AP EXAM PREP

Ace Your AP Exams

First-principles mastery for AP Chemistry, Physics, Biology, Calculus, and Statistics. Know the why, not just the what.

Days to AP Exams
0
Questions Practiced
3h 15m
Exam Duration
60
MCQ Questions
7
FRQ Questions
9
Units Covered

AP Chemistry Unit Weights

Exam score weighting guides where to focus your study time.

Atomic Structure & Properties
7-9%
Molecular & Ionic Bonding
7-9%
Intermolecular Forces & Properties
18-22%
Chemical Reactions
7-9%
Kinetics
7-9%
Thermodynamics
7-9%
Equilibrium
11-15%
Acids & Bases
11-15%
Electrochemistry
7-9%
High-Yield

IMF & Properties is King

At 18-22%, intermolecular forces and properties is the largest unit. Master polarity, hydrogen bonding, London dispersion forces, and their effect on boiling points, solubility, and viscosity.

High-Yield

Equilibrium + Acids/Bases = 26%

Together these units make up over a quarter of the exam. Deeply understand Le Chatelier's principle, ICE tables, Ka/Kb relationships, and buffer calculations.

Common Trap

Don't Neglect Electrochemistry

Students often skip this unit since it seems hard. But it's 7-9% and the FRQs are very predictable — cell notation, Nernst equation, and electrolysis calculations appear nearly every year.

Key Concepts by Unit

What you must understand deeply — not just memorize.

⚛️ Atomic Structure & Periodicity
  • Electron configuration: Aufbau principle, Hund's rule, and Pauli exclusion. Exceptions: Cr, Cu, Mo.
  • Periodic trends: Atomic radius decreases across a period (increasing nuclear charge). Ionization energy increases across a period.
  • Photoelectron spectroscopy: PES peaks map to subshells; intensity = number of electrons in subshell.
  • First principles: All periodic trends arise from two forces — nuclear attraction and electron-electron repulsion (shielding).
🔗 Bonding & Molecular Structure
  • VSEPR: Electron geometry vs. molecular geometry. Lone pairs compress bond angles more than bonding pairs.
  • Bond polarity: Electronegativity difference determines polarity. Symmetrical polar bonds cancel out (CO₂ nonpolar, H₂O polar).
  • Resonance: Delocalized electrons — the true structure is an average. Ozone, benzene, nitrate.
  • Formal charge: Assign to determine best Lewis structure. Minimize magnitude, negative charge on most electronegative atom.
⚖️ Equilibrium
  • ICE tables: Initial → Change → Equilibrium. The workhorse of equilibrium problems.
  • Q vs. K: If Q < K, reaction proceeds forward; if Q > K, reaction shifts reverse.
  • Le Chatelier: Adding reactant shifts forward. Increasing pressure favors fewer moles of gas. Increasing temp shifts endothermic direction.
  • First principles: Equilibrium is dynamic — forward and reverse reactions still occur, just at equal rates. It's not "reactions stopped".
🧪 Acids & Bases
  • pH = -log[H⁺]. For strong acids, [H⁺] = molarity. For weak acids, set up Ka expression.
  • Buffer equation: pH = pKa + log([A⁻]/[HA]) — Henderson-Hasselbalch. Buffer works best when pH ≈ pKa.
  • Titration curves: Equivalence point pH depends on salt formed. Strong-strong = pH 7; weak acid + strong base = pH > 7.
  • Kw = Ka × Kb = 1.0×10⁻¹⁴ at 25°C. Conjugate pairs are linked.
⚡ Electrochemistry
  • Cell notation: Anode (oxidation) | solution || solution | cathode (reduction). Salt bridge allows ion flow.
  • Standard cell potential: E°cell = E°cathode − E°anode. Positive E°cell means spontaneous.
  • Nernst equation: E = E° − (RT/nF)ln(Q). At 25°C: E = E° − (0.0592/n)log(Q).
  • ΔG° = −nFE°. Links thermodynamics to electrochemistry. Spontaneous if ΔG° < 0 and E° > 0.

AP Chemistry Formula Reference

All formulas provided on the AP exam — but you need to know what they mean and when to use them.

FormulaWhat It MeansWhen to Use
PV = nRTIdeal gas law: pressure × volume = moles × R × temp (K)Any gas behavior problem; combined gas law situations
pH = -log[H⁺]pH is the negative log of hydrogen ion concentrationAcid-base calculations, titrations, buffer problems
Ka × Kb = KwConjugate acid-base pair product equals water's KwFinding Ka of conjugate acid from Kb of base
ΔG° = -RT ln KLinks Gibbs energy to equilibrium constantPredicting spontaneity from K; finding K from ΔG°
ΔG° = ΔH° - TΔS°Gibbs energy: enthalpy minus entropy contributionDetermining spontaneity at any temperature
ΔH°rxn = Σ ΔH°f(products) - Σ ΔH°f(reactants)Hess's Law via formation enthalpiesAny enthalpy of reaction calculation
E = E° - (0.0592/n) log QNernst equation at 25°C: cell potential under non-standard conditionsGalvanic cells with non-standard concentrations
ln[A]t = -kt + ln[A]0First-order integrated rate lawRadioactive decay, first-order kinetics
t½ = 0.693/kHalf-life for first-order reactionsDecay problems, time for half to react
q = mcΔTHeat = mass × specific heat × temperature changeCalorimetry problems

AP Chemistry Practice Questions

AP-style multiple choice with instant explanations.

