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Final Exam with Solution Key - Intermediate Algebra | MATH 1010, Exams of Mathematics

Utah State University (USU)Mathematics

Material Type: Exam; Class: INTERMEDIATE ALGEBRA(SSS); Subject: Mathematics; University: Utah State University; Term: Spring 2008;

Typology: Exams

Pre 2010

Uploaded on 07/30/2009

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MATH1010 FINAL EXAM SPRING 2008
A Number: A_______________________ Name ______________________________________
Instructor__________________________ Section ______________
Instructions: Write your name and student ID number on your Scan-Tron sheet and on
this test booklet. DO NOT USE A CALCULATOR. Mark your answers on your Scan-Tron
sheet AND on this test booklet.
MULTIPLE CHOICE. Circle the correct choice on this test booklet AND mark your
answer on your Scan-Tron sheet.
1. Factor completely.
100425
2222
rssr
Which is NOT a factor?
(a)
5r
(b) s − 2 (c) r − 2 (d) s + 2 (e) r + 5
2. For
325)(
2
xxxf
, find
5
2
f
.
(a)
5
7
(b)
5
7
(c)
3
(d)
5
(e)
3. In interval notation, the solution set for the inequality
357.0 x
is
(a)
)50,( 
(b)
)5,( 
(c)
),5[
(d)
),50(
(e)
),50[
MATH 1010 Spring 2007
1
pf3
pf4
pf5
pf8
pf9
pfa

Partial preview of the text

Download Final Exam with Solution Key - Intermediate Algebra | MATH 1010 and more Exams Mathematics in PDF only on Docsity!

A Number: A_______________________ Name ______________________________________

Instructor__________________________ Section ______________

Instructions: Write your name and student ID number on your Scan-Tron sheet and on

this test booklet. DO NOT USE A CALCULATOR. Mark your answers on your Scan-Tron

sheet AND on this test booklet.

MULTIPLE CHOICE. Circle the correct choice on this test booklet AND mark your

answer on your Scan-Tron sheet.

1. Factor completely. 25

2 2 2 2

r s  s  r  Which is^ NOT^ a factor?

(a) r^ ^5 (b) s − 2 (c) r − 2 (d) s + 2 (e) r + 5

2. For (^ )^523

2

f x  x  x  , find 

f .

(a)

(b)

 (c)  3 (d) 5 (e)

3. In interval notation, the solution set for the inequality  0. 7 x  35 is

(a) (^ ^ ,^50 ) (b) (^ ^ ,^5 ) (c) [^ ^5 ,) (d) (^ ^50 ,) (e)

[  50 , )

4. Simplify:

2

3

3

6

y

x

y

x

(a)

y

x

2

9

2

(b)

y

x

2

2

(c)

y

x

2

3

(d)

5

9

32 y

x

(e)

y

x

2

9

3

5. Simplify:

4 2 9 11 48 x y z

(a)

2 34 2

2 y z 3 x yz (b)

2 24 2

2 y z 3 x yz (c)

2 24 2 3 2 y z 3 x yz

(d)

2 34 2 3

2 y z 3 x yz (e)

(^4 ) 4 xy z 3 yz

6. An equation of the line through the point (1,4) and (−3, −2) is

(a) 3 x^ ^2 y ^5 (b) 2 x^ ^3 y ^10 (c) x ^ y ^5

(d) 2 x^ ^3 y ^14 (e) x ^ y ^3

7. The domain of the function f^ (^ x )^8 ^4 x is the interval

(a) [^2 ,)^ (b) (^2 ,)^ (c) [^ ^2 ,) (d) (^ ,^2 ] (e) (^ ,^2 ]

12. Find the quotient:

i

i

(a) i

 (b) 1  i (c) i

 (d) i

 (e) 1  i

13. Write in simplest form.

x

x

y

x

y

2

(a)

yx

1

(b)

xy

1

(c)

xy

1

(d)

xy

 1

(e)

xy

1

14. Solve the equation:

x

x

x x

x

. The solution set is

(a) ^ ^6 ,^2  (b) ^ ^2 ,^6  (c)

6 , (d)

(e) ^ ^3 ,^3 

15. Solve for x : 2 2 x^ ^10  x ^7. Check your answers. The solution set is

(a) ^3 ^ (b) ^ ^3 ,^1  (c) ^1 ^ (d) ^ ^3  (e)^ 

16. Solve the inequality 2 x^ ^4 ^7. The solution set is

(a)

(b)

(c)

(d) 

  

    

  

   , 2

11

2

3

, (e)

 

  

    

  

   , 2

3

2

11 ,

17. A sign has a diagonal length of 60” with sides in a ratio of 3:1.

Find the area of the sign.

