Olympic College Math 94 – Test on Topics 9 to 11
Math 94 – Test on Topics 9 to 11
1.
Simplify the following expressions (The answers are to have only positive exponents.):
3
4
(a) (4x )(5x )
=
(b)
12a 9
3a 3
(c)
(– 4x )
=
(d)
6x 2 y
2y3
=
(e)
 5x 
 2
 2x 
=
3 2
2
=
(f) (2 x 3 y 2 ) 2 (3x 3 y) =
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Olympic College Math 94 – Test on Topics 9 to 11
2.
Simplify the following expressions (The answers are to have only positive exponents.):
(a)
3
z6
z 4
=
(b)
x 
(c)
4x y
(d)
10 x 3 y 2
2 x 0 y 3
2 3
–3 5
=
=
=
Express each number in scientific notation:
(a)
87,000
=
(b)
0.0023
=
4. Express each number without exponents:
(a) 5.2 X 10
(b) 4.6 X 10
5
–3
=
=
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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Olympic College Math 94 – Test on Topics 9 to 11
6. Express each polynomial in descending order. Give the degree of each polynomial:
2
3
(a) 2x – x + 7x =
(b) t – 3t2 – 4
=
3
3
2
7. Add: (3x – 5x) + (7x + 9x )
2
2
8. Subtract: (5x – 3x + 1) – (x + 3x – 1)
9.
Multiply each of the following
(a) 5(4x – 2)
=
2
(b) 3x (2x – 6) =
(c)
3
2
2x (4x – x + 3) =
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Olympic College Math 94 – Test on Topics 9 to 11
10. Multiply each of the following
(a)
(3x + 1)(2x – 3)
(b)
(4x – 5y)(2x + 3y)
=
=
11. Simplify the following
(a)
18 x  9
=
3
10 x 4  15 x 3  20 x 2
(b)
5x 2
=
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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)
12a 9
(b)
3a 3
(c)
(– 4x3)2
=
20 x3 + 4 =
20 x7
=
4a 9
a3
4a6
=
(– 4)2 (x3)2 =
=
6x 2 y
3x 2 y
(d)
=
=
y3
2y3
 5x 
(e) 
2 
 2x 
2
2
(f) (2 x 3 y 2 ) 2 (3x 3 y) =
2.
3x 2
y2
 5 
  =
 2x 
=
52
=
(2 x) 2
(4 x6 y4 )(3x3 y ) =
25
4x 2
12 x6 + 3 y4 + 1 =
12 x9 y5
Simplify the following expressions (The answers are to have only positive exponents.):
z6
(a)
z 4
(b)
(c)
x 
2 3
–3 5
4x y
=
z6 – (– 4) =
z10
=
x2(–3)
x –6 =
=
4y5
x3
=
10 x 3 y 2
30 2( 3)
(d)
=5 x y
=
0 3
2x y
3
16 x6
1
x6
5 x 3 y1 =
5 x3 y
Express each number in scientific notation:
(a)
87,000
=
8.7 x 104
(b)
0.0023
=
2.3 x 10 - 3
4. Express each number without exponents:
(a) 5.2 X 105
= 520,000
(b) 4.6 X 10 – 3
= 0.0046
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Olympic College Math 94 – Test on Topics 9 to 11
5. There are approximately 5.9 X 1012 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) =
=
=
9.
5x2 – 3x + 1 – x2 – 3x + 1
5x2 – x2 – 3x – 3x + 1+ 1
4x2 – 6x + 2
Multiply each of the following
(a) 5(4x – 2)
=
20x - 10
(b) 3x2(2x – 6) =
6x2 + 1 – 18x2
(c) 2x3(4x2 – x + 3) =
8x3+2 – 2x3 +1 + 6x3
=
6x3 – 18x2
=
8x5 – 2x4 + 6x3
10. Multiply each of the following
(a)
(3x + 1)(2x – 3)
(b) (4x – 5y)(2x + 3y)
=
6x2 – 9x + 2x – 3 =
6x2 – 7x – 3
=
8x2 + 12xy – 10xy – 15y2 =
8x2 + 2xy – 15y2
11. Simplify the following
(a)
18 x  9
=
3
18 x 9
 =
3
3
10 x 4  15 x 3  20 x 2
(b)
5x 2
6x – 3
=
10 x 4 15 x 3 20 x 2


=
5x 2
5x 2
5x 2
2x2 – 3x + 4
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