🎯 Drill by Topic

Free Response Question (FRQ) Strategy

FRQs are 50% of your score. Master the format.

Strategy

Long FRQ: Show Every Step

Long FRQs are worth 10 points. Write out every step even if you think it's obvious. Partial credit is generous — you can get 7/10 even with an arithmetic error if your setup is correct.

Strategy

Short FRQs: Be Precise

Short FRQs (4 pts each) often ask to "justify" or "explain." Vague answers get zero. Write the specific chemical reasoning: e.g., "increasing [H⁺] shifts equilibrium right via Le Chatelier's principle."

Common Error

"Because the rate increases"

Never say something "because it increases/decreases" — that's circular. Always explain why at the particle level: activation energy, effective collisions, concentration effect.

Must Know

Particulate Diagrams

AP Chem frequently shows particulate-level diagrams. Practice interpreting molecules, ions, and phases at the particle level. Know what aqueous vs. molecular solutions look like.


✍️ Practice FRQs
FRQ 1 — Equilibrium & Le Chatelier's Principle
Typical point value: 10 pts (Long FRQ) | No calculator
Context

Consider the equilibrium: N₂(g) + 3H₂(g) ⇌ 2NH₃(g) ΔH° = −92 kJ/mol. At 500°C, Kp = 6.0 × 10⁻². A sealed flask initially contains N₂ at 2.0 atm and H₂ at 4.0 atm with no NH₃.

Part (a) — 4 pts

Using an ICE table, set up the expression for Kp in terms of the change in pressure x. You do not need to solve for x.

Full credit (4 pts): Set up ICE: N₂ starts 2.0 atm (changes −x), H₂ starts 4.0 atm (changes −3x), NH₃ starts 0 (changes +2x). Equilibrium pressures: N₂ = (2−x), H₂ = (4−3x), NH₃ = 2x. Kp expression: (2x)² / [(2−x)(4−3x)³] = 6.0 × 10⁻². Partial credit: 1 pt for correct ICE table setup; 1 pt for correct stoichiometric changes; 1 pt for correct equilibrium expressions; 1 pt for correct Kp setup.
Part (b) — 2 pts

The system reaches equilibrium. Then the temperature is increased to 600°C. Predict whether K increases, decreases, or stays the same. Justify your answer using Le Chatelier's principle.

Full credit (2 pts): K decreases. The forward reaction is exothermic (ΔH° = −92 kJ/mol < 0). Treating heat as a product, increasing temperature shifts equilibrium toward reactants (Le Chatelier's). Fewer products and more reactants means the ratio [products]/[reactants] decreases, so K decreases. Common error: Saying "equilibrium shifts left" without connecting to K changing — must explicitly state the effect on K.
Part (c) — 4 pts

At equilibrium at 500°C, more N₂ is added to the flask. (i) Predict the direction the reaction will shift. (ii) Predict whether the final mole fraction of NH₃ is greater than, less than, or equal to its value before N₂ was added. Justify each response.

(i): Shift right/forward (toward NH₃). Adding a reactant increases Q below K, so the reaction proceeds forward to restore equilibrium. (ii): Mole fraction of NH₃ increases. Although adding N₂ increases total moles, the forward shift produces proportionally more NH₃. Alternatively: the new equilibrium has higher P_NH₃ relative to total pressure than before. Must justify both answers with reasoning.
FRQ 2 — Acid-Base: Titration and Buffers
Typical point value: 4 pts (Short FRQ) | Calculator permitted
Context

A 25.0 mL sample of 0.150 M propanoic acid (Ka = 1.3 × 10⁻⁵) is titrated with 0.150 M NaOH solution.

Part (a) — 2 pts

Calculate the pH of the solution after 12.5 mL of NaOH has been added. Show all work.

Full credit (2 pts): After 12.5 mL NaOH: moles NaOH = 0.0125 L × 0.150 mol/L = 0.001875 mol. Original moles HA = 0.025 L × 0.150 mol/L = 0.00375 mol. Half neutralized: [HA] = [A⁻] (0.001875 mol each in ~37.5 mL). pH = pKa = −log(1.3 × 10⁻⁵) = 4.89. This is the half-equivalence point — maximum buffering capacity.
Part (b) — 2 pts

Explain why the solution described in part (a) resists pH change when small amounts of strong acid or strong base are added.

