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Handouts
changelog (previous: changelog-20191213)
last modified: 2022 January 08 01:00

Source files (text and figures) can be downloaded from my DropBox folder.

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To the extent possible under law, David Liao has waived all copyright and related or neighboring rights to every handout linked to on this page and every source file for every handout linked to on this page. This work is published from: United States.

Practice

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Problems

Physics

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Create and solve AP Physics 1/2 problems

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Summer Mechanics

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AP Physics 1

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AP Physics 2

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SAT Physics

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AP Physics C Mechanics

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AP Physics C Electricity & Magnetism

Math

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AP Precalculus

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Ridge-iculously hard Honors Precalculus

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Make AP Calculus cribsheets

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AP Calculus AB

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AP Calculus BC

Reading and reasoning

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Critical reading & reasoning for middle school

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Critical reading & reasoning for STEM and law

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Writing

Quantitative finance

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Quant interviewing

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Introduction to arbitrage-free pricing

Low-latency audio

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https://lowlatency.audio

Dedication | Top

This collection is dedicated to George F. Schuttinger, Ken Crowther, Professor Richard C. Haskell, Professor Robert J. Cave, Professor Robert H. Austin, and Professor Thea D. Tlsty.

Quant interviewing | Top

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1.1 Counting

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1.2 Probability & conditional probability

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1.3 Agile probabilistic reasoning

Introduction to arbitrage-free pricing | Top

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0.0 Connections between arbitrage-free pricing and equilibrium statistical mechanics

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1.1 IBL Constructing arbitrage portfolios

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1.1 No arbitrage & constancy of price ratios for deterministic final prices

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1.2 Motivation for risk-neutral pricing ansatz (single-branch example)

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2.1 Qualitative graphical estimation of risk-neutral price function

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2.2 Black-Scholes

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3.1 Option-price duality

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4.1 Construct arbitrage portfolios with forwards

Problems | Top

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2020-0403 14h19 End of 2019-2020 FRQs (some require high cognitive load)

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2020-0521 FRQ bank (some require high cognitive load)

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2021-0507 EoY FRQ Practice Packet

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End of 2019-2020 FRQs (some require high cognitive load)

Create and solve AP Physics 1/2 problems | Top

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T.0 SiQuENC for AP Physics

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T.0 SiQuENC for AP Physics 2018-0326

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T.0.2 Production system algebra-based physics

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T.0.2.1 Production system uses

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T.0.2.3 Summer mechanics production system

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T.0.3 Writing arguments for FRQs

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T.0.4 Writing templates for FRQs

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T.1 AP Physics 1 & 2 FRQ problem types

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T.1.2 Experimental design

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T.2 AP Physics 1 & 2 Problem scenario maker

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T.2.1 Make problems with the help of REASoN and SiQuENC

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T.3 AP Physics 1 Problem categorization

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T.4 SiQuENC rubric

Summer Mechanics | Top

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0 Physics for non-readers

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0 Recipes

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0 SiQuENC

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1 K 01 x-displacement

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1 K 02 Average x-velocity

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1 K 03 Instantaneous x-velocity

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1 K 04 x-displacement as area under vx-t plot

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1 K 05 Average x-acceleration

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1 K 06 Instantaneous x-acceleration

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1 K 07 change in x-velocity as area under ax-t plot

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1 K 08 UAM equations

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1 K 09 Distance between two points

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1 K 10 Total distance traveled

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1 K 11 Average speed

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1 K 12 Instantaneous speed

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1 K 13 Magnitude of a vector in terms of its components

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1 K SiQuENC for Kinematics (Motion)

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2 D 01 Newton's 3rd Law (N3L)

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2 D 02 Gravitational force by nearby Earth

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2 D 03 Tension force with which a taut string pulls

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2 D 04 Normal force with which a flat surface presses

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2 D 05 Static friction force exerted by a stuck surface

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2 D 06 Kinetic friction force exerted by a surface during sliding

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2 D 07 Newton's 2nd Law (N2L)

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2 D SiQuENC for Dynamics (Forces)

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3 M 01 Impulse delivered by a force

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3 M 02 Momentum

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3 M 03 Impulse-momentum theorem

