Download algebra ii final exam review

ALGEBRA II FINAL EXAM REVIEW
Name:____________________________________________
Date:___________________
Show all work!
Possible 100 pts
1) (3pts) Given the sequence 6, 11, 18, 27, 38, 51
Determine the model (type and actual function)
(2pts) Use
2) ( 2pts) Evaluate f(3).
f(x) = 3x+1
x2 -3x+ 1,
3) ( 2pts)
the model to determine the 20th term
Simplify (3x-3)4
x<3
x≥3
f(3) =
4) (3pts) Simplify:
2a3b-4 -2ab -4
×
(4b)4 20a 6
5) (3pts)
Solve for x. 5-2⋅5x+5⋅53 = 52x
15
6) (3pts) Find the balance in an account if you deposit $10,000 paying 5.25% annual interest,
compounded monthly after 5 years.
7) (3pts) Evaluate (64)2/3 (Show all steps)
8) Given f(x) = 2 x  1  4
State the Domain and Range
(1 pt each)
Domain:
Range:
9) (3pts Solve the equation -2 + 2x - 3 = 5
11) (3pts) Solve for x.
logx 27 = 3
10) (3pts Solve the equation
1 23
x - 5 = 27
2
12) (2pts) Is f(x) = 4-2t an example of exponential
growth or decay?
19
1
13) Solve for x: log8 - log x = log1- log2
2
14) Evaluate log383 to three decimal places.
(2 pts)
(4 pts)
15) You deposit $8500 into an account that pays
(4 pts 6.5% compounded quarterly. How long will
it take for the balance to be $10,000?
.
16) Graph the function, f(x) = (x + 3)2 - 2.
List at least five ordered pairs, including the
vertex.
(4 pts)
X
Y
14
17) Given the following polynomial function, determine the left and right hand behaviors,
possible number of turning points and possible number of zeros/solutions (1 pt each)
P ( x )  x 4  4 x 3  x 2  12x  2
Right Hand Behavior
Left Hand Behavior
Possible number of
turning points
Possible number of
solutions/zeros
18)
Factor completely with respect to
the integers.
x3 - 2x2 - 9x + 18
19)
20) Factor completely the following polynomial
4 x 2  20x  24
(2 pts)
21)
(3 pts)
(3 pts)
(2 pts)
Find all real-number solutions.
x3 + 2x2 - x - 2 = 0
Use synthetic division to evaluate the
function.
F(x) = x3 + 2x2 + 4x - 12
at x = -3
14
22) (3 pts) Write a polynomial whose graph has
the given x-intercepts and has a leading
coefficient of 1.
(4, 0), (-3, 0), (2, 0)
24) (3 pts) Simplify
x 2 - 2x - 35
x 2 - 49
26) (4 pts) Solve the equation.
2x - 9 x
5
+ =
x-7 2 x-7
23) (2 pts) One root of the equation is x = -3.
Find the other roots
2x3 + 11x2 + 18x + 9 = 0
25) (3 pts) Perform the indicated operation and
simplify.
x 2 - x - 2 x 2 - 6x + 8
¸
3x 2
3x -12
27)
(3 pts)
Add and simplify.
2
3
+
2
3x
6x
18
28) Evaluate the six trig functions of the
angle
(lower right angle is
29)
Given a right triangle ABC with
m
)
A=
and b = 8, find the
missing angle ( nearest whole
(round to 4 decimal places)
number) and the other two sides.
2
(nearest hundredth)
5
(1/2 pt each)
Sin
(1 pt each)
=
Csc
Cos
=
Sec
Tan
=
Cot
=
m
A=
a=
=
m
B= 90
b= 8
=
m
C=
c=
6
30) (2 pts) Convert the following degree
31)
(2 pts)
measure to radian measure :
32) Find the arc length and area of a sector if
Convert the following radian
measure to degrees.
33) Given the position ordered pair ( 4 , -3 )
find all six trig ratios:
the radius = 4 inches and the central angle
is
(1 pt each)
(2 pts each)
Sin
=
Csc
=
Cos
=
Sec
=
Tan
=
Cot
=
Are Length:
Area of Sector:
14