Module 3

Directions: Please show all of your work for each problem.  If applicable, you may find Microsoft Word’s equation editor helpful in creating mathematical expressions in Word.  There is a tutorial on using this equation editor in Module 1 Lecture Notes.  You also have the option of hand writing your work and scanning it.

1.      Simplify.     (a⁶b⁷)⁶

2.      Simplify.    

3.      Classify the following as a monomial, binomial or trinomial, where possible.  

4.      Classify the following as a monomial, binomial or trinomial, where possible.

5.      Classify the following as a monomial, binomial or trinomial, where possible.

6.      Write in descending order and give the degree.            7x³ + 10x⁴ + 10

7.      Evaluate –x² – 10x – 6 for x = 3.

8.      True or False?     The degree of a trinomial is never 4.

9.      Evaluate (assume x does not equal 0).   8x⁰

10.    Write using positive exponents and simplify, if possible.    5^–3

11.    Simplify and write your answer with only positive exponents.

12.    Simplify.  Write your answer with only positive exponents.    

13.    Express the number in scientific notation.  The diameter of Neptune: 49,600,000 m

14.    Perform the indicated calculations.  Write your result in scientific notation.

15.    The distance from a star to a planet is 7.4 · 10¹⁸ m.  How long does it take light, traveling at 10¹⁶ m/year, to travel from the star to the planet?

16.    Add 6m² – 2m – 4 and 10m² + 3m – 6.

17.    Remove the parentheses and simplify.     7y – (–10y – 9x)

18.    Subtract 4d² + 9d – 10 from 10d² – 3d + 7.

19.    Perform the indicated operations.  [(6y² + 2y – 2) – (–y² – 10y + 2)] – (–4y² + 3y + 3)

20.    A census study shows that the population from 1990 to 1998 of the only large town in a certain county can be modeled by the formula 102t² – 225t + 3090 where t = 0 represents the year 1990 and that over the same years, the population of the surrounding county (not including the town) can be modeled by the formula 125t² + 72t + 4978 where t = 0 represents the year 1990.  Find a model for the total population of the county during the years 1990 to 1997.

21.    Multiply.    –6x(–4x – 7)

22.    Multiply.     (5m – 3)(4m + 7)

23.    Multiply.     (–4x – 2)²

24.    Divide.   

25.    Divide.   

26.    Write 7.7x10^8 in standard notation.

27.    Evaluate 4x^0+5

28.    Simplify and write using positive exponents.  (-6)^-2

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29.    Simplify x^-7/y^-2

30.    Multiply (x-9)(x+9)