Full credit (2 pts): The solution contains approximately equal concentrations of propanoic acid (weak acid) and sodium propanoate (conjugate base). If strong acid is added, the conjugate base (A⁻) reacts with it: A⁻ + H₃O⁺ → HA + H₂O, consuming the added H⁺. If strong base is added, the weak acid reacts: HA + OH⁻ → A⁻ + H₂O. Both components act as "reservoirs" to neutralize added acid or base. Common error: Saying "the buffer neutralizes acid/base" without explaining the specific reactions involved.
📝 FRQ Question Types That Appear Every Year
  • Equilibrium ICE Table: Set up ICE, solve for x, find Kc or Kp. Use small-x approximation when K is very small.
  • Acid-Base Titration: Calculate pH before/during/at equivalence point. Henderson-Hasselbalch for buffer region.
  • Electrochemistry: Write cell notation, calculate E°cell, find ΔG°, apply Nernst equation.
  • Kinetics: Determine rate law from data, find rate constant, integrated rate law graph analysis.
  • Thermodynamics: Calculate ΔH from Hess's Law, find ΔG at non-standard conditions, predict spontaneity.

AP Chemistry Prep Checklist

Check off what you've mastered. Track your readiness.

Electron configurations (including exceptions: Cr, Cu)Atomic Structure Unit 1
Lewis structures, VSEPR, molecular geometryBonding Unit 2
Intermolecular forces and their effect on physical propertiesIMF Unit 3 — highest weight
Stoichiometry, limiting reagent, percent yieldChemical Reactions Unit 4
Rate laws, integrated rate laws, Arrhenius equationKinetics Unit 5
Hess's Law, bond enthalpies, ΔG = ΔH - TΔSThermodynamics Unit 6
ICE tables, Le Chatelier, Kp vs. KcEquilibrium Unit 7
pH, Ka/Kb, buffers, Henderson-Hasselbalch, titration curvesAcids & Bases Unit 8
Galvanic cells, standard reduction potentials, Nernst equationElectrochemistry Unit 9
Practiced at least 3 full FRQ sets under timed conditionsExam Practice

AP Chemistry — My Progress

Track your practice scores and see your estimated AP score (1–5).

No quiz history yet. Complete some practice questions to see your progress here!
3h 15m
Exam Duration
50
MCQ Questions
5
FRQ Questions
7
Units (C: Mech)

AP Physics 1 Unit Weights

Physics 1 is algebra-based. Focus on conceptual understanding and proportional reasoning.

Kinematics
10-16%
Forces & Newton's Laws
16-24%
Work, Energy & Power
18-26%
Linear Momentum
10-16%
Rotation & Torque
10-16%
Oscillations
4-6%
Gravitation
4-6%
High-Yield

Forces = 20% of Exam

Newton's Second Law (ΣF = ma) is the foundation of almost every mechanics problem. Mastering free body diagrams and net force analysis will earn you the most points.

High-Yield

Energy Conservation

Energy is the most powerful tool in physics. "Work-energy theorem" and "conservation of energy" solve problems that would be impossible with kinematics alone.

AP Physics 1 Trap

Rotation is NOT Optional

Many students skip rotation. But rotational kinematics, torque, and angular momentum make up 10-16%. The concepts mirror linear mechanics — treat them as a translation.

Key Concepts by Unit

Deep understanding over memorization — AP Physics tests application, not recall.

🏃 Kinematics
  • Big Five equations connect v, v₀, a, t, Δx. Each has one variable missing — pick the equation that matches what you know.
  • Projectile motion: Horizontal and vertical components are independent. vₓ is constant; vy changes at 9.8 m/s² downward.
  • Graphs: Slope of position-time = velocity. Slope of velocity-time = acceleration. Area under v-t = displacement.
  • First principles: Kinematics is purely descriptive — it tells you HOW objects move, not WHY.
⚡ Forces & Newton's Laws
  • Free body diagrams: Draw every force acting ON the object. Never include forces the object exerts on others.
  • Net force = ma. If ΣF = 0, acceleration = 0 (equilibrium). Object can still be moving at constant velocity.
  • Friction: Static (fs ≤ μsN) keeps objects at rest. Kinetic (fk = μkN) acts while sliding. μk < μs always.
  • Newton's 3rd Law: Forces come in equal-and-opposite action-reaction pairs on different objects. Never add them together in the same FBD.
⚡ Energy & Momentum
  • Work-energy theorem: Wnet = ΔKE. All forces do work; only conservative forces have potential energy.
  • Conservation of energy: Total mechanical energy constant if only conservative forces. Add heat losses for friction.
  • Impulse-momentum: J = Δp = FΔt. Impulse equals change in momentum.
  • Collisions: Momentum always conserved. Kinetic energy conserved only in perfectly elastic collisions.

