Summer Work for
Honors Physics
Newport High School
Summer 2014
Haven’t you heard? Physics is cool!
It’s true, we will be doing a lot of fun things in
Honors Physics next year. In addition to the
written work we will be doing, I have planned
a number of exciting labs and demonstrations
that will help you connect the principles we
learn in the classroom with real life. The
central purpose of physics is to explore the
way the world works. We want to understand why things act the way
they do, especially when that behavior is counterintuitive. In our class, it
will always be important to ask “why?” Once we understand why the
world works the way it does, then our capacity to control the world is
increased. (Think of light bulbs, airplanes, and computers. The list goes
on...)
Interesting topics we will explore include many of the following:
free fall
vectors
projectiles
inertia and
forces
Newton’s laws
of motion
friction
circular
motion
terminal
velocity
work, energy,
and power
conservation
laws
momentum
impulse
rocket
propulsion
rotational
motion
torque
gyroscopes
springs
pendulums
law of gravity
planetary
motion
Page 2 of 26
Table of Contents
Assignment Title
Page
1
Seven Qualities of an Honor Student
4
2
Ten Reasons Every High School Student Should Study Physics
6
3
The Scientific Method
8
4
The Engineering Process
10
5
Seven Fundamental Measures
12
6
The Metric System
13
7
Significant Figures
15
8
Math Review: Fractions
17
9
Math Review: Exponents
18
10
Math Review: Scientific Notation
19
11
Math Review: Products of Sums
21
12
Math Review: Geometry
22
13
Math Review: Trigonometry
23
14
Math Review: True or False?
25
Page 3 of 26
Honors Physics Summer Packet
Assignment 1: Seven Qualities of an Honor Student
Intelligence
•This quality is not just about being “smart”. It is being “smart” enough to identify what you do not know or understand
and then actively seeking sources of help. This also includes knowing when you “get it” and when you need to ask for
extra help during class or after school.
Self-Motivation
•This quality describes your attitude and your mindset. Enrollment in this “honor” level class is voluntary. Your desire to
learn the material should be your chief motivation, not your desire to get an "A". You must understand that your teacher
will not plead or beg an honors level student to do the assigned work. You should be ready and willing to learn each day.
Integrity / Character
•This quality is about doing the right thing in all situations. If you have integrity, you do not cheat on any assignment, be it
a test, quiz, project or homework. You do your own work. If you have integrity it means you do not help others to cheat,
be it providing homework for someone to copy or providing the questions / answers for a test or quiz in class or for
another class.
Work Ethic / Industriousness
•This quality means that the work you turn in is of your highest quality. You show complete and organized work on all
assignments (tests, quizzes, homework, projects) clearly identifying how you arrived at the solutions. Showing just
answers does not show any work ethic at all and is unacceptable. Industriousness means that you use all available time to
learn and improve. This could simply be starting your homework if there is time left in class. It could mean asking
questions about a concept of which you are unsure. When given an extended problem / project / reading assignment
industriousness means that you start on the assignment promptly and not wait until the night before the due date to
begin. This quality means you do not do work for another class or play games on your iPad during class time.
Safety
•Honors students treat the lab and lab materials with respect. While they may not yet know all the safety regulations, they
do know that horsing around or misbehaving in the lab can potentially cause injury or worse to themselves and their
peers. Honors students do not need to be told how to behave properly in a lab, or when to appropriately observe safe
and correct lab techniques. Honors students ensure the lab is cleaner than when they found it. Labs should be read, at a
minimum, the night before. You should highlight and write notes on your procedure. All prelab assignments should be
done promptly and if there are questions you should discuss those with your teacher BEFORE the class period in which
you are supposed to perform the lab.
Inquisitiveness
•This quality means that if you have a question you ask the question as soon as possible. An honors student does not just
sit there and take notes, they think: Did I understand? Does it make sense? What if? Do not make the mistake of
assuming that a concept you do not understand now in class will all make sense later on. Being inquisitive also means
taking advantage of all opportunities to help yourself including: your teacher in and out of class, your textbook, online
resources, other students who understand the concept, etc.
Ingenuity
•This quality is about applying knowledge, not just rote memorization. An honors student is able to devise solutions to
problems they have never seen before. They are able to take what they have cumulatively learned in this class and all of
their current and previous classes and apply it toward the solution of a new problem.
Page 4 of 26
Honors Physics Summer Packet
Assignment 1: Seven Qualities of an Honor Student
1.) While reading the 7 Qualities of an Honor Student, it would be natural for someone to self-reflect and consider to
what extent she or he embodies each quality. Using a 5-point scale where a 1 means “Not Like Me” and a 5 means “A
Lot Like Me”, circle the number that best represents how you would rate yourself. Remember, for any self-reflection to be
helpful, it must be honest. Your responses are between you and your teacher and no judgments will be made.
