Download PRE-CALCULUS WORKSHEET P

PRE-CALCULUS WORKSHEET 2.1 – 2.5
NAME
PERFORM THE INDICATED OPERATION AND WRITE THE RESULT IN STANDARD FORM.
1.
(-2 + 6i) + (4 + i)
2.
(-2 + 6i) – (4 + i)
3.
3 – (5 – 4i) + (-2 + 7i)
4.
-8i(2i – 7)
5.
(3 – 6i)(2 + 7i)
6.
(3 + 5i)(3 – 5i)
7.
3
4i
8.
2  7i
4  3i
9.
 64   25
10.
5  8  3  18
11.
( 3  5 )(  4  12 )
12.
 12
SOLVE THE FOLLOWING USING THE QUADRATIC FORMULA.
13.
x2 – 6x + 10 = 0
14.
3x2 = 8x – 7

4  2

FOR THE FOLLOWING:
A)
FIND THE COORDINATES OF THE VERTEX
B)
FIND THE x-INTERCEPT(S)
C)
FIND THE y-INTERCEPT
D)
FIND THE AXIS OF SYMMETRY
E)
USE (A) – (D) TO GRAPH THE PARABOLA
15.
y = (x – 3)2 + 1
16.
f(x) = -x2 + 2x + 3
A)
A)
B)
B)
C)
C)
D)
D)
SOLVE THE FOLLOWING BY SETTING UP A QUADRATIC FUNCTION TO BE MAXIMIZED OR
MINIMIZED. SHOW ALL WORK.
17.
Among all pairs of numbers whose sum is 16, find a pair whose product is as large as possible. What is
the maximum product?
18.
You have 50 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that
maximize the enclosed area. What is the maximum area?
FOR THE FOLLOWING:
A)
DETERMINE THE GRAPH’S END BEHAVIORS
B)
FIND THE x-INTERCEPTS AND STATE WHETHER THE GRAPH CROSSES THE x-AXIS,
OR TOUCHES THE x-AXIS AND TURNS AROUND AT EACH INTERCEPT.
C)
FIND THE y-INTERCEPT
D)
STATE WHETHER THE GRAPH HAS y-AXIS SYMMETRY, ORIGIN SYMMETRY, OR
NEITHER
E)
STATE THE MAXIMUM NUMBER OF TURNING POINTS
F)
SKETCH THE GRAPH
19.
f(x) = x4 – 9x2
20.
f(x) = (x + 3)(x + 1)3(x + 4)
A)
A)
B)
B)
C)
C)
D)
D)
E)
E)
F)
F)
DIVIDE USING POLYNOMIAL LONG DIVISION. SHOW ALL WORK.
21.
(6x3 + 13x2 – 11x – 15) ÷ (3x2 – x – 3)
22.
(x4 – 81) ÷ (x – 3)
DIVIDE USING SYNTHETIC DIVISION. SHOW ALL WORK.
23.
(4x3 – 3x2 + 3x – 1) ÷ (x + 2)
24.
(x5 + x3 – 2) ÷ (x – 1)
FOR THE FOLLOWING:
A)
LIST THE TOTAL NUMBER OF ZEROS
B)
LIST THE POSSIBLE RATIONAL ZEROS
C)
LIST THE NUMBER OF POSITIVE ZEROS
D)
LIST THE NUMBER OF NEGATIVE ZEROS
E)
FIND ALL ZEROS
25.
f(x) = 3x4 – 11x3 – x2 + 19x + 6
26.
x4 – x3 + 2x2 – 4x – 8 = 0
A)
A)
B)
B)
C)
C)
D)
D)
E)
E)