MAC 1990/FALL2007
IntensiveCollege Algebra
FINAL EXAM Review/sample questions(SQ)
** To answer all questions in FINAL EXAM, you must need to be the master of everything that I covered in
sections P.2-P.7, 1.1-1.7, 2.1, 2.2, 2.4, 3.1- 3.7, 4.1(light), 4.2(long division ONLY), 5.1-5.4 and 6.1
Do all homework problems listed below, read class notes, and quizzes
Exam1 review
§ P.2 # 2, 16, 18, 26, 34, 36, 38, 40, 42, 44, 46, 50, 54, 56
§ P.3 # 2, 4, 8, 10, 12, 14, 16, 18, 20, 24, 28, 30, 38, 40, 46, 50
§ P.4 # 10, 12, 16, 24, 30, 36, 40, 42, 50, 54, 60, 62
§ P.5 # 2, 4, 14, 16, 18, 24, 28, 32, 34, 40, 44, 46
§ P.6 # 4, 6, 10, 12, 18, 20, 24, 26, 30, 34, 40, 44, 46, 50, 60, 66, 80, 86
§ P.7 # 16, 20, 24, 32, 40, 48, 50
§ 1.1 # 4, 6, 10, 12, 14, 18, 20, 24, 26, 28, 32, 34, 46, 48, 52, 50, 62, 64, 68, 80, 82
§ 1.2 #6, 10, 18, 22, 36, 34, 48
§ 1.3 # 4, 6, 12, 14, 20, 22¸28, 30, 34, 36, 48, 62, 82
§ 1.4 # 2, 4, 6, 8, 10, 16, 20, 28, 30, 36, 38, 42, 48, 50, 54, 58, 60
§ 1.5 # 2, 8, 10, 12, 14, 16, 20, 28, 32, 44, 56
§ 1.6 # 4, 10, 12, 14, 18, 26, 28, 32, 34, 36, , 44, 48, 52, 56, 60
§ 1.7 # 2, 6, 8, 18, 20, 24, 26, 32, 36, 42
§ 2.1 # 8, 10, 20, 24, 26, 32, 34
§ 2.2 # 4, 8, 10, 12, 26, 34, 36, 40, 46, 48, 50, 6, 58, 64, 66, 70
§2.4 # 2, 4, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 42, 50, 52
SampleQ1. Solve the equation:
100  4 p 5 p  6

6
3
4
3
4
1
b)
 
x( x  3) x x  3
2
2
c) ( x  2)  x  4( x  1)
a)
(2 x  1) 2  4( x 2  x  1)
4
3
1
e)


x x  6 x( x  6)
d)
SampleQ2. Application problems: read section 1.2, do examples 1-6, and do all assigned hw problems
SampleQ3. Solve the quadratic equation:
 12 x 2  2 x  24  0
SampleQ4. Solve the quadratic equation: x  5 x  3
2
SampleQ5. Determine the number of real solutions to the quadratic equation.
a) 3 x  4 x  2  0
2
b) x  6 x  5  3 x  1
2
MAC 1990 FINAL EXAM Review - M. RAHMAN
Page 2
SampleQ6. A rocket is launched from atop a 105-ft cliff with an initial velocity of 158 feet per second. The height
of the rocket t seconds after launch is given by the equation h  16t  158t  105 . Find the time it will take
for the rocket to land.
2
SampleQ7. Solve the following equations:
a) x  3x  4 x  12  0
3
2
b) x  1  0
4
c) 2 x  9 x  9 x  0
3
2
d)  4 x  12 x  16 x
4
2
3
SampleQ8. Solve the equations provided below. Be sure to check your answers.
x 2  5x  13  3
x  14  x  16
a)
b)
SampleQ9. Solve the following equations:
9
 8
x2
x
7

