Math 860 Exam 2 Review Summer 2011
Exam 2 will be on Monday, June 27 and will cover Chapters 3, 4. You should practice MANY more than this for the exam:
1.
Solve the following systems of equations using any method you choose: a) b)




2 x
 y
 
 x

4 y

12
3 x
 y

7
6
9 x

2 y

1

 c)

3( x
 y )
 x

3

 y

2 x

3
3
2.
The elevation in Denver, CO, is 13 times higher than that of Waikapu, HI. The
3.
 with one that is 30% sunflower seeds to make 50 pounds of a mixture that is 20% sunflower seeds. How many pounds of each type of seed should he use?
4.
An airplane can fly 500 miles in 2 hours when flying with the wind. When flying against the wind, it takes the plane 4 hours to complete the same journey. Find the speed of the wind and the speed of the plane (in still air).
5.
Barb invested a total of $25,000 in two accounts. One account has an annual interest rate of 3.5% while the other has an annual rate of 6%. She earned $1,257 in interest in one year. How much did she invest in each account?
6.
Henry is comparing the cost of two cell phone plans. The first plan costs $30 per month for unlimited calls and no text messages, but if he sends a text message, each will cost 10¢. The second plan costs $35 per month for unlimited calls and no text messages, but texts are 5¢ each. Find how many texts Henry will have to send per month to break even on the two plans.
7.
Solve each inequality. Graph the solution set and write it in interval notation: a)
4(5
 x )

20 b) x

2

3 or x

6
 
10

3

4

3 x

 c) a)

2
5
8.
Solve each absolute value equation:
2 x

1

3

0

 b) c) x x
2


5
 
1
5

3( x

3)

 d) 3

1
2
1
2 x

4

2
9.
Solve each absolute value inequality. Graph the solution set and write it in interval notation. a)
3 x

2


 b)
0.5
x

1
 
23 c)
2

3 x
 
8 d)
15 x

45

7

7
Answers to Practice Problems
1.
a)
b) x
 
4, y

2 x

1, y
 
4 c) infinitely many solutions, dependent equations
2.
Waikapu 400 feet, Denver 5200 feet
3.
31.25 lb of the 14% sunflower seed, 18.75 lb of the 30% sunflower seed
4.
speed of plane = 187.5 mph, speed of wind = 62.5 mph
5.
$9720 invested at 3.5%, $15280 invested at 6%
6.
Henry will break even if he sends 100 texts only.




7. a)
b)
c)
 
 
,

4


2,
19
3


 
1,

8. a) x
 
1 or x

2
, b)  , c)
9. a)



,

2
3





2
3
,



b) no solution, x

7 or x

1
d)
 c)
 
,
 
d) 3
   x

4 or x

12