AP Physics Formula Reference

FormulaWhat It MeansWhen to Use
v = v₀ + atVelocity after constant acceleration for time tMissing displacement; find final velocity
Δx = v₀t + ½at²Displacement with initial velocity and accelerationMissing final velocity
v² = v₀² + 2aΔxRelates velocity to displacement without timeMissing time variable
ΣF = maNet force equals mass times accelerationAll force problems; the cornerstone equation
W = Fd cos θWork = force × displacement × cosine of angle between themCalculating work done by a force
KE = ½mv²Kinetic energy of a moving objectEnergy conservation problems
PE = mghGravitational potential energy near Earth's surfaceEnergy conservation; height problems
p = mvMomentum = mass × velocityCollisions and impulse problems
J = FΔt = ΔpImpulse equals change in momentumForce over time; collision duration
τ = rF sin θTorque = lever arm × forceRotational equilibrium and dynamics

AP Physics Practice Questions

🎯 Drill by Topic

FRQ Strategy for AP Physics

Strategy

Experimental Design FRQ

AP Physics 1 includes experimental design questions worth 12 points. Practice identifying variables, explaining controls, describing measurements, and analyzing data with uncertainty.

Strategy

Paragraph-Length Response

New to AP Physics 1: a 4-point paragraph response. Write like a physicist: claim → evidence → reasoning. One clear paragraph beats three vague ones.

Common Error

No Units = Lost Points

Every numerical answer needs units. Every time. Graders deduct for missing units even if your number is right. Circle or highlight units in your answer.


✍️ Practice FRQs
FRQ 1 — Energy Conservation & Work
Typical point value: 7 pts | No calculator
Context

A 2 kg block is released from rest at the top of a ramp that is 3 m high and 5 m long (measured along the ramp). The coefficient of kinetic friction between the block and ramp is μk = 0.1. g = 10 m/s².

Part (a) — 3 pts

Draw a free-body diagram showing all forces on the block while it is sliding down the ramp. Label each force.

Full credit (3 pts): Must show: (1) Weight mg = 20 N downward (1 pt). (2) Normal force N perpendicular to the ramp surface (1 pt). (3) Kinetic friction force directed up the ramp, opposing motion (1 pt). Common errors: friction pointing down the ramp (−1 pt), including "applied force" or "centripetal force" which don't exist here.
Part (b) — 4 pts

Calculate the speed of the block at the bottom of the ramp using energy methods. Show all work clearly.

Full credit (4 pts): sin θ = 3/5, cos θ = 4/5. Normal force: N = mg cos θ = 2(10)(4/5) = 16 N. Friction force: f = μk N = 0.1 × 16 = 1.6 N. Work done by friction: Wf = −f × d = −1.6 × 5 = −8 J. Energy: ΔKE = Wgravity + Wfriction → ½mv² = mgh + Wf = 2(10)(3) − 8 = 52 J → v² = 52, v = √52 ≈ 7.2 m/s. Partial credit: Correct N and friction force (2 pts), correct energy setup (1 pt), correct final answer (1 pt).
FRQ 2 — Experimental Design (12-pt style)
Typical point value: 12 pts | Calculator permitted
Context

A student wants to determine the spring constant k of an unknown spring using only: a ruler, a known mass set (with values in kg), a stand with a clamp, and the spring.

Part (a) — 4 pts

Describe a procedure to determine k. Include: what measurements to take, how to record them, and how to calculate k from the data.

Full credit (4 pts): Hang the spring vertically from the clamp. Measure the natural length of the spring (x₀) with no mass. Add masses one at a time, record the mass m and the new equilibrium length x for each. Calculate stretch Δx = x − x₀. At equilibrium: kΔx = mg → k = mg/Δx. Record a table of m vs. Δx. 1 pt each: measuring natural length; varying masses systematically; using equilibrium condition; computing k from at least 3 data points.
Part (b) — 4 pts

Describe how to use a graph of the data to determine k. What should be on each axis, and how is k found from the graph?

Full credit (4 pts): Plot mg (or F = mg) on the y-axis vs. Δx on the x-axis. The relationship is linear: F = kΔx, so the graph is a straight line through the origin. The slope of the line equals k. Using a best-fit line (not connecting dots) improves accuracy. 1 pt: correct axes; 1 pt: linear relationship predicted; 1 pt: slope = k; 1 pt: mention best-fit line.
Part (c) — 4 pts

Identify one source of systematic error in this experiment and explain how it would affect the measured value of k.

Acceptable answers (4 pts): (1) Mass of the spring itself not accounted for → measured Δx is larger than predicted → k appears smaller than true value. (2) Measuring spring length while masses are still swinging → Δx measurements are inconsistent. (3) Spring stretched beyond its elastic limit → Hooke's Law no longer applies → k appears to decrease for large masses. Must identify specific error AND explain the direction of effect on k.

