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Mastery
Worksheets
MAT 1033
Test 5
 Radical Equations
 Square Root Property and the Definition of i
 Completing the Square
 Quadratic Formula
MAT 1033
Mastery
Worksheet
MY NAME IS:
Radical Equations
Test 4
Worksheet 20
Practice Session #
/ /
Date:
Steps for solving a radical equation:
Step 1
Isolate the radical (i.e. get one radical alone on one side of the equation).
Step 2
Raise both sides of the equation to a power equal to the index on the radical.
Step 3
Solve the resulting equation. If the equation still has a radical, repeat steps 1 and 2.
Step 4
CHECK all possible solutions in the original equation
Let’s get to work…
Solve the radical equation with one radical and check your answer.
1
3
x  4  10
3
x 2  11  3
CHECK:
2
x  4  10
CHECK:
CHECK:
1
Test 4 Radical Equations
Worksheet 20
4
CHECK:
3x  1  x  3
Solve a radical equation with two radicals.
5
6
How do I feel?
x  8  3x
CHECK:
x6  x2 4
CHECK:
 Awesome!
I Aced it!
 I need help with…
Easy
Medium
Hard
2
MAT 1033
Mastery
Worksheet
MY NAME IS:
Square Root Property and the Definition of i
Test 4
Worksheet 21
Practice Session #
/ /
Date:
Square Root Property: For any real number, k, if 𝑥 2 = 𝑘, then 𝑥 = √𝑘 or 𝑥 = −√𝑘.
The solution may also be written as ±√𝑘, reads “plus or minus the square root of k.”
i  1
Definition of i:
From the definition of i, it follows that i 2  1
Let’s get to work…
Solve the quadratic equations by using the square root property.
1
4
x 2  25
9n2  81
How do I feel?
 Awesome!
I Aced it!
2
5
3
k 2  11
 3x  2 
2
5  0
6
16v 2  81
t  7
2
 14
 I need help with…
Easy
Medium
Hard
1
MAT 1033
Mastery
Worksheet
MY NAME IS:
Completing the Square
Test 4
Worksheet 22
Practice Session #
Date:
/ /
Solve ax2 + bx + c = 0 by Completing the Square
Completing the square:
1.
2.
3.
4.
5.
The Leading coefficient on x 2 must be 1.
Move Variables to the left, constant to the right.
Take half the coefficient of the x term, square it, and add it to both sides.
Rewrite the polynomial on the left as (
) 2.
Solve using the square root property.
Let’s get to work…
Find the value of a such that the expression is a perfect square trinomial. Factor the trinomial.
1
2
x2  8x  a
x2  7 x  a
Solve by completing the square.
3
5
4
x2  6 x  1  0
x2  2 x  2  0
x2  16 x  3  0
How do I feel?
 Awesome!
I Aced it!
 I need help with…
Easy
Medium
Hard
1
Mastery
Worksheet
MAT 1033
MY NAME IS:
Quadratic Formula
Test 4
Worksheet 23
Practice Session #
Date:
If ax 2  bx  c  0 (a ≠ 0) then x 
/ /
b  b 2  4ac
2a
Let’s get to work…
Solve by using the quadratic formula.
1
3
2
3x 2  2 x  8  0
4 x2  5x 1  0
x2  10 x  29  0
How do I feel?
 Awesome!
I Aced it!
 I need help with…
Easy
Medium
Hard
1

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