A
Lot
Like
Me
Quality
4
5
Safety
1
2
3
4
5
3
4
5
Inquisitiveness
1
2
3
4
5
2
3
4
5
Ingenuity
1
2
3
4
5
2
3
4
5
Quality
Not
Like
Me
Intelligence
1
2
3
Self-Motivation
1
2
Integrity / Character
1
Work Ethic / Craftsmanship
1
CIRCLE YOUR
RATING
CIRCLE
YOUR
RATING
Not
Like
Me
A Lot
Like
Me
2.) Which of the 7 qualities is your greatest strength? __________________________________________
In complete sentences, explain your choice using specific examples.
3.) Which of the 7 qualities is your biggest area for growth? _____________________________________
In complete sentences, explain your choice using specific examples.
4.) As you think about this particular area of growth, what might be some things you can do to develop this quality?
Again, be specific and use complete sentences.
Page 5 of 26
Honors Physics Summer Packet
Assignment 2: Ten Reasons Every High School Student Should Study Physics
For most students taking a high school physics class is a challenge, but it's well worth the effort for the following reasons:
A. Most modern technology involves physics. Any technology involving electricity, magnetism, force, pressure, heat, light, energy, sound, optics,
etc. comes from physics. Even though the basic knowledge required for products like fertilizers, drugs, plastics, and chemicals comes from
chemistry and biology, these items have to eventually be manufactured, and manufacturing is dominated by physics-based technology.
B. An understanding of physics leads to a better understanding of almost any other science. Like technology, virtually all branches of science
contain at least some physics. Physics has been called the most basic science and in many cases is required in order to understand concepts in
other sciences. Physics sharpens skill at performing experiments, as does Biology and Chemistry. However, it differs in that most commonly used
sensors are based on a principle of physics. This includes simple pressure and temperature measuring devices all the way to complex devices like
mass spectrometers (used in chemical analysis), MRI imaging machines, and electron microscopes. Physics is the basis for all types of analytical and
measuring systems.
C. Physics classes help polish the skills needed to score well on the ACT and the SAT. Physics classes provide practice in both algebra and
geometry. These are the types of mathematics most likely to occur on the ACT and the SAT. However, physics is not just a math class. To work
physics problems, students must be able to read and comprehend short paragraphs then develop problem solving strategies from them. Physics
helps develop both math and verbal skills.
D. College recruiters recognize the value of physics classes. College recruiters tend to be favorably impressed by transcripts containing challenging
classes like physics. They know it is relatively easy to attain a high GPA by taking a light course load. Some technically oriented college programs will
deny entrance to students who have not taken high school physics.
E. College success for virtually all science, computing, engineering, and premedical majors depends in part on passing physics. College physics is
required or all of these majors. Engineering is largely applied physics. Pre-medicine majors typically must take the same number of physics as
biology classes! About 25% of the science knowledge required for the MCAT (Medical College Admission Test) is based on physics. Studies indicate
that a high quality high school physics course helps significantly reduce the failure rate in college-level physics. Students themselves typically
indicate that high school physics is a significant factor in their ability to handle college-level physics material.
F. Physics classes hone thinking skills. Physics is a whole brain subject requiring students to use both right and left brain regions for translating
complex verbal information into pictures and finally into mathematical models in order to solve problems. In addition to the subject's content
knowledge, physics requires students to develop higher level thinking--a useful skill in any endeavor.
G. The job market for people with skills in physics is strong. Engineers are applied physicists and comprise the second largest profession in
America (second only to teaching) with about 1.4 million members. By comparison, there are about 600 thousand medical doctors and only around
100 thousand biologists. However, even medical doctors and most biologists have to take college-level physics courses. Knowledge of physics is a
prerequisite for many forms of employment.
H. A knowledge of physics is helpful for understanding the arts. Physics is the science of sound and is needed for understanding how musical
instruments work. Physics is also the science of light and is key to understanding visual artwork including paintings, photograph, stage lighting,
filmmaking, etc. Even literary works have been influenced by physics. William Faulkner, for example, used the symbolism of time dilation in The
Sound and the Fury. Many commonly used expressions in everyday language come from physics, including quantum leap, free fall, light years, black
holes, resonance, and being on the same wave length.
I. To understand physics is to better understand politics, history, and culture. Due to global warming, the supply and use of energy is a highprofile 21st century issue. However, it's always been a defining issue--even in primitive cultures. The bow and arrow, for example, profoundly
altered the effectiveness of hunting and warfare by giving people a device that stored energy then released it suddenly as a deadly projectile.