AP Physics 1 Prep Checklist

Kinematic equations and graph interpretationUnit 1
Free body diagrams for all force typesUnit 2
Work-energy theorem and conservation of energyUnit 3
Impulse-momentum theorem, elastic vs. inelastic collisionsUnit 4
Torque, rotational kinematics, angular momentumUnit 5-6
Simple harmonic motion and Hooke's LawUnit 6
Practiced experimental design questionsExam Skill
Practiced paragraph-length response questionsExam Skill

AP Physics — My Progress

Track your practice scores and see your estimated AP score (1–5).

No quiz history yet. Complete some practice questions to see your progress here!
3h 15m
Exam Duration
60
MCQ Questions
6
FRQ Questions
4
Big Ideas

AP Biology Unit Weights

Chemistry of Life
8-11%
Cell Structure & Function
10-13%
Cellular Energetics
12-16%
Cell Communication & Cycle
10-15%
Heredity & Genetics
8-11%
Gene Expression & Regulation
12-16%
Natural Selection & Evolution
13-20%
Ecology
10-15%
High-Yield

Evolution is 20% — Master It

Natural selection, Hardy-Weinberg equilibrium, phylogenetics, and speciation are tested more heavily than any other unit. Understand the logic of evolution, don't just memorize facts.

High-Yield

Gene Expression = Modern Biology

Transcription, translation, operons, epigenetics, and CRISPR. AP Bio is increasingly focused on molecular mechanisms. Know every step of the central dogma cold.

Key Concepts by Unit

🧬 Cellular Energetics (Photosynthesis & Respiration)
  • Photosynthesis: Light reactions (thylakoid) → NADPH + ATP. Calvin cycle (stroma) → G3P using CO₂. Light reactions split water; oxygen is a byproduct.
  • Cellular respiration: Glycolysis (cytoplasm) → Krebs cycle (matrix) → ETC (inner membrane). Net: ~30-32 ATP per glucose.
  • Chemiosmosis: H⁺ gradient across membrane drives ATP synthase. The same mechanism in chloroplasts and mitochondria.
  • First principles: Both processes are about moving electrons to lower energy states. Energy is captured when electrons "fall" to more electronegative atoms.
🧫 Gene Expression & Regulation
  • Transcription: DNA → mRNA via RNA polymerase. Promoters, enhancers, and silencers regulate when and how much.
  • Translation: mRNA → protein at ribosomes. tRNA anticodons match codons; start codon AUG, stop codons UAA/UAG/UGA.
  • Operons (prokaryotes): lac operon (inducible — sugar turns on genes) vs. trp operon (repressible — amino acid turns off genes).
  • Eukaryotic regulation: Histone modification (acetylation loosens chromatin), methylation, miRNA, alternative splicing.
🌿 Evolution & Natural Selection
  • Hardy-Weinberg: p² + 2pq + q² = 1 and p + q = 1. Equilibrium requires no selection, mutation, migration, drift, or non-random mating.
  • Types of selection: Directional (one extreme favored), stabilizing (middle favored), disruptive (both extremes favored).
  • Speciation: Allopatric (geographic barrier) vs. sympatric (same location, e.g., polyploidy in plants).
  • Phylogenetics: Parsimony — simplest tree explaining data is preferred. Shared derived characters (synapomorphies) define clades.

AP Biology Practice Questions

🎯 Drill by Topic

FRQ Strategy for AP Biology

Strategy

Data Analysis FRQs

AP Bio loves graphs, bar charts, and data tables. Practice describing patterns (not just reading numbers), identifying controls, calculating percent change, and evaluating experimental design.

Strategy

Write Mechanistically

Say HOW, not just WHAT. Instead of "more ATP is produced," write "electrons from NADH pass through Complex I, III, IV, creating a proton gradient that drives ATP synthase to synthesize ATP."

Common Error

Don't Say "It Wants To"

Organisms don't "want" to do anything. Evolution doesn't "try" to create better organisms. Lose anthropomorphic language — it costs points. Write in terms of selection pressures and fitness.


✍️ Practice FRQs
FRQ 1 — Hardy-Weinberg & Natural Selection
Typical point value: 8 pts | Calculator permitted
Context

In a population of 1000 mice, 360 are white (homozygous recessive, bb) and 640 are dark (B_). Assume the population is in Hardy-Weinberg equilibrium.

Part (a) — 3 pts

Calculate the frequencies of both alleles and the expected number of heterozygous individuals. Show all work.

Full credit (3 pts): q² = 360/1000 = 0.36 → q = 0.6 (frequency of b). p = 1 − 0.6 = 0.4 (frequency of B). Heterozygotes = 2pq = 2(0.4)(0.6) = 0.48, or 480 mice expected. Must show: q² → q calculation (1 pt); p = 1−q (1 pt); 2pq × 1000 (1 pt).
Part (b) — 3 pts

Suppose owls preferentially prey on white mice because they are more visible in dark forests. Predict and explain what would happen to the allele frequencies over 10 generations. Name the type of selection occurring.

