Algebra 2 HonorsName______
Hour______
Write a formula for the measures of all angles coterminal with the given angle. Then use the formula to find two angles, one positive and one negative, that are coterminal with the given angle. NC
1. 2.
Express in either “Decimal Degrees” or in “Degrees Minutes Seconds” to the nearest second. SC
3. 4.
Find a first-quadrant angle , for which an angle five times as large as will be in the given quadrant. NC
5. Quadrant 26. Quadrant 4
7. Find the six trig functions of NC8. If , and find the
other five trig functions. NC
Find the exact value for . NC
9. 10. 11.
12. 13.
Draw a picture for each! Round all answers to the nearest thousandth. SC
14. An airplane is at an elevation of ft when it begins its approach to an airport. Its angle of
descent is . What is the approximate air distance between the plane and the airport?
15. A window washer 50 ft above the ground sees a parked car 153 ft away. What is the angle of
depression from the window washer to the car?
16. Find the measures of the angles of an isosceles triangle whose sides are , and .
17. Two farmers stand on the same side of a silo 10 feet apart. The angles of elevation to the top
of the silo are 25 and 30 respectively. How far is each farmer from the silo? How high is the silo?
18. While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation
to the peak is . After you drive miles closer to the mountain, the angle of elevation
is . Approximate the height of the mountain.
Convert from Radians to Degrees, or Degrees to Radians. NC
19. 20. 21. 22.
From the information given, find the quadrant in which lies. NC
23. 24.
Find the exact value of the function. NC
25. 26. 27.
28. 29. 30.
31. Find the value of all six trig functions at each quadrantal angle. NC
Express as the function of an acute angle. NC
32. 33.
34. Find the if and .35. Find when .
Are the following points on the unit circle? Show your work. NC
36. 37.
Solve the following triangles. Round all answers to the nearest tenth. SC
38. 39.
40. 41.
42. In 43. In
Find t Find t
44. Two snowmobilers start from the same point and drive at 8 km/h and 13 km/h, respectively, diverging at
an angle of . Three hours after leaving, they find that their radio transmissions are barely audible.
How far apart are they at that time? Round to the nearest thousandth. SC
45. A triangle has sides of lengths 7, 12 and 10. Find the measure of the smallest angle to the nearest
tenth of a degree. SC
46. Jan is flying a plane on a triangular course at 450 mi/h. She flies due east for four hours and then turns
right through a angle. How long after turning will she be exactly southeast of where she started? SC
47. Find the length of an arc that subtends48. Find the area of a sector with central angle
a central angle of in a circle with in a circle with radius 3 mi. SC
radius 10 m. SC
49. A woman is riding a bicycle whose wheels are 28 in. in diameter. If the wheels rotate at 130 revolutions
per minute (rpm), find the speed at which she is traveling in mi/h. SC
50. A boy rotates a stone in a 3 ft. long sling at the rate of 15 revolutions every 10 seconds.
Find the linear and angular velocities of the stone. SC
Determine whether each function is even, odd, or neither. NC
51. 52. 53. 54.
State the amplitude, period, vertical shift and phase shift. Graph and Identify the Domain & Range. NC
55.
Amplitude:
Period:
Phase Shift:
Vertical Shift:
56.
Amplitude:
Period:
Phase Shift:
Vertical Shift:
57.
Amplitude:
Period:
Phase Shift:
Vertical Shift:
58.
Amplitude:
Period:
Phase Shift:
Vertical Shift:
59.
Amplitude:
Period:
Phase Shift:
Vertical Shift:
60.
Amplitude:
Period:
Phase Shift:
Vertical Shift:
Find the EXACT value of each expression, if it is defined. Please leave answers in radians. NC
61. 62. 63.
64. 65. 66.
67. 68. 69.
70. 71. 72.
73. 74. 75.
Simplify. NC
76. 77.
78. 79.
80. 81.
82. 83.
Use the sum and difference formulas to find the exact value. SC
84. 85.
Find and from the given information. SC
86. ; 87. x in quadrant II
Use the half-angle formulas to find the exact value. SC
88. 89. 90.
Solve for Solve for Round your answer to the nearest thousandth. SC
91. 92.
Find the formulas giving the general solution for each given and Your answers must be exact. NC
93. 94.
95. 96.
97. 98.
Find all solutions of the equation in the interval. NC
99. 100.
101. 102.
Algebra 2 HonorsName______
Hour______SC
1. A briefcase lock has 3 rotating cylinders each containing 10 digits. How many numerical codes
are possible?
2. Allan is playing the role of Oliver in his school’s production of Oliver Twist. The wardrobe crew has
presented Allan with 5 pairs of pants and 4 shirtsthat he can wear. How many possible costumes
consisting of a pair of pantsand a shirt does Allan have to choose from?
