KEY Review for Test 3 (over Pie 3)
- Tests are cumulative. There will be about six (6) problems from material covered in Pie 1 and 2. Those problems are not included on this review. Use the Review from Test 1 and Test 2, and Test 1 and Test 2 to prepare for these questions.
- The following problems are examples of what will be on the test, not including the “review” problems from the material learned prior to Pie 3. The test will have 20 problems.
- These problems are organized by the “main ideas” of the course to help you continue to learn the concepts of the course. However, the test will not include the main ideas, that is, there will just be problems.
- The HINTS on the review will be included as part of Test 3. You cannot use notes on Test 3. You can use a scientific calculator.
I. Real Numbers (In Pie 1)
1. The circle graph below shows how the combined annual income for a certain family is spent. If the amount budgeted for Auto, Housing, and Food combined is $54,000, what is the total family income?
Answer:
2. The price of a notebook has dropped to $3.15 today. Yesterday's price was $3.65. Find the percentage decrease. Round your answer to the nearest tenth of a percent.
Answer:
3. A circus track has a ring shape with an inner circle of radius 15 yd
and an outer circle of radius 20 yd. (The track is represented by the
shaded region in the figure.) A circus worker has to cover the track with
sand. If one bag of sand can cover 3 sq yd, how many bags of sand does the
worker need to buy to cover the track? Note that sand can be bought only by
the bag, so the number of bags must be a whole number. (Let
.)
Answer:
4. Given the figure below, find the values of x and z.
Answer:.
5. Graph, on the number
line, all points x for which 
.
Answer:.
In this problem you are asked to express the answer on the number line.
6. Solve the following:
Answer:.
IV. Systems of Linear Equations
7. For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent," and answer the question about its solutions.
Answer:.
8. Solve the system of equations:
9. Solve the system of equations:
10. Solve the system of equations:
11. Solve the system of equations:
12. Solve the system of equations:
13. Find the value of k such that the system of equations does not have a solution.
14. Graph the solution set of
“Think” of the inequality signs is equal signs and graph the two equations. Then pick a point in each region of the graph, substitute in both inequalities to see if the resulting inequality is true, and shade the region where the point is true for both inequalities.
15. Graph the solution set of
16. Find two numbers whose sum is 132, and the larger number is 6 more than twice the smaller.
17. Five hundred tickers were sold for a fundraising dinner. The receipts totaled $3312.50. Adult tickets were $7.50 each and children’s tickets were $4.00 each. How many tickets of each type were sold?
18. A bakery with two stores buys three large delivery trucks and six small delivery trucks. One store receives one large delivery truck and four small delivery trucks for a total cost of $118,000. The second store receives two large delivery trucks and two small delivery tricks for a total cost of $107,000. What is the cost of each type of delivery truck?
19. The total cost of 8 gallons of regular gasoline and 12 gallons of premium gasoline is $27.84. Premium gasoline costs $0.17 more per gallon than regular gasoline. Find the price per gallon for each grade of gasoline.
20. An airplane flying into a headwind travels 1800 miles in 3 hours and 36 minutes. On the return flight, the same distance is traveled in 3 hours. Find the speed of the plane in still air and the speed of the wind, assuming that both remain constant throughout the round trip.
21. How many liters of a 35% alcohol solution must be mixed with a 60% solution to obtain 10 liters of a 50% solution?
22. You invest a total of $24,000 in two bonds that pay 6% and 9.5% simple interest. Your goal is to have a total annual interest income of $2000. How much should you invest at 6% and 9.5% in order to meet your objective?
23. A theater group made appearances in two countries. The hotel charges before tax in the second country were $1000 lower than in the first. The tax on the hotel was 7.5% in the first country and 6.5% in the second. After the trip, the total tax paid on accommodation expenses was $425. How much was the hotel bill in the first country before tax?
VI. Rational Expressions and Functions
24.
Reduce the following
expression to its lowest terms:
Answer:
25.
Reduce the following
expression to its lowest terms:
Answer:
26.
Reduce the following
expression to its lowest terms:
Answer:
27. Perform the indicated operation and simplify:
Answer: 
28. Perform the indicated operation and simplify:
Answer:
29. Perform the indicated operation and simplify:
Answer:
30. Perform the indicated operation and simplify:
Answer:
31. Perform the indicated operation and simplify:
Answer: 
32. Perform the indicated operation and simplify:
Answer:
33. Perform the indicated operation and simplify:
Answer:
34. Solve for x:
35. Solve for x:
36. Solve for x:
37. Solve for x:
38. Solve for x:
39. The ratio of yes votes to no votes in an election was 5 to 6. How many no votes were cast if there were a total of 8393 votes cast?
Answer:
40. A swimming pool holds 540,000 liters of water. The pool has two drainage pipes. When the pool is completely full, the first pipe alone can empty it in 225 minutes, and the second pipe alone can empty it in 150 minutes. When both pipes are draining together, how long does it take them to empty the pool?
Answer:
41. Solve for x:
42. Solve for x:
43. Solve for x:
VII. Radicals and Quadratic Equations
44. Simplify
(Assume that the variable z
represents a
positive real number.) 
Answer: 
45.
Simplify. 
Answer:
46.
Simplify. 
Answer:
47.
Perform the following multiplication and simplify:
Answer:
48.
Perform the following multiplication and simplify:
Answer:
49.
Rationalize the denominator and simplify:
Answer: 
50.
Rationalize the denominator and simplify:
Answer: 
51.
Evaluate: a) 
b)
Answer: a)
b)
52.
Solve 
where
y is a
real number. Simplify your answer as much as possible leaving it in radical
form.
Answer:
53. Solve
where
y is a real
number. Write your answer in simplified radical form.
Answer:
54. Solve for x:
Write your answer in simplified radical form.
Answer:
55. Solve for x:
Write
your answer in simplified radical form.
Answer:
56. Solve for x:
Write
your answer in simplified radical form.
Answer:
57. Solve for x:
Write
your answer in simplified radical form.
Answer:
