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Pre-Calculus A
2.1.1
2.1.2
Final Exam Review
16x  12 y  17
Solve the system 
5x  2 y  1
4 x  2 y  8
Solve the system 
using a
y  2x  1
graphing calculator.
10x  6 y  0
Solve the system 
by using
 7 x  2 y  31
matrix equations.
2.3.4
 x  y  2z  7

2.3.5 Solve the system 2x  y  z  8 by using a
x
z 5

matrix equation and a graphing calculator.
 1 0
3  4  7
6  10
Given A  
, B
, C


 , and
0
1.2.2
  5 2
1 8
4  1 
2 4
3

D  0.5  2 5  find:
  1 0  3
2.2.1
Fall 2012
(a) A + 2C
If f ( x )  x 2  2 and g( x )  2x  1 , find:
(a) ( f  g )( x )
(b) ( f  g )( x )
c) (g  f )(3)
(b) CA
d) (f  g )( x )
(c) BD
2.3.1
(a) A
(b) detD
(c) C 1
- Page 1 of 4
3.1.1
Draw a graph of an even function.
3.1.2
Draw a graph of an odd function.
3.1.3
Draw a function that is neither even nor
odd.
3.1.4
3.2.1
Determine any symmetries of the graph
of y 2  x .
To be changed
3.7.1
Find the x and y intercepts
of y  x 2  5x  6 .
3.7.2
To be changed
3.7.3
To be changed
3.8.1
x 2  5, x  1
Given f ( x )  
, find
4

3
x
,
x


1

Give an example of an equation resulting
from reflecting the parent curve of an
absolute value function about the x-axis
and shrinking it vertically.
3.3.1
Find the inverse of f ( x )  ( x  2 )2  4 .
3.4.1
Write the equation that results if the
1
parent curve f ( x )  is translated left 2
x
units and up three units and then draw
it.
3.4.2
3.6.2
Find the vertical and horizontal
asymptotes of
a) f (5)
3.6.1
a. f ( x ) 
5x  1
.
2x  3
b. f ( x ) 
5
2x  3
b) f ( 1)
c) f (2)
Find the vertical and slant asymptotes of
5 x 1
x3
2
a. f ( x) 
- Page 2 of 4
4.1.1
Which of the following expressions is not
a polynomial?
(a)
x2  5
(b)
5
(c)
x2 
2
x
4.1.2
Write a polynomial of least degree with
the roots  3i and 2.
4.2.1
Find the solutions of 1  4x 2  40x .
4.2.2
If ( 6  4i ) is a root of P(x), name another
root.
4.3.1
Find the remainder of
( 2x 3  2x  3 )  ( x  1 )
4.3.2
5.1.1
Name one positive angle and one negative
7
angle that are coterminal with
.
8
5.2.1
Find the degree measure of the central
angle whose intercepted arc measures
12.5 cm in a circle of radius 8 cm. Round
your answer to the nearest tenth.
5.2.2
The second hand of an analog clock is 12
cm long. What is the linear velocity of the
outer tip of the second hand, expressed in
cm
? Round your answer to the nearest
s
hundredth.
5.3.1
If csc   2 and the terminal side of the
angle lies in quadrant III, find cos  .
5.4.1
Evaluate rounding your answer to four
decimal places.
a. cos( 25 )
b. sin 1 (0.879)
 2 
c. cot

 5 
Which binomial is a factor of
f (x )  x 4  x 2  12 ?
(a) ( x  1 )
(b) ( x  3 )
(c) ( x  2 )
(d) ( x  1 )
4.6.1
Solve
4.7.1
Solve
1 6 x  9 3x  3


.
3x
3x
x
8x  12  6x  4  3 .
- Page 3 of 4
5.6.1
5.7.1
5.8.1
For ABC ,   25 26' ,   78  , and a =
13.7. Find b to the nearest hundredth.
For ABC , a = 14, b = 15, and c = 16.
Solve for all the missing parts of ABC .
Specify any angles accurate to the
nearest minute.
Find the area of ABC if b = 10,   42  ,
and   51 . Round to the nearest tenth.
6.2.1
State the amplitude, period, and phase

shift of f ( x )  3 tan( 2  ) .
6
6.2.2
State the amplitude, period, and phase
shift of f ( x )  5 cos(3  45) .
6.2.3
Write an equation of the sine function
with amplitude = 4, period = 480º, and
phase shift = -60 º.
6.4.1
Evaluate. cos (tan 1 0.36 ) Round your
answer to the nearest ten-thousandth.
6.4.2 Evaluate the following:
 3

a. Sin 1 

2


b. Tan 1 (1)
6.5.1
6.1.1 State the domain, range, and period of:
f ( x )  sin 
f ( x )  tan 
- Page 4 of 4
Describe the changes in the graph of
y  cos 3  1 relative to the parent graph.
Graph both equations.
f ( x )  cos 