# 004 Sample Final A

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 ${\displaystyle f^{-1}(x)}$ for ${\displaystyle f(x)={\frac {3x-1}{4x+2}}}$

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

Question 3  Solve. Provide your solution in interval notation.     ${\displaystyle \vert 4x+7\vert \geq 5}$

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

Question 5  Describe how the graph of ${\displaystyle f(x)=3^{(x+1)}-2}$ 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.      ${\displaystyle {\frac {1}{3x+6}}-{\frac {x}{x^{2}-4}}+{\frac {3}{x-2}}}$

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

Question 8  a) List all the possible rational zeros of the function ${\displaystyle f(x)=x^{4}-4x^{3}-7x^{2}+34x-24}$.
b) Find all the zeros, that is, solve ${\displaystyle f(x)=0}$

Question 9  Graph the function. Give equations of any asymptotes, and list any intercepts.     ${\displaystyle y={\frac {6}{x^{2}-x-2}}}$

Question 10  Decompose into separate partial fractions.      ${\displaystyle {\frac {6x^{2}+27x+31}{(x+3)^{2}(x-1)}}}$

Question 11  Find and simplify the difference quotient  ${\displaystyle {\frac {f(x+h)-f(x)}{h}}}$  for ${\displaystyle f(x)={\sqrt {x-3}}}$

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

Question 14  a) Find an equation of the line passing through ${\displaystyle (-4,2)}$ and ${\displaystyle (3,6)}$.
b) Find the slope of any line perpendicular to your answer from a)

Question 15  Solve. ${\displaystyle \log(x+8)+\log(x-1)=1}$

Question 16  Solve. ${\displaystyle {\sqrt {x-3}}+5=x}$

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