How to study for USAPhO and IPhO
The
United States Physics Olympiad (USAPhO) and
International Physics Olympiad (IPhO) are competitions
in which high school students are tested on their knowledge of physics,
generally at the high school and undergraduate level, and their problem-solving
skills. In the US, 6000 students sit the qualifying exam called the F=ma exam,
of whom 400 sit the semi-final exam called the USAPhO exam,
of whom 20 are invited to the US Physics Team Camp, of whom 5 are selected to
represent the US at the International Physics Olympiad. It is a giant
commitment to try to make it to IPhO and
get a gold medal, and I assume this is your goal when I write the following
program.
Starting
from scratch
I'd
suggest to start preparing for this
competition before high school, if possible. Therefore, the program assumes
you're starting from scratch:
1. High school math. A background of 8th grade math means you're
comfortable with Algebra 1. It's super important to gain more experience with
algebra so that it becomes your second language. Here are links to Khan
Academy, the best resource for learning any high school subject:
I don’t think any of these courses will take more than 40 hours to
complete and master.
2. First taste of physics. The only prerequisites for high school/AP
physics are the math prerequisites completed in step 1. Let’s just skip non-AP
physics since it’s unnecessary. Khan Academy’s AP Physics 2 is incomplete so I’ll link AP Chemistry instead—Chemistry
and Physics 2 have a bit of material overlap, and the skills gained from
Chemistry are very helpful to physics. These may take ~40 hours each to complete
and master.
3. Do this step concurrently with step 2. Mathematical intuition and
problem-solving skills are absolutely vital to
Physics Olympiad. This is why it’s so
helpful to grind out hard math while preparing for Physics Olympiad. My
favorite resource for this is AoPS Alcumus—an online program where you solve problems in
various areas of math and gain experience points and a rating kind of like in
Madden. Use the AoPS wiki when you
encounter problems you don’t know how to solve. The wiki will have helpful
tricks and formulas for this purpose. Aim to solve 2 problems (~20 minutes) for
every hour you spend on step 2. Once you’ve finished step 2, continue
grinding Alcumus by doing a few problems a
week. For reference if you want to set a goal, I’ve completed 1200 problems, my
overall rating is 95.5, and my overall level is level 13.
4. At this point, you could score well on the F=ma exam, but you may
not pass it. The next step is to dial in your physics grinding. However, you
will need to learn calculus first. Calc AB will suffice, no need to do Calc BC.
If you want a challenge, do MIT OCW’s single variable calculus instead.
a. AP Calc AB – necessary. Probably around
50 hours to complete.
b. MIT single variable calculus –
challenging replacement for AP Calc AB. Roughly 80 hours.
5. Calc-based physics. Now we’ll switch to MIT OCW as our main
resource since we’re at the college level. It’s also nice that their courses
are rigorous and challenging, prepping your brain for the feat of intelligence
that is the Physics Olympiad. The first physics course is Classical Mechanics
1, which overlaps with AP Physics 1 but is more in-depth. This could easily
take 80 hours to complete. Also use Kleppner and Kolenkow (KK) mechanics to source some great problems.
a. Classical Mechanics - necessary
b.
Don’t be discouraged if this is hard. Just take it slowly. I rushed
through it and had to redo the course twice because I struggled so much.
Steps
1-5 total time: roughly between 250-400 hours (plus weekly Alcumus), depending on the choices you make. This is
overkill if you just want to pass the F=ma, but again, I’m assuming you want to
go to IPhO, so you need this backbone.
Checkpoint
1: you’re ready for the F=ma exam.
The
F=ma exam tests only over mechanics, so a mastery of calc-based classical mechanics
is enough to pass the F=ma exam. To ensure you pass, practice the test using
old F=ma exams on this website. Do a full
practice test emulating real exam conditions, grade the test, and make
corrections. Compare your score to the cutoff score (look this up, it changes
every year but is usually around 13-18). I’d suggest just one or two practice
tests per week, and never cram practice tests in the 3-7 days preceding test
day—that will fatigue you and make you perform worse. And don’t forget to keep
grinding Alcumus!
6. More math prerequisites. Concepts of multivariable calculus,
linear algebra, and differential equations will be incredibly helpful. Each
course will take around 80 hours to complete, so be patient.
a. Multivariable Calculus - recommended
b. Linear Algebra - recommended
c. Differential Equations - recommended
7. The fun
stuff. Let’s first expand our horizons before we re-relearn mechanics. E&M
will use your math prerequisites, but the others won’t really need it yet.
Also, we are running out of OCW resources, so we will resort to textbooks.
a. Electricity & Magnetism - necessary. This
is also available on edX for free. Probably 80 hours.
b. Thermodynamics
– chapters 18-20 of Resnick, Halliday, and Walker (RHW) – necessary. Maybe 20
hours.
c. Waves
and optics – chapters 16, 17, 34-36 of RHW – necessary. Maybe 30 hours.
