Question 1

Solve the problem.
-Maria and Charlie can deliver 100 papers in 2 hours. How long would it take them to deliver 105 papers?

Accepted Answer

A) 210 hours 
B) 3.2 hours 
C) 1.9 hours 
D) 2.1 hours 
A) 210 hours 
B) 3.2 hours 
C) 1.9 hours 
D) 2.1 hours

Question 2

Find the ratio. Simplify, if possible.
-Mara can type 2040 words in $\frac { 2 } { 3 }$ hour (40 minutes). How many words per minute can she type?

Accepted Answer

A)  1360 words/minute 
B)  77 words/minute 
C)  51 words/minute 
D)  34 words $/ \mathrm { minute }$ 
A)  1360 words/minute 
B)  77 words/minute 
C)  51 words/minute 
D)  34 words $/ \mathrm { minute }$

Question 3

Perform the indicated operation. Simplify, if possible.
-$\frac { 5 x } { x - 2 } - \frac { 6 x - 7 } { 2 - x } - \frac { 4 x } { x - 2 }$

Accepted Answer

A)  $\frac { 7 x - 7 } { x - 2 }$ 
B)  $\frac { 7 x - 7 } { 3 x + 6 }$ 
C)  $\frac { 15 x + 7 } { x - 2 }$ 
D)  $\frac { 15 x - 7 } { x + 2 }$ 
A)  $\frac { 7 x - 7 } { x - 2 }$ 
B)  $\frac { 7 x - 7 } { 3 x + 6 }$ 
C)  $\frac { 15 x + 7 } { x - 2 }$ 
D)  $\frac { 15 x - 7 } { x + 2 }$

Question 4

Solve the equation.
-$$\frac { 6 } { x - 6 } = \frac { x } { x - 6 }$$

Accepted Answer

A)  6 
B)  0 
C)  No solution 
D)  $- 6$ 
A)  6 
B)  0 
C)  No solution 
D)  $- 6$

Question 5

Solve the problem.
-Tom Quig traveled 260 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one period of time he was slowed to 20 mph due to a major accident. If the total time of travel was 7 hours, how many miles Did he drive at the reduced speed?

Accepted Answer

A) 100 miles 
B) 75 miles 
C) 80 miles 
D) 90 miles 
A) 100 miles 
B) 75 miles 
C) 80 miles 
D) 90 miles

Question 6

Find all numbers for which the rational expression is not defined.
-$$\frac { 3 } { b + 4 }$$

Accepted Answer

A) b = 0 
B) b = 4 
C) b = -4 
D) None 
A) b = 0 
B) b = 4 
C) b = -4 
D) None

Question 7

Solve the equation.
-$$\frac { x } { 3 } - \frac { x } { 8 } = 7$$

Accepted Answer

A)  $\frac { 168 } { 5 }$ 
B)  21 
C)  56 
D)  24 
A)  $\frac { 168 } { 5 }$ 
B)  21 
C)  56 
D)  24

Question 8

Find the LCM.
-$r ^ { 2 } + 14 r + 49 , r ^ { 2 } + 7 r$

Accepted Answer

A)  $r ( r + 7 )$ 
B)  $( r + 7 ) ^ { 2 }$ 
C)  $r ( r + 7 ) ^ { 2 }$ 
D)  $r ( r + 1 ) ( r + 7 )$ 
A)  $r ( r + 7 )$ 
B)  $( r + 7 ) ^ { 2 }$ 
C)  $r ( r + 7 ) ^ { 2 }$ 
D)  $r ( r + 1 ) ( r + 7 )$

Question 9

Simplify.
-$\frac { 40 \mathrm {~m} ^ { 5 } \mathrm { p } ^ { 2 } } { 10 \mathrm {~m} ^ { 10 } \mathrm { p } }$

Accepted Answer

A)  $4 \mathrm { mp }$ 
B)  $4 m ^ { 5 } p ^ { 2 }$ 
C)  $\frac { 4 m ^ { 5 } } { p }$ 
D)  $\frac { 4 p } { m ^ { 5 } }$ 
A)  $4 \mathrm { mp }$ 
B)  $4 m ^ { 5 } p ^ { 2 }$ 
C)  $\frac { 4 m ^ { 5 } } { p }$ 
D)  $\frac { 4 p } { m ^ { 5 } }$

