Math 134 - Intermediate Algebra
Name: _____________________________
Final Comprehensive Exam
Date: ______________________________
Fall 2010
Instructor: __________________________
College Center: ______________________
For Instructor Use Only
Final Exam Grade: _________
Final Course Grade: ________
Read Each Problem Carefully.
Show All Your Work Neatly In The Space Provided.
No cell phones allowed on this exam.
No graphing calculators allowed on this exam.
Scientific calculators are permitted.
The following equations may be useful while taking this exam.
Slope-Intercept Form: y  mx  b
y y
Slope Formula: m  2 1
x2  x1
Point-Slope Form: y  y1  m  x  x1 
Special Products:
 a  b  a  b   a 2  b 2
 a  b 2  a2  2ab  b2
 a  b 2  a2  2ab  b2
Special Forms:
a 2  b 2   a  b  a  b 
a2  2ab  b2   a  b 
2
a 2  2ab  b2   a  b 
2


a3  b3   a  b   a 2  ab  b2 
a3  b3   a  b  a 2  ab  b2
Algebraically find the x- and y-intercepts. Use the x- and y-intercepts to graph the equation of the line.
Do Not Use A Table. Label and assign values to all axes.
1. (5pt) 4 x  3 y  12
Write the equation in slope-intercept form. Determine the slope and the y-intercept.
2. 3 x  5 y  15 (a) (2pt) Slope: _________
(b) (2pt) y-intercept: ____________
(c) (2pt) Sketch the graph of the line.
Find the slope of the line passing through the given points. Show all your work.
3. (3pt)
 4,3 and  2, 6
Write the equation of the line passing through the given point and given slope.
Show all your work.
4. (5pt)
 5, 4 
and m  
2
No decimal answers.
5
Write the equation of the line passing through the given points.
Show all your work.
5. (5pt)
 7, 3 and 1, 2
Graph the line given the point and the slope. Label and assign values to all axes.
6. (3pt)
 4, 4 ,
m is undefined
Graph the equation of the line. Label and assign values to all axes.
7. (5pt)
 4, 4 ,
m0
Application Problem.
8. The dollar cost, as a function of time t in hours, for computer repair is given by R  t   50t  35 .
a.) (2pt) What is the slope?
b.) (2pt) In a well-structured sentence, explain what the slope represents in the context of the
problem.
c.) (1pt) What is the y-intercept?
d.) (2pt) In a well-structured sentence, explain what the y-intercept represents in the context of
the problem.
Application Problem.
9. A real estate office handles an apartment complex with 50 units. When the rent per unit is $580 per
month, all 50 units are occupied. However, when the rent is $625 per month, the average number of
occupied units drops to 47 units. Assume that the relationship between the monthly rent p and the
demand x is linear.
a.) (2pt) Represent the given information as two ordered pairs of the form  x, p  .
b.) (3pt) Write a linear equation in slope intercept form that relates the monthly rent p to the
demand x.
c.) (2pt) Use the equation from part (b) to predict the number of units occupied if the rent is
raised to $655.
Simplify by applying the Laws of Exponents. Write the results with positive exponents.
No Decimal Answers.
a 4  b2 
10. (4pt)
 
b  a3 
12. (4pt)
2
11. (4pt)
3x y  2 x y 
4 2
5 3
12 x3 y 4
8 x 7 y 6
 5 x 2 y 8 
13. (4pt) 

 10 x10 y 4 


4
Evaluate. Write the answer in scientific notation and in decimal notation.
14.
8 106  2 102 
 4 102 
a. (2pt) Scientific notation: ____________________
b. (2pt) Decimal notation : _____________________
Application Problem.
15.
The mass of Earth is 5.98 1024 kg. The mass of the dwarf planet Pluto is about 0.002 times the
mass of the Earth. What is the mass of Pluto?
a.) (2pt) Write an algebraic expression to find the mass.
b.) (2pt) Evaluate the expression and write the result in scientific notation.
c.) (1pt) Write a well-structured sentence with units correctly stated.
Perform the indicated operations and simplify. Show all your work.
16. (4pt) 8 x  7   x  4   6 x 

 
17. (4pt) 4  5  x   5 x 2  3  x 2  3x
Application Problem.
18.
The average number of M words memorized in t minutes can be modeled by
M  0.001t 3  0.1t 2 .
a.) (2pt) Use the model to estimate the number of words memorized after 14 minutes.
b.) (1pt) Write a well-structured sentence with the units correctly stated.
Perform the indicated operations and simplify. Show all your work.
19. (4pt)
 3x  4 2 x  5
20. (4pt) 5x  3x 1 2 x  3
21. (4pt)
 3 x  5 2
22. (4pt)
 x  1  x 2  x  1
Perform the indicated operations and simplify. Show all your work.
12 x3  26 x 2  8 x
23. (3pt)
2x
Use Long Division to divide the polynomials. Show all your work.
6 x 2  8 x  13
24. (4pt)
3x  2
No credit unless long division is shown.
Use Synthetic Division to divide the polynomials. Show all your work.
25. (4pt)
3 x3  7 x 2  4 x  3
No credit unless synthetic division is shown.
x3
Application Problem.
26.
The height of a rectangular door is  x  5 feet and its area is 2 x 2  13 x  15 square feet.
What is the length of the door?
1.) (2pt) Write an algebraic equation to find the length.
2.) (2pt) Solve the equation.
3.) (1pt) Write a well-structured sentence with the units correctly stated.

Solve each equation by completely factoring the polynomial and applying the Zero Factor Property.
No Decimal Answers.
27. (6pt) 2 x2  9 x  0
28. (6pt) x 2  8 x  12  0
Solve each equation by completely factoring the polynomial and applying the Zero Factor Property.
No Decimal Answers.
29. (6pt) 3 x 2  10 x  8  0
30. (6pt) 81x 2  64  0
Solve each equation by completely factoring the polynomial and applying the Zero Factor Property.
No Decimal Answers.
31. (6pt)
 x  2 2  9
33. (6pt) x  x  3  28
32. (6pt) 36a 2  9a
34. (6pt) 2 x3  7 x 2  15 x
Application Problem
35. A penny is dropped from the roof of a building 256 feet above the ground. The height h (in feet) of
the penny after t seconds is modeled by the equation
h  16t 2  256 .
How long does it take for the penny to reach the ground?
1.) (2pt) Write an algebraic equation using the given position equation.
2.) (2pt) Solve the equation.
3.) (1pt) Write a well-structured sentence with the units correctly stated.
Application Problem
36.
The rectangular floor of a storage shed has an area of 540 square feet. The length of the floor is 7
feet more than its width. What are the dimensions of the floor?
1.) (2pt) Write an algebraic equation to find the dimensions.
2.) (2pt) Solve the equation.
3.) (1pt) Write a well-structured sentence with the units correctly stated.