Name_________________________ Test 2, Math 109



Name_________________________ Test 2, Math 109

For multiple choice questions, circle the best answer. For all other problems, clearly show work, or no credit will be given. Circle all answers. GOOD LUCK!!!

1. For [pic], Find f(3)

a. 2 b. 6 c. 2 and 6 d. 0 e. none of the answers a-d

2. Without solving the system, find the number of solutions to the following systems of equations: [pic] This systems has

a. one solution b. no solution c. many solutions d. two solutions

3. Without solving the system, find the number of solutions to the following systems of equations:

[pic] This systems has

a. one solution b. no solution c. many solutions d. two solutions

4. A shopkeeper has two types of coffee beans: Hazelnut and Vanilla. The hazelnut sells for $5.20 per pound and the vanilla sells for $5.80 a pound. How many pounds of each type must be mixed to make 16 pounds of coffee that will sell for $5.50 per pound? Show all your work and write your final answer in a sentence.

5. a. Construct a piecewise defined tax function, Tax paid=f(i), if the tax amount is 5% on the first $50,000 of income and 8% on any income in excess of $50,000, where i=the amount of income .

[pic]

b. Find the amount of tax a person would pay if she made $70,000. Circle your answer.

c. Another method of taxation is paying 6.5% on all income. Find an equation for the tax paid, g(i) using this method where i=the amount of income. Circle your answer.

d. Comparing 5a to 5c, what amount of income would pay the same amount of taxes under the two plans? Circle your answer.

6. Find an equation for the piecewise defined function graphed below.

[pic]

[pic]

7. Solve the following systems of equations algebraically (elimination or substitution). Show all work and write your answer as a point if possible. Check your answer.

a. [pic] b. [pic]

8. Construct a system of equations (not anywhere on this exam) where there is no solution to the system.

9. For what x values is the following true:

[pic] [pic]

a. x=-1, 0 ,1 b. x=-1, 1 c. 0 ................
................

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