Changes in energy use and supply produced the industrial revolution in the 1800s and ushered in all kinds of inventions from reliable internal
combustion engines to practical electrical devices. The most significant historic event of the 20th Century, WWII, began for the United States, with
the bombing of Pearl Harbor by the Japanese using battle tactics shaped by an understanding of projectile motion physics and ended with a nuclear
bomb blast enabled by physicists.
J. Physics offers a deep and unique perspective in itself: There is quite simply no other area of study quite like it.
Page 6 of 26
Honors Physics Summer Packet
Assignment 2: Ten Reasons Every High School Student Should Study Physics
5.) As you consider the ten reasons listed in the article, which 3 would you say appeal to you the most? Using complete
sentences, explain why using specific examples.
6.) What are some reasons you signed up for this course? Again, using complete sentences, list and explain at least 3
reasons why.
7.) As a student who has been in school for many years, what are your expectations of me as your teacher? Yep,
complete sentences again.
Page 7 of 26
Honors Physics Summer Packet
Assignment 3: The Scientific Method
What is the Scientific Method? It is a series of steps used to help solve a problem.
Step 1. Make an Observation. After making an observation of the natural world, define the problem and make sure only one
problem is being studied. ALL scientific experimentation starts with observation.
Step 2. Research the problem (question). Use all available resources to collect data on the subject being covered. Libraries, Internet,
books, magazines, personal interviews, etc.
Step 3. Develop a hypothesis (educated guess). Make it a short definitive statement. It may be an "if-then" statement. The “if” part
will become the hypothesis and the “then” part should be the results received at the end of the controlled experiment. Remember
your hypothesis can be changed if the results do not support it.
Step 4. Develop a controlled experiment. A controlled experiment is an experiment that contains only one experimental
variable. An experimental or independent variable is the thing being tested (what the scientist changes). Everything else in the
experiment or all other variables must be the same. These variables are also called the controlled variables. Keeping these variables
the same allows the experimenter to show that it was the experimental variable that caused the results. The dependent variable is
what changes when the independent variable changes - the dependent variable depends on the outcome of the independent
variable. Data should be organized into charts, tables, or graphs.
Step 5. Analyze the data and come up with a conclusion. Data may be quantitative (numbers) or qualitative (appearance,
properties, etc.). The conclusion may or may not support the hypothesis. Additional experimentation must then take place to build
documentation concerning the problem. If the hypothesis is proven wrong, change the hypothesis, not the data. Scientists must be
unbiased.
WHAT FOLLOWS: Scientific research must be published, but first it must be reviewed by peers (other scientists) and verified for
accuracy. Research may result in a scientific theory or law.
Read each scenario below & use your knowledge of the scientific method to help answer the questions.
8.) Flower Flourish
Jeremy has decided that he really likes Candace. He wants to start a flower garden
so he can grow lots of flowers to give to her. He bought a special fertilizer called
Flower Flourish to see if will help his plants produce more flowers. To test this, he
planted two plants of the same size in separate containers with the same amount of
potting soil. He then placed one plant in a sunny window and watered it every day
with fertilized water and he placed the other plant on a shelf in a closet and watered
it with plain water every other day.
Will this experiment help Jeremy answer the question of whether the fertilizer help produce more flowers? If you
answered “Yes,” then identify the independent, dependent, and controlled variables. If you answered “No,” then what
advice would you offer Jeremy to improve his experimental design. Explain.
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Honors Physics Summer Packet
Assignment 3: The Scientific Method
9.) Snack Crackers
Dr. Doofenschmirtz is not the smartest evil villain in the Tri-state area, but he believes he can improve his brain power
by eating his new snack crackers called Cheesy Brain Enlargenators. In order to test this hypothesis, he recruits several
of his evil friends to help him with an experiment. He created an intelligence test and gave it to his
evil friends at the beginning of the experiment and then his evil friends ate one snack with each meal
every day for three weeks. Afterwards, they took the test again. Analyze the data in the chart.
Based on the data, did the Cheesy Brain Enlargenator snack crackers help his evil friends become
smarter? Explain your answer.
Test Scores
Friend
Before
Hans
64%
Rolf
78%
Fritz
82%
Dieter
72%
After
80%
78%
84%
70%
10.) Mega-Bubble
Phineas and Ferb know what they are going to do today. They are going to compete in
the Danville Mega-Bubble Contest. In order to win, they need to know which bubble
gum will make the biggest bubbles. To prepare for the contest, they purchased five
different brands of bubble gum. They need your help to decide which brand to use
during the contest. Write an experiment to test the bubble size of the five bubble gum
brands so they can win the contest. Where’s Perry?
Page 9 of 26
Honors Physics Summer Packet
Assignment 4: The Engineering Process
The engineering design process is a series of steps that engineering teams use to guide them as they solve problems.
