Math 012

Midterm Exam Page 3

*Please remember to show all work on every problem.*

1) Solve the equation using the methods discussed in Chapter 2 of our text. If the equation has a unique solution, please show the complete check of your answer.

2) Solve the equation using the methods discussed in Chapter 2 of our text. If the equation has a unique solution, please show the complete check of your answer.

3) Solve the equation using the methods discussed in Chapter 2 of our text. If the equation has a unique solution, please show the complete check of your answer.

4) Solve the inequality using the methods discussed in Chapter 2 of our text. Write your answer in interval notation and graph the solution set on a number line.

5) Solve the inequality using the methods discussed in Chapter 2 of our text. Write your answer in interval notation and graph the solution set on a number line.

6) Solve the inequality using the methods discussed in Chapter 2 of our text. Write your answer in interval notation and graph the solution set on a number line.

7) Solve the inequality using the methods discussed in Chapter 2 of our text. Write your answer in interval notation and graph the solution set on a number line.

8) After Amanda received a 4.5% raise, her new annual salary was $75,240. What was her annual salary before the raise?

9) Patrick wins $900,000 (after taxes) in the lottery and decides to invest half of it in a 5-year CD that pays 6.72% interest compounded quarterly. He invests the other half in a money market fund that unfortunately turns out to average only 2.4% interest compounded annually over the 5-year period. How much money will he have altogether in the two accounts at the end of the 5-year period?

10) The average annual tuition and fees at public 4-year institutions in the US in 2005 was $13,847 and in 2010 was $16,384. Let y be the average tuition and fees in the year x, where x = 0 represents the year 2005.

a) Write a linear equation that models the growth in average tuition and fees at public 4-year institutions in the US in terms of the year x.

b) Use this equation to predict the average tuition and fees at public 4-year institutions in the US in the year 2020.

c) Explain what the slope of this line means in the context of the problem.

11) Given the linear equation :

a) Find both intercepts of the equation. Show all work and state intercepts as ordered pairs.

x-intercept =

y-intercept =

b) Use the intercepts to find the slope of the line. Show all work.

12) Given the following two linear equations, determine whether the lines are parallel, perpendicular, or neither. Show the work that leads to your conclusion.

13) Write an equation of a line through the point (5, -2) that is perpendicular to the y-axis. Graph the line on the grid below or create your own graph. State the slope of the line.

14) Given the linear equation , answer the following questions, showing all work:

a) Find the slope of a line perpendicular to the given line.

b) Write an equation in point-slope form of the line perpendicular to the given line through the point (4, -3).

c) Convert the equation found in part (b) to slope-intercept form.

d) Convert the equation found in part (b) to standard form.

e) Graph both lines. You may use the grid provided or create your own graph.

15) Given the function :

a) Find at least 5 ordered pairs that belong to the function. Show all work below.

b) Graph the function. You may use the grid provided or create your own graph.

c) State the domain and range of the function.

*End of exam: please do not forget to write and sign (or type) the required statement explained on Page 1 of the exam.*

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