# 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 for

## 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

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

## Question 4

Solve. Provide your solution in interval notation.

## Question 5

Graph the system of inequalities

## Question 6

Sketch . Give coordinates of each of the 4 vertices of the graph.

## Question 7

Solve

## Question 8

Given a sequence use formulae to compute and .

## Question 9

a) List all the possible rational zeros of the function

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

## Question 11

Decompose into separate partial fractions

## Question 12

Find and simplify the difference quotient for f(x) =

## 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

## 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.

## Question 17

Compute the following trig ratios: a) b) c)

## Question 18

Compute

## Question 19

Compute . Provide your answer in radians.