Download AP Statistics PBHS Summer Packet 2015

PBHS
AP Statistics
Summer Packet 2015
Name: ________________
To all students enrolled in AP Statistics and their parents/guardians:
Congratulations on your decision to take AP Statistics in the upcoming school year. You
have joined the growing ranks of students who recognize the value of an introductory
statistics course. A course such as this is typically required of many college majors including
those in the social sciences, health sciences, and business. Throughout the course of the year,
AP Statistics will expose you to four themes: exploring data; sampling and experimentation;
anticipating patterns; and statistical inference.
AP Statistics is not a typical math class. In this course you will combine verbal and
mathematical skills to describe the qualitative world around us in a quantitative manner.
Unlike other math classes, we will focus on what your calculations and results mean, as
opposed to how you do the calculations. You will be provided with the AP Statistics
formula sheet for all your assessments, and you will NEED a graphing calculator with builtin statistics packages; any TI-83 or TI-84 will be fine. You can check the College Board
website for a list of approved calculators (http://apcentral.collegeboard.com/home). In
fact, this website can answer most questions you have about AP Statistics. Paint Branch
does have a limited number of graphing calculators available for students to borrow, but if
possible, please come to class with your own.
How can you prepare for this class? To be successful in AP Statistics, you need a strong
background in the skills of Algebra II. You should be comfortable with the skills listed
below:
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Calculating percent and proportions
Substituting values into equations and simplifying
Solving equations for a given variable
Solving linear, quadratic, and exponential equations
Graphing linear, quadratic, and exponential functions
Writing and interpreting linear equations
Creating a scatterplot
Properties of functions
Interpreting simple data displays: pie charts, bar graphs, etc.
Calculating the mean, median, mode and range of a set of data
Calculating simple probabilities
I encourage you to complete the summer packet by the first day of class. There are many
excellent on-line resources to assist you with questions you may have on problems in the
packet. Do not start working on this packet in June; enjoy a break from schoolwork and start
working on this in mid-July. It is important that the techniques practiced in this packet are
fresh in your mind come the first day of school. This packet will not be collected, but I will
assume you have mastery of the skills reviewed in this packet.
If you have any questions, feel free to email me at [email protected]. Have
a great summer and I look forward to seeing you in the fall.
Mrs. Mamana
Part I – Math Skills Review
1. Solve each equation on a separate sheet of paper:
a. 2 x  9  21
2 x  10  x  1
b.
c. 2 x  1  14
d. 4( x  2)  32  x
e.
1
n3 n2
3
f.
2
8
y
3
13
g. x2  8x  7  0
m 5 5
 
12 6 24
h.
i.
1
2
𝑥2 − 8 = 0
j. −3𝑥 2 + 343 = 0
2
k. 𝑦 = 83
l. 9𝑥 = 81
2.
Write equations of the horizontal and vertical lines that pass through the
point (-3, 4).
Horizontal:_______________
3.
Vertical:__________________
Find the slope and y-intercept of the line. Sketch the line.
2
a. y  (2 x  4)
3
b.
1
y  6x  4
3
4. Find the slope and write the equation of the line containing the points (6, -2)
and (0, 5).
5. What is the slope of the line that is parallel to 2𝑥 + 3𝑦 = 9?
5
6. What is the slope of any line that is perpendicular to the line 𝑦 = 2 𝑥 + 2?
7. A line has the equation 𝑦 = 2𝑥 − 3. Does the point (4,3) lie on this line? Justify.
8. Plot the data using a scatter plot then decide if the data is linear, exponential,
quadratic, or absolute value. Label each scatterplot.
a.
b.
c.
d.
(-3, 4) (-2, 3.5) (-1, 3) (0, 2.5) (1, 2) (2, 1.5) (3, 1)
(-3, 4) (-2, 3) (-1, 2) (0, 1) (1, 2) (2, 3) (3, 4)
(-3, 4) (-2, 2) (-1, 1) (0, ½ ) (1, ¼ ) (2, 1/8 ) (3, 1/16 )
(-3, 4) (-2, 7/3) (-1, 4/3) (0, 1) (1, 4/3) (2, 7/3) (3, 4)
a.__________________________
b.__________________________
c.__________________________
d.___________________________
9. For each function, find f(x) for 𝑥 = −3, 0, 𝑎𝑛𝑑 2.
a. 𝑓(𝑥) = 4𝑥 − 2
b. 𝑓(𝑥) = (𝑥 − 3)2 + 1
f(-3) = __________
f(-3) = _________
f(0) = __________
f(0) = _________
f(2) = __________
f(2) = _________
10. Evaluate g(f(-2)) and f(g(3)) for each of the following functions.
a. f(x)=3x; g(x)=2x+3
g(f(-2)) = _____________
f(g(3)) = _____________
b. f(x)=-x; g(x)=x2+5
g(f(-2)) = _____________
f(g(3)) = _____________
11. Sketch each of the following on the grids provided. You may use your calculator
to help you, but you should label important features such as x/y intercepts,
max/mins, etc. Be sure to include a scale on your graphs.
a.
𝒚 = −𝒙𝟐 + 𝟐
c. 𝒚 = √𝒙 − 𝟗
b.
d.
𝒚 = 𝟑|𝒙 − 𝟐| + 𝟏
𝒚 = 𝟒𝒙 − 𝟐
12. Each of the members of a recent high school graduating class was asked to
name his/her favorite among these subjects: English, foreign language, history,
mathematics, science. The results are shown in the table. Construct a bar
graph that shows these results. Label your axes.
English
Foreign Language
History
Mathematics
Science
62
40
40
18
33
Part II – Basic Probability Review
13. A special lottery is to be held to select the student who will live in the only
deluxe room in a dormitory. There are 100 seniors, 150 juniors, and 200
sophomores who applied. Each senior's name is placed in the lottery 3 times;
each junior's name, 2 times; and each sophomore's name, 1 time. What is the
probability that a senior's name will be chosen?
A. 1/8
B. 2/9
C. 2/ 7
D. 3/8
E. 1/2
14. Which of the following has a probability closest to 0.5?
A.
B.
C.
D.
E.
The sun will rise tomorrow.
It will rain tomorrow.
You will see a dog with only three legs when you leave the room.
A fair die will come up with a score of 6 four times in a row.
There will be a plane crash somewhere in the world within
the next five minutes.
15. A famous advertisement reads “4 out of 5 dentists surveyed recommend Brand
X Sugarless gum for their patients who chew gum.” What is the best
interpretation of this claim?
A. That 80% of dentists recommend that their patients chew gum.
B. That of the 5 dentists surveyed, 4 of them recommend Brand X gum.
C. That while dentists don’t generally recommend that their patients chew
gum, for those that insist on doing so, 80% of them recommend
Brand X.
D. 80% of all dentist patients chew gum.
18. The probability of flipping a coin and getting heads is 0.5. What does this
mean?
A.
B.
C.
D.
Every time you flip a coin, you’ll get exactly 0.5 heads.
Over time, you can expect 50% of all coin tosses to be heads.
For every two coins you toss, you’ll get one head.
You have to toss a coin more than 10 times to see these results, but
once you do, you’ll get an equal number of heads and tails.
19. Which of the following in NOT a plausible probability?
A.
B.
C.
D.
E.
0
0.0001
0.50
0.998
1.01