Test 1
Test Grade________
MAT 122 spring 2015
Name:
Directions: This take home exam is intended to measure each individual student’s mastery of the topics in chapter 7. Please
do not seek help from any individuals except your instructor and please do not use any resources except your textbook, class
notes, homework, and class handouts. If there is evidence of one student copying answers from another student’s exam, then
all students involved will be docked a significant amount of points on the exam.
If appropriate work is not shown, you will NOT receive credit. This test is due by midnight on February 9th . It can be
submitted in Canvas (ONLY .pdf or .docx files).
1. (4 pts) When is the function
x+5
undefined?
x−8
x 2 − 16
2. (6 pts) Simplify 2
x − x − 12
3. (8 pts) Multiply. Express answer in lowest terms.
4. (9 pts) Divide
x 2 − 5x + 6
x 2 + 6x − 16
÷
x 2 − 10x + 21 x 2 − 2x − 35
x+2
x−3
⋅ 2
x − 4 x − 12 x − 9
2
Test 1
MAT 122 spring 2015
Problems 5-10 are True/False questions. Indicate whether the statement is true or false. (2 pts each)
5.
6.
7.
8.
9.
10.
To solve
1
1
2
+3=
, multiply each term by x − 4 .
x−2
x+2
A rational expression is undefined whenever its denominator is zero.
The two triangles below are similar. The height of the larger triangle is
The expression
2+ x
is a rational expression.
x −1
The domain of
2x + 5
is All Real Numbers except x = 9 .
(x − 9)(2x + 1)
The rational expression
24
.
5
5x + 2
x+2
reduces to
.
15
3
11. (9 pts) Lee can shovel the driveway in three hours and Susan can shovel the driveway in two hours. How
long will it take them working together?
Test 1
MAT 122 spring 2015
1
2
3
+
= 2
12. (12 pts) Solve x x + 2 x + 2x and check your solutions by graphing.
13. (10 pts) The ratio of pickups to cars sold at a dealership is 2 to 3. If the dealership sold 142 more cars
than pickups in 1999, then how many of each did it sell?
Test 1
MAT 122 spring 2015
14. (10 pts) Pollution in the Tickfaw River has been blamed primarily on pesticide runoff from area farms.
4, 000, 000 p
The formula C =
has been used to model the cost in dollars for removing p% of the pollution
100 − p
in the river. If the state gets a $1 million federal grant for cleaning up the river, then what percentage of the
pollution can be removed?
15. (10 pts) A motorboat travels 18 mph in still water. If the boat travels 52 miles upstream in the same time
that it takes to travel 80 miles downstream, then what is the rate of the current?
Test 1
MAT 122 spring 2015
Problems 16-20 are Matching questions. Match each term with its definition. (2 pts each)
16)
y = 2400
a) If y varies jointly as x and z .
17)
y=6
b) If y varies jointly as x and z squared.
18)
y = kxz
c) If y varies jointly as x cubed and z .
19)
y = kx z
d) If y varies jointly as x and z squared, and y = 225 when x = 4 and
z = 3 , find y when x = 6 and z = 8 .
20)
y = kxz 2
3
e) If y varies jointly as x and z , and y = 12 when x = 9 and z = 3 ,
find y when x = 15 and z = 109 .
EXTRA CREDIT
1. Find the exact value of:
1
1
1+
1
1+
1
1+
2
x−3
.
2x + 1
Round answers to 4 decimal places. What can you conclude about the value of R as x gets larger and larger?
2. Use a calculator to find R when x = 2, 30,500,9000, and 80000 for the rational expression R =