 1
b) 2
x 9 x3
a) x 
SampleQ10. Solve the inequality and write the solution using interval notation:
a)  2( x  3)  2 x  5
6  3x
2
5
c) 2 x  5  7
b)  6 
7  6x  3
d)
c) x  x  12  0
2
SampleQ11. Solve the following rational inequality:
5
1
x3
x 1
0
b)
x5
a)
SampleQ 12. Decide whether or not the following equation has a circle as its graph. If it does, give the center and
the radius:
x 2  8 x  y 2  6 y  16  0
SampleQ13. Find an equation of the line that passes through the point (3, -1) and is
perpendicular to the line 2 x  3 y  5 . Write the equation in slope-intercept form.
Exam2 review
-----------------§3.1 # 16, 20, 22, 24, 26, 28, 30, 32, 36, 38, 40, 42, 44, 46, 48, 50, 54
§3.2 # 24, 38, 40, 42, 56, 58, 78, 80
§3.4 # 2, 4, 6, 8, 10, 12, 14, 16, 18, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 70
F2007 Copyright 2007 University of North Florida
MAC 1990 FINAL EXAM Review - M. RAHMAN
Page 3
§3.5 # 6, 8, 10, 12, 18, 22, 30, 40, 42
§3.6 # 2, 4, 6, 8, 10, 18, 20, 22, 24, 26, 28, 30,34, 38, 40, 50
§3.7 # 8, 10, 12, 18, 24, 30, 34, 36, 38, 40, 44
§4.2 # 6, 10, 14(Long Division)
§5.1 # 2, 14, 16, 18, 20, 22, 30, 32
§5.2 # 2, 4, 6, 8, 10, 12, 16, 22, 24, 26, 28, 30, 50, 54, 60
§5.3 # 1, 4, 6, 8, 14, 16, 18, 22, 24, 26, 32, 40, 42, 44, 50, 52
§5.4 # 2, 4, 6, 8, 10, 12, 16, 18, 20, 22, 24, 28, 0, 32, 34, 36, 8, 40, 42, 44, 46, 48, 50, 68, 74
SQ1. Find the domain of the following functions:
i) f ( x)  7  3x
ii) g ( x) 
x
2x  x  1
2
2 x  3, x  1
iii) f ( x)  
. Sketch the graph of f (x ) .
3  x, x  1
SQ2. If g ( x)  5 x  2, calculate g (2), g ( 2  h), and
g ( x  h)  g ( x )
.
h
SQ3. Evaluate ( f  g )(2) and ( g  f )(-1) for the following functions
f (x)  x 2  5 ;
g ( x) 
x2
SQ4. Find domain and range of f , g , ( f  g ), and ( g  f ) for the following function
f (x)  x  5 ;
7
g ( x)  2
x 4
SQ5. For the function f ( x)  2 x  4 , check whether the function is one-to-one or not. If one-to-one write an
equation for the inverse. Give the domain and range of f(x) and
f
1
f
1
( x) . Verify that f ( f
( f ( x))  x .
SQ6. Find the vertex, domain, and range of the following quadratic functions
a) h(x) 
b)
 ( x  3) 2  2
h( x)  5x 2  10 x  3
SQ7. Find the quotient and remainder using long division.
3x 4  5 x 3  20 x  5
x3  x  3
x
SQ8. a. Graph the function f ( x)  2  1 .
b.
Find domain, range, and horizontal asymptote.
F2007 Copyright 2007 University of North Florida
1
( x))  x and
MAC 1990 FINAL EXAM Review - M. RAHMAN
Page 4
c.
d.
Solve for x: 2
Solve for x:
4
3 y
x2
8
 2 3 x 3
SQ9. a. Graph the function f ( x)  log 2 x .
b. Find domain, range, and vertical asymptote.
c. Write the following expression as a sum and/or difference of logarithms. Express power as factor:
x3 x  1
( x  2) 2
d. Solve for x: -2 log 4 x  log 4 9
e. Solve for x: log 4 ( x  6)  log 4 ( x  2)  log 4 x
log
NEW MATERIAL
§6.1 # 2, 10, 18(LONG DIVISION)
F2007 Copyright 2007 University of North Florida