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MAT 1101 Spring 2009 Test 3 - Algebra - Prof. Nancy Molik, Exams of Mathematics

A mathematics test focusing on algebra concepts, including simplifying expressions, adding and subtracting fractions, exponents, and multiplying and factoring expressions. Students are required to show their work.

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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Test 3 MAT 1101 Spring 2009 Name ________________________
Simplify all answers and show your work!
1) When we have a variable with an exponent raised to another exponent, what do we do with those
exponents? (Ex: (x3)2 )_____________________________________________________________
2) To add and subtract fractions, they must have a _________________________________________.
3 ) Exponents are a shortcut for repeated ______________________________________.
4) Why can we not simplify 4x – 5y any further? __________________________________________
_________________________________________________________________________________.
5) Combine like terms: 4x2 – 5x + 3x – 2x2 + 9 + 12
6) Add: (5x4 + 3x + 8) + (6x4 + 21x – 5) 7) Subtract: (8x2 – x – 5) – (4x2 – 5x + 6)
Simplify the following:
8) 54
23
15
25
yx
yx 9)
3
92
75
2
yx
yx 10) 462 )3( yx
11) 2
5
4
12) 2 4 5 – 3 • 5 5 • 2 – 1 13) 1178
xxx
Multiply the following:
14) 3x2y(2xy2 – 3x3y3 + xy) 15) (2x – 3)(3x + 2) 16) (3x – 4)(2x2 + 5x + 7)
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Test 3 MAT 1101 Spring 2009 Name ________________________

Simplify all answers and show your work!

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

exponents? (Ex: (x^3 )^2 )_____________________________________________________________

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

3 ) Exponents are a shortcut for repeated ______________________________________.

  1. Why can we not simplify 4x – 5y any further? __________________________________________

_________________________________________________________________________________.

  1. Combine like terms: 4x^2 – 5x + 3x – 2x^2 + 9 + 12

  2. Add: (5x^4 + 3x + 8) + (6x^4 + 21x – 5) 7) Subtract: (8x^2 – x – 5) – (4x^2 – 5x + 6)

Simplify the following:

3 2

15

x y

x y

3

2 9

x y

x y

  1. ( 3 x −^2 y^6 )−^4

5 4

  1. 2 4 • 5 – 3^ • 5 5 • 2 – 1^ 13) x^8 • x^7 • x −^11

Multiply the following:

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

Factor the following completely:

  1. 12x^3 y^4 + 36x^5 y^6 + 48x^4 y^5 18) x^2 – 12x – 28 19) x^2 – 64

  2. 12x^3 – 6x^2 + 10x – 5 21) 2x^2 – 7x – 30

  3. Simplify: 3 6

x

x x

  1. Multiply and simplify: x

x x x x

x x 2

2

  1. Divide and simplify: 3

2

2

÷

x

x x x

x x

  1. Add and simplify: 5

x x

  1. Subtract and simplify: 3

xx

  1. Solve the inequality: 3 < 2x – 8 < 10