Chapter 4. Exponents & Radicals
Try Your Best FIRST, Then Look At The Explanation
AAT Section
11
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
28 ____.
If
_____________________________
x−1
x2 −1
__
= 5, what is the value of x?
𝟏𝟎
𝟗
28 ____.
If
x+1
x2 −1
_____________________________
= 9, what is the value of x?
−
28 ____.
If
x+1
x2 −1
𝟒
𝟓
_____________________________
= 12, what is the value of x?
𝟏𝟑
𝟏𝟐
12
__
__
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
38 ____.
If
x
y
_____________________________
= 12 and
3𝑥
𝑝𝑦
__
= 360, what is the value of p?
𝟏
𝟏𝟎
38 ____.
If
x
y
_____________________________
= 4 and
5𝑥
𝑝𝑦
__
= 100, what is the value of p?
𝟏
𝟓
38 ____.
If
x
y
_____________________________
= 16 and
8𝑥
𝑝𝑦
__
= 8, what is the value of p?
𝟒
13
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
38 ____.
_____________________________
2
2
3x (7 + 11x) = 𝑔𝑥 + 𝑗𝑥
__
3
In the above equation, g and j are constant values.
Knowing that the equation is true for all values of input
values of x, what is the value of a - b?
-12
38 ____.
_____________________________
__
5 (8x 2 + 2x) = 𝑧𝑥 2 + 𝑣𝑥 3
Variables z and v are constants in the above model.
Keeping in mind that the equation is true for all values
of x, what is the value of a * b?
400
38 ____.
_____________________________
__
3x (10 + 5𝑥 2 ) = 𝑎𝑥 3 + 𝑏𝑥 2
In the equation shown above, a and b are constants.
What is the value of a + b, considering all values for x
keep the equation true?
45
14
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
29 ____.
_____________________________
__
2
x −3
x − √3
Which of the following values is equal to the
expression above if x ≠ √3?
A) x-2
B) x+2
C) x-√3
D) x+√𝟑
29 ____.
_____________________________
__
2
x −5
x − √5
Which of the following values is equal to the
expression above if x ≠ √5?
A) x-3
B) x+3
C) x-√5
D) x+√𝟓
29 ____.
_____________________________
__
2
x −7
x − √7
Which of the following values is equal to the
expression above if x ≠ √7?
A)
B)
C)
D)
x-5
x+5
x-√7
x+√𝟕
15
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
29 ____.
_____________________________
__
2
𝑥 + 8𝑥 + 17
The above expression is rewritten in the form 𝑔2 + ℎ2 ,
where h is an expression and g is a constant value.
Which of the following is the correct expression for h
and value for g?
A) h = x + 4, g = 1
B) h = x + 4, g = 2
C) h = x + 8, g = 2
D) h = x + 4, g = 1
29 ____.
_____________________________
__
The trinomial 𝑥 2 + 10𝑥 + 29 can be expressed in the
format 𝑓 2 + 𝑧 2 , where f is an expression and z is a
constant value. Which of the following gives the correct
version of each variable?
A) f = x + 5, z = 2
B) f = x + 5, z = 4
C) f = x + 10, z = 4
D) f = x + 10, z = 2
29 ____.
_____________________________
__
2
𝑥 + 14𝑥 + 65
The above polynomial can be rewritten in the format
a2 + 𝑏 2, where a is an expression and b is a constant
value. Which of the following is the correct values for
the variables?
A)
B)
C)
D)
16
a = x + 7, b = 2
a = x + 7, b = 4
a = x + 9, b = 4
a = x + 9, b = 2
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
29 ____.
_____________________________
__
3x – 6y = 6
2x + 12y = -12
The above system of equation’s solution is (x, y). What
is the value of the expression 4x – y?
A)
B)
C)
D)
-1
0
1
6
29 ____.
_____________________________
__
5x – 8y = -6
4x + 8y = 24
The above system of equation’s solution is (x, y). What
is the value of the expression 3x + 2y?