3. A Mexican restaurant offers chicken, beef, or vegetarian fajitas wrappedwith either corn or flour tortillas,
and topped with either mild, medium orhot salsa. How many different choices of fajitas does a customer
have?
4. How many 7-digit phone numbers can be formed if the first digit cannot be 0 or 1, and no digit can
be repeated?
5. How can 8 students be seated in 8 seats in the front row of the school auditorium?
6. How many ways can you check out 3 library books from a list of 8 books for a research paper?
7. How many ways can you elect 4 candidates to a municipal planning board from a field of 7 candidates?
8. How many ways can 10 contestants finish a race in first, second, and third place?
9. A student council has 5 seniors, 4 juniors, 3 sophomores and 2 freshmen as members. In how many
ways can a 4-member council committee be formed that includes one member from each class?
10. How many ways are there to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 if no
digit is used more than once?
11. Six representatives from a senior class of 350 students are to be chosen for the student council.
In how many ways can these students be chosen to represent the senior class on the student council?
Find the number of possible 5-card hands that contain the cards specified from a standard 52-card deck.
12. 4 kings and one other card 13. 5 hearts or 5 diamonds
Find the number of distinguishable permutations in the following words.
14. PROBABILITY15. PERMUTATION16. BEEKEEPER
A letter is selected at random from those in the word TRIANGLE. Find the probability of each event.
16. It is a vowel.18. It is from theupper half of the alphabet.
A card is randomly selected from a standard deck of 52 cards. Find the probability of drawing the given card.
19. A red king20. A diamond or a 321. Not a club
Two cards are drawn at random from a 52-card deck without replacement. Find the probability of each event.
22. Both are hearts.23. Both are jacks.
24. Neither is red.25. Neither is a spade.
Two six sided dice are rolled, one blue and one red. Find the probability of the given event.
26. The sum is 3 or 9.27. The sum is greater than 7 and less than 11.
Find the odds in favor of an event, given the probability of the event.
28. 29. 30.
Find the probability of an event occurring, given the odds of the event.
31. 32. 33.
34. There are 3 nickels, 3 dimes and 5 quarters in a purse. Three coins are selected in succession at
random. Find the probability of:
a. Drawing a nickel, then a dime, then a quarter if no replacement occurs
b. Drawing three quarters if replacement occurs
c. Drawing a nickel and then two quarters if no replacement occurs
d. Drawing three quarters if no replacement occurs
35. Serena is creating a painting. She wants to use 2 more colors. She choosesrandomly from 6 shades of
red, 10 shades of green, 4 shadesof yellow, 4 shadesof purple and 6 shades of blue. What is the
probability that she chooses 2 shades of green?
36. Becky’s mother is shopping at the bakery. The owner offers Becky acookie froma jar containing 22
chocolate chip cookies, 18 sugar cookiesand 15 oatmeal cookies. Without looking, Becky selects one,
drops it back in, and then randomly selects another. What is the probability that neither selection was a
chocolate chip cookie?
Algebra 2 HonorsName______
Hour______SC
Find a formula for the nth term, of each sequence.
1. 18, 11, 4, -3, . . .2. 16, 24, 36, 54, . . .
Given the arithmetic sequence find each of the following.
3. The value of 4. Which term is ?5. Find
Write a rule for the nth term of the arithmetic sequence.
6. 7.
8. Insert three arithmetic means between 6 and 26.
Write a rule for the nth term of the geometric sequence.
9. 10.
11. Find of the geometric sequence
12. The temperature of water in a kettle is when it is placed on the stove. Its temperature n
seconds after being placed on the stove is is 7% more than 1 second earlier. Find the
temperature of the water a) 20 seconds and b) 1 minute after it is placed on the stove.
Is this realistic?
13. Find the sum of the first 20 terms of the geometric series
14. Find the geometric mean of .
15. Insert 4 geometric means between -4 and -972.
Evaluate. You must use a formula when appropriate.
16. 17. 18.
19. Find the sum of the series:
Write in sigma notation.
20. 21.
Find the sum of each series. Note, for arithmetic and geometric series, you may use the formula. You must use other methods to find non-arithmetic and non-geometric sums.
22. Odd integers from 100-350.
23. The positive four-digit integers divisible by 12.
Use Arithmetic and Geometric Sequences and Series to solve the following applications.
24. A small hardware store makes a profit of $10,000 during its first year. The store owner sets a
goal of increasing profits by $700 each year for 7 years. Assuming that this goal is met, find
the total profit during the first 8 years of business.