Full credit (3 pts): Directional selection (1 pt). White mice (bb) have lower fitness because they are eaten more often. Over generations, the b allele decreases in frequency and B allele increases (1 pt). Hardy-Weinberg equilibrium is violated because one condition (no natural selection) is broken — the population will evolve (1 pt). Avoid: "Mice want to be darker" (anthropomorphism). Write in terms of survival, reproduction, and fitness.
Part (c) — 2 pts

Name TWO other conditions required for Hardy-Weinberg equilibrium that are NOT natural selection. For each, explain what would happen if that condition were violated.

Full credit (2 pts, 1 each): Any two of: No genetic drift (small population → random fluctuations change allele frequencies). No mutation (new mutations introduce new alleles, shifting frequencies). No gene flow/migration (immigration/emigration changes allele frequencies). Random mating (non-random mating, e.g., by phenotype, changes genotype frequencies without changing allele frequencies).
FRQ 2 — Gene Expression: Central Dogma
Typical point value: 6 pts | No calculator
Context

The following DNA template strand corresponds to part of a gene: 3'-TACGCAATGGCTCGAAAG-5'

Part (a) — 2 pts

Write the sequence of the mRNA transcribed from this template strand. Label the 5' and 3' ends.

Full credit (2 pts): mRNA: 5'-AUGCGUUACCGAGCUUUC-3'. Rules: RNA is complementary to template DNA and antiparallel. T → A, A → U, G → C, C → G. mRNA runs 5'→3' opposite to template (which runs 3'→5'). Must label 5' and 3' ends (1 pt), must have correct U substitutions (1 pt).
Part (b) — 2 pts

Use the mRNA sequence from part (a) to determine the first four amino acids in the polypeptide. The first codon AUG codes for Met.

Full credit (2 pts): Codons: AUG (Met) — CGU (Arg) — UAC (Tyr) — CGA (Arg). Students need a codon chart for this (provided on AP exam). Credit for correctly reading codons in triplets (1 pt) and correctly identifying the amino acids from the chart (1 pt).
Part (c) — 2 pts

A mutation changes the 6th base of the template strand from A to T (so the mRNA codon changes from CGU to CAU). Predict and explain the effect on the protein.

Full credit (2 pts): The codon changes from CGU (Arg) to CAU (His) — a missense mutation (1 pt). Effect: Arginine is replaced by Histidine at position 2 in the protein. This is a nonsynonymous substitution that may alter protein structure and function, especially if it occurs in a critical domain or active site (1 pt). Contrast: if the change had resulted in the same amino acid (synonymous/silent mutation), there would be no effect on the protein.

AP Biology Prep Checklist

Macromolecules: structure and function of proteins, lipids, carbs, nucleic acidsUnit 1
Cell organelles and membrane structure (fluid mosaic model)Unit 2
Photosynthesis and cellular respiration (both in detail)Unit 3
Cell cycle, mitosis, meiosis, and cancer connectionsUnit 4
Mendelian genetics, non-Mendelian inheritance, chi-square testUnit 5
Central dogma, gene expression, operons, epigeneticsUnit 6
Hardy-Weinberg, types of selection, speciationUnit 7
Population ecology, community interactions, nutrient cyclesUnit 8
Practiced data analysis FRQs with graphsExam Skill

AP Biology — My Progress

Track your practice scores and see your estimated AP score (1–5).

No quiz history yet. Complete some practice questions to see your progress here!
3h 15m
Exam Duration
45
MCQ Questions
6
FRQ Questions
4
Big Ideas

AP Calculus AB Unit Weights

Limits & Continuity
10-12%
Differentiation (Basic Rules)
10-12%
Differentiation (Composite/Implicit)
9-13%
Contextual Applications of Differentiation
10-15%
Analytical Applications of Differentiation
15-18%
Integration & Accumulation
17-20%
Differential Equations
6-12%
Applications of Integration
10-15%
Core Insight

The Fundamental Theorem

The Fundamental Theorem of Calculus connects derivatives and integrals — they are inverses. This is the single most important idea in all of calculus. Every other concept builds from it.

High-Yield

Integration = 32% of Exam

Units 6 and 8 together are nearly a third of your score. Master u-substitution, the Fundamental Theorem, area between curves, and accumulation functions.

