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Math 095 Exam 2 Study Guide

1. The exam covers Sections 3.3-3.8, 4.1-4.5. The exam will be closed book, closed notes, and turned off cell phones. Calculators are allowed .

2. Practice doing problems without using the book or your notes. I will only test you on ideas that we have covered in class and on your homework.

3. Review the topics and do the problems listed below. Review homework and in-class worksheets. If a certain problem type is difficult for you, do some other problems like it in the book for more practice.

4. Do not wait until the night before the exam to begin studying.

5. Make sure to show all your work.

6. Do not skip an exam. Check my syllabus for exam policy.

Fraction Review

subtract ing-multiplying.html">Add , subtract, multiply , divide fractions and mixed numbers:

1.

2.

3.

Solve Linear Equations

Solve linear equations :

4. -3x - 17 + 4x = 5

5. 2(2x - 5) = 3(x + 4)

6.

Section 3.3

Solve a formula for the specified variable :

7. for h

8. P = 2L + 2W for L

9. ax + by + c = 0 for x

Solve for y; put the resulting equation into y = mx + b form:

10. 2x + 5y = 10

11. 3x = 4y + 11

12. 3x - y = 5x + 3y

Section 3.4 and 3.5

Solve application problems: set up a variable, write an equation, solve the equation, and then answer the question.

13. A 6 foot board is cut into 2 pieces so one piece is 2 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

14. For a four number lottery, a person's first three picks were consecutive odd integers, and the fourth was the sum of the first three numbers. If the fourth number was 45, what are the first three numbers.

15. One angle of a triangular banner is 20 degrees greater than the first angle. The third angle is twice as large as the first angle. What are the measures of the three angles?

16. How much pure acid (100%) should be mixed with 2 gallons of a 50% acid solution in order to get an 80% acid solution.

17. The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate-covered raisins, which usually sells for $3 per pound, and macadamia nuts, which usually sells for $8 per pound. They have a 60-pound barrel of the raisins. How many pounds of the nuts should they mix with the barrel of raisins so they hit their target value of $6 per pound for the mixture?

Section 3.6 and 3.7

Solve inequalities and compound inequalities. Graph the solution set AND write it in interval notation.

18. 7x + 1 ≥15

19. 5 -y > 0

20. 3 -2x ≥-2x + 1

21. 2x + 7 < 3 + 5x

22. 3(x + 4) > 2x -3

23. -2x + 18≤-2(5x ?3)

*24. - 7≤-2x + 3 < -3

25. x -2 > 3 and x -5 < 4

26. 2x + 3 ≥-1 and 3x + 6 < 21

27. -x -5 > 0 or 3x -2 ≥1

28. -x -6 ≥3 or 4x + 3 > 5

Section 3.8: *BONUS MATERIAL

Solve basic absolute value equations; graph basic absolute value inequalities.

(We will go over these in class on the review day.)

*29. | x | + 2 = 5

*30. | x | 2

*31. | x | 7

Sections 4.1, 4.2, and 4.3

1. Find slopes of given lines.

2. De termine the slope and y- intercept of given equations.

3. Determine if lines are parallel, perpendicular or neither.

4. Graph equations.

32. Complete the ordered pair so that it is a true solution of the given linear equation:

3x + y = 2 ( ___, 8 ), ( ___, -4 ), ( 0, ___)

Write each equation in slope intercept form and determine the slope and y-intercept:

33. 2x + 3y = 14 34. 13x+34y-9=0

Determine the slopes of the given equations:

35. 3x = 12

36.-y = -8

Two points of two lines are given; determine if the lines are parallel, perpendicular, or neither.

37.
L
1: (3, 5) and (-2, 1)
L2: (-6, 9) and (-1, 13)

38.
L
1
: (4, 8) and (1, -2)

L2: (-3, 5) and (2, 2)

The equations of two lines are given; determine if the lines are parallel, perpendicular, or neither.

39.
L
1: 3y = 5 -2x
L
2: y = 3/2x + 9

40.
L
1
: y = 5x -3
L2: y = -5x + 3

Use the slope-intercept form to graph the equations:

41. y = -4x -7

42. 5x + 4y = 20 43. x -3 = 4

44. y = -3x + 4

45. x + 3y -y = 0

Section 4.4

Write equations in slope-intercept form given information.

Try problems like:

Write the equation of the line in slope-intercept form given the fol lowing information .

46. m = - 3, (2, 5)

47. m = -1/3, (-6, 3)

48. m is undefined, (6, 8)

49. m is zero , (6, 8)

50. (4, 7) and (6, 11)

51. (4, 0) and (2, 5)

Section 4.5

1. Graph linear inequalities.

2. Graph compound linear inequalities.

Try problems like:

52. y ≤1/2x -5

53. 4x + 5y > 20

54. 2x -5y ≥10

55. y ≤-x + 3 and y ≤2x + 1

56. -x + 4y < 12 or x ≥2

Solutions:

Fraction Review:

1. 11/24

2. 7 1/18

3. 3/10

Solve Linear Equations:

4. x = 22 5. x = 22 6. x = -2

Section 3.3:

7.

8.

9.

10.

11.

12.

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