Anyone can do it! To determine how to build something (skyscraper, amusement park ride, bicycle, music player),
engineers gather information and conduct research to understand the needs of the challenge to be addressed. Then
they brainstorm many imaginative possible solutions. They select the most promising idea and embark upon a design
that includes drawings, and analytical decisions on the materials and construction, manufacturing and fabrication
technologies to use. They create and test many prototypes, making improvements until the product design is good
enough to meet their needs.
Engineers design and build all types of structures, systems and products that are important in our everyday lives. The
engineering design process is a series of steps that engineering teams use to guide them as they solve problems:






Understand the need: What is the problem? What do we want to
accomplish? What are the project requirements? What are the
limitations? Who is the customer? What is our goal? Gather information
and conduct research - talking to people from many different
backgrounds.
Brainstorm different designs: Imagine and brainstorm ideas. Be creative;
build upon the wild and crazy ideas of others. Investigate existing
technologies and methods to use. Explore, compare and analyze many
possible solutions.
Select a design: Based on the needs identified, select the most promising idea.
Plan: Draw a diagram of your idea. How will it work? What environmental and cultural considerations will you
evaluate? What materials and tools are needed? What analyses must you do? How will you test it to make sure
it works?
Create: Assign team tasks. Build a prototype and test it against your design objectives. Push yourself for
creativity, imagination and excellence in design. Does it work? Analyze and talk about what works, what doesn't
and what could be improved.
Improve: Discuss how you could improve your product. Make revisions. Draw new designs. Iterate your design
to make your product the best it can be.
Engineers use their science and math knowledge to explore all possible options and compare many design ideas. This is
called open-ended design because when you start to solve a problem, you don't know what the best solution will be to
meet the requirements. The process is cyclical and may begin at, and return to, any step.
The use of prototypes, or early versions of the design (or a model or mock-up) helps move the design process forward
by improving your team's understanding of the problem, identifying missing requirements, evaluating design objectives
and product features, and getting feedback from others.
Engineers select the solution that best uses the available resources and best meets the project's requirements. They
consider many factors before they implement a design: Cost to make and use, quality, reliability, environmental
consideration, safety, functionality, ease of use, aesthetics, ethics, social and cultural impact, maintainability, testability,
ease/cost of construction and manufacturability. They also consider sustainability - how the development, use and
ultimate disposal of the product might impact people and our planet.
Page 10 of 26
Honors Physics Summer Packet
Assignment 4: The Engineering Process
11.) NASA Scientists are currently planning for a manned landing on the planet Mars. One device that would be useful
to the astronauts that travel to Mars would be a device that takes waste water and purifies it so the astronauts can
reuse it. Using the engineering process described on the previous page, describe the process the engineers might use to
develop this piece of equipment. Use complete sentences, and your imagination!!
Page 11 of 26
Honors Physics Summer Packet
Assignment 5: The Seven Fundamental Measures
In Honors Physics, good measuring techniques will be required in order to be successful in lab activities. Obtaining
accurate and precise data through measurement is a critical skill to learn, develop, and refine. There are a wide variety
of physical quantities which can be measured, but there are only seven fundamental measures. A fundamental measure
is a measurement that is not based on any other unit of measure. For example, speed is not a fundamental measure
because it is based on distance and time (think miles per hour). Units of measure that are based on other measures are
called derived units.
Do a little research and find the name, unit, and definition of the seven fundamental measures. Record your answers in
the chart below:
Name
Unit
Definition
12
13
14
15
16
17
18
Page 12 of 26
Honors Physics Summer Packet
Assignment 6: The Metric System
The International System of Units – the Metric System – is usually referred as the SI. The metric system is used by scientists throughout the world,
and is based on units of ten. Each unit is ten times larger or ten times smaller than the next unit, and these units are specified by the use of
prefixes.
Symbol
K
Ha
C
C
A
V

J
N
Hz
m
g
t
W
Pa
Gy
Sv
Bq
a
d
h
min
s
L
Unit
Kelvin
Hectare
Degree Celsius
Coulomb
Ampere
Volt
Ohm
Joule
Newton
Hertz
Metre (meter)
Gram
Tonne, metric ton
Watt
Pascal
Gray
Sievert
becquerel
Year
Day
Hour
Minute
Second
Litre
Quantity
Absolute temperature
Area
Celsius temperature
Electric charge
Electric current
Electric potential energy
Electric resistance
Energy, work
Force
Frequency
Length
Mass
Mass
Power
Pressure, stress
Radiation (absorbed dose)
Radiation (does equivalent)
Radioactivity
Time
Time
Time
Time
Time
Volume
Prefix
Exa
Peta
Tera
Giga
Mega
Kilo
Hecto
Deca
Symbol
E
P
T
G
M
k
h
Da
Deci
Centi
Milli
Micro
Nano
Pico
Femto
Atto
d
c
m
METRIC
2.54 cm
1m
1 km
1L
250 mL
1 kg
28.3 g
C
Some commonly used Metric Units
Length: the distance from one point to another
Meter (m)
A meter is slightly longer than a yard
1 m = 1000 mm
1 m = 100 cm
Mass: the amount of mass in an object
Gram (g)
A paper clip has a mass close to a gram
1000 g = 1 kg

n
p
f
a
Mult. Factor
1018
1015
1012
109
106
103
102
101
100
10-1
10-2
10-3
10-6
10-9
10-12
10-15
10-18
Example
106 m = 1 Mm
103 g = 1 kg
m
10-2 m = 1 cm
10-3 m = 1 mm
10-6 m = 1 m
ENGLISH
= 1 inch (in.)
