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MAT 1101 Winter 2009 Exam: Algebra and Exponents - Prof. Nancy Molik, Exams of Mathematics

The winter 2009 exam for mat 1101, a college-level algebra and exponents course. The exam covers topics such as adding and subtracting fractions, simplifying expressions, multiplying and factoring polynomials, and dividing and simplifying expressions. Students are required to simplify their answers and show their work.

Typology: Exams

Pre 2010

Uploaded on 08/17/2009

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Test 3 MAT 1101 Winter 2009 Name ________________________
Simplify all answers and show your work!
1) To add and subtract fractions, they must have a __common denominator____.
2) Why can we not simplify 2x + 3y and further? Because 2x and 3y aren’t like terms._
3) Exponents are a shortcut for repeated ___multiplication_______.
4) When we have a variable with an exponent raised to another exponent, what do we do with those
exponents? (Ex: (x3)2 )____We multiply the exponents._____
5) Combine like terms: 2xy + 3x2y – 12x2y + 17xy – 12xy 7xy – 9x2y
6) Add: (4x3 + 5x2 – 7) + (8x3 – 11x2 + 9) 7) Subtract: (7x2 – 2x – 8) – (3x2 – x + 5)
12x3 – 6x2 + 2 4x2 – x – 13
Simplify the following:
8) 75
62
yx16
yx4
9)
3
35
24
yx2
yx3
10) 324 )yx4(
y
x
4
3
33
8
27
yx
12
6
64
x
y
11) 3
4
27
12) 4 3 3 – 2 • 4 – 1 • 3 4 13) 1276
x
x
x
81
1 144 x11
Multiply the following:
14) 4x2(3x2y + 5xy4 – 4xy) 15) (x – 4)(x + 7) 16) (3x – 5)(6x + 8)
12x4y + 20x3y4 – 16x3y x2 + 3x – 28 18x2 – 6x – 40
17) (3x + 2)2 18) (5x – 6)(x2 – 2x + 3)
9x2 + 12x + 4 5x3 – 16x2 + 27x – 18
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Test 3 MAT 1101 Winter 2009 Name ________________________

Simplify all answers and show your work!

  1. To add and subtract fractions, they must have a __common denominator____.

  2. Why can we not simplify 2x + 3y and further? Because 2x and 3y aren’t like terms._

  3. Exponents are a shortcut for repeated ___multiplication_______.

  4. When we have a variable with an exponent raised to another exponent, what do we do with those

exponents? (Ex: (x^3 )^2 )____We multiply the exponents._____

  1. Combine like terms: 2xy + 3x^2 y – 12x^2 y + 17xy – 12xy 7xy – 9x^2 y

  2. Add: (4x^3 + 5x^2 – 7) + (8x^3 – 11x^2 + 9) 7) Subtract: (7x^2 – 2x – 8) – (3x^2 – x + 5)

12x^3 – 6x^2 + 2 4x^2 – x – 13

Simplify the following:

2 6

16 x y

4 x y −

3

5 3

4 2

2 x y

3 x y  

  1. ( 4 x^4 y−^2 )−^3

y

x 4

3

8 3 3

x y^12

6

64 x

y

4 27

  1. 4 3 • 3 – 2^ • 4 – 1^ • 3 4 13) x 6 • x−^7 • x^12

144 x^11

Multiply the following:

  1. 4x^2 (3x^2 y + 5xy^4 – 4xy) 15) (x – 4)(x + 7) 16) (3x – 5)(6x + 8)

12x^4 y + 20x^3 y^4 – 16x^3 y x^2 + 3x – 28 18x^2 – 6x – 40

  1. (3x + 2)^2 18) (5x – 6)(x^2 – 2x + 3)

9x^2 + 12x + 4 5x^3 – 16x^2 + 27x – 18

Factor the following completely:

  1. 25x^4 y^7 + 40x^3 y^5 + 35x^8 y^6 20) x^2 + x – 30 21) x^2 – 81

5x^3 y^5 (5xy^2 + 8 + 7x^5 y) (x + 6)(x – 5) (x + 9)(x – 9)

  1. 9x^2 – 64 23) 15x^3 – 2x^2 + 30x – 4 24) 4x^2 – 4x – 15

(3x – 8)(3x + 8) (15x – 2)(x^2 + 2) (2x – 5)(2x + 3)

  1. Simplify: x x 6

x 3 x 10 2

2

  1. Multiply and simplify: x 3 x 4

2 x 14 x 4 x 21

x 4 x 2 2

2

x

x ( 3 )( 1 )

x + x

x

  1. Divide and simplify: x 5 x

x 6 x 5

3 x 18 x 2

2

÷

  1. Add and simplify: (^) 2 2 x

x

3x^22

x

  1. Subtract and simplify: x 3

x 3

4 x −