Download FST - Pascack Valley Regional High School District

FST
Name: _______________________
Final Exam Review Guide
Period: ____ Date:
_____________
Trigonometry Unit:
I.
Triangles
a. Right Triangle Trig (SOH-CAH-TOA)
b. Law of Sines and Law of Cosines
II.
Angles
a. Drawing positive and negative
b. Finding coterminal angles
c. Converting from degrees to radians/radians to degrees
d. Finding reference angles
III. Evaluating trig functions
a. No calculator
b. ASTC
IV.
Graphing trig functions
a. Amplitude
b. Period
c. Vertical and horizontal (phase) shifts
You will be given the following information on the test:

6
2
3

2
1
4

60
o
1
Law of Sines:
1
sinA
a

sinB
b

45
o
sinC
c
3
Round to the tenth.
 45
o
 60o
S A
T C
Law of Cosines: c 2  a 2  b 2  2ab cosC
In addition, I will give you a unit circle.
1. Solve for x.
 30o
a)
b)
21
x
o
16
c)
x
64
45
14.5
19o
2. Two boats leave the same port at the same time.
91o
x
46o
The angle between
their paths is 46o . One boat is traveling at a speed of 49 km/hr and
the other boat is traveling at a speed of 34 km/hr. How far apart
are the boats after 2.5 hours?
3. Nick and Patty are walking down a straight path in the woods. Nick
is 100 yards ahead of Patty. In the distance, they each see a bald
eagle in a tree.
Patty’s line of sight to the bird makes an angle
of 28o with the ground and Nick’s line of sight makes an angle of 52o
with the ground. What is the altitude of the bald eagle in the tree?
Convert measures in degrees to radians and measures in radians to degrees.
4. 120o
5. 42o
6.
5
3
7. 
2
9
Find a coterminal angle x such that 0  x  360o or 0  x  2 .
8. 273o
9. 825o
10.
17
3
11. 
43
8
Find the reference angle for the given angles.
12. 300o
13. 540o
14. 135o
15.
16.
17.
13
6
7
12
4
5
18. 42o
19.
11
12
20. 
14
3
Draw the following angles on a coordinate plane.
21. 750o
22. 145o
23. 370o
24.
4
5
25. 
8
3
All answers must be between 0 and 360 degrees.
26.
the sin  0.8192.
(No Calc)
If sin125o  0.8192, find another angle,  , such that
27.
the tan  0.6249.
If tan148o  0.6249, find another angle,  , such that
28.
the sec  1.0223.
If sec12o  1.0223, find another angle,  , such that
29.
Find all values of  such that sin  
1
2
.
Evaluate the function. (No Calc)
30.
sin240o
31.
csc135o
32.
sec225o
33.
tan(150o )
34.
cos(420o )
35.
 3 
sin  

 4
36.
tan
7
4
Answer the questions below. (No Calc)
37.
If cos   
38.
If tan 
39.
If csc   
4
3
5
13
and 180    360, then find sin and cot  .
and 0    180, then find csc  and sec  .
25
7
and 90    270, then find tan and cos  .
(Remember: 72  242  252 )
Find the sine, cosine, and tangent values based upon the following points.
(No Calc)
40.
41.
24, 7  Remember: 7  24  25
6, 8 Remember: 6  8  10
2
2
2
2
2
2
Graph the following functions on the interval [0  2 ] .
scaled appropriately and labeled.
42.
43.
44.
45.
46.
y
y
y
y
y
All axes must be
 2sinx
 cos3x
 4cos2x
 5sin2x
 2  cos2x


47. y  3  sin  x  
4

48. y 
1
4
cos
1
4
x


49. y  2  3sin2  x  
2

Graph the following functions until two full cycles are complete.
axes must be scaled appropriately and labeled.
1
50. y  cos x
3
51. y  5sin3x
Write the equation of the function from the graph or the given
information.
52.
53. y = asinbx
amplitude = 5
period = 6
54. y = acosbx
amplitude = 4
period =

2
vertical shift: up 2 units
Statistics Unit
1. Determine if any of the data sets contain outliers.
All
Cars99
CityMPG HwyMpg FuelCapacity Acc030 Acc060 QtrMile
17
19
20.5
23
30
S1 = min  
S2 = Q1  
CityMPG
S3 = median 
S4 = Q3  
S5 = max  
23
26
28.5
31
38
10.3
14.5
16.2
18.45
23.7
2.4
3.3
3.5
3.9
4.5
5.6
8.8
9.5
10.9
12.5
14.1
16.8
17.4
18.2
19.1

