The questions, answered first.

Equations, inequalities, functions, and the rules that keep them balanced.

• what is the difference between domain and range
• why does a negative exponent mean reciprocal
• how do you find a hole in a rational function
• what is the difference between a vertical and a horizontal asymptote
• how to solve an exponential equation with different bases
• why do logarithms turn multiplication into addition
• what does the discriminant tell you
• when do you complete the square instead of using the quadratic formula
• how do you know which way a parabola opens
• why does the horizontal line test tell you a function has an inverse
• how to find the inverse of a function
• what is an extraneous solution and why does it happen
• why can't you divide by zero
• when do you flip the inequality sign

Limits, derivatives, and integrals, and knowing which one a question wants.

• what is the difference between a sequence and a series
• how do you know when a series converges
• how do you set up a related rates problem
• why does the second derivative tell you concavity
• what is the difference between a local max and an inflection point
• what does the fundamental theorem of calculus actually say
• how to choose u and dv in integration by parts
• why do you add + C to an indefinite integral
• when do you use u-substitution
• how do you know if a function is continuous
• what is the difference between a limit not existing and being infinite
• when do you use the chain rule vs the product rule
• when can you use L'Hopital's rule
• why does 0/0 mean you can factor and cancel
• what does implicit differentiation actually do
• why is the derivative of e^x itself
• what is the derivative of the inverse trig functions

Reactions, equilibrium, bonding, and the arithmetic that holds them together.

• why is water polar
• how do you know if a reaction is endothermic or exothermic
• why does atomic radius decrease across a period
• why do electrons fill 4s before 3d
• why is pH 7 neutral
• why do you convert to moles before comparing amounts
• when is a reaction spontaneous using Gibbs free energy
• what does an oxidation number actually mean
• how to tell if a molecule is polar from its shape
• how does a buffer resist pH change
• what is the difference between a strong acid and a weak acid
• how to find the limiting reactant
• why is entropy positive when a solid becomes a gas
• what is the difference between Kc and Kp
• why doesn't adding a solid change the equilibrium constant
• does adding a catalyst shift equilibrium
• why does Le Chatelier's principle shift toward products

Cells, genetics, and the systems that keep an organism running.

• what is the difference between transcription and translation
• why do enzymes stop working when they get too hot
• what is the difference between natural selection and genetic drift
• where does most of the ATP come from in cellular respiration
• why is ATP called the energy currency of the cell
• how to read a Punnett square for two traits
• what is the difference between genotype and phenotype
• why do cells burst in a hypotonic solution
• how does osmosis differ from diffusion
• why does the lagging strand need Okazaki fragments
• why is DNA replication called semiconservative
• what is the difference between mRNA, tRNA, and rRNA
• why does meiosis produce genetic variation
• what is the difference between mitosis and meiosis
• why do plants release oxygen if they need it to respire

Forces, energy, circuits, and the sign conventions that trip everyone up.

• what is the difference between velocity and speed
• why do you draw a free body diagram
• why does current stay the same in a series circuit
• what is the difference between series and parallel circuits
• why is acceleration still negative at the top of a throw
• how do you choose a sign convention in kinematics
• why is the work zero when you carry something at constant height
• what is the difference between elastic and inelastic collisions
• when is momentum conserved but kinetic energy is not
• is centrifugal force real
• why does centripetal force point inward
• what is the difference between mass and weight
• why is the normal force not always equal to weight

Distributions, tests, and telling a real effect from a lucky sample.

• when should you use the median instead of the mean
• how do you tell if a distribution is skewed left or right
• how do you interpret a 95% confidence interval
• what is the difference between standard deviation and standard error
• what does R squared tell you
• what is the difference between correlation and causation
• what does the central limit theorem actually say
• why do you divide by n-1 for sample variance
• when do you use a t-test instead of a z-test
• what is the difference between a type I and type II error
• what does a p-value actually mean

Supply, demand, elasticity, and why the curve moves rather than slides.

• why do firms produce where marginal revenue equals marginal cost
• what is deadweight loss and why does it happen
• what is the difference between fiscal and monetary policy
• why does marginal cost cross average total cost at its minimum
• what is the difference between nominal and real GDP
• why does a price ceiling cause a shortage
• what is opportunity cost, with an example
• why is price elasticity of demand negative but reported as positive
• what does elastic demand actually mean
• what is the difference between a shift and a movement along the demand curve

Causes, consequences, and the arguments historians are still having.

• what does checks and balances actually mean
• why did the Industrial Revolution start in Britain
• what was the purpose of the Marshall Plan
• what is the difference between communism and socialism
• why did the Roman Empire fall
• what was the Columbian Exchange
• what is the difference between the House and the Senate
• what actually caused World War I

Grammar, rhetoric, and how to say what a passage is actually doing.

• how do you analyze a poem you have never seen before
• what is dramatic irony
• what is the difference between a metaphor and a simile
• what is the difference between active and passive voice
• when do you use a semicolon instead of a comma
• what is the difference between ethos, pathos, and logos
• how do you write a thesis statement that isn't just a summary
• what is the difference between tone and mood

Complexity, data structures, and why the fast solution is fast.

• what is a race condition
• why is binary search O(log n)
• what is the difference between a compiled and an interpreted language
• why does 0.1 + 0.2 not equal 0.3
• what is recursion and how does it know when to stop
• what is the difference between a stack and a queue
• why are hash table lookups O(1)
• what is the difference between an array and a linked list
• what does Big O notation actually measure