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MAT0056
Name:___________________________
PRACTICE FINAL
Solve each equation.
Multiply.
1.
7(2 x  3)  6 x  1  7 x
10. (4x + 3) (2x − 5)
2.
3
x  2  1  3x
7
11. (5x − 3)2
12. (4x + 9y) (4x − 9y)
Simplify each expression.
3.
3 5 0
4 2
4.
( x y z )( x y )
5.
(a 7b2c0 )3
6.
7.
Divide.
(2r 3 s 2t )(5st 6 )
x2 y6 z3
x11 yz 4
13.
18 x3 y  27 x 2 y 2  36 xy 3
9 xy
14.
16a 4b3  12a3b2  8a 2b
4a 2 b
Factor out the GCF (greatest common factor).
15. 5x2y3 − 15x3y + 10xy2
Convert each number as indicated.
a)
Write in scientific notation: 207,000
b)
Write in standard form: 4.2 × 10−4
16. 16 x5 y 2  8x4 y 2  4 x3 y 2
Factor by grouping.
8.
Evaluate the polynomial for the given values
of x and y.
x2 − 2xy + 3y2; x = −2 and y = −1
17. 9y − 3x + 3y2 − xy
18. ax − a + bx − b
Factor each expression completely.
Subtract.
9.
2
2
(x + 2x − 5) − (6x − 4x − 1)
19. 64a4 − 9b2
20. 25x2 − 16y2
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MAT0056 – Practice Final
Solve each equation.
Multiply. Then simplify.
21. 3y2 − 4y − 15 = 0
28.

3 2 3  21

22. 4a2  9a  5  0
29. Find the x- and y-intercepts of the given
lines.
Simplify each expression.
23.
24.
2 x2  7 x  4
x 2  16
x2  4x  3
x2  1
a)
2x − 5y = 10
b)
3x + 6y = −18
Graph each linear equation.
25. Simplify. Assume each variable represents a
non-negative number.
30. y = −4x − 5
6
5
4
3
2
1
6
a)
60a
b)
144 x7 y 4
-6 -5 -4 -3 -2 -1
Simplify. Then add or subtract.
26.
3  2 75  27
-1
-2
-3
-4
-5
-6
y
x
1 2 3 4 5 6
27. 4 5  6 45  80
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MAT0056 – Practice Final
ANSWER KEY
1.
2.
3.
4
3

7
6


10
r 3 st 5
20. (5x + 4y) (5x − 4y)
5
21. y   , y  3
3
5
22. a  , a  1
4
23.
2x  1
x4
24.
x3
x 1
7
4.
y
x
5.
b6
a 21
6.
y5
x9 z
7.
25. a) 2a3 15
b) 12 x3 y 2 x
a) 2.07 × 105
26. 12 3
b) 0.00042
27. 10 5
8.
3
9.
−5x2 + 6x − 4
28. 6  3 7
10. 8x2 − 14x − 15
29. a) (5, 0) and (0, −2)
11. 25x2 − 30x + 9
b) (−6, 0) and (0−3)
12. 16x2 – 81y2
30. y = −4x − 5
13. 2x2 − 3xy – 4y2
6
5
4
3
2
1
14. 4a2b2 + 3ab + 2
15. 5xy (xy2 − 3x2 + 2y)
16. 4x3y2 (4x2 − 2x + 1)
-6 -5 -4 -3 -2 -1-1
-2
-3
-4
-5
-6
17. (3 + y) (3y − x)
18. (x − 1) (a + b)
19. (8a2 + 3b)(8a2 − 3b)
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y
x
1 2 3 4 5 6
MAT0056 – Practice Final