1. Study the questions from Exams #1-#5.

2. Graph the following:

3. Write sec θ in terms of sin θ where θ is in

quadrant II.

4. For

a) Use the Elimination Method to solve

the above system.

5. For

a) Convert the above system to a matrix

equation.

b) Find the inverse of the coefficient

matrix.

c) Use the result of part b) to find to

solve the system.

6. A biologist has two alcohol solutions, one

solution containing 5% methane and the

other containing 20% methane. How many

milliliter of each solution should he mix to

produce 1L of a solution that contains 14%

methane? For practice use the Matrix

Method and the inverse of the matrix.

7. Two straight roads diverge at an angle of

75°. Two cars leave the intersection at 2:00

P.M., one traveling at 55 mph and the other

at 30 mph. How far apart are the cars at

3:30 PM?

8. For ,

a) Find the amplitude

b) Find the period

c) Find the phase shift of the function

d) Sketch the graph

9. Solve the logarithmic equation for x :

10. Let

a) List all of the possible rational roots .

b) Use the Descartes’ rule of signs to

determine the possible number of

positive and negative real zeros.

c) Find the upper and the lower bound

d) Without actually factoring,

determine how many positive real

zeros, negative real zeros , and

imaginary zeros we could have.

e) Using the synthetic division and the

information above to find all of the

roots including the real and complex

roots.

11. Let

a) Find the x- intercept .

b) Find the y-intercept.

c) Find the asymptotes.

d) Use the above information to graph.

12. Find a fourth-degree polynomial with

integer coefficients that has zeros 2i and -2

with -2 a zero of multiplicity 3.

13. Factor the following expressions

completely:

14. Solve each inequality . Sketch the solution

on a real number line, and write the solution

using the interval notation:

15. A ball is thrown straight upward at an initial

speed of 40 ft/s. How high is the highest

point the ball reaches? Use the formula

discussed in the lecture and

the discriminant of the quadratic formula.

16. Use the property of Inverse Functions to

find the range and domain of the

following . What two

assumptions do we have to find the inverse

function?

17. Find the expansion of

a) Using the Pascal’s triangle.

b) Using the Binomial Theorem .

18. Find the sum of 1+3+9+…+2187

19. The common ratio in a geometric sequence

is , and the fourth term is
. Find the

fifteenth term.

20. Write the sum using sigma notation

for .

21. Graph

22. Convert the polar equation to

the rectangular coordinates .

23. Find parametric equations for the line of

slope 3 that passes through the point (2, 6).

24. Find the area of the largest rectangle that can

be inscribed in a right triangle with legs 3

cm and 4 cm if two sides of the rectangle lie

along the legs as show below.