Key Concepts — The Big Ideas

📐 Limits & Continuity
  • Limit definition: lim(x→a) f(x) = L means f(x) gets arbitrarily close to L as x approaches a. The function doesn't need to equal L at a.
  • L'Hôpital's Rule: If limit gives 0/0 or ∞/∞, take derivative of numerator and denominator separately, then re-evaluate.
  • Continuity: f is continuous at a if (1) f(a) exists, (2) the limit exists, and (3) they're equal. All three conditions must hold.
  • IVT: If f is continuous on [a,b] and k is between f(a) and f(b), then there exists c in (a,b) where f(c) = k.
📈 Derivatives
  • Definition: f'(x) = lim(h→0) [f(x+h)-f(x)]/h. The derivative is the instantaneous rate of change — the slope of the tangent line.
  • Chain rule: d/dx[f(g(x))] = f'(g(x)) · g'(x). Work from outside in. "Derivative of outside times derivative of inside."
  • Implicit differentiation: Differentiate both sides with respect to x; treat y as a function of x, so dy/dx appears whenever you differentiate y.
  • Optimization: Set f'(x) = 0 to find critical points. Use second derivative or first derivative sign test to classify as max/min.
∫ Integration
  • FTC Part 1: d/dx ∫ₐˣ f(t)dt = f(x). The derivative of an accumulation function gives back the integrand.
  • FTC Part 2: ∫ₐᵇ f(x)dx = F(b) - F(a) where F is any antiderivative. Net change = final - initial.
  • u-substitution: Let u = inside function, du = derivative × dx. Rewrite integral entirely in terms of u. The chain rule in reverse.
  • Area between curves: ∫[top - bottom]dx. Always integrate the upper function minus the lower. Set up limits at intersection points.

Essential Derivatives & Integrals

Function f(x)Derivative f'(x)Notes
xⁿnxⁿ⁻¹Power rule — most used rule in calculus
sin xcos xTrig derivatives cycle: sin→cos→-sin→-cos
cos x-sin xNote the negative sign
e is the unique base where f = f'
ln x1/xDomain: x > 0
tan xsec² xMemorize this one
f(g(x))f'(g(x)) · g'(x)Chain rule — most common mistake is forgetting g'(x)
IntegrandAntiderivativeNotes
xⁿ (n≠-1)xⁿ⁺¹/(n+1) + CReverse power rule
1/xln|x| + CNote absolute value
eˣ + Ceˣ is its own antiderivative
sin x-cos x + CNote negative sign
cos xsin x + C
sec² xtan x + CReverse of tan derivative

AP Calculus Practice Questions

🎯 Drill by Topic

AP Calculus AB Prep Checklist

Evaluating limits algebraically and graphicallyUnit 1
Power, product, quotient, chain rule derivativesUnit 2-3
Implicit differentiation and related ratesUnit 3
Optimization and curve sketching (f, f', f'' analysis)Unit 5
Fundamental Theorem of Calculus (both parts)Unit 6
u-substitution for integrationUnit 6
Separable differential equations and slope fieldsUnit 7
Area between curves, volume with disk/washer methodUnit 8

FRQ Strategy for AP Calculus

FRQs are 50% of your score — 3 with calculator, 3 without.

Strategy

Show All Work

AP Calculus graders give credit for process, not just answers. Write every step: set up, integrate/differentiate, evaluate. Even a wrong final answer earns most points if the method is correct.

Strategy

No Calculator? Exact Answers

On the no-calculator FRQ sections, leave answers in exact form: ln(3), π/4, √2. Never approximate unless the problem says to. Rounding prematurely loses points.

Common Trap

Forgetting the Constant of Integration

Every indefinite integral needs + C. On differential equations, forgetting C means you found one particular solution, not the general solution — major point loss on the setup.

Must Know

FRQ Types That Appear Every Year

Area/volume integrals; rates (slope fields / differential equations); motion on a line (position, velocity, acceleration from graphs); accumulation (FTC applied to real context).


✍️ Practice FRQs
FRQ 1 — Particle Motion
Typical point value: 9 pts | No calculator
Context

A particle moves along the x-axis so that its velocity at time t is given by v(t) = t² − 4t + 3 for 0 ≤ t ≤ 4. The particle is at position x = 5 when t = 0.

Part (a) — 3 pts

Find all values of t in [0, 4] where the particle changes direction. Justify your answer.

Full credit (3 pts): Set v(t) = 0 → t² − 4t + 3 = (t−1)(t−3) = 0 → t = 1, 3. Check sign change: v changes from + to − at t=1 (direction change), − to + at t=3 (direction change). Must state "v changes sign" for justification credit, not just "v = 0."
Part (b) — 3 pts

Find the total distance traveled by the particle from t = 0 to t = 4.

Full credit (3 pts): Total distance = ∫₀¹|v|dt + ∫₁³|v|dt + ∫₃⁴|v|dt. On [0,1] v > 0, on [1,3] v < 0, on [3,4] v > 0. Antiderivative: t³/3 − 2t² + 3t. Evaluate each piece and sum absolute values. [0,1]: t³/3−2t²+3t from 0 to 1 = 4/3. [1,3]: |0−4/3| = 4/3. [3,4]: 4/3−0 = 4/3. Total distance = 4/3 + 4/3 + 4/3 = 4.
Part (c) — 3 pts

Find the position of the particle at t = 4.

