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Mastery
Worksheets
MAT 1033
Test 4
Rational Equations
Variation
Rational Exponents
Simplifying Radical Expressions
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
x9
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
x5 x5 7
4
40
42
1
x2
x2
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
x2
x 3
2x 3
2
2
2
x 16 x 3x 4 x 5 x 4
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Mastery
Worksheet
MAT 1033
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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
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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
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Simplifying Radical Expressions
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
Test 3 Simplifying Radical Expressions
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
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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
x3
x 3
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1
…
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