End-of-Course Assessment to Prepare for the ADP Algebra 2 Test
This practice test is designed to help you prepare for the American Diploma Project (ADP) Algebra 2 Test.
Complete the following items without a calculator. For multiple choice items, write the letter of the correct response on your paper. For all other items, show or explain your work.
-
The graph of a quadratic function
f
(
x
)
f open x close is shown below.
Use the graph to solve
f
(
x
)
f open x close < 0.
-
−
1
<
x
<
3
negative 1 less than x less than 3
-
−
1
≤
x
≤
3
negative 1 less than or equal to x less than or equal to 3
-
x
<
−
1
or
x
>
3
x less than , minus 1 , or , x greater than 3
-
x
<
−
1
or
x
>
3
x less than , minus 1 , or , x greater than 3
- Newton's Law of Universal Gravitation is
F
=
G
m
1
m
2
r
2
.
f equals . fraction g , m sub 1 , m sub 2 , over r squared end fraction . . Solve this equation for r.
-
r
=
F
G
m
1
m
2
r equals . square root of fraction f , over g , m sub 1 , m sub 2 end fraction end root
-
r
=
G
m
1
m
2
F
r equals . square root of fraction g , m sub 1 , m sub 2 , over f end fraction end root
-
r
=
F
2
G
m
1
m
2
r equals . fraction f , over 2 g , m sub 1 , m sub 2 end fraction
-
r
=
G
m
1
m
2
2
F
r equals . fraction g , m sub 1 , m sub 2 , over 2 f end fraction
- Let
f
(
x
)
=
x
3
−
4
x
2
+
9
x
f open x close equals , x cubed , minus , 4 x squared , plus 9 x and let
g
(
x
)
=
6
x
3
+
x
2
−
5
x
−
g open x close equals , 6 x cubed , plus , x squared , minus 5 x minus 12. What is
f
(
x
)
−
g
(
x
)
?
f open x close minus g open x close question mark
-
−
5
x
3
−
5
x
2
+
14
x
+
12
negative 5 , x cubed , minus , 5 x squared , plus 14 x plus 12
-
−
5
x
3
−
3
x
2
+
4
x
−
12
negative 5 , x cubed , minus , 3 x squared , plus 4 x minus 12
-
7
x
3
−
3
x
2
+
4
x
−
12
7 x cubed , minus , 3 x squared , plus 4 x minus 12
-
−
5
x
4
−
5
x
3
+
14
x
2
+
12
x
negative 5 , x to the fourth , minus , 5 x cubed , plus , 14 x squared , plus 12 x
- Let
f
(
x
)
=
x
−
3
f open x close equals x minus 3 and let
g
(
x
)
=
2
x
2
−
6
.
g open x close equals , 2 x squared , minus 6 . What is
g
(
f
(
x
)
)
?
g open f open x close close question mark
-
2
x
2
−
9
2 x squared , minus 9
-
2
x
2
−
12
2 x squared , minus 12
-
2
x
2
−
12
x
+
2 x squared , minus 12 x plus 12
-
2
x
3
−
6
x
2
−
6
x
+
2 x cubed , minus , 6 x squared , minus 6 x plus 18
- Let
f
−
1
(
x
)
=
2
x
+
3
.
f super negative 1 end super , open x close equals 2 x plus 3 . What is the solution of
f
(
x
)
=
f
−
1
(
x
)
?
f open x close equals , f super negative 1 end super , open x close question mark
-
x
=
−
1
x equals negative 1 or
x
=
−
2
x equals negative 2
-
x
=
−
3
x equals negative 3
-
(
x
,
y
)
=
(
−
2
,
−
2
)
open x comma y close equals open negative 2 comma negative 2 close
-
(
x
,
y
)
=
(
−
2
,
−
3
)
open x comma y close equals open negative 2 comma negative 3 close
- Which is a simpler form of
2
3
−
2
?
fraction square root of 2 , over 3 minus square root of 2 end fraction . question mark
-
10
3
2
−
2
fraction square root of 10 , over 3 square root of 2 minus 2 end fraction
-
5
3
5
−
10
fraction 5 , over 3 square root of 5 minus 10 end fraction
-
3
5
−
10
7
fraction 3 square root of 5 minus 10 , over 7 end fraction
-
3
5
+
10
7
fraction 3 square root of 5 plus 10 , over 7 end fraction
- Suppose that
n
4
=
2
.
the fourth , root of n , , equals 2 . . What is
n
−
1
2
?
n super negative , 1 half end super . question mark
-
−
8
negative 8
-
−
4
negative 4
-
1
8
1 eighth
-
1
4
1 fourth
- What is the quotient
2
+
5
i
4
+
3
i
,
fraction 2 plus 5 i , over 4 plus 3 i end fraction . comma written in standard form?
-
1
2
+
5
3
i
1 half , plus , 5 thirds , i
-
8
25
−
12
25
i
8 twenty fifths , minus , 12 over 25 , i
-
−
7
7
+
26
7
i
negative , 7 sevenths , plus , 26 over 7 , i
-
23
25
+
14
25
i
23 over 25 , plus , 14 over 25 , i
-
Multiply
x
3
x
2
−
4
·
5
x
+
10
10
x
.
fraction x cubed , over x squared , minus 4 end fraction . middle dot . fraction 5 x plus 10 , over 10 x end fraction . .
-
5
x
4
fraction 5 x , over 4 end fraction
-
x
2
2
(
x
−
2
)
fraction x squared , over 2 . open , x minus 2 , close end fraction
-
x
2
(
x
+
2
)
2
(
x
2
−
4
)
fraction x squared . open , x plus 2 , close , over 2 . open . x squared , minus 4 . close end fraction
-
5
x
3
10
x
(
x
−
2
)
fraction 5 , x cubed , over 10 x . open , x minus 2 , close end fraction
- Which is a simpler form of the complex fraction
1
b
+
c
b
+
1
c
?
fraction 1 over b , plus c , over b plus , 1 over c end fraction . question mark
- 1
-
c
b
c over b
-
(
1
b
+
c
)
2
open , 1 over b , plus c close squared
-
(
1
+
c
)
(
b
+
1
)
open 1 plus c close open b plus 1 close
- What is the sum of the x-intercepts of the graph of the quadratic function
y
=
x
2
−
4
x
−
12
?
y equals , x squared , minus 4 x minus 12 question mark
- 6
- 4
-
−
1
negative 1
-
−
4
negative 4
