Math 95 Exam 3 Study Guide
Exam will consist of a sampling of questions similar to the ones below
Solving Equations for Variables:
1. Solve for b:
W = b − 3a − c
2. Solve for z:
r = 4yz
3. Solve for y:
z = 2y − 9x
4. Solve for w:
3w + x = A
5. Solve for x:
y = 2(x − 1)
6. Solve for b:
5(b + 8) = a
7. Solve for g:
g−h+k
f=
2
8. Solve for A:
3
B = (C − A)
5
Geometry and Formulas:
9. Find the perimeter of the following polygon:
10. Find the perimeter and area of a rectangular field that has a width of 22 yards and a
length of 77 yards. If we wanted to cover the field with artificial turf, which measure
would be used in finding the amount of turf needed?
11. Find the length of the missing side in the following figure:
12. Find the area of the following figure:
13. The area of a rectangular paining is 3150 square centimeters. If the width of the
painting is 54 centimeters, what is the length?
14. The perimeter of a rectangular field is 360 yards. If the width of the field is 84 yards,
what is its length?
15. The length of a rectangle is five times its width. If the area of the rectangle is 405
square feet, find its perimeter
16. The length of a rectangle is six times its width. If the perimeter of the rectangle is 84
inches, find its area.
17. Andy rides his bicycle at a speed of 9.6 miles per hour for 3 hours. For how many
miles does he ride?
18. Tom walks 3.2 miles in 2 hours. What is his speed?
Linear expressions and equations:
19. Translate the phrase into an algebraic expression:
The sum of x and 3
20. Translate the phrase into an algebraic expression:
The product of y and 2
21. Translate the phrase into an algebraic expression:
Two more then the product of 12 and a number
22. Translate the phrase into an algebraic expression:
67 less than twice a number
23. Translate the phrase into an algebraic equation, and solve the equation:
45 is the sum of 18 and a number
24. Translate the phrase into an algebraic equation, and solve the equation:
Twice the sum of a number and 7 is 3
25. Translate the phrase into an algebraic equation, and solve the equation:
Three less than the product of 8 and a number is 5
26. Write an inequality for the following statement:
y is greater than 7
27. Write an inequality for the following statement:
Twice x is at most 15
28. Write an inequality for the following statement:
y increased by 3 is at least -15
29. Write a single compound inequality for the following statement:
y is less than 7 and greater than or equal to -4
30. Write a single compound inequality for the following statement:
8 is greater than x, and 3 is less than x
Applications:
31. On Thursday, a local hamburger shop sold a combined total of 318 hamburgers and
cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Thursday?
32. A total of 632 tickets were sold for the school play. They were either adult tickets or
student tickets. There were 68 fewer student tickets sold than adult tickets. How many
adult tickets were sold?
33. Joe has scored 79, 95, 68, 64, and 94 on his previous 5 tests. What score does he need
on his next test so that his mean is 77?
Solving Percent Equations:
34. What is 60% of 94?
35. A saleswoman earns 7% commission on all the merchandise that she sells. Last month
she sold $5000 worth of merchandise. How much commission (in dollars) did she earn
last month?
36. Carlos needs to make a total of 40 deliveries this week. So far he has completed 14 of
them. What percentage of his total deliveries has Carlos completed?
37. 85% of what number is 34?
38. 33 is what percent of 60?
39. Last year, Maya opened an investment account with $5800 . At the end of the year, the
amount in the account had increased by 6.5% . How much money was in her account
at the end of last year?
40. The next model of a sports car will cost 14.5% less than the current model. The current
model costs $43,000 . What will be the price of the next model?
41. The price of an item has been reduced by 45% . The original price was $60 . What is
the price of the item now?
42. The wholesale price for a chair is $180 . A certain furniture store marks up the
wholesale price by 21% . Find the price of the chair in the furniture store.
43. This year, a small business had a total revenue of $29,900 . If this is 15% more than
their total revenue the previous year, what was their total revenue the previous year?
44. Today only, a table is being sold at a 35% discount. The sale price is $624. What was
the price yesterday?
