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Worksheets11MA End of S1 Review
Total questions: 148
Worksheet time: 5hrs 56mins
A cable news show displays the results of a poll for a two-candidate runoff election between candidate A and candidate B. The poll shows that candidate A is leading with 53% of the vote. In small print at the bottom of the graphic, it says ±4.9%. Which of these statements is true about this poll?
Candidate A will win because the mean percentage for the poll is greater than 50%.
Candidate A cannot get more than 58% of the vote.
The poll predicts that between 48.1% and 57.9% of voters will select candidate A in the election.
The poll should not be trusted since it has a margin of error attached to it.
In the 1940s, the U.S. Department of Commerce reported a new way to test the tensile strength, in pounds per square inch, of concrete. Several samples of concrete specimens were used to estimate the mean tensile strength of 430 pounds per square inch with a margin of error of 10 pounds per square inch. After the study was published, another group proposes to run the same test on concrete specimens but with samples including many more concrete specimens in each sample. Which of these statements is most likely to be true about the second study?
The estimated mean will be greater than 440 pounds per square inch.
The margin of error for the second study will likely be around 10 pounds per square inch.
The margin of error for the second study will likely be greater than 10 pounds per square inch.
The margin of error for the second study will likely be less than 10 pounds per square inch.
Forty volunteer drivers are separated into two groups of 20 drivers each at random. The first group is asked to pay particular attention to braking smoothly when approaching a red light or stop sign. The second group is given no special instructions. All drivers report, at the end of a month, the gallons of gasoline used. The mean for the first group is 43.16 gallons of gas. The mean for the second group is 54.63 gallons of gas. The difference in means for the two groups is -11.47 gallons of gas. The data for both groups are combined and redistributed at random into two groups of 20. The means for each redistributed group are calculated, and the difference in means is recorded. The differences are represented in the histogram. Which of these conclusions and justifications is the most reasonable?
A. The difference in means for the two treatment groups is likely due to the random assignment since the difference is negative.
B. The difference in means for the two treatment groups is likely due to the random assignment since there is at least one value in the histogram with a greater absolute difference than 11.47 gallons of gas.
C. The randomization distribution does not give any evidence that the difference between the two treatment groups is due to the special instructions.
D. The randomization distribution provides strong evidence that the difference in means for the two treatment groups is due to the treatment because the difference is highly unlikely based on random assignment alone.
A student measures the wingspans of 40 local dragonfly specimens selected at random. The sample mean is 6.8 centimeters with a margin of error of 0.9 centimeters. Based on this information, what are plausible values for the mean wingspans of the population of local dragonflies?
A. between 6 cm and 7 cm
B. 6.8 cm
C. between -5.7 cm and 10 cm
D. between 5.7 cm and 7.7 cm
Which of the following best describes the difference between an observational study and an experiment?
Observational studies always have larger sample sizes
Experiments involve manipulating variables while observational studies do not
Observational studies are always more accurate
Experiments never have control groups
In a normal distribution, approximately what percentage of data falls within one standard deviation of the mean?
95%
99.7%
68%
50%
What is the primary purpose of randomization in statistical studies?
To make the study easier to conduct
To reduce the impact of confounding variables
To increase the sample size
To eliminate the need for control groups
A z-score of -2 indicates that a data point is:
At the mean
Two standard deviations below the mean
Two standard deviations above the mean
At the median
Which type of data would be considered secondary data?
Interviews you conduct personally
Data collected from government census records
Surveys you distribute to participants
Direct observations you make
When evaluating a statistical study, what is the most important consideration regarding ethics?
The sample size used
The statistical methods employed
The protection of participant privacy and consent
The cost of the study
In the equation log₂(x) = 8, what is the value of x?
256
16
64
128
Which transformation of eˣ moves it 3 units right?
e(x+3)
e(x−3)
3eˣ
eˣ + 3
Which of the following is the inverse function of f(x)=ex ?
ln(x)
e−x
−ex
ex1
The domain of log2(x−3) is:
x < 3
All real numbers
x = 3
x > 3
Solve for x: log4(x+2)=3
x = 62
x = 64
x = 14
x = 16
Which property is represented by logb(MN)=logb(M)+logb(N) ?
