Download Final Exam b, Intermediate Algebra, fall 2002 with answers

Name: _____________________
Section Number: _____
Final Exam b, Math 120, fall 2002 12/05/2005
Answers
1. A 2. D 3. D 4. C 5. A 6. B 7. B 8. A 9. A 10. D
11. approximately 4.1  10 4
12. x = 2 [x = −1 does not check.]
13. (−2, 7)
x 10
14. a) 4a 4 11a
b)
2
15.  4  2 3
(2 p  3) 2
16.
p( p  1)
y 12
17.
25x 2
18. x + .04x = 23,992. Gabriel earned $23,o69.23 before his raise.
19. Equations: x  y  8000 and .04 x  .045 y  350 . Solution (2000, 6000)
Roza should invest $2000 at 4% and $6000 at 4.5%.
20. a) (x – 4)(x + 7)
b) (3x + 1)(x + 4)
21. The width of the rectangle is 8 feet; its length is 12 feet.
22. b  15 ; b  1 . Both check.
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23.The maximum height of the ball is 1600 feet. It lands 80 feet from where it was hit.
24. The speed of the boat in still water is 7.5 mph. the speed of the current is 1.5 mph.
25. The value of the car 5 years after purchase is $11,141.12
3
1
26. y  x  Its graph is a straight line with y-intercept 14 and x-intercept  13 . Other
4
4
points on the line are (4,3 14 ), (8,6 14 )( 4,2 34 ), etc.
27. y  ( x  5) 2  15
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Part I: Questions 1 to 10 (6 points each)
1. The slope of the line joining the two points (2, 3) and (4, 1) is:
[A] 2
[B]  1
2
[C]  3
5
[D]  1
2. If f(x) = 3x – 4, then:
[A] f(3) = 4
3
[B] f(3) = 1
3
[C] f(3) = –1
[D] f(3) = 5
3. The solution to the equation 3(x + 1) = –4(x – 5) + 6x is:
[A] 23
7
[B] 23
[C]  1
3
[D] 17
4. Evaluate log 4 64
[A] 16
[B] 1.806
[C] 3
[D] 4
5. Multiply and simplify: (1 + 3 2 )(3 + 2 2 )
[A] 15 + 11 2
[B] 4 + 5 2
[C] 3 + 6 2
[D] 15
6. Evaluate 8
[A] 5.33
[B] 4
[C] 16
[D] 3 16
2
3
2
7. Which of these graphs best represents the function y = 4 x ?
[A]
[B]
A
B
[C]
y
[D]
y
x
x
C
y
D
y
x
x
8. Which of these points does not lie on the line y  2( x  1) 2  3 ?
[A] (0, 5)
[B] (1, 3)
[C] (2,15)
[D] (2, 1)
9. The solution of the inequality
[A] 3  x  5
[B] 1  x  5
[C] x  1
[D]  1  x  3
1  2x  5  5
is:
10. The vertex of the parabola described by the function y  2( x  4) 2  1 is the
point:
[A] (8, 1)
[B] (4,1)
[C] (16,1)
[D] (4, 1)
Part II: WRITE YOUR ANSWERS ON THE SPACES PROVIDED. Show your work.
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11. (8 points) Calculate: (5.065  10 7 )(8.17  10 4 )
Write your answer in scientific notation.
Answer: _______________
12. (8 points) Solve for x. Check your solution(s).
3  x  x 1
Solution(s):___________________
Checks:
13. (8 points) Find the solution to this system of equations:
3 x  2 y  20
5 x  6 y  32
answer: ________________
14. (8 points) Write in simplified form (leave no radicals in the denominator):
4
a) 2a 44a 7
answer: ____________
b)
15 x 2
6
answer: _____________
15. (8 points) Consider the quadratic equation x 2  8 x  4 = 0.
a) Write the quadratic formula:
_______________________________________
b) Use the formula to find the solutions to the above equation. Leave solutions in
simplest radical form.
solutions: ___________
16. (8 points) For the operation
4 p2  9 2 p2  p  3
÷
p
2p  3
a) factor all the numerators and denominators:
answer: ___________________________
b) divide and simplify:
answer: _____________________________
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 (5 x) 3 x 2 

17. (8 points) Simplify leaving no negative exponents:  4
2 
y
(
5
y
)


2
answer: _______________________
18. (8 points) After his 4% raise, Gabriel earned $23,992 a year. How much did he
earn before his raise?
i. Write an equation to find how much he earned before the raise.
equation: ________________________
ii. Figure how much he earned before the raise, rounded to the nearest
penny.
answer: ________________________________________________________________
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19. (10 points) Roza has $8,000 to invest. She invests part at 4% and the rest at 4.5%.
If she earns $350 in interest after one year, how much did she invest at each rate?
i. Complete the table:
4%
4.5%
Total
rates 
$ invested
Interest earned
ii.
Figure how much she invested at each rate.
answers: ________________________________________________________________
20. (10 points) Factor the following expressions completely. Check by using FOIL
multiplication
a) (4 points) x 2  3 x  28
answer: _________________
b) (6 points) 3x 2  13x  4
answer: _________________
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21. (8 points) A rectangle is 4 feet longer than it is wide. Its area is 96 square feet.
Find the dimensions of the rectangle.
answer: _____________________________________________________________
22. (8 points) Solve for b if possible
2
3
1

 . Check your answer(s).
b5 b3 b
Answer(s):_______________
Checks:
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23. (10 points) The flight of a golf ball over a level course can be modeled by the
function f ( x)   x 2  80 x , where f(x) (in feet) represents its height above the
ground and x (in feet) is the horizontal distance it travels.
a. Make a sketch of what’s happening.
b. How high is the golf ball at its maximum height?
c. How far away does it land?
24. (10 points) Adriana’s18-kilometer boat trip downriver took two hours, but the
return trip back upstream took three hours. Figure the speed of the boat in still water and
the speed of the current of the river.
answer: ________________________________________________________________
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25. (10 points) A Schwartzmobile depreciates according to the formula:
V (t )  V0 (.8) t ,
where V(t) represents the dollar value after t years, and V 0 represents the original
value of the automobile.
Figure the value of a Schwartzmobile purchased 5 years ago for $34,000.
Answer: ________________________________________________________________
26. (10 points) Write an equation of the line that has a slope of
the point (-3, -2).
3
4
and passes through
a) Equation: _________________________________
b) Graph the line on these axes. Label three points.
27. (4 points extra) Convert the quadratic equation y  x 2  10 x  10 into the form
y  a ( x  h) 2  k
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