= 39.37 inch (in.)
= 0.62 miles (mi)
= 1.06 quarts (qt)
= 1 cup (c)
= 2.2 pounds (lb)
= 1 ounce (oz)
5
  F  32 
9
Volume: the amount of space taken up by an object
Liter (L)
A meter is slightly morer than a quart
1 L = 1000 mL
Temperature: the measure of energy in an object.
Celsius ( C)
0 C freezing point of water
Kelvin ( K)
100 C boiling point of water
-273 C = 0 K lowest temp possible
19
Which metric prefix means
100?
22
If your mass is 73 kg, what is
your mass in grams?
20
Which metric prefix means
1/100?
23
How many millimeters are
there in a meter?
21
What does milli- mean?
24
How many millimeters are
there in a kilometer?
Page 13 of 26
Honors Physics Summer Packet
Assignment 6: The Metric System
Using the abbreviations for the base units on the previous page, write abbreviations for the following metric units:
25
Milligram
28
Kilogram
31
Micrometer
26
Centimeter
29
Centigram
32
Milliliter
27
Kilometer
30
Decimeter
33
Megagram
Write the name for each metric unit abbreviated below:
34
mm
37
km
40
mL
35
cg
38
cm
41
Mm
36
kg
39
dg
42
m
Calculate the equivalence between the metric units:
43
1g=
cg
48
1m=
Mm
53
1L=
L
44
1m=
km
49
1 hg =
mg
54
1 km =
m
45
1m=
cm
50
1g=
dg
55
1 am =
nm
46
1 cg =
g
51
1 mL =
L
56
1 dg =
g
47
1 kg =
g
52
1 cm =
m
57
1 Mm =
m
Calculate the equivalence between the units:
58
268 mg =
g
61
6 in. =
cm
64
0.00015 g =
g
59
500  =
M
62
0.025 m =
cm
65
36 hm =
km
60
247 km =
m
63
100 EV =
aV
66
0.05 km =
cm
What metric unit of measurement would you use to measure the following quantities?
67
68
69
70
71
72
73
The amount of juice you drank at
breakfast
The amount of water you used in
the shower this morning.
The distance from here to Las
Vegas, Nevada.
The amount of energy in a liter of
gasoline.
The thickness of a piece of
notebook paper.
The frequency of WEBN’s radio
signal.
The mass of a skateboard
74
75
76
77
The amount of salt you put on your
French fries.
The amount of water your family
uses in one year
The distance from here to the
moon.
The amount of farmland on a wheat
farm.
78
The width of a piece of paper
79
The temperature on Pluto
80
The mass of the Earth
Page 14 of 26
Honors Physics Summer Packet
Assignment 7: Significant Digits
It should be no surprise to you that in science a number with units represents some physical quantity. But did you know
that it also says something about the measurement process that produced it? For example, suppose Jill and Fred are
dancing together at the Homecoming dance, and the distance between them is determined to be about 30 cm. It would
be fair to say that the precision of the measured distance between them is on the order of tens of centimeters. In other
words, no attempt was made to measure the distance between Jill and Fred down to the nearest micron. In fact, for
reasons discussed below, it probably wouldn’t make sense even to try.
So what would you think if someone told you that he had determined that the distance between Jill and Fred was
actually 28.0026911014723 cm? That should set off red flags in your head. The inclusion of so many significant digits in
this number implies that it is precise to within about 10-15 meters—the approximate size of a proton! I can immediately
think of three big reasons why this is not likely to be the case.
A. It would be extremely difficult to measure distances on this scale without some very specialized tools. It’s pretty hard to
imagine someone trying to measure Jill and Fred with an electron tunneling microscope or a laser interferometer out on the
dance floor, but it sure is fun to try!
