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 $f^{-1}(x)$ 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: $\log _{6}{\frac {1}{36}}=x$