1. Olympic College Math 94 – Test on Topics 9 to 111.
Simplify the following expressions (The answers are to have only positive exponents.):
(a) (4x )(5x )
12a 9 =
(b)
(c)
(d) =
3a 3
3 2
6 x 2 y
2 y 3
(– 4x ) =
 5x 
 2 x  2 
2 
(e) =
(f) (2x 3 y 2 ) 2 (3x 3 y) =
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2. Olympic College Math 94 – Test on Topics 9 to 112.
Simplify the following expressions (The answers are to have only positive exponents.):
z 6
(a)
(b)
(c)
z  4
2 3
–3 5
4x y =
 x 
10 x 3 y 2
(d)
2 x 0 y 3 = 3
Express each number in scientific notation:
(a)
(b)
87,000
0.0023 =
4. Express each number without exponents: 5
– 3
(a) X 10
(b) 4.6 X 10 = 12
5. There are approximately 5.9 X 10
miles in one light year. How many miles are there in 3,500 light
years? Write your answer in scientific notation.
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3. Olympic College Math 94 – Test on Topics 9 to 11
6. Express each polynomial in descending order. Give the degree of each polynomial:
(b) t – 3t2 – 4 = 9.
Multiply each of the following
(a) 5(4x – 2) = 2
(c)
2x (4x – x + 3) =
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4. (3x + 1)(2x – 3) 10x 4  15x 3  20x 2 5x 2 11. Simplify the following
Olympic College Math 94 – Test on Topics 9 to 11
10. Multiply each of the following
(a)
(b)
(3x + 1)(2x – 3)
(4x – 5y)(2x + 3y) = =
11. Simplify the following
18x  9 3
(a) =
10x 4  15x 3  20x 2
(b) =
5x 2
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5. Olympic College Math 94 – Test on Topics 9 to 11
Solutions 1.
Simplify the following expressions (The answers are to have only positive exponents.):
(a) (4x3)(5x4) =
20 x =
20 x7
12a 9
3a 3
4a 9
a 3
(b) = =
4a6
(c)
(– 4x3)2 =
(– 4)2 (x3)2 =
16 x6
6 x 2 y
3x 2 y
3x 2
(d)
2 y 3 =
y 3 =
y 2
 5x 
 2 x  2
 5  2 52
(2 x) 2 25
4 x 2
(e) 
2 
  =
 2 x  = =
(f) (2x 3 y 2 ) 2 (3x 3 y) =
(4 x6 y4 )(3x3 y ) =
12 x6 + 3 y4 + 1 =
12 x9 y5 2.
Simplify the following expressions (The answers are to have only positive exponents.):
z 6
z  4
2 3
–3 5
z6 – (– 4) =
x2(–3) =
4 y 5
x 3
(a)
(b)
(c) =
z10
x – 6 =
 x  1
x 6
4x y
10 x 3 y 2
0 3
30
y 2( 3) =
= 5 x
5 x3 y1 =
5 x 3 y
(d)
2 x y 3
Express each number in scientific notation:
(a)
87,000 =
8.7 x 104
(b)
0.0023 =
2.3 x
4. Express each number without exponents:
(a) X 105
(b) 4.6 X 10 – 3
= 520,000 =
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6. Olympic College Math 94 – Test on Topics 9 to 11
5. There are approximately 5.9 X miles in one light year. How many miles are there in 3,500 light
years? Write your answer in scientific notation.
(5.9 x 1012) x 3500 =
2.065 x 1016
6. Express each polynomial in descending order. Give the degree of each polynomial:
(a) 2x2 – x3 + 7x =
– x3 + 2x2 + 7x
degree = highest power = 3
(b) t – 3t2 – 4 =
– 3t2 + t – 4
degree = highest power = 2
7. Add: (3x3 – 5x) + (7x3 + 9x2) = =
3x3 – 5x + 7x3 + 9x2
3x3 + 7x3 + 9x2 – 5x
10x3 + 9x2 – 5x
8. Subtract: (5x2 – 3x + 1) – (x2 + 3x – 1) = =
5x2 – 3x + 1 – x2 – 3x + 1
5x2 – x2 – 3x – 3x
4x2 – 6x + 2 9.
Multiply each of the following
(a) 5(4x – 2) =
20x - 10
(b) 3x2(2x – 6) =
6x2 + 1 – 18x2 =
6x3 – 18x2
(c) 2x3(4x2 – x + 3) =
8x3+2 – 2x x3 =
8x5 – 2x x3
10. Multiply each of the following
(a)
(3x + 1)(2x – 3) =
6x2 – 9x + 2x – 3 =
6x2 – 7x – 3
(b) (4x – 5y)(2x + 3y) =
8x2 + 12xy – 10xy – 15y2 =
8x2 + 2xy – 15y2
11. Simplify the following
18x  9 3
18x 3 9 3
(a) =  =
6x – 3
10x 4  15x 3  20x 2
5x 2
10x 4
5x 2
15x 3
5x 2
20x 2
5x 2  
(b) = =
2x2 – 3x + 4
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