CP Algebra II 5/16/16
1.
2.
Factor.
a.
x 2 - 64
b.
2x 2 - 15x - 27
c.
3xv 3 - 12xv 2 + 30x 2v 4
d.
x 2 + 13x + 36
b.
y = 2x 2 + 8x + 3
b.
h(- 2) if h(x) = - 2x 3 + 8x - 11
Graph each function.
a.
3.
y = 2(x - 1)(x + 2)
Evaluate.
a.
c.
4.
Name: ______________________ Exam Review
f (3) if f (x)  x 2  5x  1
b(x  2) if b(x)  x 2  6x  2 .
Complete the table.
d.
v(3x  1) if v(x)  2x 2  3x  7 .
degree
end
behavior
end
behavior
5.
even or odd
lim f (x) 
even or odd
lim f (x) 
even or odd
lim f (x) 
x 
x 
x 
lim f (x) 
lim f (x) 
lim f (x) 
x 
x 
x 
Simplify.
a.
c.
(3x 6  2x 4  3x 2  5)  (x 5  5x 3  6x)
3x 2(- 2x 3 - x 2 + 3x + 3)
b.
(x 2 + 2x) - (4x 2 - 2x - 2)
d.
(2 + x)(5x 2 + 3x + 2)
6.
Sketch a 3rd degree polynomial with zeros at x = –2, 3, and 5 with a max at x = 1 and a positive leading
coefficient.
7.
Write an equation for the polynomial.
8.
Match the equation to the correct graph.
a.
y  x 3  x 2  9x  9
b.
y  x 4  2x 3  7x 2  8x  12
c.
d.
y  x 4  2x 3  5x  7
y = x 3 + 4x 2 + x - 6
_________
9.
10.
_________
_________
Given g(x)  2x 3  7x 2  5x  4.
a.
List all possible rational zeros.
b.
Find all zeros of g(x ) .
c.
Sketch the graph of g(x )
Simplify each expression.
a.
6a - 12 a + 5
•
6
10a 2
b.
6x 5y 3
24y
•
2
7xy
35x 4y 3
c.
p 2 - p - 72 p 2 - p - 72
• 2
10p - 90
p - 7p - 18
d.
6n 2 - 18n
1
³
n- 3
n- 1
e.
5b
2
3b 20b - 8
f.
2
3x
+
x+ 3 x- 1
11.
Variable M varies directly with p. If M = 75 when p = 10, find M when p = 16.
12.
R varies inversely with variable T. If R is 168 when T = 24, find R when T = 30.
13.
Variable Y varies jointly with P and Q. If Y = 144 when P = 12 and Q = 8, find Y when
Q = 25.
P = 15 and
14.
In science, one theory of life expectancy states that the lifespan of mammals varies inversely to the
number of heartbeats per minute of the animal. If a gerbil's heart beats 360 times per minute and lives
an average of 3.5 years, what would be the life expectancy of a human with an average of 72 beats per
minute? Does this theory appear to hold for humans?
15.
Sketch the graph of each function.
a.
16.
y=
5
x- 3
Determine the equation of each graph.
a.
b.
b.
y=
- 2
- 3
x+1
c.
17.
Solve the triangle.
18.
The point (–4, 6) lies on the terminal side of an angle. Find the values of sin q, cos q, and tan q.
19.
In triangle ABC, a = 5, b = 7, and c = 10. Find angle C.
20.
In triangle ABC, b = 10, c = 12, and <C = 120˚. Solve the triangle.
21.
Convert 206˚ into radians.
22.
Find the area of a triangle with side lengths 8, 12, and an included angle of 102˚.
23.
Graph y  2cos(3x)  7 .
24.
Match the equation to the appropriate graph.
i.
y = sin(2x)
y = 3sin(x)
ii. y = cos(2x)
iv. y = sin(x) + 3
iii.
25.
Find
a1 in the arithmetic sequence where d  7 and a4  5.



26.
Find a14 in the arithmetic sequence where a1 = 4 and d = 3 .
27.
Find the arithmetic means in the sequence 35,_ _ _ _ _ ,_ _ _ _ _ ,_ _ _ _ _ ,19 .
28.
Find the geometric means in the sequence 4000, _ _ _ _ _ , _ _ _ _ _ ,_ _ _ _ _ , _ _ _ _ _ ,125 .
29.
Find the sum of 7  19  31  ...  199 .
30.
Find a5 for the geometric sequence where a1 = 120, and a3 = 30.

31.
 12(.5)
n 1
n 1
32.
11
 (2k k= 4
1)
33.
9
k
 1.5
k= 1
34.
Express as a single logarithm.
a.
35.
b.
b.
log6 216
log2 36  2 log2 3
c.
d.
log125 5
Solve for the given variable. Express answers to 3 decimals when appropriate.
b.
d.
log16 x =
logx e 391  391
3
4
c. ln e p = k
e.
log27 x =
5
3
Solve each equation.
a.
38.
c.
log1000
a. logx 81  4
37.
log5 40  log5 8
Simplify.
a.
36.
log5 25  log5 25
log4 x 2 = log4 169
b.
log5
100
= log5 20
w
Use logarithms to solve. Express your answers correct to 3 decimal places when appropriate.
a.
343 = 7x
b.
3 ³2x = 1
ln e 2/ 3