25. A bouncy ball is dropped from the top of a 200 foot building. It rebounds to 93% of its
original height after each successive bounce. After bouncing and rebounding 15 times, how
far has the ball traveled?
Write each of the following as a fraction.
26. 27. as a fraction.
Write the first five terms of the sequence.
28. 29.
30. 31.
32. Expand
33. Find the 5th term of 34. Find the 4th term of
35. Find the term containing in
Algebra 2 HonorsName______
Hour______NC
Determine the conic represented by the following equations. Then, find all necessary information and graph the following equations.
1. 2.
3. 4.
5. 6.
7. 8.
9. 10.
Write an equation given the following information.
11. Circle: 12. Parabola:
13. Parabola: 14. Ellipse:
15. Hyperbola:
Identify each conic section and list all of its necessary information.
16. 17.
18. 19.
Given the equation of a circle, find the center and the radius.
20. 21.
Given the equation of a parabola, find the axis of symmetry.
22. 23.
Given the equation of an ellipse, find the foci.
24. 25.
Given the equation of a hyperbola, find the length of the transverse axis.
26. 27.
Algebra 2 HonorsName______
Hour______
Sketch the system and estimate the solutions. NC
1. 2. 3.
Solve the system of equations. NC
4. 5. 6.
7. 8.
Use the following matrices to perform the indicated operation, or explain why it cannot be done. NC
9. 10. 11.
Use the following matrices to solve the matrix equation for the unknown matrix, X, or show that no solution exists. NC
12. 13. 14.
15. 16. 17.
Evaluate. Determine if an inverse will exist. Be sure that you can do the problem by hand and on the graphing calculator. SC
18. 19. 20.
Evaluate. Determine if an inverse will exist. Be sure that you can do the problem by hand and on the graphing calculator. SC
21. 22. 23.
Find the inverse of each matrix. If the matrix has no inverse, say so. NC
24. 25. 26.
Solve the system of equations using matrices. 2x2 must be done by hand, 3x3 can be done on the calculator.
27. 28.
29. 30.
Solve the system using Cramer’s Rule. 2x2 must be done by hand, 3x3 can be done on the calculator.
31. 32.
33. 34.
35. 36.
Algebra 2 HonorsName______
Hour______SC
Name the vector and write its Given the points, write the component form
component form.for each vector.
1. 2.
3.
Find the designated values for the given vectors in terms of i and j:
4. 5. 6.
Find
7. 8.
9. Find the dot product:
Determine if the following vectors are orthogonal.
10. 11.
12. Find the vector with and .
13. Find the magnitude and direction of the vector
14. Find the magnitude and direction of the vector created by
15. Given the magnitude of 35 at a direction of with the positive x-axis, find the horizontal and
vertical component of the vector.
16. Find the work done by the force F in moving an object from P to Q:
17. Find the angle between the given vectors:
18. Find the work done by the force in moving an object from P(0, 10) to Q(5, 25).
19. A constant force moves an object along a straight line from point (2, 5) to the point (11, 13). Find the work done if the distance is measured in feet and the force is measured in pounds.
20. A ship with velocity of 20 km/h has a heading of and an ocean current of 3 km/h is flowing due south.
Find its speed and true course bearing.
21. An airplane flies 600 km/h and its heading is when there is a 40 km/h wind blowing from .
With what heading and at what speed should the plane travel?
Algebra 2 HonorsName______
Hour______SC
Make a stem and leaf plot of the data and then find the mean, median, mode, and range.
1. 35, 36, 38, 36, 42, 45, 41, 482. 88, 90, 92, 75, 88, 76, 79, 85
3. 76, 102, 87, 85, 91, 92, 91, 974. 103, 155, 140, 125, 130, 140, 115
For the following sets of data find the 5 number summary, ranges, and fences. Name any outliers and then create a box and whisker plot.
5. 48, 3, 19, 17, 4, 4, 14, 3, 13, 6. 2, 31, 10, 17, 10, 11, 17, 13, 3,
19, 13, 7, 17, 10, 14 5, 41, 5, 17, 11, 17
Compare box and whisker plots A and B.
7. What is the median of each data set?
8. What is the least value in plot A?
9. What is the greatest value in plot B?
10. What is the lower quartile of each data set?
11. What is the upper quartile of each data set?
12. Which plot has the greater interquartile range?
13. Which plot illustrates the larger range of data?
14. What percent of the data in plot A is greater than 8?
15. What percent of the data in plot B is less than 18?
Using the following information, find the mean and standard deviation of each data set.
