008A 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 $f(x)=\log _{3}(x+3)-1$

 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 $x=-3y^{2}-6y+2$

                  b) Sketch the graph. Provide the focus and directrix.

 Question 4  Solve. Provide your solution in interval notation. $(x-4)(2x+1)(x-1)<0$

 Question 5  Graph the system of inequalities $y<\vert x\vert +1$           $x^{2}+y^{2}\leq 9$

 Question 6  Sketch $4x^{2}+9(y+1)^{2}=36$. Give coordinates of each of the 4 vertices of the graph.

 Question 7  Solve $2\vert 3x-4\vert -7=7$

 Question 8  Given a sequence $27,23,19,15,\ldots$ use formulae to compute $S_{10}$ and $A_{15}$.

 Question 9  a) List all the possible rational zeros of the function $f(x)=x^{4}+5x^{3}-27x^{2}+31x-10$

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 $y={\frac {x-1}{2x+2}}$

 Question 11  Decompose into separate partial fractions ${\frac {3x^{2}+6x+7}{(x+3)^{2}(x-1)}}$

 Question 12  Find and simplify the difference quotient ${\frac {f(x+h)-f(x)}{h}}$ for f(x) = ${\frac {2}{3x+1}}$

 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 $\displaystyle {\sum _{n=1}^{\infty }5\left({\frac {3}{5}}\right)^{n}}$

 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. $\log _{6}(x+2)+\log _{6}(x-3)=1$

 Question 17  Compute the following trig ratios: a) $\sec {\frac {3\pi }{4}}$       b) $\tan {\frac {11\pi }{6}}$       c) $\sin(-120)$

 Question 18  Compute $\cos(\arctan {\frac {5}{3}})$

 Question 19  Compute $\arcsin -{\frac {\sqrt {3}}{2}}$. Provide your answer in radians.