HwyMPG
FuelCapacity
Acc030
Acc060
QtrMile
2. Below is a graph of the number of losses for National League teams
during the 1999 season. Describe the distribution seen below. Also
state the relationship between the mean and median.
3. The graph below shows Skull measurements of 150 male Egyptian skulls
from 5 different time periods. Describe the distribution seen below.
Also state the relationship between the mean and median.
4. The five number summary of a data set is (17, 27, 35, 49, 90)
a) Are there any outliers in this data set?
work)
Explain.
(Show all
b) Is the mean less than, equal to, or greater than the median?
Why?
5. Since Pascack Valley High School eliminated the use of bells,
teachers have noticed an increase in tardiness. One statistics
teacher decided to collect data on the accuracy of students’ and
teachers’ watches. The ordered data from 9 randomly selected
teachers and 9 randomly selected students are shown below. Negative
values mean that the watch showed a time earlier than the true time
(in minutes), positive values indicate later than the true time.
Students
Teachers
–3.5
-6
–2
–2
–2
0
–1
0
–0.5
0.5
–0.5
1
1
1
2
1
3.5
1.5
a. Construct parallel boxplots using the given data. Show your plots
on the grid below. Be sure to properly indicate outliers if any
exist.
–6
-5
-4
-3
-2
-1
0
1
2
3
4
b. Compare the two data sets.
c. Based on the boxplots, which of these two groups, students or
teachers, tends to have watches set closer to the true time?
Explain your choice using appropriate statistical analysis.
1. The heights of all 10-year old children are normally distributed,
with a mean of 138 cm and a standard deviation of 5 cm.
a. Find the percent of heights greater than 133 cm.
b. Find the percent of heights less than 130 cm.
c. Find the percent of heights between 131 cm and 142 cm
d. Find the percent of heights between 125 cm and 135 cm
e. Find the approximate height of a 10-year old that is taller than at
than 80% of all 10-year olds.
f. Find the approximate height of a 10-year old that has 30% of the
other 10-year olds taller than him/her.
g. Find the heights of the middle 70%.
2. A school district administered IQ tests to all students in the
district and found the distribution to be normal with a mean of 102
and the standard deviation of 12.
a. Find the percent of scores between 96 and 110.
b. Find the percent of scores between 105 and 120.
c. Find the percent of scores less than 120.
d. Find the percent of scores greater than 114.
e. Find the approximate IQ score of a student that has a score less
than 65% of other students IQ scores.
f. What are the approximate IQ scores for the top 5% of the students?
g. What is the smallest range containing 20% of the scores
4. Adult female Dalmatians weigh an average of 50 pounds with a standard
deviation of 3.3 pounds. Adult female Boxers weigh an average of 57.5
pounds with a standard deviation of 1.7 pounds. One statistics
teacher owns an underweight Dalmatian and an underweight Boxer. The
Dalmatian weighs 45 pounds, and the Boxer weighs 52 pounds. Which dog
is more underweight? Explain using percents and z-scores.
5. Marks on a Chemistry test follow a normal distribution with a mean of
65 and a standard deviation of 12.
a. Approximately what percentages of the students have scores below
50?
b. What is the approximate 90th percentile of the mark distribution?
c. If the standard deviation calculated was wrong and actually 20% of
the scores were below 50, what would be the correct standard
deviation.
6.
PROBABILITY REVIEW:
1. A calculator is chosen at random from a display case that contains
four graphing calculators and eight scientific calculators. What is
the probability that the calculator is graphing?
2. The employees of a company are in six departments. 31 are in sales,
54 are in research, 42 are in marketing, 20 are in engineering, 47
are in finance and 58 are in production. If one employees paycheck
is lost, what is the probability that the employee is not in the
research department?
3. In how many ways can you order the letters A, B, C, and D?
4. A computer generates random integers from 1 through 20.
probability that the first two numbers are 5 or less?
What is the
5. There are 34 students in your homeroom. Numbers from 1 through 34
are randomly assigned to the students to determine the order in which
your school pictures will be taken. What is the probability that you
and your best friend will be there first and second to get your
pictures taken (in either order)?
6. Find the indicated probability:
P(A) 
P(B) 
1
4
1
5
P(A  B) 
P(A  B) 
2
15
?
?
7. You have time to listen to 3 songs on your iPod that contains 40
songs. If the iPod is on the random shuffle setting, what is the
probability that your three favorite songs will be the three that
play?
8. In how many ways can three letters be chosen from the alphabet?
order of the three letters is not important.
The
9. Five cards are dealt at random from a standard deck of 52 playing
cards. What is the probability that all five cards are face cards or
aces?
10.
Suppose that you decide to buy a car. Among the options you may
choose 6 paint colors (red, yellow, blue, brown, black, and white), 3
interior colors (brown, black, white), and 2 transmissions (manual,
automatic).
a. If a car dealer has, in the parking lot, one of every type of
car made using these options, how many cars are there in the
lot?
b. How many cars of each color are in the parking lot?
c. What is the probability that if you choose a car at random that
it will be red?
11.
Suppose you go out to a movie with 6 of your friends.
many ways can you form a line at the ticket booth?
In how
12.
The probability that it will rain today is 0.4, and the
probability that it will rain tomorrow is 0.2. The probability that
it will rain both days is 0.1. What is the probability that it will
rain today or tomorrow?
13.
Consider all families that have exactly 3 children. What is the
probability that a family of 3 children chosen at random has all 3
daughters?