A)
B)
C)
D)
-10
-6
6
10
29 ____.
_____________________________
__
5x – 8y = -6
4x + 8y = 24
The above system of equation’s solution is (x, y). What
is the value of the expression 3x + 2y?
E)
F)
G)
H)
-10
-6
6
10
17
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
29 ____.
_____________________________
R=1
𝑎
__
1
+
1
b
An energy consulting group uses the above equation to
calculate the total resistance X, for a schematic with
parallel resisters with separate resistances a and b,
where a ≠0 and b ≠0. Which expression accurately
values b in terms of a and R?
A)
𝑎𝑋
𝑎−𝑋
B)
1− 𝑎𝑋
𝑋
C)
𝑎− 𝑋
𝑎𝑋
D) X - a
29 ____.
_____________________________
__
R=𝑥+𝑦+𝑧
A student research team uses the above equation to
determine the total resistance R, for a circuit with
series resisters with separate resistances x, y, and z
where x ≠0, y ≠0, and z ≠ 0. Which expression
accurately depicts y in terms of x, z, and R?
A) R – x - z
B)
x−z
𝑅
C)
𝑥+ 𝑧
𝑅
D) R – x + z
18
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
3 ____.
_____________________________
__
The function g is defined by g(x) = (𝑥 + 3)2 . If g(x+a)
= 𝑥 2 − 2x + 1, where a is a constant, what is the value
of a?
A) -4
B) -2
C) 2
D) 4
3 ____.
_____________________________
__
The function f is defined by f(x) = (𝑥 + 5)2 . If g(x+a) =
𝑥 2 + 14x + 49, where a is a constant, what is the value
of a?
A) -9
B) -2
C) 2
D) 9
3 ____.
_____________________________
__
The function h is defined by h(x) = (𝑥 + 4)2 . If h(x+a)
= 𝑥 2 + 16x + 64, where a is a constant, what is the
value of a?
A) -4
B) -2
C) 2
D) 4
19
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
29 ____.
_____________________________
__
10
4
32
+ =
𝑥+1 𝑥
𝑥(𝑥 + 1)
What is the value of x for the above equation?
A)
B)
C)
D)
-2
-1
1
2
29 ____.
_____________________________
__
9
3
1
+ =
𝑥− 1 𝑥
𝑥(𝑥 − 1)
What is the value of x for the above equation?
A) -1
1
B) –
3
C)
D) 1
𝟏
E)
𝟑
29 ____.
_____________________________
__
9
3
1
+ =
𝑥− 1 𝑥
𝑥(𝑥 − 1)
What is the value of x for the above equation?
A) -1
𝟏
B) - 𝟑
C) 1
1
D) 3
20
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
29 ____.
_____________________________
__
4𝑥 3 + 𝑏𝑥 2 − 64𝑥 − 16𝑏
In the above expression, b is a constant value. Which of
the following expressions is a factor of the above
polynomial?
A)
B)
C)
D)
x+4
x+b
4𝑥 3 + b
𝑥 2 + 16
29 ____.
_____________________________
__
2𝑥 3 + 𝑏𝑥 2 − 8𝑥 − 4𝑏
In the above expression, b is a constant value. Which of
the following expressions is a factor of the above
polynomial?
A)
B)
C)
D)
x+2
x+b
2𝑥 3 + b
𝑥2 + 4
29 ____.
_____________________________
__
5𝑥 3 + 𝑏𝑥 2 − 125𝑥 − 25𝑏
In the above expression, b is a constant value. Which of
the following expressions is a factor of the above
polynomial?
A)
B)
C)
D)
x+5
x+b
5𝑥 3 + b
𝑥2 + 5
21
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
3 ____.
_____________________________
__
If 8(x + 4) = 7(x + 7) + 20, what is the value of x + 4?
A) -9
B) 11
C) 37
D) 41
3 ____.
_____________________________
__
If 11(x + 2) = 9(x + 2) + 16, what is the value of x +
2?
A) -6
B) 6
C) 8
D) 12
3 ____.