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3 M SiQuENC for Impulse and momentum

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4 E 01 Work performed by a force

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4 E 02 Kinetic energy

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4 E 03 Gravitational potential energy

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4 E 04 Spring potential energy

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4 E 05 Internal energy

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4 E 06 Generalized work-energy principle

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4 E SiQuENC for Work and energy

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Mastering Tests of Physics Reasoning

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read

AP Physics 1 | Top

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0.1 What is physics (APP1)

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0.2 Rejecting candidate explanations

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1.1 1-d Kinematics describe (APP1)

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1.2 1-d Kinematics graph interpretation

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1.2.1 1-d Kinematics graph interpretation worksheet

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1.2.2 UAM position formula derivation

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1.3 SiQuENC 1-d Kinematics

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2.1 Resolve 2-d kinematics (APP1)

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2.2.1 Vectors

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2.2.3 Resolve vector components using trigonometry

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2.3.1 SiQuENC 2-d Kinematics

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3.1 Forces figures

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3.2 Force and Newton's laws cribsheet (APP1)

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3.3 Spring force

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3.4.1 Drag force

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3.5 SiQuENC Forces

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3.5.1 Very tedious SiQuENC Forces

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3.6 Free-fall & projectile motion

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4.1 UCM cribsheet

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4.2 UCM aIN deriv

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4.3 SiQuENC Circular motion forces

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4.4 Circular motion cribsheet

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4.5 Gravitation

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4.6 Elliptical orbits

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5.0 Newt 2 can be re-expressed

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5.1 Impulse delivered by a force

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5.2 Not-necessarily-constant sums

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5.3 Parallels momentum energy (APP1)

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5.4 SiQuENC Impulse-momentum (APP1)

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5.5 Opt Momentum transfer

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6.1 Center of mass cribsheet

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7.1 Work done by a force

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7.1.1 Force sums are not always suitable for calculating work

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7.2.1 Potential energy

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7.2.3 Spherical symmetry and potential energy functions

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7.3 Internal energy

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7.4 SiQuENC Work-energy

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7.5 Types of collisions

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8.0.1 Rotational statics (APP1)

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8.0.2 SiQuENC Rotational equilibrium (APP1)

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8.1 Rotational kinematics and dynamics cribsheet (APP1)

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8.2 Torque and rotational inertia

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8.3 SiQuENC Torques and forces

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8.4 Accruing effects of varying torques

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8.5 Rotational not-necessarily-constant sums

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8.6 SiQuENC Angular impulse-momentum (APP1)

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10.1 SHM Graphs

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10.2 SHM UCM connection

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10.3 SHM cribsheet

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10.4 SHM Ignoring gravity

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10.5 Resonance

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11.1 Fluid mechanics

AP Physics 2 | Top

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0.1 AP Phy 2 Curriculum

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7.2.2 Potential energy landscapes (APP2)

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7.6 Kinetic theory of ideal gas

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11.1 Waves

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11.2 Speed of wave on string

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11.3 Doppler

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12.1 Electric charge and force

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12.2 SiQuENC Charge transfer

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12.3.1 Electric potential

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12.3.2 Electric fields and potentials

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12.3.3 Conductors near equilibrium

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12.4 Current

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12.5 DC (equilibrated) operation

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12.6 Laboratory precautions and measurements for DC circuits

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12.7 SiQuENC DC Circuits

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12.8 Capacitors

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13.1 Magnetism

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13.2 Magnetism in materials

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13.3 Mass spectrometer

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14.1 Electromagnetism

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15.1 Physical (wave) optics

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15.2 Polarization of light

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15.3 Light interrupted

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15.4 Reflections and thin-film interference

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16.1 Geometric (ray) optics

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16.2 Specular and diffuse reflection

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16.3 Raytracing to determine visibility

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16.4 Mirror and lens ray approximations

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16.5 Snell's law

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16.6 Total internal reflection

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17.1.1 Quantum physics

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17.1.2 SchrΓΆdinger equation

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17.2.1 Special relativity

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17.2.2 Special relativity steps

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17.3 Subatomic physics

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18.1 Thermo first law

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18.2 Thermo second law

SAT Physics | Top

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0.0 SAT Topics for after AP Physics 1

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5.2.1 Heating curve

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5.2.2 Thermal expansion

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18.3 Heat engines

AP Physics C Mechanics | Top

(Folder contains copies of materials common to AP Physics 1 and C Mechanics and also supplemental files unique to AP Physics C Mechanics, indicated by suffix "(APPC)").