45. The price of an item has risen to $216 today. Yesterday it was $135. Find the percentage increase.
Graphing Lines:
46. Graph the line: y = 4x
1
47. Graph the line: y = x
3
48. Graph the line: y = −3x − 2
1
49. Graph the line: y = x + 3
2
50. Graph the line: y − 3x = 3
51. Graph the line: x − y = −2
52. Graph the line: x = −1
53. Graph the line: y = 2
54. Graph the line whose x-intercept is 5 and whose y-intercept is 2.
55. Graph the line with slope −
3
passing through the point (−1, 1)
4
56. Graph the line with slope −3 and y-intercept -2
2
57. Graph the line: y − 4 = − (x − 3)
3
Properties of lines:
58. Find the x-intercept and y-intercept of the line:
−x + 2y = 2
59. Find the x-intercept and y-intercept of the line:
−3x + 4y = 9
60. Find the slope of the line passing through the points (−7, −7) and (−3, 6)
61. Find the slope of the line passing through the points (6, −9) and (2, −3)
62. Find the slope of the line passing through the points (−9, 8) and (2, 8)
63. Find the slope of the line passing through the points (−6, 2) and (−6, −6)
1
64. Find the slope and y-intercept of the line: y = − x + 7
2
65. Find the slope and y-intercept of the line: −3x − 2y = −6
66. Find the slope of a line perpendicular to y = −x + 8
5
67. Find the slope of a line parallel to y = x + 1
4
68. Find the slope of a line parallel to 5x − 6y = 7
69. Find the slope of a line perpendicular to 9x − 2y = 8
70. A construction crew is lengthening a road. Let y represent the total length of the road
(in miles). Let x represent the number of days the crew has worked. Suppose that x
and y are related by the equation y = 4x + 56.
(a) What was the road’s length when the crew started working?
(b) What is the change in the road’s length per day?
Writing equations of lines:
71. Write an equation in slope-intercept form for the line with y-intercept -4 and slope −
1
2
72. A line passes through the point (3, −8) and has a slope of −6. Write an equation in
slope-intercept form for this line.
5
73. A line passes through the point (−4, −6) and has a slope of . Write an equation in
2
slope-intercept form for this line.
74. A line passes through the point (9, 5) and has a slope of 1. Write an equation for this
line.
75. A line passes through the point (8, 2) and has a y-intercept of -4. Write an equation
in slope-intercept form for this line.
76. A line passes through the points (−1, −5) and (5, −1). Write an equation in slopeintercept form for this line.
77. A line passes through the points (−6, 1) and (4, 3). Write an equation in slope-intercept
form for this line.
78. Write the equation of the vertical line that passes through the point (−3, −4)
79. Write the equation of the horizontal line that passes through the point (5, −2)
80. Dale is a software salesman. His base salary is $2400 , and he makes an additional
$120 for every copy of English is Fun he sells. Write an equation that relates his total
pay (P ) in dollars, to the number of copies he sells (N ).
Multiple Choice Think About Questions for Exam 3
You should be able to determine the answer to these multiple choice questions by thinking
about the question and possible answers using little arithmetic computation.
Exam 3 will consist of at most 5 multiple choice questions similar to the ones below.
1. Which situation below represents the largest percent increase in Salary?
(a) A person’s salary is raised from $25,000 to $26,000
(b) A person’s salary is raised from $35,000 to $36,000
(c) A person’s salary is raised from $75,000 to $76,000
(d) A person’s salary is raised from $125,000 to $126,000
2. Which equation represents the sentence: 45% of what number is 125?
(a) 45x = 125
(b) 0.45x = 1.25
(c) 125x = 0.45
(d) 0.45x = 125
3. Which statement below is represented by the equation 3x + 1 = 10
(a) The sum of x and 1 times 3 is 10
(b) The product of 3 and x is 1 more than 10
(c) One more than the product of 3 and x is 10
4. Picture drawing a sketch of the graph, what is a reasonable x-intercept of the line that
goes through the points (−1, 6) and (−4, −3)?
(a) (9, 0)
(b) (−5, 0)
(c) (−3, 0)
(d) (0, 0)
5. Which of the following is the y-intercept of the horizontal line that passes through the
point (−2, 9)?
(a) (−2, 0)
(b) (0, 9)
(c) (0, −2)
(d) (9, 0)
6. Which of the following rectangles has the largest area?
(a) A rectangle with a perimeter of 60 and length of 5
(b) A rectangle with a perimeter of 60 and length of 20
(c) A rectangle with a perimeter of 60 and length of 29
(d) All rectangles with a perimeter of 60 have the same area
7. Which linear equation below does not have a y-intercept?
(a) 3x + y = −4
(b) x − 4 = 0
(c) y = 4x
(d) y = 4
8. Which of the following graphs could represent the linear equation y = −35x + 19?
(a)
(b)
(c)
(d)