_____________________________
__
If 10(x + 3) = 9(x + 3) + 13, what is the value of x +
3?
A) -13
B) -3
C) 3
D) 13
22
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
14 ____.
_____________________________
__
Which of the following expressions is equivalent to
√𝑥 2 + 10𝑥 + 25 for all positive values of x?
A) x + 5
B) 11x + 9
C) x + √10𝑥 + 5
D) x + √5𝑥 + 12.5
14 ____.
_____________________________
__
Which of the following expressions is equivalent to
√𝑥 2 + 8𝑥 + 16 for all positive values of x?
A) x + 4
B) 9x + 16
C) x + √8𝑥 + 4
D) x + √4𝑥 + 8
14 ____.
_____________________________
__
Which of the following expressions is equivalent to
√𝑥 2 − 6𝑥 + 9 for all positive values of x?
A) x - 3
B) 6x + 9
C) x + √−6𝑥 + 3
D) x + √−3𝑥 + 3
23
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
3 ____.
_____________________________
__
Which of the following expressions is NOT a factor of
𝑥 4 − 17𝑥 2 + 16?
A) x -2
B) x – 4
C) 𝑥 2 −16
D) 𝑥 2 −1
3 ____.
_____________________________
__
Which of the following expressions is NOT a factor of
𝑥 4 − 3𝑥 2 + 2?
A) x -1
B) x – 4
C) 𝑥 2 −2
D) 𝑥 2 −1
3 ____.
_____________________________
__
Which of the following expressions is NOT a factor of
𝑥 4 − 6𝑥 2 + 8?
A) x -1
B) x – 4
C) 𝒙𝟐 −2
D) 𝑥 2 −1
24
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
13 ____.
If
_____________________________
4
__
= 2, what is the value of x - 1?
𝑥+1
A) 0
B) 0.5
C) 1
D) 3
13 ____.
If
9
𝑥+1
_____________________________
__
= 3, what is the value of x + 1?
A) 0.5
B) 2
C) 3
D) 4
13 ____.
If
8
𝑥−1
_____________________________
__
= 5, what is the value of x + 1?
A) 1.6
B) 2.6
C) 3.6
D) 4.6
25
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
12 ____.
_____________________________
__
𝑎
𝑏
3
4
𝑎
𝑏
5
2
𝑎
𝑏
2
6
Which of the following expressions is equal to ( + )2
A)
B)
C)
D)
𝒂𝟐
𝟗
𝑎2
3
𝑎2
9
𝑎2
3
+
+
+
+
12 ____.
𝒂𝒃
𝟔
𝑎𝑏
12
+
+
𝒃𝟐
𝟏𝟔
𝑏2
4
𝑏2
16
𝑏2
4
_____________________________
__
Which of the following expressions is equal to ( + )2
A)
B)
C)
D)
𝑎2
5
𝒂𝟐
𝟐𝟓
𝑎2
25
𝑎2
5
+
+
+
+
12 ____.
𝑎𝑏
5
𝒂𝒃
𝟏𝟎
+
+
𝑏2
4
𝒃𝟐
𝟒
𝑏2
4
𝑏2
2
_____________________________
__
Which of the following expressions is equal to ( + )2
A)
B)
C)
D)
26
𝑎2
2
𝒂𝟐
𝟒
𝑎2
4
𝑎2
2
+
+
+
+
𝑎𝑏
2
𝒂𝒃
𝟏𝟐
𝑏2
36
𝑏2
6
+
+
𝑏2
36
𝒃𝟐
𝟑𝟔
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
12 ____.
_____________________________
__
Einstein’s theory of relativity depicts the relationship
between time m measured by a stationary clock and
the time t measured by a clock moving at speed s by
the formula t = m√1 − 𝑠 2 . The speed s is measured as
a proportion of the speed of light. Which of the
following equations represents the speed in terms of
time t and time m?
A) 𝑠 = √1 + 𝑚2 𝑡 2
B) 𝑠 = √1 − 𝑚2 𝑡 2
C) 𝒔 = √𝟏 −
D) 𝑠 = √1 +
12 ____.