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0.0 AP Physics C Mechanics outline

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0.1 Calculus mini intro for AP Phy C

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0.2 Rejecting candidate explanations

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1.1 1-d Kinematics describe calc (APPC)

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1.2 1-d Kinematics graph interpretation

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1.2.1 1-d Kinematics graph interpretation worksheet

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1.2.2 UAM position formula derivation

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1.3 SiQuENC 1-d Kinematics

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2.2.1 Vectors

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2.2.2 More vector details (APPC)

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2.2.3 Resolve vector components using trigonometry

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2.3 2-d Kinematics calc tiles (APPC)

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2.3.1 SiQuENC 2-d Kinematics

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3.1 Forces figures

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3.2 Force and Newton's laws cribsheet (APPC)

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3.3 Spring force

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3.4.1 Drag force

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3.4.2 Drag force integration (APPC)

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3.5 SiQuENC Forces

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3.6 Free-fall & projectile motion

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3.7 Non-inertial reference frames (APPC)

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4.1 UCM cribsheet

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4.2 UCM aIN deriv

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4.3 SiQuENC Circular motion forces

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4.4 Circular motion cribsheet

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4.5 Gravitation

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4.6 Elliptical orbits

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5.0 Newt 2 can be re-expressed

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5.1 Impulse delivered by a force

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5.2 Not-necessarily-constant sums

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5.3 Parallels momentum energy calc (APPC)

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5.4 SiQuENC Impulse-momentum calc (APPC)

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6.1 Center of mass cribsheet

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6.2 Mass-averaging over continuous mass distributions (APPC)

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7.1 Work done by a force

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7.1.1 Force sums are not always suitable for calculating work

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7.1.2 Work done along a path (APPC)

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7.2.1 Potential energy

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7.2.2 Potential energy landscapes calc (APPC)

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7.2.3 Spherical symmetry and potential energy functions

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7.2.4 Inverse-square fields have inverse-r potentials

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7.3 Internal energy

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7.4 SiQuENC Work-energy

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7.5 Types of collisions

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8.1 Rotational kinematics and dynamics cribsheet calc (APPC)

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8.2 Torque and rotational inertia

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8.3 SiQuENC Torques and forces

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8.4 Accruing effects of varying torques

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8.5 Rotational not-necessarily-constant sums

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8.6 SiQuENC Angular impulse-momentum calc (APPC)

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10.1 SHM Graphs

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10.2 SHM UCM connection

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10.3 SHM cribsheet

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10.4 SHM Ignoring gravity

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10.5 Resonance

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A.1 Spatial integrals (APPC Mech)

AP Physics C Electricity & Magnetism | Top

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0.0 AP Physics C E&M outline

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E1.1 Electric charge and force

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E1.1.1 SiQuENC Charge transfer

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E1.2 Electric fields and potentials with calculus

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E1.2.1 Integrating over charge distributions and paths to get electrostatic field quantities

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E1.2.2 Inverse-square fields have inverse-r potentials

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E1.3 Conductors near equilibrium

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E1.4 Gauss's law

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E1.5 Capacitors

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E2.1.1 Current

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E2.1.2 DC (equilibrated) operation

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E2.1.3 Laboratory precautions and measurements for DC circuits

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E2.2 Informal and formal circuit analysis

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E2.3 RC Charging

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E2.3.1 Mnemonic for exponential decays

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E2.4 Electromotive force

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M1.1 Magnetism with calculus

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M1.2 Magnetism in materials

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M1.3 Solenoids

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M1.4 Mass spectrometer

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N1.1 Electromagnetism

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N1.2 Inductors

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N1.3 LR Increasing current

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N1.4.1 LC SHO Graphs

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N1.4.2 LC and RLC

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N2.1 Maxwell's equations

AP Precalculus | Top

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LO 1.1.A Varying together (analytic)

