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Sample 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: Fall 2007;

Typology: Exams

Pre 2010

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MATH1010 SAMPLE FINAL EXAM FALL 2007

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. An equation of the line through the point

)4,2(

perpendicular to

546  yx

(a)

223  yx

(b)

1632  yx

(c)

832  yx

(d)

1423  yx

(e)

832  yx

2. Simplify:

a

(a)

(b)

(c)

(d)

(e)

3. Simplify:

3 1911

24 ba

(a)

3263

32 baba

(b)

3263

23 baba

(c)

3263

32 abba

(d)

3263

23 abba

(e)

3263

63 abba

MATH 1010 Spring 2007

Discover Exams of Mathematics Utah State University (USU)

Partial preview of the text

Download Sample 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. An equation of the line through the point (^2 ,^4 ) perpendicular to 6 x^ ^4 y ^5 is

(a) 3 x^ ^2 y ^2 (b) 2 x^ ^3 y ^16 (c) 2 x ^3 y ^8

(d) 3 x^ ^2 y ^14 (e) 2 x ^3 y ^8

2. Simplify:

b

a

b

a

(a)

b

a

(b)

b

a

(c)

b

a

(d)

a

b

(e)

3. Simplify:

3 11 19 24 a b

(a)

3 63 2

2 a b 3 a b (b)

3 63 2

3 a b 2 a b (c)

3 63 2 2 a b 3 ab

(d)

3 63 2

3 a b 2 ab (e)^

3 63 2 3 a b 6 ab

4. For (^ )^625

f x  x  x  , find 

f .

(a)

(b)

(c)

(d)

 (e)

5. Factor r 3 rs rt 3 st

   completely. One of the factors is

(a) r^ ^ s (b) r^ ^ s (c) r^ ^3 t (d) r^ ^3 s (e) r^  t

6. In interval notation, the solution set for the inequality

2  x  is

(a) 

, (b)

 

  

   6

, (c) 

(d) 

(e)

 



 

  , 6

7. The domain of the function f ( x ) 6  3 x is the interval

8. Solve the quadratic equation 3 2 0

x  x  . The solution set is

(a)

1 , (^) (b)   2 , 3  (c)   3 , 2  (d)



(e) ^1 ,^3 

9. Simplify: 75  48  3 3. The result is

(a) 9 3 (b) 6 3 (c) 4 3 (d) 3 3 (e) 5 3

10. Identify the center and radius of the circle 8 6 0

2 2

x  x  y  y .

(a) Center: (−8,6), r = 14 (b) Center: (8,−6), r = 14 (c) Center: (−4,3), r = 5

(d) Center: (4,−3), r = 25 (e) Center: (4,−3), r = 5

11. Simplify:

(a)

 3 (b)

 (c)

 (d)

 (e)



12. Find the quotient:

(a) i

 (b) i

 (c) i

 (d) i

  (e) i

13. Write in simplest form.

x y

(a)

y  x

(b)

x y

y x





(c)

x  y

(d)

x  y

 1

(e)

x y





14. Solve the equation 2

t t

. The solution set is

(a)

(b) ^ ^3  (c) ^0 ^ (d) ^3 ^ (e)^ 

18. Solve the equation: 4 8 0

x  x  . The solution set is

(a) ^ ^ i , i  (b) ^1 ^ i^ ,^1  i  (c) ^1 ^23 ,^1 ^23  (d) ^1 ^2 i^^3 ,^1 ^2 i^3  (e)

 2  2 i , 2  2 i 

19. Solve the system: 



  

  2 5

5 2 7 x y

x y

. The corresponding value of y is

(a) 11 (b) −3 (c) −11 (d) 3 (e) 7

20. Solve the nonlinear inequality 84

x  x  . The solution in interval notation is

(a) [^3 ,^4 ] (b) ^ ^ ,^ ^3 ^ ^4 , (c) ^ ^ ,^ ^4 ^ ^3 , (d) [^4 ,^3 ]

(e) [^3 ,^4 ]

21. Add:

x  x

(a)

x

(b)

x 

(c)

x 

(d)

x 

(e)

x

22. Find the distance between the points (5, −4) and (7,3).

(a) 7 (b) 53 (c) 13 (d) 61 (e) 157

23. It takes Kyle twice as long to paint a room than it takes Brendan. Working together,

they can paint the room in 2 hours. How long does it take Brendan to paint the room?

