Download Chapter 7 Practice Test

Math 107 Chapter 7 Practice Test
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Simplify the rational expression. If the rational expression cannot be simplified, so state.
x - 10
1)
x2 - 100
1)
Find the least common denominator of the rational expressions.
6
8
2)
and
- 15
2
5x
x - 4x + 3
2)
Solve.
3) The voltage across a resistor is jointly proportional to the resistance of the resistor and
the current flowing through the resistor. If the voltage across a resistor is 42 volts for a
resistor whose resistance is 7 ohms and when the current flowing through the resistor
is 6 amperes, find the voltage across a resistor whose resistance is 4 ohms and when
the current flowing through the resistor is 2 amperes.
3)
4) The amount of gas that a helicopter uses is directly proportional to the number of
hours spent flying. The helicopter flies for 3 hours and uses 30 gallons of fuel. Find the
number of gallons of fuel that the helicopter uses to fly for 6 hours.
4)
Solve the rational equation.
5-x 3 7
+ =
5)
x
4 x
5)
Multiply. Simplify if possible.
6p - 6 4p2
·
6)
p
9p - 9
6)
Two formulas that approximate the dosage of a drug prescribed for children are:
Young's Rule: C =
DA
D( A + 1 )
and Cowling's Rule: C =
.
A + 12
24
In each formula, A = the child's age in years, D = an adult dosage, and C = the proper child's dosage. The formulas
apply for ages 2 through 13. Use these formulas to solve the problem.
7) For a 5-year old child, what is the difference in the dosage given by Young's Rule and
7)
Cowling's Rule? Express the answer as a single rational (or fractional) expression in
terms of D.
Perform the indicated operation(s). Simplify if possible.
3x
x-1
1
+
8)
x2 - 5x - 36 x2 - 16 x2 - 13x + 36
8)
Solve the equation for the specified variable.
1 1 1
9) + = for c
a b c
9)
1
Simplify.
10)
x-2
x-2 - y-2
10)
Solve the rational equation.
x 2 x-7
+ =
11)
14 7
7
11)
Use a proportion to solve the problem.
12) It is recommended that there be at least 9.8 square feet of floor space in a classroom for
every student in the class. Find the minimum floor space that 23 students require.
Round to the nearest tenth if necessary.
Perform the indicated operation(s). Simplify if possible.
4x - 8
+1
13)
x+3
12)
13)
Solve.
14) While traveling at a constant speed in a car, the centrifugal acceleration passengers
feel while the car is turning is inversely proportional to the radius of the turn. If the
passengers feel an acceleration of 6 feet per second per second when the radius of the
turn is 50 feet, find the acceleration the passengers feel when the radius of the turn is
150 feet.
Perform the indicated operation(s). Simplify if possible.
2
4
15) +
x x-6
14)
15)
Simplify the rational expression. If the rational expression cannot be simplified, so state.
x2 - 25
16)
2
x + 8x + 15
Perform the indicated operation. Simplify the result, if possible.
x
3
+
17)
x+7 x-7
Simplify the rational expression. If the rational expression cannot be simplified, so state.
x+7
18)
2
x + 5x - 14
Simplify the complex fraction.
1 1
6 5
19)
1 1
8 3
16)
17)
18)
19)
2
Multiply. Simplify if possible.
y2 - z2
y
·
20)
y+z
2
y - yz
20)
3
Answer Key
Testname: MATH 107 CHAPTER 7 TEST
1)
1
x + 10
2) 5(x - 1)(x - 3)
3) 8 volts
4) 60 gallons
5) {-8}
8p
6)
3
7)
3
D
68
8)
2x2 - x - 5
(x - 9)(x + 4)(x - 4)
9) c =
10)
ab
a+b
y2
2
y - x2
11) {18}
12) 225.4 sq ft
5x - 5
13)
x+3
14) 2 feet per second per second
6x - 12
15)
x(x - 6)
16)
x-5
x+3
17)
x2 - 4x + 21
(x + 7)(x - 7)
18)
1
x-2
19)
4
25
20) 1
4