1.
Simplify (7
a
4
b
) (8
a
7
b
6
).
A.
15
a
11
b
7
B.
56
a
28
b
6
C.
15
a
28
b
6
D.
56
a
11
b
7
Hint
2.
Simplify (4
x
2
y
) (2
x
y
2
z
3
)
3
.
A.
32
x
6
y
6
z
9
B.
24
x
5
y
7
z
9
C.
32
x
5
y
7
z
9
D.
8
x
5
y
7
z
9
Hint
3.
Simplify
. Assume the denominator is not equal to zero.
A.
B.
C.
D.
Hint
4.
Arrange the terms of 4
x
2
y
3
– 2
x
4
y
+ 3
x
3
y
2
– 3 + 2
xy
so that the powers of
x
are in descending order.
A.
-3 - 2
x
4
y
+ 3
x
3
y
2
+ 4
x
2
y
3
+ 2
xy
B.
4
x
2
y
3
+ 3
x
3
y
2
- 2
x
4
y
+ 2
xy
– 3
C.
-3 + 2
xy
+ 4
x
2
y
3
+ 3
x
3
y
2
- 2
x
4
y
D.
– 2
x
4
y
+ 3
x
3
y
2
+ 4
x
2
y
3
+ 2
xy
– 3
Hint
5.
Find the difference (-3
x
3
– 7
x
2
+ 5
x
– 4) – (6
x
2
– 8).
A.
–3
x
3
– 13
x
2
+ 5
x
+ 4
B.
–3
x
3
– 13
x
2
+ 5
x
- 12
C.
–3
x
3
–
x
2
+ 5
x
- 12
D.
-11
x
8
+ 4
Hint
6.
Find the sum (4
xy
2
– 3
x
2
y
– 5
xy
– 6) + (-5
xy
2
– 2
xy
+ 3).
A.
-
xy
2
– 3
x
2
y
– 3
xy
– 3
B.
-
xy
2
– 3
x
2
y
– 7
xy
– 3
C.
4
xy
2
– 8
x
2
y
– 7
xy
– 3
D.
4
xy
2
– 7
xy
– 3
Hint
7.
Find –8
x
3
y
2
(3
xy
4
– 2
x
5
–
y
).
A.
–24
x
4
y
6
- 16
x
8
y
2
+ 8
x
3
y
3
B.
–5
x
4
y
6
- 10
x
8
y
2
- 9
x
3
y
3
C.
–24
x
4
y
6
+ 16
x
15
y
2
+ 8
x
3
y
3
D.
–24
x
4
y
6
+ 16
x
8
y
2
+ 8
x
3
y
3
Hint
8.
Find (2
y
2
+ 7
y
– 5)(3
y
2
– 5
y
+ 4).
A.
6
y
4
+ 11
y
3
– 42
y
2
+ 53
y
– 20
B.
5
y
2
+ 2
y
– 1
C.
6
y
4
+ 4
y
2
– 32
y
2
– 20
D.
6
y
4
– 35
y
2
– 20
Hint
9.
Find (
x
- 4)
2
.
A.
x
2
- 8
x
+ 16
B.
x
2
+ 16
C.
x
2
- 4
x
+ 16
D.
x
2
- 16
Hint
10.
Simplify
.
A.
x
3
y
B.
x
2
y
C.
x
3
y
2
D.
x
2
y
2
Hint
11.
Express 4.67 × 10
-7
in standard notation.
A.
0.0000000467
B.
0.00000467
C.
0.000000467
D.
46,700,000
Hint
12.
Express the result of
in
scientific
notation.
A.
343
B.
3.43 × 10
3
C.
3430
D.
3.43 × 10
2
Hint
13.
Write a polynomial to represent the area of a square with a side
x
minus the area of a triangle with a base 2
x
and a height of 5.
A.
4
x
B.
x
2
– 5
x
C.
x
2
– 10
x
D.
x
2
– 2
x
+ 5
Hint
14.
A cafeteria has two meal plans. One requires the worker to pay $20 for the card, and $1 each time
x
she uses it. The other plan requires the worker to pay $30 for the card, but only $0.50 each time
x
she uses it. After how many uses will the workers with different plans have spent the same amount of money?
A.
It will never happen.
B.
20 uses
C.
5 uses
D.
10 uses
Hint
15.
Find the product (2
x
- 3)(2
x
2
+ 5
x
- 1).
A.
4
x
3
+ 4
x
2
– 17
x
– 3
B.
4
x
3
+ 4
x
2
– 17
x
+ 3
C.
8
x
2
– 17
x
+ 3
D.
8
x
2
– 17
x
– 3
Hint
16.
Which of the following is a difference of two squares?
A.
x
2
+ 6x + 9
B.
x
2
– 8
x
– 16
C.
x
2
– 9
D.
x
2
+ 36
Hint