(a) 4.5 hours (b) 4 hours (c) 3.5 hours (d) 3 hours (e) 2.75 hours

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

(a) 6

x  x  (b)^5 x^ ^2 (c)^6

x  (d)^6

x  x  (e)

2 x  x 

25. Solve the quadratic equation 2 7 7 7 9

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 

26. Solve the system of inequalities ^ 

  

  2 2 2

2 3 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 left, 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 ) 3 x  5 and

x g x , evaluate  f  g  ( 1 ).

(a) 1 (b) 3 (c) 0 (d) 2 (e) Not a real

number

29. Find the inverse of ,^2

 x x

f x.

(a)



f x (b)



f x (c)



x f x

(d)



f x (e)



x f x

30. The pressure p (in pounds per square inch) exerted by water on a submerged object is

directly proportional to the depth d (in feet) beneath the surface. If the pressure at a

depth of 20 feet is 9 lbs per square inch, at what depth will an egg break if its shell

cannot withstand 36 pounds per square inch?

(a) 90 feet (b) 80 feet (c) 60 feet (d) 50 feet (e) 40 feet

31. Identify the equation of the exponential function whose graph is shown.

(a)

x y



 2 (b)

y  2 (c)

x y



 3 (d)  2  1

y (e)  3  1

x y

32. Evaluate

log 27 3

(a) −3 (b) −9 (c) 3 (d) 9 (e) 81

33.Rewrite as a single logarithm. ln(^1 )^2 ln^3 ln^5

x   

(a)











 

5 1 ln

2 x

(b) 

(c)











 

5 1 ln

2 x

(d) 











 (^) 

5 ( 1 ) ln

(e)











 

1 ln

2 x

38. If y varies directly with the square root of x and inversely with the cube of t and

y = 20 when x = 25 and t =5, find t when y = 5 and x = 100.

(a) t = 10 (b) t = 20 (c) t = 30 (d) t = 40 (e) t = 50

39. Which of the following relations has a v-shaped graph opening left (with its vertex

pointing right)?

(a) y^ ^  x (b) x^ ^  y (c) y^ ^  x (d) x^ ^  y (e) x^  y

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

Related documents

Partial preview of the text

Download Sample 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. An equation of the line through the point (^2 ,^4 ) perpendicular to 6 x^ ^4 y ^5 is

(a) 3 x^ ^2 y ^2 (b) 2 x^ ^3 y ^16 (c) 2 x ^3 y ^8

(d) 3 x^ ^2 y ^14 (e) 2 x ^3 y ^8

2. Simplify:

b

a

b

a

(a)

b

a

(b)

b

a

(c)

b

a

(d)

a

b

(e)

3. Simplify:

(a)

2 a b 3 a b (b)

3 a b 2 a b (c)

(d)

3 a b 2 ab (e)^

4. For (^ )^625

f x  x  x  , find 

f .

(a)

(b)

(c)

(d)

 (e)

5. Factor r 3 rs rt 3 st

   completely. One of the factors is

6. In interval notation, the solution set for the inequality

2  x  is

(a) 

, (b)

, (c) 

(d) 

(e)

7. The domain of the function f ( x ) 6  3 x is the interval

8. Solve the quadratic equation 3 2 0

x  x  . The solution set is

(a)

9. Simplify: 75  48  3 3. The result is

(a) 9 3 (b) 6 3 (c) 4 3 (d) 3 3 (e) 5 3

10. Identify the center and radius of the circle 8 6 0

x  x  y  y .

(a) Center: (−8,6), r = 14 (b) Center: (8,−6), r = 14 (c) Center: (−4,3), r = 5

(d) Center: (4,−3), r = 25 (e) Center: (4,−3), r = 5

11. Simplify:

(a)

 3 (b)

 (c)

 (d)

 (e)

12. Find the quotient:

(a) i

 (b) i

 (c) i

 (d) i

  (e) i

13. Write in simplest form.

(a)

(b)

A Number: A_ Name ________________

Instructor____________ Section