F&T: Midterm Review #1 2012
Name: _______________
1.) In a capture-recapture experiment, 25 turkeys were caught, tagged, and
released. One month later, 120 turkeys were caught, 5 of which were tagged.
Please estimate the size of the turkey population in this area.
2.) Ben earned the following scores on his first three quizzes in Functions &
Trigonometry: 88%, 96%, 79%. What must he earn on his next quiz in order to
earn an average of 89.5% on his quizzes?
3.) Mike purchased the following stocks this month. Find the average price per
share of his stocks.
Price per share
$32
$20
$15
$40
$22
# of shares
5
7
12
8
7
4.) The table below shows the favorite
leisure activities for 50 adults.
a.) How many adult women chose tv as their
favorite leisure activity?
b.) What percent of women chose sports as their
favorite lesire activity?
c.) What percent of all adults chose dance as their favorite leisure activity?
Use the following information for questions 5-9.
The frequency distribution shows the number of absences for a class of students.
# of days
10
16
20 21
22 23 24 25 26 27
28 29 30
absent
Frequency 1
1
2
1
2
3
1
5
7
6
4
2
1
5.) How many students were in the class?
6.) Please identify the measures of center, then find the values of each.
7.) Please find the 5-number-summary and create a box plot, using an appropriate
scale.
8.) Please determine if there are any outliers by using the 1.5xIQR criterion.
9.) What is the standard deviation? What does it mean?
Use f(x) = x2 - 6x - 7 following information for questions 10-14.
10.) Find f(-3) and f(h+1).
11.) Please find the vertex of the graph. You may find this manually or use your
calculator.
12.) Please identify the y-intercept of the graph.
13.) Please identify the x-intercepts of the graph. You must do this by hand.
14.) Please find the domain and range of f(x).
15.) Please find a linear model to fit the points (3, -3) and (-6, -9).
16.) Please find a quadratic model to fit the points (0, 19), (5,4), and (10, 39).
17.) Each of the numbers below represents a correlation coefficient between two
variables. Which indicates the strongest linear relation?
a. -1
b. 0
c. .5
d. .95
Use the following information for questions 18-22.
A missile is launched upward from the side of a mountain. Its height, h, in feet above
the ground can be modeled by H(t) = -16t2 + 512t + 350, where t is the time in seconds
after the launch. You may use your calculator to aide you with any of these.
18.) How high up the mountain is the launch site? (initial height!)
19.) What is the maximum height attained by the missile?
20.) What is the height of the missile after 5 seconds?
21.) How long (to the nearest tenth second) until the missile hits the ground?
22.) At what time (to the nearest tenth of a second) will the missile be at 3000 feet?
23.) A horizontal stretch of 3 and a vertical shrink of 1/8 are applied to the graph
of y = x2. What is the equation for the image?
24.) A shift to the left by 4 and a shift up by 8 are applied to the graph of y = |x|.
What is the equation for the image?
25.) Please write the translation rule that maps f(x) = x3 to g(x) = (2x-6)3 + 5.
26.) Write the following in graphing form (by completing the square). Then,
identify the vertex and x-intercept(s). y = 2x2 – 12x - 21
27.) Please find an equation for the inverse function of f(x) = ¼x + ¾.
28.) If f and g are inverse functions and (7, -5) is on the graph of f, then what
would have to be a point on the graph of g?
29.) a.) If f(x) = x2 + 5 and g(x) = ½x – 6, then find an expression for (f(g(x)).
b.) What is (f(g(14))?
30.) Evaluate: log
3
c.) What is (f(g)(-2))?
31.) Evaluate: 4lne5
81
32.) Simplify. Do not leave any negative exponents in your answer:
a.) (3x4y2)2 (2x-6y-3)
b.)
27 x 4y 7
33.) Please find the domain, range, and asymptote of y = 2x -6. Is the asymptote
horizontal or vertical? (It would help to sketch the graph first!)
34.) Please solve to the nearest tenth: 3x
5
2
= 96
35.) Please solve to the nearest thousandth: 2x = 235.
36.) In 1990, the population of PA was 11.9 million and was increasing 1.6% per year.
a.) Please create a model for the population P, in millions, y years after 1990.
b.) Use your model to estimate the population of PA in 2000.
c.) In what year will the population reach 15 million?
37.) The value of a car that you purchased for $6,500 decreases by 9.4% each year.
Write an exponential model expressing the value of your car after x years.
38.) Please solve:
4 log
3
(x-1) = 12
and
log
2
x + log
2
5 =6
for x.