12th grade advance functions
1. A manufacturer of electronics components produces precision resistors designed to have a tolerance of 1%. From quality-control testing, the manufacturer knows that about one resistor in six is actually within just 0.3% of its normal value. A customer needs two of these more precise resistors. What is the probability of finding exactly two such resistors among the first four tested?
2. The Choco-Latie Candies company makes candy-coated chocolates, 40% which are red. The production line mixes the candies randomly and packages ten per box.
a. What is the probability that less than four candies in a given box are red?
b. What is the probability that at least four candies in a given box are red?
c. Describe a second way of finding the answer to part b.
3. Suppose that 65% of families in a town own computers. If ten families are surveyed at random. What is the probability that at least five own computers?
4. Ninety percent of a country’s population are right handed. What is the probability that exactly 29 people in a group of 30 are left handed?
5. A student takes a five question multiple-choice quiz. Each question has four possible responses. The student guess at random for each question. Calculate the probability for each possible score on the test from getting 0 correct to getting 5 correct.
6. A student takes a 5 question multiple-choice quiz. Each question has four possible responses. The student guess at random for each question. Calculate the probability of getting greater than 2 questions correct.
7. Over a long period, the proportion of defective items in a manufacturing process is 5%. In a random sample of 25, find the probability of
a. No defectives
b. Exactly 2 defectives
c. More than 2 defectives
8. A company makes 1.5 volt batteries and its quality control department estimates that 0.7% of the batteries are defective. The batteries are sold in packs of 8. Find the probability that a pack contains no defective batteries.
9. A bag contains a large number of balls of which 25% are blue. The rest are yellow. If 7 balls are taken from the bag, find the probability that less than 5 are yellow.
10. Ten percent of a country’s population are left handed. What is the probability that more than 28 people in a group of 30 are right handed?
11. A Ferris wheel has a diameter of 40m. It sits 5m above ground. It makes one complete rotation every 65 seconds. Find the equation of the graph?
12. A Ferris wheel has a diameter of 48m. It sits 4m above ground. It makes one complete rotation every 55 seconds. How high is the Ferris wheel?
13. The equation that models the height of a Ferris wheel is as follows:
. How tall is the highest point on the Ferris wheel?
14. The equation that models the height of a Ferris wheel is as follows: . How tall is the highest point on the Ferris wheel?
15. The equation that models the height of a Ferris wheel is as follows: . How long is the Ferris Wheel ride?
16. A class has 10 boys and 12 girls. The teacher wants to form a committee of 3 students to plan the year-end picnic. Determine the number of committees possible if there are no boys on the committee.
17. A class has 10 boys and 12 girls. The teacher wants to form a committee of 5 students to plan the year-end picnic. Determine the number of committees possible if there must be 3 boys and 2 girls on the committee.
18. A store has 25 doughnuts, 20 cookies, and 8 cupcakes. Customers can create a party tray choosing 10 doughnuts, 8 cookies and 5 cupcakes. In how many ways can this be done?
19. In how many ways can a first, second, third prize and five identical fourth place prizes be given to 20 runners competing in a race?
20. In how many more ways can a group of 15 seniors running for president, vice president, and secretary be chosen over a group of 12 juniors running for only president and vice president?
21. If the probability of giving birth to a boy is 0.52, what is the probability of giving birth to 3 boys and 1 girl?
22. A water tower is located 410 feet from a building. From a window in the building it is observed that the angle of elevation to the top of the tower is 42 degrees and the angle of depression to the bottom of the tower is 25 degrees. Approximately how tall is the water tower?
23. Two sides of a triangle measure 14ft and 17ft, respectively. The included angle is 72°. Approximately how long is the third side of the triangle? Round to the nearest tenth.
24. The sides of a triangular lot are 158 ft, 173 ft, and 191 ft. Find the measure of the angle opposite the longest side to the nearest tenth of a degree.
25. A landscaper wants to plant begonias along the edges of a triangular plot. Two of the angles of the triangle are 95̊ and 40̊. The side between these angles is 80 feet long. What is the perimeter of this triangular plot of land?
26. During a figure skating routine, Jackie and Peter skate apart with an angle of 15̊ between them. Jackie skates for 5 meters and Peter skates for 7 meters. How far apart are these skaters?
27. A triangular playground has sides of lengths 475 feet, 595 feet, and 401 feet. What are the measures of the angles between the sides, to the nearest tenth of a degree? Write from least to greatest.
28. Frank N. Stine needs to build a wheelchair ramp to the front porch of his hardware store. If the porch is 2.4 feet high, and the angle at which the ramp is to be built is 22°, how long will the ramp be? Round to nearest foot.
29. A tree casts a shadow 21m long. The angle of elevation of the sun is 51°. What is the height of the tree? Round to nearest meter.
