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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.
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Test 3 MAT 1101 Winter 2009 Name ________________________
Simplify all answers and show your work!
To add and subtract fractions, they must have a __common denominator____.
Why can we not simplify 2x + 3y and further? Because 2x and 3y aren’t like terms._
Exponents are a shortcut for repeated ___multiplication_______.
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._____
Combine like terms: 2xy + 3x^2 y – 12x^2 y + 17xy – 12xy 7xy – 9x^2 y
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
y
x 4
3
8 3 3
x y^12
6
64 x
y
4 27
−
144 x^11
Multiply the following:
12x^4 y + 20x^3 y^4 – 16x^3 y x^2 + 3x – 28 18x^2 – 6x – 40
9x^2 + 12x + 4 5x^3 – 16x^2 + 27x – 18
Factor the following completely:
5x^3 y^5 (5xy^2 + 8 + 7x^5 y) (x + 6)(x – 5) (x + 9)(x – 9)
(3x – 8)(3x + 8) (15x – 2)(x^2 + 2) (2x – 5)(2x + 3)
x 3 x 10 2
2
2 x 14 x 4 x 21
x 4 x 2 2
2
x
x ( 3 )( 1 )
x + x −
x
x 6 x 5
3 x 18 x 2
2
−
x
3x^22
x
x 3
4 x −