Download Math 1302- Short Quiz - Angelo State University

Name __________________________________ Math 1302 – Exam II – March 6, 2006
Show Work on all problems. If you give me the answer only, I will count it wrong. Make sure to begin with #1.
You should complete every problem that appears easy to you – This test is written so that you can complete about 60- 70 %
within the first 15 minutes and the remaining 30 % in about 40 minutes. Do not spend time trying to remember how to do a
problem at the very beginning – save those for the end of class.
1. Number of absences up to today. ___________ Give me a close approximation if not sure of exact number.
A blank answer will result in points counted off.
2. State the quadratic formula that is used to solve equations of the form
ax2 + bx + c = 0
3. Assuming that
a) ( 2 – 3x ) ( 2 + 3x ) represents a difference of squares, what is the product in simplest form? _____________________
b) ( 3 + 4y)( 9 – 12y + 16y2 ) represents a sum of cubes, what is the product in simplest form ? ______________________
4. Factor each of the following polynomials (completely). If polynomial does not factor, then indicate by writing
prime.
a) 4x3 - 9y2x = ____________________
b) 5 + 40x3 = _____________________
c) ( x + 2)2 - 9 = ___________________
5. Simplify the following algebraic fractions. Perform the given operation and simplify.
a)
b)
x  1 3x  3

=
3
8
7x  2 x  6

=
3x  4 3x  4
c) ( (2 
d)
e)
1
4x 2  1
=
) 2
x 4x  2x
3 x 2 x
  =
4x
x 4
1
1
x
1
1 x
=
6. George starts at 8:00 AM and works for three hours. Al starts helping at that point and usually Al can complete
the job by himself in 9 hours. At what time will they finish ? Define your variable(s) and set up an equation in
one variable. I want the equation – not the solution. Assume that George can do the job in 12 hours if he works by
himself.
7. What quadrant is the point in ?
a) A (-2, 12 ) → ______________________
b) B( - 2, - 2 ) → ___________________
8. Write the four basic forms of in in their simplest form
____________
______________
_____________
_______
9. Write in one of the simplest forms of i n .
a) i19 = _______
c) ( i3257)4 = ________
d) i – 15 = _________
10. Simplify. Do not use your calculator on this – not even for checking purposes.
 16 + 3 -
 64 + 2  4 -
3
 8 = _____________
11. Simplify – write your final answer in the form a + bi.
( 2 – 3i) + ( 3 + 5i) = _______________
3i
= ____________
3i
2i ( 1 – 3i) = ________________
i
 _________
1  3i
12.
Plot the following complex number; - 4 + 3i . Find its modulus. _____________
13. Find the conjugate of
-4 – 2i → ____________
14.
6i → ________________
What is the imaginary part of the complex numbers
-1-2i →_____
15. Find the solution of each of the following.
a) 2x2 = 7x
c) 3x3 = 12x
b) 180 – 5x2 = 0
d) 4x2 - 3x - 7 = 0
16. More equations.
a) x4 - 3x2 - 4 = 0
→ x = ________________________
b) x ( x + 3 ) ( 2x – 1 ) ( x2 + 4 ) = 0
→
x = _________________
17. Find the value of the discriminant that corresponds to the equation
5x2 – 4x + 2 = 0 → ________________
18. Find the solution by using the quadratic formula.
x2 + 4 = 0
19. Solve by completing the square – no other method will do.
2x2 - x - 8 = 0