Quotient Property
Change of Base
Product Property
Power Property
Which equation represents exponential decay?
y=3(2x)
y=3(0.5x)
y=3x2
y = 3x
The range of f(x) = log5(x) is:
(0, ∞)
(-∞, ∞)
[0, ∞)
(-∞, 0)
Which transformation of f(x)=ex shifts the graph 2 units left?
f(x + 2)
f(x - 2)
f(x) + 2
2f(x)
The equation log₂(x − 1) = log₂(3x + 5) has how many solutions?
Two
Zero
One
Infinite
If log₄(x) = 3, then x equals:
12
64
81
16
Which represents the solution to log₂(x + 3) = 4?
x = 16
x = 13
x = 9
x = 7
The domain of f(x) = ln(x − 5) is:
x ≥ 5
x ≤ 5
x = 0
x = 1
Which is equivalent to log₃(27)?
9
6
4
3
The half-life of a radioactive substance is 12 years. Which equation models the amount remaining after t years, starting with 100 grams?
A(t) = 100(0.5)ᵗ/¹²
A(t) = 100(2)ᵗ/¹²
A(t) = 100(0.5)¹²ᵗ
A(t) = 100(2)¹²ᵗ
A study where a political pollster wishes to determine if his candidate is leading in the polls.
Survey
Observational Study
Experiment
Osman wanted to know what this weekends favorite movie was among RBHS students so he asked everyone at RBHS and counted the number of movie preferences.
Which research method is most appropriate?
Census
Sample Survey
Experiment
Biased Sample
A researcher stood at a school parking lot entrance to see if the color of a car is related to the driver not wearing a seat belt.
Which research method is most appropriate?
Observational Study
Experiment
Survey
Correlation
Ghala wanted to know what the most popular book was in the whole school, so she asked everybody in 11th grade what their favorite book was. Which research method is most appropriate?
Sample Survey
Census
Experiment
Biased Sample
graph log7(x+2)+3
Rewrite in exponential form:
log3(9)=2.
39=2
32=9
x2=9
3x=2
graph log7(x+2)+3
Graph the function y = 3(5)x
Graph the function y= 4(41)x
Graph the function y= 0.45⋅3x
James' 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.
70(2)35
70(2)5
2(70)5
5(70)2
A=10(1.01)3
3log2x - log2y + log2z
f(x) = log2(x)
R: y > 0
Range: all real numbers
Range: all real numbers
Range: y < 0
Solve for x:
2(3)x+1 = 36
log53 + log56 + log59
log (4x − 5) = log (2x − 1)
What is the Asymptote?
x=5
x=0
y=0
x=1
x=3
Exponential functions have ____________ asymptotes.
horizontal
vertical
diagonal
log52+log53=
log55
log56
log105
log105
Find the domain of the logarithmic function f(x)=ln(2−x) .
(-∞, 2) or (2, ∞)
(-∞, 0)
(-∞, 2)
(-2, ∞)
(0, ∞)
In an exponential function, what does the 'a' represent?
SLOPE
RATE OF CHANGE
Y-INTERCEPT
COMMON RATIO
Which function models this table?
f(x)=2⋅4x
f(x)=4x
f(x)=4⋅2x
f(x)=8x
A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?
$5,884.00
$5,178.97
$2,992.96
$2,957.04
Describe the transformations of f(x)= -log2(x+1)
left one & y-axis reflection
right one & y-axis reflection
left one & x-axis reflection
right one & x-axis reflection
5-3x - 1 = 25
4p+2 = 64
Solve log2(x+8)=log264
x=16
x=24
x=56
x=40
Solve log6x+log69=log654
x=6
x=45
x=7
x=36
Solve
log7n=32log78
n=1
n=3
n=6
n=4
Write an exponential function in the form y=abx that goes through points (0,13) and (5,416).
y=13(32)x
y=13(2)x
y=13(5)x
y=2(13)x
Write an exponential function in the form y=abx that goes through points (0,9) and (3,72).
y=9(3)x
y=2(9)x
y=9(2)x
y=8(3)x
What is the Asymptote?
x=5
x=0
y=0
x=1
x=3
Describe the transformations of f(x)= -log2(x+1)
left 1
left one & reflected over the y-axis
left one & reflected over the x-axis
right one & reflected over the x axis
Exponential functions have ____________ asymptotes.
