Difference between revisions of "004 Sample Final A"

Latest revision as of 10:43, 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 $f^{-1}(x)$ for $f(x)={\frac {3x-1}{4x+2}}$

Question 2

a) Find the vertex, standard graphing form, and x-intercepts for $f(x)={\frac {1}{3}}x^{2}+2x-3$
b) Sketch the graph. Provide the y-intercept.

Question 3

Solve. Provide your solution in interval notation. $\vert 4x+7\vert \geq 5$

Question 4

Graph the system of inequalities. $y>2x-3\qquad y\leq 4-x^{2}$

Question 5

Describe how the graph of $f(x)=3^{(x+1)}-2$ can be obtained from a basic graph. Then sketch the graph. Provide at least two ordered pairs, and the equation of any asymptote.

Question 6

Simplify. ${\frac {1}{3x+6}}-{\frac {x}{x^{2}-4}}+{\frac {3}{x-2}}$

Question 7

Given a sequence $10,7,4,1,\ldots$ use formulae on the back page to compute $S_{20}$

Question 8

a) List all the possible rational zeros of the function $f(x)=x^{4}-4x^{3}-7x^{2}+34x-24$ .
b) Find all the zeros, that is, solve $f(x)=0$

Question 9

Graph the function. Give equations of any asymptotes, and list any intercepts. $y={\frac {6}{x^{2}-x-2}}$

Question 10

Decompose into separate partial fractions. ${\frac {6x^{2}+27x+31}{(x+3)^{2}(x-1)}}$

Question 11

Find and simplify the difference quotient ${\frac {f(x+h)-f(x)}{h}}$ for $f(x)={\sqrt {x-3}}$

Question 12

Set up, but do not solve the following word problem. Two private airplanes travel toward each other from cities that are 780 km apart at speeds of 190 km/hr and 200 km/hr. They left at the same time. In how many hours will they meet?

Question 13

Compute $\displaystyle {\sum _{n=1}^{6}4\left({\frac {1}{2}}\right)^{n}}$

Question 14

a) Find an equation of the line passing through $(-4,2)$ and $(3,6)$ .
b) Find the slope of any line perpendicular to your answer from a)

Question 15

Solve. $\log(x+8)+\log(x-1)=1$

Question 16

Solve. ${\sqrt {x-3}}+5=x$

Question 17

How many ways can a committee of four people can be selected from five married couples if no committee is to include both husband-and-wife pairs? (simplify your answer to a single number)

Question 18

Ten teams are entered in a bowling tournament. In how many ways can first, second, and third prizes be awarded? (simplify your answer to a single number)