Question 10

Perform the indicated operation. Simplify, if possible.
-$$\frac { 2 x + 9 } { x + 1 } + \frac { x + 2 } { x + 4 } - \frac { 5 x + 26 } { ( x + 1 ) ( x + 4 ) }$$

Accepted Answer

A)  $\frac { 1 } { ( x + 1 ) ( x + 4 ) }$ 
B)  $\frac { 3 } { ( x + 1 ) ( x + 4 ) }$ 
C)  $\frac { 2 } { ( x + 1 ) }$ 
D)  3 
A)  $\frac { 1 } { ( x + 1 ) ( x + 4 ) }$ 
B)  $\frac { 3 } { ( x + 1 ) ( x + 4 ) }$ 
C)  $\frac { 2 } { ( x + 1 ) }$ 
D)  3

Question 11

Solve the problem.
-Martha can rake the leaves in her yard in 2 hours. Her younger brother can do the job in 3 hours. How long will it take them to do the job if they work together?

Accepted Answer

A)  $\frac { 6 } { 5 } \mathrm { hr }$ 
B)  $6 \mathrm { hr }$ 
C)  $\frac { 5 } { 6 } \mathrm { hr }$ 
D)  $3 \mathrm { hr }$ 
A)  $\frac { 6 } { 5 } \mathrm { hr }$ 
B)  $6 \mathrm { hr }$ 
C)  $\frac { 5 } { 6 } \mathrm { hr }$ 
D)  $3 \mathrm { hr }$

Question 12

Solve.
-The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 2 amperes when the resistance is 564 ohms. What is the current when the resistance is 336 ohms? Round to the
Nearest hundredths when necessary.

Accepted Answer

A) 0.3 amperes 
B) 3.36 amperes 
C) 0.84 amperes 
D) 1.19 amperes 
A) 0.3 amperes 
B) 3.36 amperes 
C) 0.84 amperes 
D) 1.19 amperes

Question 13

Find the reciprocal.
-$\frac { 11 } { x ^ { 2 } + y ^ { 2 } }$

Accepted Answer

A)  $- \frac { 11 } { x ^ { 2 } + y ^ { 2 } }$ 
B)  $\frac { 1 } { 11 x ^ { 2 } + y ^ { 2 } }$ 
C)  $\frac { x ^ { 2 } + y ^ { 2 } } { 11 }$ 
D)  $\frac { 1 } { 11 x ^ { 2 } + 11 y ^ { 2 } x }$ 
A)  $- \frac { 11 } { x ^ { 2 } + y ^ { 2 } }$ 
B)  $\frac { 1 } { 11 x ^ { 2 } + y ^ { 2 } }$ 
C)  $\frac { x ^ { 2 } + y ^ { 2 } } { 11 }$ 
D)  $\frac { 1 } { 11 x ^ { 2 } + 11 y ^ { 2 } x }$

Question 14

Find the equation of variation if the following is true.
-Suppose $m$ varies directly as $p$ and $m = 36$ when $p = 9$.

Accepted Answer

A)  $m = 45 p$ 
B)  $m = \frac { 1 } { 4 } \mathrm { p }$ 
C)  $m = 27 p$ 
D)  $m = 4 p$ 
A)  $m = 45 p$ 
B)  $m = \frac { 1 } { 4 } \mathrm { p }$ 
C)  $m = 27 p$ 
D)  $m = 4 p$

Question 15

Solve.
-The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 4 foot candles, find the intensity on a screen 20 ft from the light.
Express the answer as a fraction.

Accepted Answer

A)  4 foot-candles 
B)  $\frac { 1 } { 5 }$ foot-candle 
C)  $\frac { 1 } { 4 }$ foot-candle 
D)  2 foot-candles 
A)  4 foot-candles 
B)  $\frac { 1 } { 5 }$ foot-candle 
C)  $\frac { 1 } { 4 }$ foot-candle 
D)  2 foot-candles

Question 16

Simplify.
-$$\frac { \frac { 6 } { x + 2 } + \frac { 1 } { x } } { \frac { 4 } { x + 2 } + \frac { 3 } { x } }$$

Accepted Answer

A)  1 
B)  $\frac { 7 x + 2 } { 7 x + 6 }$ 
C)  $\frac { 7 x + 2 } { 7 x }$ 
D)  $\frac { 7 x + 12 } { 7 x + 8 }$ 
A)  1 
B)  $\frac { 7 x + 2 } { 7 x + 6 }$ 
C)  $\frac { 7 x + 2 } { 7 x }$ 
D)  $\frac { 7 x + 12 } { 7 x + 8 }$

Question 17

Answer the question.
-Explain in your own words how to divide rational expressions. (How would you explain this to a student in this class who was absent from class?).