30. FOOTBALL: The winning scores for the first 34 Super Bowls are 35, 33, 16, 23,17, 24, 14, 24, 16, 21, 32, 27, 35, 21, 27, 26, 27, 38, 38, 46, 39, 42, 20, 55, 20, 37, 52, 30, 49, 27, 35, 31, 34, and 23.
a. Find the range of the data .
b. What is the mean of the data?
c. What is the median of the data?
d. What is the mode of the data?
e. Create a histogram with the data using classes of 10.
31. NUTRITION: The grams of fat in various sandwiches served by national fast-food restaurants are listed below:
18, 27, 15, 23, 27, 14, 15, 1, 39, 53, 31, 29, 12, 43, 38, 4, 10, 9, 21, 31, 31, 25, 28, 20, 22, 46, 15, 31, 16, 20, 30, 8, 18, 15, 7, 9, 5,8
a. What is the range of the data?
b. What is the mean of the data?
c. What is the median of the data?
d. What is the mode of the data?
e. Create a histogram with the data using classes of 10.
32. BASEBALL: The greatest numbers of stolen bases for a single player are listed.
Year |
‘90 |
‘91 |
‘92 |
‘93 |
‘94 |
’95 |
‘96 |
‘97 |
‘98 |
‘99 |
American League |
65 |
58 |
66 |
70 |
60 |
54 |
75 |
74 |
66 |
44 |
National League |
77 |
76 |
78 |
58 |
39 |
56 |
53 |
60 |
58 |
72 |
a. What is the range of the American League? National League?
b. What is the mean of the American League? National League?
c. What is the median of the American League? National League?
d. What is the mode of the American League? National League?
e. Create a histogram using all of the data.
33. A company tries to develop a cost equation based on the quantity of the product produced in a day. They collected the following data:
Quantity Produced |
20 |
35 |
50 |
65 |
80 |
95 |
110 |
Cost |
642.35 |
766.48 |
858.82 |
928.83 |
1005.32 |
1078.82 |
1140.79 |
a. Determine whether a linear, quadratic, or exponential function would be a good model for the data.
b. According to the model, how much will producing 195 units cost the company?
c. How any units could be produced for $800?
34. After winter break, 3 students came to school sick with the flu. The following table shows the number of students infected with the flu depending on the number of days after the winter break.
Time (days) |
0 |
5 |
10 |
15 |
20 |
25 |
30 |
# of infected students |
3 |
6 |
14 |
23 |
23 |
21 |
9 |
a. Find the quadratic and quartic model that fit this data. Which model appears to better fit the data?
b. Using the better model, find the day at which the number of infected students will reach the maximum.
c. When will the number of infected students drop to zero?
35. Describe how the graph of can be translated to .
36. Describe the transformation of to .
37. Which translation when applied to the graph of results in the graph of?
38. The graph of was translated 2 units to the right and 6 units down, resulting in the graph of g(x). Which function represents g(x)?
39. The graph of was translated 2 units to the right, 7 units up and flipped over the y-axis resulting in the graph of . Which is an equation of ?
a.
b.
c.
d.
40. The function was replaced with resulting in the function. What is the distance between the y-intercept of and the y-intercept of?
a. 6 units
b. 5 units
c. 3 units
d. 20 units
41. Which translation would move the vertex of f(x) up 7 units?
a.
b.
c.
d.
42. The function was replaced with resulting in the function. Which statement correctly states what has happened to the graph?
a. The graph of g(x) has moved 4 units to the left of f(x).
b. The graph of g(x) has moved 4 units to the right of f(x).
c. The graph of g(x) has moved 4 units higher than f(x).
d. The graph of g(x) has moved 4 units lower than f(x).
43. The function underwent a translation resulting in the function. Which describes the translation that resulted in g(x)?
a. A shift up 2 units
b. A shift down 2 units
c. A shift left 2 units
d. A shift right 2 units
44. The function, was shifted 2 units up, resulting in the function g(x). What is the y-intercept of g(x)?
a. (0,-1)
b. (0,-5)
c. (0,2)
d. (0,5)
45. A Ferris wheel has a diameter of 80 feet. Riders enter the Ferris wheel at its lowest point, 5 feet above the ground, at time t = 0 seconds. One complete rotation takes 65 seconds. What is the equation that models the vertical height of a rider at time t? What is the maximum height that a rider will go?
46.
A=__________
Period=___________
Phase Shift=_________
Vertical Shift=_________
47.
A=__________
Period=___________
Phase Shift=_________
Vertical Shift=_________
48.
A=__________
Period=___________
Phase Shift=_________
Vertical Shift=_________
Use the figure below to answer the questions #49-51. Round all answers to the nearest whole value. Drawing is not to scale.