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Mastery
Worksheets
MAT 1033
Test 4
 Rational Equations
 Variation
 Rational Exponents
 Rationalizing the Denominator
Mastery
Worksheet
MAT 1033
MY NAME IS:
Rational Equations
Test 3
Worksheet 14
Practice Session #
Date:
/ /
To determine which values cannot be a solution to a rational equation set the denominator equal to zero
and solve the equation.
Let’s get to work…
Determine the values that make the rational expression undefined.
1
2
x9
4 x
To solve a rational equation without factoring:
1.
2.
3.
x 2  4 x  45
x2  9
Identify the LCD of the equation.
Multiply both sides of the equation by the LCD.
Solve and check solution(s).
Let’s get to work…
Solve.
3
6
8
4

x5 x5 7
4
40
42
1 
x2
x2
1
Test 3 Rational Equations
Worksheet 14
To solve a rational equation with factoring:
1.
2.
3.
4.
Factor the denominator of all rational expressions.
Identify the LCD of the equation.
Multiply both sides of the equation by LCD.
Solve and Check solution(s).
Let’s get to work…
Solve.
5
6
x
8 x  28
x 3
 2

x  4 x  7 x  12 x  6
x2
x 3
2x  3
 2
 2
2
x  16 x  3x  4 x  5 x  4
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Mastery
Worksheet
MAT 1033
MY NAME IS:
Variation
Test 3
Worksheet 16
Direct Variation
Practice Session #
y  kx is equivalent to the statements
Date:
/ /
y varies directly as x.
y is directly proportional to x.
Let’s get to work…
Find the constant of variation and write the equation of variation.
1
2
The variable y varies directly as x and y = 20 when x = 80.
Suppose that y is directly proportional to x and y = 15 when x = 3.
Inverse Variation
y
k
is equivalent to the statements
x
y varies inversely as x.
y is inversely proportional to x.
Find the constant of variation and write the equation of variation.
3
4
Suppose that y is inversely proportional to x and y = 0.5 when x = 3.8
The variable z varies inversely as t and z = 2.3 when t = 72.
1
Test 3 Variation
Worksheet 16
5
6
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The number of patients Dr. Wong can see varies directly as the time it takes her to see them. If she
can see 11 patients in 3 hours, how long would it take her to see 66 patients?
The speed of a vehicle varies inversely as the time it takes to travel a fixed distance. If a vehicle
travels a fixed distance at 20 miles per hour in 60 minutes, how fast must it travel to cover the same
distance in 25 minutes?
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Mastery
Worksheet
MAT 1033
MY NAME IS:
Rational Exponents
Test 4
Worksheet 17
Definition of x m / n :
Practice Session #
x m/ n  n x m or
 x
n
/ /
Date:
m
m, n positive integers and share no common factors
Let’s get to work…
Evaluate.
1
2
271/3
Properties of Exponents:
5
8
6
 4x 
6 1/2
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9
 16 
1/4
xA
 x A B
B
x
x A x B  x A B
x3/4 x 2/3
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3
161/4
x 1/4 x3/4
x1/8 y 2/3
x1/4
4
x 
A B
 64 
2/3
 x AB
7
x1/4 x 1/3
x 2/3
10
6x 3/4
x 1/4
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MAT 1033
Mastery
Worksheet
MY NAME IS:
Test 4
Worksheet 18
Practice Session #
For x and y real numbers and
n
n
x and
Date:
/ /
y real numbers : n xy  n x  n y
Let’s get to work…
Simplify.
1
4
6
8
10
4×3
3
27×8
2 27  5 75
10 40  5 50  3 90
12 50  3 2
2
3
54×3
5
7
9
11
3
20×3 y 5
12 x 3
3x
5 3 16  18 3 2
x 20 x  4 45×3
3 3 4 x  2 3 2 x2
1
Worksheet 18
12
14
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3 2 12  10 10

5 8

5 8
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13

2
7 5 3

7 4 3

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MAT 1033
Mastery
Worksheet
MY NAME IS:
Rationalizing the Denominator
Test 4
Worksheet 19
Practice Session #
For x and y real numbers and
n
x and
Date:
n
y real numbers:
n
x

y
n
n
/ /
x
y
Let’s get to work…
Rationalize the denominator and simplify.
1
5
2x
4
14
3 5
6
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2
3
4
3
2x
2
5
8
3xy 2
8
3 1
x3
x 3
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