Math Assignment

This is your first assignment! It is to be handed in to your instructor on Friday, August 27th. Use standard 8.5" x 11" paper, but not paper with a ragged edge torn from a composition notebook. Write legibly in pencil or erasable ink. Arrange problems in numerical order. Do not use a calculator. Show your work. Simplify all expressions and circle your answers.

1. Multiply: . 2. Subtract: .

3. Divide: . 4. Divide twenty-four by one-half.

5. Simplify: . 6. Simplify: .

7. If , find the value of .

8. Suppose a friend covers the total bill including a tip of 20% at Perkins restaurant, but you want to reimburse her for the tip. If the total was $18, how much should you reimburse her?

9. If you drive to Nashville from CBU, a distance of 210 miles, and it takes you three-and-a-half hours, what was your average speed?

10. Simplify: 3x - {2x - 2[x - (x - 1)] + 2} . 11. Solve: .

12. Solve: . 13. Find all solutions of the inequality: .

14. Solve for x: (x - 4)(x + 8) = 7 - (3 - x)(x + 5) . 15. Multiply a2x4 + a4x2 - 2a4 by 2x - 3a .

16. Suppose your scores on the first three math exams are: 80, 90, 100. What score would you need to make on the fourth exam in order to end up with a 91 average?

 

In Problems 17 through 20, factor the following expressions:

17. 18.

19. 20.

In Problems 21 through 26, perform the indicated operations on the following fractions and simplify:

21. 22.

23. 24.

25. 26.

27. Find if and .

28. The conversion of Celsius temperatures C  to Fahrenheit temperatures F  is given by the formula . Find the Celsius temperature corresponding to .

29. Consider the algebraic expression 7x3y2 - 3xy + 4x2 - y +12.

  1. What is the coefficient of the second term?

  2. What are the factors of the first term?

  3. What is the degree of this expression?

In Problems 30 through 35, simplify the expressions with radicals and/or negative exponents so that there are only expressions with positive fractional exponents remaining.

30. 31.

32. 33.

34. (x-2 + y-2)-2 35.

Problems 36 and 37 concern graphing equations.

36. The following parts are about the equation .

  1. Write the equation in slope-intercept form.

  2. Determine its slope.

  3. Graph the equation on the set of axes and label it.

  4. Where does the graph cross the x-axis?

  5. Where does the graph cross the y-axis?

  6. Graph the equation and label it to distinguish it from the graph in (c).

  7. What is the slope of the equation in (f)?

 

 

37. The following parts are about the equation .

  1. What type of function is it?

  2. ;

  3. If , what type of equation would you have?

  4. Solve the equation in (c).

  5. What are the zeros of the function?

  6. Graph and label the function on the set of axes.

  7. Label the x- and y-intercepts of the function.

  8. Find the vertex and label it on the graph.