B. How does one determine endpoints for such a measurement? The thickness of a person can easily be 10 cm. Keeping
this in mind, it really doesn’t make sense to try and measure the distance between Jill and Fred to any accuracy better than
tenths of meters. If you wanted to be really careful, you could define a person’s position to be at their center of mass. If
you had a way of determining where that was, you could start talking about more precise measurements of the distance
between Jill and Fred.
C. Even with precise endpoints for your measurement, it still would not be practical to try and measure the distance
between Jill and Fred to the nearest femtometer. Even the slightest breath of air on either of their parts would probably
change the result of the measurement by a distance on the order of a millimeter. (That’s
a trillion femtometers!) And even if you could convince them to stop breathing, you’d still have their pulses to deal with.
With Jill and Fred dancing, you can bet that the distance between their center of masses is always changing on a scale even
bigger than that.
81.) Do a little research and find the rules for counting significant figures. Write them in the space below:
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Honors Physics Summer Packet
Assignment 7: Significant Digits
In our honors physics course, most of the numbers we use will have three significant digits. So, before you start the
course, it is a good idea to make sure you know how to round numbers correctly to three significant digits. You probably
think it’s a snap, and in most cases it is, but there are two special cases that seem to confuse students.
A. For some reason, people tend to want to round a number like 6.999942 down. If we were rounding to five significant
digits, then that would be the right thing to do (giving us 6.9999). But we want to round this number to three significant
figures. The correct answer is 7.00, not 6.99. Make sure you understand why.
B. The second case involves what I like to call “hanging 5’s”. A hanging 5 shows up whenever the number you are trying to
round is exactly half way between two values you might choose to round it to. For example, if you’re rounding to three
significant figures, then 69.35 has a hanging 5 (because it’s exactly half way between 69.3 and 69.4), whereas 69.351 does
not (because it’s closer to 69.4). In elementary school you probably learned that you should always round 5’s up. That’s
one simple approach to rounding, but it probably isn’t the best from a statistical standpoint because it introduces a bias
into your data. What does that mean? Essentially, it means that, on the average, you round up more than you round
down. A better approach involves rounding hanging 5’s up half of the time, and down the other half of the time. In honors
physics, we will accomplish this by rounding hanging 5’s such that the last significant digit of our rounded number is even.
In other words, 69.35 would be rounded up to 69.4, but 69.25 would be rounded down to 69.2.
How many significant figures do the following numbers have?
82
1234
87
1090.0010
83
0.023
88
0.00120
84
890
89
340000
85
91010
90
0.00090
86
9010.0
91
0.09010
Round the following measurements to three significant figures.
92
0.003115
97
0.0001554
93
1020012
98
8125
94
780.5
99
0.000065979
95
1699
100
0.003908
96
918.010
101
72.0015
Page 16 of 26
Honors Physics Summer Packet
Assignment 8: Math Review – Fractions
In my experience, students have more trouble with the algebra in Honors Physics than they do with the physics! Your
algebra, geometry, and trig skills should be well-polished. So, the remaining material in this packet will all focus on
these areas.
The first area I have noticed Honors Physics students struggle in deals with the manipulation of fractions. As practice,
express the following quantities as a single fraction. No fractions should appear inside the numerator or denominator of
your answer.
x
y
y
x
1
102
c c

b a
107
103
A/B
2
C /D
108
t 3  t sint
 tant
cos t
109
ax
xy
xy
ay
 k r  /  kr 
1
104
1
k2r 2
1
105
3  x  x2
2
x
110
m / n2
m2 / n
106
y  y 1
111
G 2G

M M
Page 17 of 26
Honors Physics Summer Packet
Assignment 9: Math Review – Exponents
It is also very common for students to struggle with exponents. Again, practice is really the best way to get your head
around the meaning of an exponent. The Laws of Exponents are summarized below:
Express each of the following quantities as x to some power.
112
1
x
117
1
x b
122
113
x 
118
x5
x4
123
114
xa xb
119
1
124
115
x
120
1
x
125
116
x
121
x 
126
3 2
a b
Page 18 of 26
x2
x 2
3
x
1
xa
x3
xx
x2
Honors Physics Summer Packet
Assignment 10: Math Review – Scientific Notation
In both scientific and engineering work, it is very common to have to work with extremely large or extremely small
numbers. For example, the Sun has a mass of 1,988,000,000,000,000,000,000,000,000,000 kg. When scientists and
engineers are plotting the path of a spacecraft traveling to another planet, the gravity of the sun must be taken into
account and calculations involving the sun’s mass must be done. It would be very inconvenient to have to write that
extremely long number. Similarly, a scientist might need to complete a calculation involving the mass of a proton, which
is 0.000000000000000000000000001672621636 kg. It would be miserable to have to write that number when doing
calculations. Instead, scientists and engineers take advantage of the powers of 10 and write the numbers more
concisely.
