MATH QUIZ 4
juniorquijada
quiz4.docxIN ORDER TO GET FULL CREDIT FOR EACH PROBLEM, PLEASE SHOW ALL WORK AND WRITE EVERYTHING OUT CORRECTLY USING THE LANGUAGE OF MATH.
The quiz is worth 100 points. Each problem is worth 5 points.
For #1 through #6, please put the answer in a + bi form.
1. Add (3 – 2i) + (-4 – 4i)
2. Subtract (3 - 2i) - (-4 - 4i)
5. Square (1 – i)2
To do #6, below, I would use the following table:
|
REMAINDER |
ANSWER |
|
0 |
1 |
|
1 |
i |
|
2 |
-1 |
|
3 |
-i |
FOR EXAMPLE:
Let’s simplify i10. We divide whatever the exponent is by 4.
So, doing so, we have
2
8
2
We get a remainder of 2, so the answer is -1. So, we can say that i10 is -1.
#6 (a) Simplify i715
(b) Simplify (-3i)6
7. Solve x2 + 25 = 0
8. Solve 3x3 + x2 – 12x – 4 = 0
9. Solve 4x2 - 10x = -3 by completing the square. Then,
please leave your answer(s) as APPROXIMATE DECIMAL.
Then, please check your answer(s) under the word, CHECK,
below.
CHECK:
10. Solve -5x2 + 2x + 1 = 0 by using the quadratic formula.
Then, please leave your answer(s) as EXACT.
11. Using any method you wish, solve x2 = x.
12. Solve m6 + 16m3 + 64 = 0
13. Consider the parabola given by the function
f( x ) = 4x2 – 5x + 9 , and use f( x ) to do each of the following
parts.
(a) Find the vertex of f( x ).
(b) Determine whether there is a minimum or maximum
of f and then, use that vertex to find the minimum or maximum of f( x ).
(c) Find the interval where f( x ) is increasing.
14. Consider the parabola given by the function
y = -2(x – 1)2 - 4 .
(a) Find the vertex.
(b) Determine whether there is a minimum or maximum
and then, use that vertex to find the minimum or maximum.
(c) Find the interval where the function is decreasing.
Please choose the best possible answer for the solution.
A. -13
B. -1, 7
C. 7
D. No solution
20. Charcoal Gurney has 100 yd of fencing with which to completely enclose
her rectangular space of briskets.
(a) If the width of the space is x yards, express the area of the space as a function of the width.
(b) Use the function in (a) to find the maximum possible area of the space.
410
1122
xx
+=-
12
1
x
x
-=
1
3
4
x
=
111
Fmp
=+
1
2
T
g
p
=
(32)(44)
ii
-·--
32
44
i
i
-
--
410
