Written Assignment 1

Answer all assigned exercises, and show all work.

1. Let set A = . List all the elements of A that belong to the set of rational numbers. (See section R.2, Example 1.) [2 points]

2. Evaluate each expression. (See section R.2, Example 3.) [4 points]

a.

b.

3. Evaluate each expression for p = –4, q = 8, and r = –10. (See section R2, Example 4.) [4 points]

a.

b.

4. Use the distributive property to rewrite the sum as a product. (See section R.2, Example 6.) [2 points]

5. Let x = –4 and y = 2. Evaluate each expression. (See section R.2, Example 9.) [4 points]

a.

b.

6. Simplify the expression. Assume variables represent nonzero real numbers. (See section R.3, Examples 1–3.) [2 points]

7. Identify the expression as a polynomial or not a polynomial. If a polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. (See section R.3, Example 4.) [2 points]

8. Find the sum or difference. (See section R.3, Example 5.) [2 points]

9. Find the product. (See section R.3, Examples 6–8.) [2 points]

10. Find the product. (See section R.3, Examples 8 and 9.) [2 points]

11. Perform the indicated operations. (See section R.3, Examples 5–9.) [4 points]

a.

b.

12. Perform the indicated operation. (See section R.3, Examples 10 and 11.) [2 points]

13. Factor out the greatest common factor for each polynomial. (See section R.4, Examples 1 and 2.) [4 points]

a.

b.

14. Factor the polynomial by grouping. (See section R.4, Example 2.) [2 points]

15. Factor each trinomial, if possible. (See section R.4, Examples 3 and 4.) [4 points]

a.

b.

16. Factor each polynomial. (See section R.4, Examples 5 and 6.) [4 points]

a.

b.

17. Factor each polynomial by substitution. (See section R.4, Example 7.) [4 points]

a.

b.

18. Factor by any method. (See section R.4, Examples 1–7.) [2 points]

19. Find the domain of the rational expression. (See section R.5, Example 1.) [2 points]

20. Write the rational expression in lowest terms. (See section R.5, Example 2.) [2 points]

21. Find the product or quotient. (See section R.5, Example 3.) [4 points]

a.

b.

22. Perform each addition or subtraction. (See section R.5, Example 4.) [4 points]

a.

b.

23. Simplify the expression. (See section R.5, Example 5.) [2 points]

24. (Modeling) Distance from the Origin of the Nile River. [2 points]

The Nile River in Africa is about 4000 mi long. The Nile begins as an outlet of Lake Victoria at an altitude of 7000 ft above sea level and empties into the Mediterranean Sea at sea level (0 ft). The distance from its origin in thousands of miles is related to its height above sea level in thousands of feet (x) by the following expression.

For example, when the river is at an altitude of 600 ft, x = 0.6 (thousand), and the instance from its origin is

, which represents 3000 mi.

(Source: World Almanac and Book of Facts.)

What is the distance from the origin of the Nile when the river has an altitude of 1200 ft?

25. Match the following expression with its equivalent expression, (a)–(h) [2 points]

a. b.

c. d.

e. f.

g. h.

26. Perform the indicated operations. Write each answer using only positive exponents. Assume all variables represent positive real numbers. (See section R.6, Examples 5 and 6.) [8 points]

a.

b.

c.

d.

27. Find the product. Assume all variables represent positive real numbers. (See section R.6, Example 6(e), and section R.3, Example 7.) [2 points]

28. Factor, using the given common factor. Assume all variables represent positive real numbers. (See section R.6, Example 7.) [4 points]

a.

b.

29. If the expression is in exponential form, write it in radical form. If it is in radical form, write it in exponential form. Assume all variables represent positive real numbers. (See section R.7, Examples 2 and 3.) [4 points]

a.

b.

30. Simplify each expression. Assume all variables represent positive real numbers. (See section R.7, Examples 1, 4–6, and 8–11.) [4 points]

a.

b.

31. Simplify each expression. Assume all variables represent positive real numbers. (See section R.7, Examples 7, 9 and 11.) [6 points]

a.

b.

c.

32. Rationalize the denominator of the radical expression. Assume all variables represent nonnegative numbers and that no denominators are 0. (See section R.7, Example 12.) [2 points]