For example, the mass of the sun is equal to 1,988 x 1,000,000,000,000,000,000,000,000,000 (which is 10 27). So the
mass could be written as 1,988 x 1027 kg. However, scientists have agreed to make the first number in this “shortcut” a
number bigger than or equal to 1 and less than 10. So the 1,988 would be converted to 1.988 x 1000 making the mass of
the sun 1.988 x 1030 kg. This shortcut way of writing numbers is called scientific notation.
127.) How would you write the mass of a proton in scientific notation? _______________________________________
The rules for converting numbers between standard notation and scientific notation are summarized here:
Standard Notation  Scientific Notation
1. Move the decimal in the original number to the right of the first nonzero digit to
obtain a number > 1 and < 10.
2. Count the number of places moved to determine the exponent.
a. Original number 10 or >10 - - - - positive exponent
b. Original numer < 1 - - - - negative exponent
3. Multiply the number obtained in step 1 by 10 to the power (exponent) found in step 2.
Scientific Notation  Standard Notation
Observe the exponent
1. Positive exponent - - - - move the decimal to the right the same number of places as the
exponent and drop the power of 10.
2. Negative exponent - - - - move the decimal to the left the same number of places as the
exponent and drop the power of 10.
Page 19 of 26
Engineering notation is very similar to scientific notation. The difference is that engineers use powers of 10 that are
divisible by 3. This means that the first number can be any number >1 and < 1,000.
Page 20 of 26
Honors Physics Summer Packet
Assignment 10: Math Review – Scientific Notation
Directions: Indicate whether the sentence or statement is true or false. If a question is false, write the correct
answer to make the statement true.
128
129
104 is the same as
10,000.
T F
101 is the same as
100.
T F
100 is the same as 1.
T F
130
131
132
10- 5 is the same as
0.00001
T F
10- 2 is the same as
0.02.
T F
T F
133
The long form of
500, 000 is equal to
the scientific
notation 5 X 105.
T F
134
The long form of
0.0089 is equal to
the scientific notation
8.9 X 10-4.
T F
135
The long form of
23.76 is equal to the
scientific notation
2.376 X 101.
T F
136
The long form of
1386 is equal to the
scientific notation
1.386 X 103.
T F
137
The long form of
0.0084 is equal to the
scientific notation 8.4
X 10-4.
T F
138
The scientific notation
2.376 X 104 is equal to
the long form of
237,600.
T F
139
The scientific notation
7.844 X 106 is equal to
the long form of
78,440,000.
T F
140
The scientific notation
4.95 X 10-3 is equal to
the long form of
0.000495.
T F
141
The scientific notation
3.9 X 106 is equal to
the long form of
390,000.
T F
142
The scientific notation
2.894452 X 10-2 is
equal to the long
form of 289.4452.
Write these numbers in scientific notation
Write these numbers in standard notation.
143
1,230,000
148
1.57 x 107
144
0.00237
149
6.32 x 104
145
4,267,000,000,000
150
7.2 x 10-3
146
0.0000000068877
151
3 x 10-6
147
6,700,100,000,000
152
9.7361x 10-5
Page 21 of 26
Honors Physics Summer Packet
Assignment 11: Math Review – Products of Sums
Do you know how to FOIL? You should. Expand the following products, term by term. When you’re done, all quantities
should be expressed as a sum of products, rather than as a product of sums.
 a  b  a  b 
153
5s  s 2  5 
154
 mx  b
2
155
m
n
 11  m n 
156
A
2
 B2  A2  B2 
157
 z  1  z 2  z  1
158
Page 22 of 26
Honors Physics Summer Packet
Assignment 12: Math Review – Geometry
In order to model real-world situations, we will need to be able to represent objects using geometric figures. Calculating
the perimeter and area of plane figures as well as the surface area and volume of three dimensional solids will be
important. Make sure you have these geometric formulas committed to memory since we will be using them frequently
in class.
Write down the geometric expression for each of the following:
159
Area of a circle
with radius r
168
Perimeter of a
right triangle with
horizontal leg b
and vertical leg a
160
Circumference of
a circle with
radius r
169
Area of a square
with side length s
161
Volume of a
sphere with
radius r
170
Perimeter of a
square with side
length s
162
Surface area of a
sphere with
radius r
171
Volume of a cube
with edge length
s
163
Volume of a
cylinder with
base radius r and
height h
172
Surface area of a
cube with edge
length s
164
Surface area of a
cylinder with
base radius r and
height h
173
Area of a
rhombus with
base b and height
h
165
Area of a triangle
with base length
b and height h
174
Volume of a cone
with base radius r
and height h
166
Area of a
rectangle with
width w and
height h
175
Volume of a
pyramid with
base area A and
height h
167
Perimeter of a
rectangle with
width w and
height h
176
Area of a
trapezoid with
base b, top a, and
height h
Page 23 of 26
Honors Physics Summer Packet
Assignment 13: Math Review – Trigonometry
You should know the value of the sine and cosine functions at each of the following first quadrant angles:
0 ,30 ,45 ,60 , and 90 . In case you don’t remember, it’s actually pretty easy to learn these because of a neat pattern
that emerges.

