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.
a) Find the vertex, standard graphing form, and x-intercepts for
b) Sketch the graph. Provide the y-intercept.
Solve. Provide your solution in interval notation.
== Question 4 == Graph the system of inequalities.
== Question 5 == Describe how the graph of 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.
== Question 7 == Given a sequence use formulae on the back page to compute
== Question 8 == a) List all the possible rational zeros of the function .
b) Find all the zeros, that is, solve
== Question 9 == Graph the function. Give equations of any asymptotes, and list any intercepts.
== Question 10 == Decompose into separate partial fractions.
== Question 11 == Find and simplify the difference quotient for
== 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
== Question 14 == a) Find an equation of the line passing through and .
b) Find the slope of any line perpendicular to your answer from a)
== Question 15 == Solve.
== Question 16 == Solve.
== 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: