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Alg/Geometry Honors
Ch 8 Alg Review
Name ___________________
1. Simplify: (xy 8 )(3x 6y 2 )
1.
___________
3x7y10
2. Simplify: (x 3 )2
2.
x6
___________
2 
3. Simplify:  h 2 
3 
16
4
h
3. ___________
81
4. Simplify: (4x 2y )3  4x 2y 3  4(x 2y )3
Change problem!! 4.
54x 2y 5
5. Simplify:
9x 6y 2
5.
6.
 2x 3y 2z 
7. Simplify: 

4
 3x z 
8. Simplify:
 7x
3
y 3
6 3
2
7.
6y 3
x
___________
4
7.2x 10 5
4x 10 3
10. Arrange the terms of 2x + 6 + 4x5 + 7x6
9. Evaluate:
so the powers of x are in ascending order
h
x
___________
2
9x 2 y 4
___________
4
y
1
x 5 y 4
2 3
68x y + 4x y
___________
4
36x 7
6. Simplify:
9x 5
8
8.
7x 2
___________
9.
1.8 x 10-2
___________
6+2x+4x5+7x6
10. ___________
11. Find the degree of : m2n2 + m2 -nm2
4
11. ____________
12. Simplify: (8x 2  4x  2)  (2x 2  x  6)
2
+3x+4
12. 10x
___________
13. Simplify: (x 2  x  1)  (5  5x 2  5x )
-4x2+4x+4
13.____________
14. Simplify: 5n 2 (x  6)  2x (3x 2  x  6)  7(x 2  3)
-x3-25x2+12x-21
14. ___________
2
15. Simplify: (x+4)(x+1)
x +5x+4
15. ___________
16. Simplify: (2x-7)(4x+4)
16. ___________
8x2-20x-28
17. Simplify: (4x2 + 2y2)(2x2 - y2)
17. ___________
8x4-2y4
18 Simplify: (y - 2)2
y -4y+4
18. ___________
20. Simplify: (2x - 3y)(2x + 3y)
4x -9y
20. ___________
21. Simplify: (x + 3)(x2 - 2x +4)
21. ___________
x3+x2-2x+12
22. Solve: y(y-6) = (5y2 - 36) - (4y2 - 3y)
22. ___________
y=4
23. Solve: 2(4y + 3) + 2 = -4(y + 1)
23. ___________
y = -1
2
2
1
33x y
24. ___________
24. Write in radical form: 33xy 2
25. Write in rational exponent form:
26. Simplify:
6
4096
1
 16  4
27. Simplify: 

 625 
28. Simplify: 243
1
5
2
4
1296
1
12964
25. ___________
26.
4 or 4
___________
6
6
2
27. ___________
5
28. ___________
3
29. Solve: 11x 1  1331
29. ___________
x=4
30. Solve: 5x = 15625
30. ___________
x=6
31. The number of three-letter words that can be formed with the English alphabet is 26 3. The
number of five-letter words that can be formed is 265. How many times more
676
five-letter words can be formed than three-letter words?
31. ____________
32. Consider a dust mite that measures 10-3 millimeters
in length and a caterpillar that measures 10 cm long.
How many times as long as the mite is the caterpillar?
10
32. ____________
33. The height above the ground of a ball thrown up with a
velocity of 96 feet per second from a height of 6 feet
is 6 + 96t -16t2, where t is the time in seconds. Using
this model, how high is the ball after 7 seconds?
-106 (SKIP)
33. ______________
34. The measures of two sides of a triangle are (3x + 4y) and
(5x –y). If the perimeter is (10x + 5y), find the
measure of the third side.
2x + 2y
34. _______________
5
35. The profit P of a company in thousands of dollars can be
modeled by
P  12.75 5 c 2
, where c is the number of
customers in hundreds. If the profit of the company is
$51,000, how many customers do they have?
3200 customers
35. _____________
36. A rectangle with an area of 24 square inches is formed
by cutting strips of equal width from a rectangular piece
of paper. Find the dimensions of the new rectangle if the
original rectangle measures 8 in by 6 in.
36. ________________
37. Marlene is buying a new plasma tv. The height of the
screen of the tv is one half the width plus 5 inches.
The width is 30 inches. Find the height of the screen.
37. ______________
6x4
20 inches
38. A high school wrestling mat must be a square with 38 foot sides and contain two
circles, as shown. Suppose the inner circle has a radius of r feet, and the radius
of the outer circle is 9 feet longer than the inner circle.
(38r2 +56.52r+254.3)ft2
a) Write an expression for the area of the larger circle.
38a) ___________
b) Write an expression for the area of the portion of
(1190 - 3.14r2 – 56.52r)ft2
the square outside the larger circle.
38b) ___________
c) Write an expression for the total shaded area
2
38c) (1190-56.52r)ft
___________
a) A=(r + 9)2
simplify using 3.14 for 
b) 382 – (answer from a)
c) (b) + area of small
circle