0
30
sin
Pattern:
Simplifies to:
0
0 /2
1/2
1 /2
cos 
Pattern:
Simplifies to:
1
4 /2
3 /2
3 /2
45
2 /2
2 /2
2 /2
60
3 /2
1 /2
90
4 /2
3 /2
1
2 /2
1/2
0 /2
0
You should also know the value of the sine and cosine functions at the analogous angles in each of the other three
quadrants, namely: 120 , 135 , 150 , 180 , 210 , 225 , 240 , 270 , 300 , 315 , 330 , and 360 . The results in
these three quadrants actually don’t require any additional memorization because they’re so similar to the values in the
first quadrant (given in the table above). There are only two potential differences. The sign may be different, and the
order that the values appear in the table may be reversed. So how can you be sure? I like to imagine little plots of the
sine and cosine functions in my head. That way, it’s immediately obvious to me what the correct sign should be (positive
whenever the function is above the x-axis and negative whenever it is below the x-axis), and whether the values should
be increasing or decreasing as  increases (increasing if the slope is positive and decreasing if the slope is negative).
Another useful tool is the unit circle (a circle with a radius of 1 that happens to be centered at the origin). Since cos  is
the x-coordinate of the position of a point on the circle, the cosine is negative in the second and third quadrants (on the
left side of the unit circle, where x is less than zero), while the cosine is positive in the first and fourth quadrants (on the
right side of the unit circle, where x is greater than zero). Likewise, since sin  is the y-coordinate of the position of a
point on the circle, the sine is negative in the third and fourth quadrants (on the bottom half of the circle, where y is less
than zero), while the sine is positive in the first and second quadrants (on the top half of the circle, where y is greater
than zero). Similar arguments can help you determine where sine and cosine are each increasing (with increasing  )
and where each of them is decreasing.
Page 24 of 26
Honors Physics Summer Packet
Assignment 13: Math Review – Trigonometry
sin
1
1
cos
, sec 
, csc 
, and cot 
for all values of  , you should be able
cos
cos
sin
sin
to quickly evaluate each of the six trig functions at each of these angles (without a calculator). As practice, evaluate the
following trigonometric functions without looking at the chart or diagrams above.
Then, knowing that tan 
177
sin 45
182
cot 135
178
tan 60
183
csc 330
179
sin 30
184
cos 150
180
cos 240
185
sec 270
181
sec 0
186
tan 210
Page 25 of 26
Honors Physics Summer Packet
Assignment 14: Math Review – True or False?
Real problems frequently involve several mathematical and/or scientific principles at once. In practice, it can be easy to
make little mistakes, even when you understand the associated principles fairly well. When this happens, it usually leads
to a wrong answer. That’s why it’s always important to ask yourself if your answer makes sense. You should check both
the numerical value of your answer, and the associated units. For example, of the following three statements, two are
obviously wrong. Can you spot which ones?
A. The amount of time it takes to fly from Baton Rouge to Dallas is approximately 5.4  103 s.
B. The radius of Earth’s orbit around the sun is approximately 3.19  102 m.
C. The speed of a bullet is approximately 1000 m/km.
Once you’ve determined that an answer is wrong, you should go back and check your work to try and determine where
you made the first mistake (so that you can correct it!). Consequently, it’s important for you to be able to identify little
mistakes when you review your work. Hone your mistake-sniffing skills by determining which of the following
statements are true (‘T’) and which are false (‘F’). You should also try to identify what the mistake was that lead to any
false statements. Good luck!
187
ab
a b
 
c
c c
T
F
197
f 3 f 3  0
T
F
188
j  j  j2  j   j  j 3  j2
T
F
198
s2  
1
s2
T
F
189
b x b x 2  b x  x 2
T
F
199
x 
 x5
T
F
190
e2x  e x  e x
T
F
200
1
s2
T
F
2 3
s 2 
191
 K  3
 K 2  32
T
F
201
3  x  10   3x  10
T
F
192
 K  3
 K 2  32
T
F
202
yk y z  ykz
T
F
2
2
193
x log  x  1  log  x  x  1 
T
F
203
p3 px 1  px 4
T
F
194
x
x x
 
yz
y z
T
F
204
h2h2  1
T
F
T
F
205
T
F
T
F
206
T
F
1
H
195
H 1 
196
2325  215
Page 26 of 26
x 
y z
x
y 
z
sin2 x   sin x 
2