Question 19

Solve for x: $\log _{6}{\frac {1}{36}}=x$

Contributions to this page were made by Kayla Murray

@@ Line 3: / Line 3: @@
 <div class="noautonum">__TOC__</div>
 <span class="exam">
-==[[004 Sample Final A, Problem 1|<span class = "biglink">&nbsp;Question 1&nbsp;</span>]]==
+==[[004 Sample Final A, Problem 1|<span class = "biglink" style="font-size:80%">&nbsp;Question 1&nbsp;</span>]]==
 <span class="exam"> Find <math style = "vertical-align: -17%;">f^{-1}(x)</math> for <math style = "vertical-align: -17%;>f(x) = \frac{3x-1}{4x+2}</math>
-==[[004 Sample Final A, Problem 2|<span class = "biglink">&nbsp;Question 2&nbsp;</span>]]==
+==[[004 Sample Final A, Problem 2|<span class = "biglink" style="font-size:80%">&nbsp;Question 2&nbsp;</span>]]==
-<span class="exam"> a) Find the vertex, standard graphing form, and ''x''-intercepts for <math>f(x) = \frac{1}{3}x^2 + 2x - 3</math><br>
+<span class="exam"> a) Find the vertex, standard graphing form, and ''x''-intercepts for <math>f(x) = \frac{1}{3}x^2 + 2x - 3</math></span><br>
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<span class="exam"> b) Sketch the graph. Provide the ''y''-intercept.</span>
-b) Sketch the graph. Provide the ''y''-intercept.
+==[[004 Sample Final A, Problem 3|<span class = "biglink" style="font-size:80%">&nbsp;Question 3&nbsp;</span>]]==
+<span class="exam"> Solve. Provide your solution in interval notation. &nbsp;&nbsp;&nbsp;&nbsp;<math>\vert 4x + 7\vert \ge 5</math>
-==[[004 Sample Final A, Problem 3|<span class = "biglink">&nbsp;Question 3&nbsp;</span>]]==
+==[[004 Sample Final A, Problem 4|<span class = "biglink" style="font-size:80%">&nbsp;Question 4&nbsp;</span>]]==
-<span class="exam"> Solve. Provide your solution in interval notation. &nbsp;&nbsp;&nbsp;&nbsp;<math>\vert 4x + 7\vert \ge 5</math>
+<span class="exam"> Graph the system of inequalities. <math>y > 2x - 3 \qquad y \le 4-x^2</math>
+==[[004 Sample Final A, Problem 5|<span class = "biglink" style="font-size:80%">&nbsp;Question 5&nbsp;</span>]]==
+<span class="exam"> Describe how the graph of <math>f(x) = 3^{(x+1)} - 2</math> can be obtained from a basic graph. Then sketch the graph. Provide at least two ordered pairs, and the equation of any asymptote.
-==[[004 Sample Final A, Problem 4|<span class = "biglink">&nbsp;Question 4&nbsp;</span>]]== <span class="exam"> Graph the system of inequalities. <math>y > 2x - 3 \qquad y \le 4-x^2</math>
+==[[004 Sample Final A, Problem 6|<span class = "biglink" style="font-size:80%">&nbsp;Question 6&nbsp;</span>]]==
+<span class="exam"> Simplify. &nbsp;&nbsp;&nbsp;&nbsp; <math>\frac{1}{3x + 6} - \frac{x}{x^2-4} + \frac{3}{x-2}</math>
-==[[004 Sample Final A, Problem 5|<span class = "biglink">&nbsp;Question 5&nbsp;</span>]]== <span class="exam"> Describe how the graph of <math>f(x) = 3^{(x+1)} - 2</math> can be obtained from a basic graph. Then sketch the graph. Provide at least two ordered pairs, and the equation of any asymptote.
+==[[004 Sample Final A, Problem 7|<span class = "biglink" style="font-size:80%">&nbsp;Question 7&nbsp;</span>]]==
+<span class="exam"> Given a sequence <math>10, 7, 4, 1, \ldots</math> use formulae on the back page to compute <math>S_{20}</math>
-==[[004 Sample Final A, Problem 6|<span class = "biglink">&nbsp;Question 6&nbsp;</span>]]== <span class="exam"> Simplify. &nbsp;&nbsp;&nbsp;&nbsp; <math>\frac{1}{3x + 6} - \frac{x}{x^2-4} + \frac{3}{x-2}</math>
+==[[004 Sample Final A, Problem 8|<span class = "biglink" style="font-size:80%">&nbsp;Question 8&nbsp;</span>]]==
+<span class="exam">  a) List all the possible rational zeros of the function <math> f(x)=x^4-4x^3-7x^2+34x-24</math>. </span><br>
+<span class="exam">  b) Find all the zeros, that is, solve <math>f(x) = 0</math>
-==[[004 Sample Final A, Problem 7|<span class = "biglink">&nbsp;Question 7&nbsp;</span>]]== <span class="exam"> Given a sequence <math>10, 7, 4, 1, \ldots</math> use formulae on the back page to compute <math>S_{20}</math>
+==[[004 Sample Final A, Problem 9|<span class = "biglink" style="font-size:80%">&nbsp;Question 9&nbsp;</span> ]]==
+<span class="exam"> Graph the function. Give equations of any asymptotes, and list any intercepts. &nbsp;&nbsp;&nbsp;&nbsp;<math>y = \frac{6}{x^2 - x - 2}</math>
-==[[004 Sample Final A, Problem 8|<span class = "biglink">&nbsp;Question 8&nbsp;</span>]]== <span class="exam"> a) List all the possible rational zeros of the function <math> f(x)=x^4-4x^3-7x^2+34x-24</math>.<br>
+==[[004 Sample Final A, Problem 10|<span class = "biglink" style="font-size:80%">&nbsp;Question 10&nbsp;</span>]]==
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; b) Find all the zeros, that is, solve <math>f(x) = 0</math>
+<span class="exam"> Decompose into separate partial fractions. &nbsp;&nbsp;&nbsp;&nbsp; <math>\frac{6x^2 + 27x + 31}{(x + 3)^2(x-1)}</math>
-==[[004 Sample Final A, Problem 9|<span class = "biglink">&nbsp;Question 9&nbsp;</span> ]]== <span class="exam"> Graph the function. Give equations of any asymptotes, and list any intercepts. &nbsp;&nbsp;&nbsp;&nbsp;<math>y = \frac{6}{x^2 - x - 2}</math>