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LO 1.1.B Varying together (graphical)

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LO 1.2.A IROC

Ridge-iculously hard Honors Precalculus | Top

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R1.0 GREAT method

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R1.0.1 Domain restriction

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R1.1 Make sadistic problems

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R1.2 How to make a painful precalculus problem

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R1.3 Beware of challenging problems

Make AP Calculus cribsheets | Top

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0.1 AP Calculus cribsheet maker

AP Calculus AB | Top

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1.1 Limit definitions

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1.3 Calculating limits

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1.4 Continuity and IVT

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2.1 Derivatives

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2.2.1 Derivatives of circle functions intuitive

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2.2.2 Derivatives of circle functions

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2.3 l'Hospital's rule

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2.4 Extrema

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2.5 Rolle & MVT

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2.6 Derivative tests

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2.6.1 Derivative tests sentences worksheet

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2.7 Curve sketching

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2.8 Related rates & Optimization

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3.1 Definite integrals and area

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3.2.1 RAM

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3.2.2 Matching definite integrals with limits of Riemann sums

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3.2.3 TAM

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3.2.4 Integration table

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3.3.1 Fundamental theorem of calculus

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3.3.1.1 u-sub is backwards chain

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3.3.2 Fundamental theorem of calculus flashcard

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3.3.3 Fundamental theorem of calculus keeping track

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3.4.1 Derivatives inverse functions

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3.4.2 Exponentials and logarithms calc

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4.1 Derivatives and integrals in kinematics

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4.2 Using integrals for areas

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4.3 Using integrals for volumes

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4.4 IVPs and DEs

AP Calculus BC | Top

(Supplement for AB packet)

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0.1 AP Calc BC Curriculum

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3.6 Integration by parts

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3.7 Partial fractions and intro logistic growth

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3.8 Improper integrals

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3.9 Euler method

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4.5 Parametric

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4.6 Arc lengths and surfaces of revolution

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4.7 Polar calculus

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5.1 Series, tests, and remainders

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5.2 Common Taylor series

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5.3.1 Series calculus tricks Recognize summation

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5.3.2 Series calculus tricks Obtaining series

Critical reading and reasoning for middle school | Top

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0 Links to problems

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1 Steps for parsing word problems

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2 Steps for parsing LSAT logic games

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4 Use CER to audit explanations (for middle school)

Critical reading and reasoning for STEM and legal professions | Top

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0.1 Make digestible lectures

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1 Learning and applying for STEM and legal professions

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1.1 Learn and apply STEM knowledge

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2 Reading for STEM and legal professions

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2.1 Quiz Reading like a lawyer

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2.1 Reading with SiQuENC

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2.1.0 Reading cards

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2.1.1 Reading card large

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2.1.1 Taking notes using multiple representations

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2.1.1.1 Taking AP notes using multiple representations

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2.1.1.2 Taking notes using multiple representations (not just AP)

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2.1.2 Computationalize rules before writing proofs

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2.2 Precis assignment

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2.3.0 Recipes

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2.3.1 Rule chart

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2.3.1.1 Rule chart (Dark)

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2.3.2 Note-taking for proof-based courses

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2.3.3 STEM SiQuENC cribsheet maker

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2.3.3 SiQuENC science steps

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2.3.4 STEM SiQuENC explanation maker

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2.3.5 STEM SiQuENC explanation & cribsheet maker

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2.3.6 STEM SiQuENC & REASoN (wide)

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2.3.6 STEM SiQuENC & REASoN ntbk wide

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2.3.6 STEM SiQuENC & REASoN pg

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2.3.7 STEM SiQuENC & REASoN (wide) dark

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2.3.8 Legal for Etkina and proofs

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3 REASoN grid

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4 Robotic reasoning for STEM and legal professions

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4.0.1 Because worksheet

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4.1 Quiz Reading math word problems

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4.2 Proof writing

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4.2.1 Proof writing poster

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5.0 Generate knowledge

Writing | Top

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1.0 Impact essays (11th grade)

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2.0 Composing essays

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2.1 Expository structure

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2.1 Forensics case table

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2.2 Hierarchical taxonomy

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2.3 Linked argument