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Algebra Diagnostic Pre-Test
50 questions – 60 minutes
Multiple Choice
Use the answer “NOTA” (which stands for None Of The Above) if the answer is not listed
1
...


B) 196

B) 9

2 3

D) 225

E) 135

C) 4x4y6

E) NOTA

(3x – 2)(4x + 1) =
A)12x2 – 8x – 2

B) 12x2 + 5x – 2

2
D) 12x – 5x – 2

E) NOTA

C) x2 – 5x – 2

2 -3
(4xy ) =

A) – 64 x3y6
D) –

6
...


E) NOTA

(4x2y3)2 =
A) 8x4y5

4
...


C) 392

4
x y6
3

B)

1
4 x3 y 6

C)

1
64 x3 y 6

E) NOTA

(x – 4)(x + 4) =
2
A) x – 16

B) x2 + 16

D) x2 + 8x + 16

E) NOTA

C) x2 – 8x + 16

7
...
The total number of students in
that freshman class is 259
...


9
...


E) NOTA

(-5) + 9
(-9) + 5
9+5
5 + (-9) + 4
9 – (-5)

Solve the system of equations: 3x + 4y = 11
x – 2y = – 3
A) x = 1
y=2
3
B) x = -1 y =
4
C) x = 2
y=–3
D) x = 1

y=–2

E) NOTA
11
...


Solve: 2x2 + 5x – 3 = 0
A) 3, 2

13
...


Solve:

D) 3,

7
13

C) –2

D)

C) 99

D) 96

B) 11

1
2

E) NOTA

E) – 1

E) NOTA

Solve: 3x + 17 – 5x = 12 – (6x + 3)
B) 4

C) 0

D) – 4

E) NOTA

You and three friends are eating a pizza with 12 pieces
...
Let x represent the number
of pieces each person eats
...


3
,1
2

1
y + 28 = −5
3

A)2

16
...


1
2

B) –3,

1
x = 12
4

B)

1
x = 12
3

C) 4x = 12

E) NOTA

2
(3x + 4) =

A) 9x2 + 12x + 16

B) 9x2 + 16

D)

E) 25x2

9x + 16

C) 9x2 + 24x + 16

18
...


E) NOTA

One of the solutions of the equation:
B) −

A) 0

5
C) − , 4, 0
3

11
3

C) 4

3x2 + 11x = 4
D)

1
3

is
E) NOTA

20
...


C) 9c7d22

E) 27c7d22

Simplify: (4c4 + 1) – (7c3 – 3) + (2c4 + 5c3)
A) 6c4 + 2c3 – 4

B) 6c4 – 2c3 + 4

4
3
D) 2c – 2c – 2

E) 4c + 4

C) 6c4 – 2c3 – 2

22
...
The answer
has to be between which two numbers?
A)
B)
C)
D)
E)
23
...
27

B)

1
4

C)

3
8

D)

2
11

E) 11%

24
...


B) −18

C) −12

D) 12

E) 18

Which is closest to the distance between A and B on the number
line?
A

B
-4

A) -9

0

B) -5

C) 13

4

D) 5

E) 12

26
...
Then 2 ~ 3 =
A) 108

B) 27

C) 99

D) 117

E) 89

27
...
Which of the following best describes the circled part of the
statement?
7x + 9 = 40
A)
B)
C)
D)
E)

Coefficient
Variable
Term
Expression
Solution

29
...
Solve for r:
A)

D)

31
...
1 x 10

33
...


A = p + prt

Factor:

B) 21 x 1020
7

C) 2
...
Find a possible middle term to make this polynomial factorable:
2
x + ______ + 20

A) 12x

35
...


37
...
Find the x-coordinate of the system:
3x + 3y = 4
x – 3y = 1
A)

39
...
Find the slope and y-intercept of the line whose equation is
3
y =− x+4
2
A) slope = 2, y-int =

3
2

C) slope = 2, y-int = −3

E) slope =

3
, y-int = −2
2

3
B) slope = − , y-int = 4
2

D) slope = −2, y-int =

3
2

41
...
Solve:

C) y = − 4x − 24

4x + 5 ≤ 3 + 6x

A) x ≤ – 4

B) x ≥ 1

D) x ≥ – 4

E) x ≥ 4

C) x ≤ 4

43
...

The solutions to x2 + 2x − 12 = − 12 are:
A) 0, − 2

B) −4, 6

C) −6, 4

D) 12, 2

E) NOTA

45
...
Which pair of lines represent graphs that are perpendicular?
A) y = −3x + 7
y = –3x + 2

B) y = 5x + 5
y = 10x + 5

D) y = 9
x=5

E) y = x
y=3

C) 2y = 4x − 16
y = 2x – 8

47
...
Which equation is graphed to the right?
A) x + y = 2

B) 2x – y = 3

D) 2 x − y = 5

E) 3x + y = 2

C) 2x + y = 3

49
...
A boy is mowing a rectangular lawn 40 ft
...
wide
...
long and 15 ft
...
What fractional part of the lawn remains uncut?
A)

1
4

B)

2
5

C)

3
125

D)

3
4

E) NOTA

Answers for
Algebra
Diagnostic
Pretest

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25

C
C
E
D
C
A
B
B
B
A
C
B
A
E
E
C
C
C
D
E
B
B
E
B
C

26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50

C
E
D
A
C
A
E
E
A
B
E
E
D
D
B
D
B
B
A
E
D
D
B
C
A



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