Math 3

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Allied American University

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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. 53

5

y z

     

3. Classify the following as a monomial, binomial or trinomial, where possible. 2

2 vw

−

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

4x2 – 3xy + y2 5. Classify the following as a monomial, binomial or trinomial, where possible.

y7 + y6 + 8y5+ 2 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. 5

20

m m

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

–53

–43

r

r r

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.

( )( ) ( )( )

8 3

14 15

8 10 5.4 10

2.7 10 2 10

× ×

× ×

15. The distance from a star to a planet is 7.4 • 1018 m. How long does it take light, traveling

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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. 3 250 – 70 10

x x x

25. Divide. 4 2

2

– 10 + 31 – 5

x x x

26. Write 7.7x10^8 in standard notation. 27. Evaluate 4x^0+5 28. Simplify and write using positive exponents. (-6)^-2 29. Simplify x^-7/y^-2 30. Multiply (x-9)(x+9)