8. On top
of your weekly Alcumus practice, we can now
add a physics version of this. Use older IPhO
theoretical problems (from years before about 2000), and
do a few problems each week. The specific number depends on your circumstances
but let’s say 3-6 problems per week.
a. Old IPhO Questions - necessary
9. The
hardcore stuff. Now, we’ll have to pull out our math prerequisites to tackle
these courses. David Morin is important because his problems are incredible. If
you can do 3- and 4-star problems consistently, then you’re practically
guaranteed a spot at training camp. Do at least 20 problems from each chapter
(if there are 20 problems) before moving on to the next. Each book will likely
take 120+ hours to complete thoroughly.
a. Mechanics
and Relativity – Introduction to Classical Mechanics by David Morin (MM), all
chapters – necessary. Do chapter 11 (relativistic kinematics) before you get to
chapter 5 of the following book (PM).
b. E&M
– Electricity and Magnetism by Edward Purcell and David Morin (PM), all
chapters except the last 2 – necessary
c. Thermodynamics,
Waves, Modern – Kevin Zhou’s
handouts. They’re in his “Teaching” section. Do them in order: T1, T2, T3,
W1, X1. W2 has no solutions yet.
Steps 6-9 total time: ~600 hours (plus weekly Alcumus and IPhO,
roughly a combined 6h/wk), including all the math prerequisites.
You could shave a hundred hours off this time if you rush the math
prerequisites since they aren’t absolutely essential.
Be ready to spend your summers locked in, grinding out physics—in addition to some
time every day during the school year.
Checkpoint
2 – you can finesse the USAPhO exam and
move on to training camp.
At this
point, you will probably be able to reach the USAPhO exam
and perform well enough to make it to the training camp. In the months leading
up to the USAPhO, practice with old exams
from this website. Do a full
practice test simulating exam conditions, grade the test, and make
corrections. I’m pretty sure a good goal is to get a 70%, though they never
release cutoff scores to be invited to the training camp. I’d suggest just one
or two practice tests per week, and never cram practice tests in the 3-7 days
preceding test day—that will fatigue you and make you perform worse. Beyond
this point, I can only speculate how to move on since I have yet to make it
past training camp.
Do
these three steps concurrently:
10. Keep doing previous IPhO questions.
You’ll find they’re easier than the USAPhO.
Do a couple each week, grade them, and make corrections. Aim for the moon and
set a goal to hit 8+ points per question (out of 10 total). Use newer exams
(from 2000 or earlier).
a. Old IPhO problems and solutions. This website
also has the experimental portions if you want to look at them. 100 minutes per
problem time limit, but I find the older ones take less time.
11. Kevin Zhou’s Physics Olympiad handouts. This guy is an absolute hero
for the work he has done with these handouts. You could do them in order, but
they take a long time, so I’d suggest starting with your weak points.
a. Kevin
Zhou. Scroll down to his Physics Olympiad handouts under the “Teaching”
section. The time commitment to complete all of these is on the order of 300
hours.
12. Lab skills. Look at old experimental portions of the IPhO. Email a professor at a local university and ask if
you can borrow the physics lab to try doing these experiments with him. If you
can find simulation labs that you can run from home, do those. IPhO 2022 has two sim labs, and the Online Physics Olympiad
(OPhO) will have some.
a. IPhO 2022
b. OPhO
Archive
Steps
10-12 total time: ~10^2.5 hours (plus weekly Alcumus
and IPhO, roughly a combined 6h/wk).
I’m being vague here since I’m unsure. Plus, there’s wide variation between
individuals at these steps. All these 12 steps are probably enough to make IPhO gold. You’ll know based on your scores on old IPhO questions—consistently scoring at least 8 points per
theoretical problem puts you in a very safe spot; I averaged about 6 points per
problem!
Steps
1-12 total time: 1000-2000 hours. Most of us land in this range. For reference,
that’s an average of an hour or two a day for three (full) years. If you study
hard during the summer, you won’t need to spend much time studying on school
days!
Senior
year – going above and beyond
At this point, you may want
to branch out to other activities like research or different Olympiads. But in
case you still want to try very hard on the Physics Olympiad—perhaps aiming for
IPhO Winner—here are more ideas:
a.
Finish Kevin’s handouts (do this first)
b.
Previous IPhO exams
c.
Asian Physics Olympiad (APhO). This is
harder than the IPhO.
d.
Physics Olympiad Hub
Resources. These include other countries’ Olympiads. The Chinese finals should
be harder than the IPhO.
e.
International Young Physicists’
Tournament
f.
Mathematical
Contest in Modeling (Not super physics-y, but they’re very good problems!)