60” x

3 x

(a) 1080 sq. in. (b) 6 10 sq. in. (c) 48 10 sq. in. (d) 360 sq. in. (e) 1440 sq. in.

22. Rationalize the denominator:

(a) 9  3 7 (b) 6  3 7 (c) 6  3 7 (d) 9  3 7 (e) 18  6 7

23. Solve the quadratic equation 3 5 9 2 5 7

2 2

x  x   x  x . The solution set is

(a) ^ ^4 ,^4  (b) ^ ^4 i^ ,^4 i  (c) ^ ^2 ,^2  (d) ^ ^16 ,^16  (e)

  i 2 , i 2 

24. Let f^ (^ x )^3 x ^5 and g^ (^ x )^2 x ^3. Find (^ fg^ )( x ).

(a) 5 x  2 (b) 6

2

x  x  (c)^6

2

x  x  (d)^6

2

x  x  (e)^6

2 xx

25. Two cyclists take off in opposite directions riding at constant speeds. One cyclist is

riding 5 miles an hour faster than the other. If they are 80 miles apart after 2 hours,

what is the speed of the slower cyclist?

(a) 17 mph (b) 17.5 mph (c) 18 mph (d) 18.5 mph (e) 20 mph

26. Solve the system of inequalities ^ 

  

   2 0

2 2 AND x y

x y

(a) (b) (c) (d) (e)

27. If the graph of y^ ^ x is translated 5 units upward and 3 units to the right, then the

equation of that curve is

(a) y^ ^5  x ^3 (b) y^ ^5 x ^3 (c) y ^ x ^3 ^5

(d) y^ ^5  x ^3 (e) y ^ x ^3 ^5

28. If f^ (^ x )^2 x ^6 and

x

x

g x , evaluate (^ g^  f )(^5 )

(a) 1 (b) 0 (c) −3 (d) 23 (e) Undefined

29. Find the inverse of

x

f x.

(a)

1

x

f x (b)

x

f x (c)

x f x

(d)

x

f x (e) ( ) 5 4

1  

f x x

30. Hooke’s Law states that the force required to compress a spring is directly proportional to

the change in length of the spring. If a force of 20 pounds is required to compress a spring 2

inches, what force is required to compress the spring 8 inches?

2

3 28

2 2

 

 

y x

x y

34. Rewrite in exponential form: y^ log^2 x.

(a)

x

y  2 (b)

2

x  y (c)

2

y  x (d)

x

2  y (e)

y x  2

35. Solve the system of equations. The solutions are

(a) (−2, −4) and (3, 1) (b) (−2, −4) and (−3, −5) (c) (0, −2) and (1, −1)

(d) (−3, −5) and ) (2, 0) (e) (2,0) and ) (3, 1)

36. The equation of the circle with radius 2 centered at the point (3, −5) is

(a) (^3 ) (^5 )^4

2 2

x   y   (b) ( 3 ) ( 5 ) 4

2 2

x   y   (c) ( 3 ) ( 5 ) 8

2 2 x   y  

(d) (^3 ) (^5 )^16

2 2

x   y   (e) ( 3 ) ( 5 ) 16

2 2 x   y  

37. Rewrite in logarithmic form:

y

(a) 7 log^ y^21 (b) y^ log 721 (c) 7 log^21 y (d) y^ log 217 (e) 21 log y^7

38. Suppose y varies directly with x and inversely with the square root of t ( t > 0). If

y = 60 when x = 4 and t = 25, find t when y = 50 and x = 2.

(a) t = 3 5 (b) t = 5 (c) t = 9 (d) t = 12 (e) t = 4 3

39. Which of the following relations is a parabola opening right?

(a)

2

y   x (b)

2

y  x (c)

2

x  y (d)

2

x  3  y (e) 5

2 xy

40. Which of the following is the graph of f^ (^ x )^2  x ^3?

(a) (b)

(c) (d)

(e) None of the above END OF

EXAM