Download Spring Benchmark #2 REVIEW 1) You want to estimate the mean

Spring Benchmark #2 REVIEW
1) You want to estimate the mean EOCT score for a population of Ola High School Sophomore
students with a 95% confidence interval. Assume that the population standard deviation is  = 250.
If you want the margin of error to be approximately 20, you will need a sample size of ____________
20 = 1.96
The average ACT score for Ola High School students is 21 with a standard deviation of 3.4. A random
sample of 50 students is taken.
2) What are the mean and the standard deviation of the sampling distribution?
Mean (rate) = ________
Std. Dev. = ______
3) What does the Central Limit Theorem state?
4) What is the probability that a random sample of 50 students will have an average ACT score above 23?
5) A specific sample of 50 students had an average ACT score of 22. Find and interpret a 90%
confidence interval for the average ACT scores for all of Ola High School based upon this sample.
6) Find the indicated term of the sequence.
7) Find the sum.
8) Find the sum of the infinite series.
9) Write the first five terms of the arithmetic sequence.
10) Write the first five terms of the geometric sequence.
11) Write an explicit formula and recursive formula for the following sequence: 18, 6, 2, , …
12) Write an explicit formula and recursive formula for the following sequence: 4, 7, 10, …
13) Intervals of increasing and decreasing:
14) Properly factor the following:
15) Graph the function. Include any asymptotes (dotted line), holes, zeros, and y-intercepts.
a. Domain:
b. HA:
c. VA:
d. SA:
e. Holes:
f.
Zeroes (x – intercepts):
g. Y-Intercept:
16) Graph the function. Include any asymptotes (dotted line), holes, zeros, and y-intercepts.
a. Domain:
b. HA:
c. VA:
d. SA:
e. Holes:
f.
Zeroes (x – intercepts):
g. Y-Intercept:
h. End behavior:
Find the inverse of the following functions:
17)
18)
19) a) What is the domain and range of the following function:
b) What is the domain and range of the inverse of the function? _____________________
Solve each equation:
20)
21)
21)
Find the intervals that satisfy the following rational inequalities:
22)
23)
24) Let be an acute angle in standard position. Find the quadrant containing the terminal side of ,
if csc  < 0 and sec  < 0.
25) Using the unit circle, find the exact value of
.
Use the triangle to the right for # 26 and 27.
B
c
a
26) Find the value of B, if c = 11.5 and b = 6.8
A
b
27) Find the value of a if B = 43 and b = 3.5
28) What is the period and amplitude of y  3 sin( 5 x) ?
29) Let be an acute angle such that sin  
30) If sin  
24
. Find the value of tan .
25
1
and tan   0 , what is cos ?
5
31) If the point (5, -12) is on the terminal side of , what is sin ?
C
32) Which of the following is the graph of y  4 cos 12 x ?
33) Identify the amplitude, period, phase shift, and vertical shift of the function AND GRAPH,
34) Use the information in the table below to find the trigonometric model (equation) to represent the
data.
t (time)
y (depth)
Midnight
(0)
2.55
2 A.M.
4 A.M.
6 A.M.
8 A.M.
10 A.M.
3.80
4.40
3.80
2.55
1.80
35) State the amplitude, period, and vertical-shift AND GRAPH y  3csc 3x  2
Noon
2.27