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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. Evaluate m 7 + 3mnwhenm= 8 andn= 14
A) 84 B) 196 C) 392 D) 168 E) NOTA
- Simplify: 675 ÷ (6 + 9 ÷ 3)
A) 15 B) 9 C) 75 D) 225 E) 135
- (4x
2
y
3
2
A) 8x
4
y
5
B) 16x
4
y
5
C) 4x
4
y
6
D) 16x
2
y
3
E) NOTA
- (3x – 2)(4x + 1) =
A)12x
2
2
2
D) 12x
2
- (4xy
2
A) – 64
x
3
y
6
B)
3 6
x y
C)
3 6
x y
D) –
3 6
x y
E) NOTA
- (x – 4)(x + 4) =
A) x
2
2
2
D) x
2
- Find the equation that best represents the following word problem:
In a certain freshman class, the number of girls is 83 less than
twice the number of boys (b). The total number of students in
that freshman class is 259. How many boys and girls are in that
class?
A) b + 2b = 259 - 83 B) b + 2b – 83 = 259
C) b + 83 – 2b = 259 D) b + 2b = 259
E) NOTA
- Factor: 6x
2
A) (6x + 5)(x – 1) B) (3x + 1)(2x – 5)
C) (6x – 1)(x + 5) D) (2x – 1)(3x + 5) E) NOTA
- Which one of the following equals a negative number?
A) (-5) + 9
B) (-9) + 5
C) 9 + 5
D) 5 + (-9) + 4
E) 9 – (-5)
- Solve the system of equations:3x + 4y = 11
x – 2y = – 3
A) x = 1 y = 2
B) x = -1 y =
C) x = 2 y = – 3
D) x = 1 y = – 2
E) NOTA
- Factor: 25x
2
2
A) (5x – 4y)
2
B) 5 (5x – 4y) C) (5x + 4y)(5x – 4y)
D) (5x + 2y)(5x – 8y) E) NOTA
- Solve: 3x (x – 4)(3x + 5) = 0
A) 4,
− B) – 4,
− , 3, 0 C)
D) 4, –5, 0 E) NOTA
- One of the solutions of the equation: 3x
2
A) 0 B)
− C) 4 D)
E) NOTA
- Simplify: (3cd
6
3
(cd)
4
A) 27c
7
d
10
B) 27c
7
d
13
C) 9c
7
d
22
D) 27c
12
d
72
E) 27c
7
d
22
- Simplify: (4c
4
3
4
3
A) 6c
4
3
4
3
4
3
D) 2c
4
3
- The number ten is raised to a power between 0 and 1. The answer
has to be between which two numbers?
A) 0 and 1
B) 1 and 10
C) 10 and 100 but not 5
D) 0 and 100 but not 50
E) – 10 and 0
- Which of the following is the least?
A) .27 B)
C)
D)
E) 11%
If
x
= 2 and
y
=−3, then−
x y
A) − 36 B)− 18 C)− 12 D) 12 E) 18
- Which is closest to the distance between A and B on the number
line?
A) -9 B) -5 C) 13 D) 5 E) 12
Define p ~ q by the equation p ~ q = p
2
q
3
A) 108 B) 27 C) 99 D) 117 E) 89
- If 7x + 4 = -19 + 5x, then 2x – 14 equals
A) 23 B) -23 C) -3 D) 16 E) NOTA
- Which of the following best describes the circled part of the
statement?
7x + 9 = 40
A) Coefficient
B) Variable
C) Term
D) Expression
E) Solution
- Solve for x:
5x – 10 = 2 – 2x + 10(x – 3)
A) 6 B) 3 C) - 3 D) - 14 E) NOTA
A B
-4 0 4
- (y² + 2y – 3) – (4y² – 5y – 2) =
A) – 3y² – 9y + 5 B) – 3y² – 9y + 1 C) – 3y² – y + 5
D) – 3y² + y – 5 E) – 3y² + 7y – 1
The solutions of the equation 2
x
2
x
− 8 = 0 are:
A) − 4 and 1 B) 2, 4 and− 1 C) − 2 and
D)
and 2 E) − 1 and 4
- Find the x-coordinate of the system:
3x + 3y = 4
x – 3y = 1
A)
B)
C) 1 D)
E)
- Find the slope of the line that passes through (4, 7) and (1, 3)
A)
B)
C)
D)
E) 2
- Find the slope and y-intercept of the line whose equation is
y =− x +
A) slope = 2, y-int =
B) slope =
− , y-int = 4
C) slope = 2, y-int =− 3 D) slope =−2, y-int =
E) slope =
, y-int =− 2
Find the equation of the line containing the point (−3, 5) and
having slope: 4
A) y = 4x− 7 B) y = 4x C) y =− 4x− 24
D) y = 4x + 17 E) NOTA
Solve: 4
x
A) x≤ – 4 B) x≥ 1 C) x≤ 4
D) x≥ – 4 E) x≥ 4
- Which of the following graphs represents the solution of
2 x 3 1
A)
B)
C)
D)
E)
The solutions to x
2
A) 0,− 2 B)−4, 6 C)−6, 4 D) 12, 2 E) NOTA
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
-5 -4 -3 -2 -1 0 1 2 3 4 5
1 C 26 C
2 C 27 E
3 E 28 D
4 D 29 A
5 C 30 C
6 A 31 A
7 B 32 E
8 B 33 E
9 B 34 A
10 A 35 B
11 C 36 E
12 B 37 E
13 A 38 D
14 E 39 D
15 E 40 B
16 C 41 D
17 C 42 B
18 C 43 B
19 D 44 A
20 E 45 E
21 B 46 D
22 B 47 D
23 E 48 B
24 B 49 C
25 C 50 A
Answers for
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