𝒕𝟐
𝒎𝟐
𝑡2
𝑚2
_____________________________
__
Einstein’s theory of relativity depicts the relationship
between time m measured by a stationary clock and
the time t measured by a clock moving at speed s by
the formula m = s√𝑡 2 + 1. The speed s is measured as
a proportion of the speed of light. Which of the
following equations represents the time t in terms of
time m and speed s?
A) 𝑡 = √𝑚2 𝑡 2 + 1
B) 𝑡 = √ 𝑚2 𝑡 2 − 1
𝒎𝟐
C) 𝒕 = √
𝒔𝟐
𝑚2
D) 𝑡 = √
𝑠2
−𝟏
+1
27
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
29 ____.
_____________________________
𝑎=
__
3
+7
𝑥−4
The above equation models the relationship between
the numbers a and x, where x is not equal to 0 and a >
7. Which of the following appropriately depicts x in
terms of a?
A) 𝑛 =
B) 𝑛 =
C) 𝒏 =
D) 𝑛 =
29 ____.
𝑎
3
𝑎
3
−7
+7
𝟑
𝒂−𝟕
3
𝑎+7
+4
-4
_____________________________
𝑎=
__
2𝑏 + 5
+1
4
The above equation models the relationship between
the numbers a and b. Which of the following correctly
depicts b in terms of a?
𝟗
A) 𝒃 = 𝟐𝒂 −
B) 𝑏 = 4𝑎 +
𝟐
9
2
C) 𝑏 = 4𝑎 – 9
D) 𝑏 = 2𝑎 − 9
28
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
29 ____.
_____________________________
__
𝑥 2 − 𝑥 − 12 𝑥 + 4
∗
; 𝑥 ≠ −4, 0, 4
𝑥 2 − 16
𝑥
Which of the following expressions is equal to the one
above?
A)
B)
C)
D)
𝑥−3
𝑥
𝒙+𝟑
𝒙
𝑥 2 −4
𝑥 2 −2𝑥−15
𝑥 2 −3
𝑥 2 −4𝑥−16
29 ____.
_____________________________
__
𝑥 2 − 4𝑥 − 12 𝑥 − 2
∗
; 𝑥 ≠ −2, 0, 2
𝑥2 − 4
𝑥
Which of the following expressions is equal to the one
above?
A)
B)
C)
D)
𝒙−𝟔
𝒙
𝑥+6
𝑥
𝑥 2 −4
𝑥 2 −2𝑥−15
𝑥 2 −3
𝑥 2 −4𝑥−16
29
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
3 ____.
_____________________________
__
Which of the following expressions is a factor of 12 xy 3x +8y -2
A) 3x -2
B) 3x +2
C) 4y +2
D) 4y -2
3 ____.
_____________________________
__
Which of the following expressions is a factor of 8 xy 20x +6y -15
A) 4x -3
B) 4x +3
C) 2y +2
D) 2y -2
3 ____.
_____________________________
__
Which of the following expressions is a factor of 10 xy
+30x -8y -24
A) 5x + 4
B) 5x – 4
C) 2y – 6
D) 2y - 4
30
Try Your Best FIRST, Then Look At The Explanation
Chapter 4. Exponents & Radicals
29 ____.
_____________________________
__
𝑥 2 − 12𝑥 − 4 = −36
For the above equation, t and u are the solutions. If u >
t, what is the value of u-t ?
A) 2
B) 4
C) 6
D) 8
29 ____.
_____________________________
__
𝑥 2 − 9𝑥 − 8 = −28
For the above equation, t and u are the solutions. If u >
t, what is the value of u+t ?
A)
B)
C)
D)
2
5
9
11
29 ____.
_____________________________
__
𝑥 2 − 8𝑥 − 18 = −30
For the above equation, t and u are the solutions. If u >
t, what is the value of u+t ?
A) 2
B) 6
C) 8
D) 10
31