Lesson Quizzes
Preview
10-1 Inverse Variation
10-2 Rational Functions
10-3 Simplifying Rational Expressions
10-4 Multiplying and Dividing Rational Expressions
10-5 Adding and Subtracting Rational Expressions
10-6 Dividing Polynomials
10-7 Solving Rational Equations
10-8 Applying Rational Equations
10-1 Inverse Variation
Lesson Quiz: Part I
1. Write and graph the inverse variation in which
y = 0.25 when x = 12.
10-1 Inverse Variation
Lesson Quiz: Part II
2. The inverse variation xy = 210 relates the length
y in cm to the width x in cm of a rectangle with
an area of 210 cm2. Determine a reasonable
domain and range and then graph this inverse
variation.
10-1 Inverse Variation
Lesson Quiz: Part III
3. Let x1= 12, y1 = –4, and y2 = 6, and let y vary
inversely as x. Find x2.
–8
10-2 Rational Functions
Lesson Quiz: Part I
Identify the exceeded value for each rational
function.
1.
0
5
2.
3. Identify the asymptotes of
graph the function.
and then
x = –4; y = 0
10-2 Rational Functions
Lesson Quiz: Part II
4. You have $100 to spend on CDs. A CD club
advertises 6 free CDs for anyone who
becomes a member. The number of CDs y
that you can receive is given by y =
where x is the average price per CD.
,
a. Describe the reasonable domain and range
values.
D: x > 0
R: natural numbers > 6
10-2 Rational Functions
Lesson Quiz: Part III
b. Graph the function.
10-3 Simplifying Rational Expressions
Lesson Quiz: Part I
Find any excluded values of each rational
expression.
1.
0
2.
0, 2
Simplify each rational expression, if possible.
3.
5.
4.
10-3 Simplifying Rational Expressions
Lesson Quiz: Part II
6. Calvino is building a rectangular tree house. The
length is 10 feet longer than the width. His friend
Fabio is also building a tree house, but his is
square. The sides of Fabio’s tree house are equal
to the width of Calvino’s tree house.
a. What is the ratio of the area of Calvino’s tree
house to the area of Fabio’s tree house?
b. Use this ratio to find the ratio of the areas
if the width of Calvino’s tree house is 14
feet.
10-4 Multiplying and Dividing Rational Expressions
Lesson Quiz: Part I
Multiply. Simplify your answer.
1.
2
2.
3.
Divide. Simplify your answer.
4.
5.
10-4 Multiplying and Dividing Rational Expressions
Lesson Quiz: Part II
6. A bag contains purple and green toy cars.
There are 9 more purple cars than green
cars.
a. Write and simplify an expression to represent the
probability that someone will pick a purple car
and a green car.
b. What is the probability of someone picking a
purple car and a green car if there are 12 green
cars before the first pick? Round to the nearest
hundredth.
0.24
10-5 Adding and Subtracting Rational Expressions
Lesson Quiz: Part I
Add or subtract. Simplify your answer.
1.
2.
3.
4.
5.
10-5 Adding and Subtracting Rational Expressions
Lesson Quiz: Part II
6. Vong drove 98 miles on interstate highways and
80 miles on state roads. He drove 25% faster on
the interstate highways than on the state roads.
Let r represent his rate on the state roads in
miles per hour.
a. Write and simplify an expression that
represents the number of hours Vong drove in
terms of r.
b. Find Vong’s driving time if he averaged 55
miles per hour on the state roads.
about 2 h 53 min
10-6 Dividing Polynomials
Lesson Quiz: Part I
Add or Subtract. Simplify your answer.
1. (12x2 – 4x2 + 20x) ÷ 4x
2.
2x + 3
3.
x–2
4.
x+3
3x2 – x + 5
10-6 Dividing Polynomials
Lesson Quiz: Part II
Divide using long division.
5. (x2 + 4x + 7)  (x + 1)
6. (8x2 + 2x3 + 7)  (x + 3)
10-7 Solving Rational Equations
Lesson Quiz
Solve each equation. Check your answer.
1.
24
–4, 3
2.
3.
4. Solve
Check your answer.
–5
.
10-8 Applying Rational Equations
Lesson Quiz
1. Pipe A can fill a storage tank in 40 minutes.
Pipe B can fill the tank in 80 minutes. How long
does it take to fill the tank using both pipes at
the same time?
min, or 26 min 40 s
2. An 8 oz smoothie is made up of 50%
strawberries and 50% yogurt. How many
ounces of strawberries should be added to
make a smoothie that is 60% strawberries? 2 oz
3. Carlos bikes 3 mi/h faster than Tim. It takes
Tim 1 hour longer than Carlos to bike 36
miles. How long does it take Carlos to bike 36
miles? 3 h