Accepted Answer

To divide rational expressions, you woul

Question 18

Solve the problem.
-A loaded moving truck is traveling 25 mph faster than a freight train. In the time it takes the train to travel 90 miles, the truck travels 140 miles. Find the speed of the truck.

Accepted Answer

A) 14 mph 
B) 140 mph 
C) 70 mph 
D) 25 mph 
A) 14 mph 
B) 140 mph 
C) 70 mph 
D) 25 mph

Question 19

Solve.
-The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft
Apart?

Accepted Answer

A) 1 lb 
B) 2 lb 
C) 4 lb 
D) 3 lb 
A) 1 lb 
B) 2 lb 
C) 4 lb 
D) 3 lb

Question 20

Solve the problem.
-Dr. Wong can see 8 patients in 2 hours. At this rate, how long would it take her to see 48 patients?

Accepted Answer

A) 11 hours 
B) 192 hours 
C) 12 hours 
D) 16 hours 
A) 11 hours 
B) 192 hours 
C) 12 hours 
D) 16 hours

Solve the problem. -Maria and Charlie can deliver 100 papers in 2 hours. How long would it take them to deliver 105 papers?

Find the ratio. Simplify, if possible. -Mara can type 2040 words in $\frac { 2 } { 3 }$ hour (40 minutes). How many words per minute can she type?

Perform the indicated operation. Simplify, if possible. - $\frac { 5 x } { x - 2 } - \frac { 6 x - 7 } { 2 - x } - \frac { 4 x } { x - 2 }$

Solve the equation. - $\frac { 6 } { x - 6 } = \frac { x } { x - 6 }$

Solve the problem. -Tom Quig traveled 260 miles east of St. Louis. For most of the trip he averaged 60 mph, but for one period of time he was slowed to 20 mph due to a major accident. If the total time of travel was 7 hours, how many miles Did he drive at the reduced speed?

Find all numbers for which the rational expression is not defined. - $\frac { 3 } { b + 4 }$

Solve the equation. - $\frac { x } { 3 } - \frac { x } { 8 } = 7$

Find the LCM. - $r ^ { 2 } + 14 r + 49 , r ^ { 2 } + 7 r$

Simplify. - $\frac { 40 \mathrm {~m} ^ { 5 } \mathrm { p } ^ { 2 } } { 10 \mathrm {~m} ^ { 10 } \mathrm { p } }$

Perform the indicated operation. Simplify, if possible. - $\frac { 2 x + 9 } { x + 1 } + \frac { x + 2 } { x + 4 } - \frac { 5 x + 26 } { ( x + 1 ) ( x + 4 ) }$

Solve the problem. -Martha can rake the leaves in her yard in 2 hours. Her younger brother can do the job in 3 hours. How long will it take them to do the job if they work together?

Solve. -The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 2 amperes when the resistance is 564 ohms. What is the current when the resistance is 336 ohms? Round to the Nearest hundredths when necessary.

Find the reciprocal. - $\frac { 11 } { x ^ { 2 } + y ^ { 2 } }$

Find the equation of variation if the following is true. -Suppose $m$ varies directly as $p$ and $m = 36$ when $p = 9$ .

Solve. -The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 5 ft from a light is 4 foot candles, find the intensity on a screen 20 ft from the light. Express the answer as a fraction.

Simplify. - $\frac { \frac { 6 } { x + 2 } + \frac { 1 } { x } } { \frac { 4 } { x + 2 } + \frac { 3 } { x } }$

Answer the question. -Explain in your own words how to divide rational expressions. (How would you explain this to a student in this class who was absent from class?).

Solve the problem. -A loaded moving truck is traveling 25 mph faster than a freight train. In the time it takes the train to travel 90 miles, the truck travels 140 miles. Find the speed of the truck.

Solve. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft Apart?

Solve the problem. -Dr. Wong can see 8 patients in 2 hours. At this rate, how long would it take her to see 48 patients?

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Polynomials: Factoring

Graphs, Functions, and Applications

Systems of Equations

More on Inequalities

Radical Expressions, Equations, and Functions

Quadratic Equations and Functions

Exponential Functions and Logarithmic Functions

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Exam 6: Rational Expressions and Equations