16. 74, 101, 87, 89, 23, 92, 84, 9717. 35, 36, 32, 36, 42, 47, 41, 50
18. A Calculus test given last week can be summarized by the following: the scores were
normally distributed with a mean of 81 and a standard deviation of 4.
a. Construct a normal distribution of the data.
b. What percent of the students scored at most 81?
c. What percent of the students scored higher than an 89?
d. Between which pairs of scores do 97.5% of the students fall?
e. What is the z-score for a test grade of an 88?
f. What is the probability of scoring at most a 68?
g. What is the probability of scoring higher than a 95?
19. The number of times a robin chirps in a day is normally distributed with a mean of 45,700 chirps
and a standard deviation of 300 chirps.
a. Find the z-score for 46,520 chirps.
b. What is the probability that a robin will chirp less than 46,520 in a day?
c. What is the probability that a robin will chirp more than 46,520 in a day?
d. What is the probability that a robin will chirp 45,000 times or less in a day?
20. Find the margin of error for a survey that has the given sample size.
a. 824b. 6745
c. 20000d. 155
21. Using the margin of errors for number 20, find the interval that is likely to contain the exact
percent of the total population if for each situation 47% of the sample agreed with the question
asked.
a. b.
c.d.
22. Find the sample size required to achieve the given margin of error.
a. ±2.9%b. ±10.2%
c. ±1.2%d. ±5.7%
ANSWERS – Trigonometry
1. 2.
3. 4. 5. 6.
7.
8. 9.
10. 11. 12. 13.
14. 859,829.517 feet15. 16.
17. Farmers: 41.994 and 51.994 feet from silo. Height: 24.245 feet18. 1.974 mi
19. 20. 21. 22. 23. Q2
24. Q225. 26. -127. 28. -1
29. 30.
31.
32. 33. 34. 35. 36-37. Yes, See Work
38. No Solution39.
40.
41. 42. t = 18.6 43. t = 21.744. 48.360 km
45. 46. 32 hrs. 27 min.47. 48.
49. 10.83 mi/hr50. 50. Angular: 9.42 radians/sec Linear: 28.27 ft/sec51. Neither
52. Neither53. Even54. Odd55.
56. 57.
58. 59.
60. 61. 62. 63.
64. 65. 66. 67. 68.
69. 70. 171. 72. 73.
74. 75. 76. 77. 78.
79. 80. 81. 82. 83.
ANSWERS – Probability
1. 1,0002. 203. 184. 483,8405. 40,320
6. 567. 358. 7209. 12010. 60
11. 12. 4813. 2,57414. 9,979,20015. 19,958,400
16. 3,02417. 18. 19. 20.
21. 22. 23. 24. 25.
26. 27. 28. 3:429. 4:130. 1:14
31. 32. 33. 34a. 34b.
34c. 34d. 35. 36.
ANSWERS – Sequences and Series
1. 2. 3. 4. n = 49 5.
6. 7. 8. 6, 11, 16, 21, 269. 10.
11. 12.
13. 14. 15. -4, -12, -36, -108, -324, -97216. 249,991
17. 59,04018. 19. 2020. 21.
22. 28,12523. 4,126,50024. $99,60025. 3,724.96 feet26.
27. 28. 4, 13, 22, 31, 4029. 8, 40, 200, 1000, 500030. 2, 4, 12, 48, 240
31. 32.
33. 34. 35.
ANSWERS – Conics
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. 12. 13.
14. 15.
16.
17.
18.
19.
20. 21. 22.
23. 24. 25. 26. Trans Axis: 4
27. Trans Axis: 4
ANSWERS – Matrices
1. No Solution2. 3.
4. 5. 6. 7.
8. 9. 10. 11. 12.
13. 14. 15. Not Possible
16. Not Possible 17. 18. 19.
20. 21. 22. 23.
24. 25. 26. No Inverse Exists27.
28. 29. 30. 31.
32. 33. No Solution34. InfiniteSolutions35.
36.
ANSWERS – Vectors
1. 2. 3. 4. 5. 6
6.
7.
8.
9. -4410. yes11. No12.
13. 14.
15. 16. 17.
18. 19. 20.
21.
ANSWERS – Statistics
1. 2.
3. 4.
5.
6.
7. A: 8 B: 18. 29. 2410. A: 4 B: 811. A: 16 B: 18
12. A13. B14. 50%15. 75%
16. 17. 18a. See Picture
18b. 50%18c. 2.5%18d. 73-100 or 0-8918e. 1.7518f. 0.5%
18g. 0.2%19a. 2.719b. 99.65%19c. 0.35%19d. 1.07%
20a. 20b. 20c. 20d. 21a. 43.52% - 50.48%
21b. 45.78% - 48.22%21c. 46.29% - 47.71%21d. 38.97% - 55.03%
22a. 22b. 22c. 22d.