+==[[004 Sample Final A, Problem 11|<span class = "biglink" style="font-size:80%">&nbsp;Question 11&nbsp;</span> ]] ==
+<span class="exam"> Find and simplify the difference quotient &thinsp;<math>\frac{f(x + h) - f(x)}{h}</math>&thinsp; for <math>f(x) = \sqrt{x - 3}</math>
-==[[004 Sample Final A, Problem 10|<span class = "biglink">&nbsp;Question 10&nbsp;</span>]]== <span class="exam"> Decompose into separate partial fractions. &nbsp;&nbsp;&nbsp;&nbsp; <math>\frac{6x^2 + 27x + 31}{(x + 3)^2(x-1)}</math>
+==[[004 Sample Final A, Problem 12|<span class = "biglink" style="font-size:80%">&nbsp;Question 12&nbsp;</span>]]==
+<span class="exam"> Set up, but do not solve the following word problem. Two private airplanes travel toward each other from cities that are 780 km apart at speeds of 190 km/hr and 200 km/hr. They left at the same time. In how many hours will they meet?
-==[[004 Sample Final A, Problem 11|<span class = "biglink">&nbsp;Question 11&nbsp;</span> ]] ==<span class="exam"> Find and simplify the difference quotient &thinsp;<math>\frac{f(x + h) - f(x)}{h}</math>&thinsp; for <math>f(x) = \sqrt{x - 3}</math>
+==[[004 Sample Final A, Problem 13|<span class = "biglink" style="font-size:80%">&nbsp;Question 13&nbsp;</span>]]==
+<span class="exam"> Compute <math>\displaystyle{\sum_{n = 1}^6 4\left(\frac{1}{2}\right)^n}</math>
-==[[004 Sample Final A, Problem 12|<span class = "biglink">&nbsp;Question 12&nbsp;</span>]]== <span class="exam"> Set up, but do not solve the following word problem. Two private airplanes travel toward each other from cities that are 780 km apart at speeds of 190 km/hr and 200 km/hr. They left at the same time. In how many hours will they meet?
+==[[004 Sample Final A, Problem 14|<span class = "biglink" style="font-size:80%">&nbsp;Question 14&nbsp;</span>]]==
+<span class="exam"> a) Find an equation of the line passing through <math>(-4, 2)</math> and <math>(3, 6)</math>.</span><br>
+<span class="exam"> b) Find the slope of any line perpendicular to your answer from a)
-==[[004 Sample Final A, Problem 13|<span class = "biglink">&nbsp;Question 13&nbsp;</span>]]== <span class="exam"> Compute <math>\displaystyle{\sum_{n = 1}^6 4\left(\frac{1}{2}\right)^n}</math>
+==[[004 Sample Final A, Problem 15|<span class = "biglink" style="font-size:80%">&nbsp;Question 15&nbsp;</span>]]==
+<span class="exam"> Solve. <math>\log(x + 8) + \log(x - 1) = 1</math>
-==[[004 Sample Final A, Problem 14|<span class = "biglink">&nbsp;Question 14&nbsp;</span>]]== <span class="exam"> a) Find an equation of the line passing through <math>(-4, 2)</math> and <math>(3, 6)</math>.<br>
+==[[004 Sample Final A, Problem 16|<span class = "biglink" style="font-size:80%">&nbsp;Question 16&nbsp;</span>]]==
-&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
+<span class="exam"> Solve. <math>\sqrt{x - 3} + 5 = x</math>
-b) Find the slope of any line perpendicular to your answer from a)
-==[[004 Sample Final A, Problem 15|<span class = "biglink">&nbsp;Question 15&nbsp;</span>]]== <span class="exam"> Solve. <math>\log(x + 8) + \log(x - 1) = 1</math>
+==[[004 Sample Final A, Problem 17|<span class = "biglink" style="font-size:80%">&nbsp;Question 17&nbsp;</span>]]==
+<span class="exam"> How many ways can a committee of four people can be selected from five married couples if no committee is to include both husband-and-wife pairs? (simplify your answer to a single number)
-==[[004 Sample Final A, Problem 16|<span class = "biglink">&nbsp;Question 16&nbsp;</span>]]== <span class="exam"> Solve. <math>\sqrt{x - 3} + 5 = x</math>
+==[[004 Sample Final A, Problem 18|<span class = "biglink" style="font-size:80%">&nbsp;Question 18&nbsp;</span>]]==
+<span class="exam"> Ten teams are entered in a bowling tournament. In how many ways can first, second, and third prizes be awarded? (simplify your answer to a single number)
-==[[004 Sample Final A, Problem 17|<span class = "biglink">&nbsp;Question 17&nbsp;</span>]]== <span class="exam"> How many ways can a committee of four people can be selected from five married couples if no committee is to include both husband-and-wife pairs? (simplify your answer to a single number)
+==[[004 Sample Final A, Problem 19|<span class = "biglink" style="font-size:80%">&nbsp;Question 19&nbsp;</span>]]==
+<span class="exam"> Solve for ''x'': <math>\log_6 \frac{1}{36} = x</math>
-==[[004 Sample Final A, Problem 18|<span class = "biglink">&nbsp;Question 18&nbsp;</span>]]== <span class="exam"> Ten teams are entered in a bowling tournament. In how many ways can first, second, and third prizes be awarded? (simplify your answer to a single number)
-==[[004 Sample Final A, Problem 19|<span class = "biglink">&nbsp;Question 19&nbsp;</span>]]== <span class="exam"> Solve for ''x'': <math>\log_6 \frac{1}{36} = x</math>
+'''Contributions to this page were made by [[Contributors|Kayla Murray]]'''