) \sin\left(\frac{-32\pi}{3}\right) \qquad \qquad (c)\sec\left(\frac{-17\pi}{6}\right)</math>
-==[[005 Sample Final A, Question 14|<span class = "biglink"style="font-size:80%">&nbsp;Question 14&nbsp;</span>]]==
+==[[005 Sample Final A, Question 14|<span class = "biglink" style="font-size:80%">&nbsp;Question 14&nbsp;</span>]]==
 <span class="exam"> Prove the following identity, <br>
 <center><math>\frac{1-\sin(\theta)}{\cos(\theta)}=\frac{\cos(\theta)}{1+\sin(\theta)}</math></center>
-==[[005 Sample Final A, Question 15|<span class = "biglink"style="font-size:80%">&nbsp;Question 15&nbsp;</span>]]==
+==[[005 Sample Final A, Question 15|<span class = "biglink" style="font-size:80%">&nbsp;Question 15&nbsp;</span>]]==
 <span class="exam"> Find an equivalent algebraic expression for the following, <center><math> \cos(\tan^{-1}(x))</math></center></span>
-==[[005 Sample Final A, Question 16|<span class = "biglink"style="font-size:80%">&nbsp;Question 16&nbsp;</span> ]]==
+==[[005 Sample Final A, Question 16|<span class = "biglink" style="font-size:80%">&nbsp;Question 16&nbsp;</span> ]]==
 <span class="exam"> Graph the following, </span><center><math> -x^2+4y^2-2x-16y+11=0</math></center></span>
-==[[005 Sample Final A, Question 17|<span class = "biglink"style="font-size:80%">&nbsp;Question 17&nbsp;</span>]]==
+==[[005 Sample Final A, Question 17|<span class = "biglink" style="font-size:80%">&nbsp;Question 17&nbsp;</span>]]==
 <span class="exam"> Graph the following function, <center><math>f(x) = \log_2(x+1) + 2</math></center> </span> <br>
 <span class="exam">Make sure to label any asymptotes, and at least two points on the graph. </span>

@@ Line 14: / Line 14: @@
 <span class = "exam">Find the domain of the following function. Your answer should be in interval notation <math> f(x) = \frac{1}{\sqrt{x^2-x-2}}</math> <br>
-==[[005 Sample Final A, Question 3|<span class = "biglink"style="font-size:80%">&nbsp;Question 3&nbsp;</span>]]==
+==[[005 Sample Final A, Question 3|<span class = "biglink">&nbsp;Question 3&nbsp;</span>]]==
 <span class = "exam">Find f <math>\circ</math> g and its domain if <math>f(x) = x^2+1 \qquad g(x)=\sqrt{x-1}</math>

@@ Line 61: / Line 61: @@
 ==[[005 Sample Final A, Question 17|<span class = "biglink">&nbsp;Question 17&nbsp;</span>]]==
-<span class="exam"> Graph the following function, <center><math>f(x) = \log_2(x+1) + 2</math></center> <br>
+<span class="exam"> Graph the following function, <center><math>f(x) = \log_2(x+1) + 2</math></center> </span> <br>
-Make sure to label any asymptotes, and at least two points on the graph. </span>
+<span class="exam">Make sure to label any asymptotes, and at least two points on the graph. </span>
 ==[[005 Sample Final A, Question 18|<span class = "biglink">&nbsp;Question 18&nbsp;</span>]]==
@@ Line 69: / Line 69: @@
 ==[[005 Sample Final A, Question 19|<span class = "biglink">&nbsp;Question 19&nbsp;</span>]]==
-<span class="exam"> Consider the following function, <center><math>f(x) = -\sin\left(3x+\frac{\pi}{2}\right)+1</math></center><br>
+<span class="exam"> Consider the following function, <center><math>f(x) = -\sin\left(3x+\frac{\pi}{2}\right)+1</math></center></span><br>
-&nbsp;&nbsp;&nbsp;&nbsp; a. What is the amplitude?<br>
+&nbsp;&nbsp;&nbsp;&nbsp;<span class="exam"> a. What is the amplitude?</span><br>
-&nbsp;&nbsp;&nbsp;&nbsp; b. What is the period? <br>
+&nbsp;&nbsp;&nbsp;&nbsp;<span class="exam"> b. What is the period? </span><br>
-&nbsp;&nbsp;&nbsp;&nbsp; c. What is the phase shift? <br>
+&nbsp;&nbsp;&nbsp;&nbsp;<span class="exam"> c. What is the phase shift? </span><br>
-&nbsp;&nbsp;&nbsp;&nbsp; d. What is the vertical shift? <br>
+&nbsp;&nbsp;&nbsp;&nbsp;<span class="exam"> d. What is the vertical shift? </span><br>
-&nbsp;&nbsp;&nbsp;&nbsp; e. Graph one cycle of f(x). Make sure to label five key points.</span>
+&nbsp;&nbsp;&nbsp;&nbsp;<span class="exam"> e. Graph one cycle of f(x). Make sure to label five key points.</span>
 ==[[005 Sample Final A, Question 20|<span class = "biglink">&nbsp;Question 20&nbsp;</span>]]==
 <span class="exam"> Consider the following rational function,
-<center><math>f(x) = \frac{x^2+x-2}{x^2-1}</math></center> <br>
+<center><math>f(x) = \frac{x^2+x-2}{x^2-1}</math></center></span> <br>
+<span class="exam">
 &nbsp;&nbsp;&nbsp;&nbsp; a. What is the domain of f? <br>
 &nbsp;&nbsp;&nbsp;&nbsp; b. What are the x and y-intercepts of f? <br>

@@ Line 65: / Line 65: @@
 ==[[005 Sample Final A, Question 18|<span class = "biglink">&nbsp;Question 18&nbsp;</span>]]==
-<span class="exam"> Graph the following function, <center><math>f(x) = \left(\frac{1}{3}\right)^{x+1} + 1</math></center> <br>
+<span class="exam"> Graph the following function, <center><math>f(x) = \left(\frac{1}{3}\right)^{x+1} + 1</math></center> </span> <br>
-Make sure to label any asymptotes, and at least two points on the graph.</span>
+Make sure to label any asymptotes, and at least two points on the graph.
 ==[[005 Sample Final A, Question 19|<span class = "biglink">&nbsp;Question 19&nbsp;</span>]]==