horizontal
vertical
diagonal
Exponential functions have a restricted ______________.
domain
range
Logarithmic functions have a restricted _____________.
domain
range
left one & reflected
stretch and left
right one and reflected
f(x)=log5(x+4) - 2
Describe the asymptote
Horizontal Asymptote x = -4
Vertical Asymptote x = -4
Horizontal Asymptote x = 4
Vertical Asymptote x = 4
f(x)=log5(x+4) - 2
Describe the transformation
translation 4 units to the right, 2 units down
translation 4 units to the left, 2 units down
translation 4 units to the up, 2 units right
translation 4 units to the up, 2 units left
What is the asymptote for the logarithmic function
f(x)=log(x−1)
x=1
x=-1
y=1
y=-1
What is the transformation of the logarithmic function
f(x)=log (x+3)−1
left 3, right 1
right 3, down 1
right 3, up 1
left 3, down 1
Write the equation of the function f(x)=log3x after the following transformations:
Translate 6 units left and 4 units up.
g(x)=log3(x+6)+4
g(x)=log3(x+4)-6
g(x)=log3(x-6)+4
g(x)=3log(x+6)+4
What are the transformations of this function?
vertical compression by 1/3, down 8
vertical stretch by 1/3, down 8
vertical compression by 1/3, right 8
reflection across the x-axis, right 8
Describe the transformations in the logarithmic function
y=4log3x +7up 4 units, left 7 units
left 4 units, up 7 units
vertical stretch by 4, up 7 units
vertical compression by 4, left 7 units
What is the domain of log(x)?
(-∞, ∞)
[0, ∞)
(0, ∞)
(∞, -∞)
What is the range of log(x)?
(-2, 4)
(-∞, ∞)
(-∞, 0)
(∞, -∞)
In the general log function
y = a*logb(x-c)+d, what letter tells us if the function has stretched, compressed, or reflected?
a
b
c
d
In the general log function
y = a*logb(x-c)+d, what letter tells us if the function has moved up or down?
a
b
c
d
In the general log function
y = a*logb(x-c)+d, what letter tells us if the function has moved left or right?
a
b
c
d
Convert Log3(x) = 4 to an exponent
3x = 4
34 = x
x3 = 4
4x = 3
Convert 16 = 2x to a Log
Log2(x) = 16
Log2(16) = x
Log16(x) = 2
Logx(16) = 2
log636 = 2
Rewrite in exponential form:
log9x=2
9x=2
2x=9
29=x
92=x
Write 6x = 8 in log form.
log6 8 = x
log8 6 = x
log6 x = 8
log8 x = 6
Change to logarithmic form.
3h = w
logw3 = h
log3w = h
logh3 = w
log3h = w
Convert 3x = 12 to the equivalent log form.
312 = x
logx 3 = 12
log3 x = 12
log3 12 = x
Change to exponential form.
loga2 = 5
a2 = 5
52 = a
a5 = 2
25 = a
Which functions is a model of exponential growth?
f(x) = 3(.99)x
f(x) = .99(3)x
f(x) = .99(3)-x
f(x) = .99(1 - 0.3)x
Most automobiles depreciate as they get older. Suppose an automobile that originally costs $14,000 depreciates by 20% of its value every year.
What exponential equation can we create to model this situation?
y=14000(.20)x
y=14000(.80)x
y=14000(1.20)x
y=14000(1.80)x
The amount of money in an account at any given time is modeled by the equation A = 4100(1.45)x. How does the amount of money in the account change each year?
It increases by 145%.
It increases by 45%.
It decreases by 145%.
In decreases by 45%.
Describe the transformations that change the graph of y=2x to the graph of y=2x+4+5
Left 4, Up 5
Right 4, Up 5
Left 4, Down 5
Right 4, Down 5
What type of function is f(x)=2(71)x ?
Exponential Growth
Linear
Exponential Decay
None of the Abovee
52 = 25
log232 = 5
log381
log416
Use the graph to help!
Range: y>0
Range: y>1
Range: y>0
Range: y>0
5-3x - 1 = 25
log6(3x - 2) = log6(5x - 8)
3x = 27
104x+1 > 100x - 2
x > 10
x > -2/5
x < -5/2
x > -5/2