Full credit (3 pts): x(4) = x(0) + ∫₀⁴ v(t) dt = 5 + [t³/3 − 2t² + 3t]₀⁴ = 5 + (64/3 − 32 + 12) = 5 + 4/3 = 19/3. Key: use x(0) = 5 as initial condition.
FRQ 2 — Area Between Curves
Typical point value: 9 pts | Calculator permitted
Context

Let f(x) = 3 − x² and g(x) = x + 1. Let R be the region enclosed by the graphs of f and g.

Part (a) — 3 pts

Find the x-coordinates of the points of intersection of f and g. Show the work leading to your answer.

Full credit (3 pts): Set equal: 3 − x² = x + 1 → x² + x − 2 = 0 → (x+2)(x−1) = 0 → x = −2, x = 1. Must show algebraic setup for credit.
Part (b) — 3 pts

Find the area of region R.

Full credit (3 pts): Area = ∫₋₂¹ [f(x) − g(x)] dx = ∫₋₂¹ (3 − x² − x − 1) dx = ∫₋₂¹ (2 − x² − x) dx = [2x − x³/3 − x²/2]₋₂¹ = (2 − 1/3 − 1/2) − (−4 + 8/3 − 2) = 9/2. Answer: 9/2 square units.
Part (c) — 3 pts

Write, but do not evaluate, an integral expression for the volume of the solid generated when R is rotated about the x-axis.

Full credit (3 pts): Washer method: V = π ∫₋₂¹ [f(x)² − g(x)²] dx = π ∫₋₂¹ [(3−x²)² − (x+1)²] dx. Must use washer (not disk) because there is a gap between the x-axis and both curves. Clearly label the outer and inner radii.

AP Calculus — My Progress

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3h
Exam Duration
40
MCQ Questions
6
FRQ Questions
4
Big Ideas

AP Statistics Unit Weights

Exploring One-Variable Data
15-23%
Exploring Two-Variable Data
5-7%
Collecting Data
12-15%
Probability, Random Variables
10-20%
Sampling Distributions
7-12%
Inference for Categorical Data
12-15%
Inference for Quantitative Data
10-18%
Inference for Regression
6-10%
Core Insight

Inference is 50%+ of the Exam

Units 6, 7, and 8 together cover confidence intervals and hypothesis tests — more than half the exam. Know when to use each test (z, t, chi-square, F) and be able to write full conclusions in context.

Common Trap

Context is Non-Negotiable

Every single answer must reference the context of the problem. Never write "the mean is 42" — write "the mean exam score of students is 42 points." Graders require context for full credit.

Key Concepts by Unit

📊 Exploring Data
  • Shape, center, spread: Always describe distributions with all three. Shape: symmetric/skewed left or right. Center: mean or median. Spread: range, IQR, or standard deviation.
  • Outlier rule: Q1 − 1.5×IQR and Q3 + 1.5×IQR. Points outside this range are outliers.
  • Normal distribution: 68-95-99.7 rule. Z-score = (x − μ)/σ. Z-table gives area to the LEFT.
  • Skewness and center: In right-skewed data, mean > median. In left-skewed, mean < median. Median is resistant to outliers.
🎲 Probability & Sampling Distributions
  • Law of Large Numbers: As sample size increases, sample mean approaches population mean. Does NOT say results "balance out."
  • Central Limit Theorem: For n ≥ 30 (or any n if population is normal), the sampling distribution of x̄ is approximately normal with mean μ and std dev σ/√n.
  • Binomial distribution: Fixed n trials, binary outcome, constant p, independent trials. Mean = np, SD = √(np(1-p)).
  • First principles: A sampling distribution is NOT data — it's the distribution of a statistic across all possible samples.
🔬 Inference: Hypothesis Testing
  • Four steps: (1) State hypotheses, (2) Check conditions, (3) Calculate test statistic and p-value, (4) Make conclusion in context.
  • p-value: The probability of getting a result at least as extreme as observed, IF H₀ is true. It is NOT the probability H₀ is true.
  • Type I error: Rejecting a true H₀ (false positive). Type II error: Failing to reject a false H₀ (false negative). Power = 1 - P(Type II).
  • AP-required phrase: "We (reject/fail to reject) H₀. There (is/is not) convincing evidence that [context statement in terms of population]."
📏 Confidence Intervals
  • Formula: statistic ± (critical value) × (standard error). Always: point estimate ± margin of error.
  • Interpretation: "We are 95% confident the true [parameter] is between [L] and [U]." Not "there's a 95% chance" — the parameter is fixed.
  • Increasing width: Higher confidence level OR smaller sample size → wider interval. More precision requires larger n.
  • Conditions for z-interval: (1) Random sample, (2) n ≥ 30 or normal population, (3) n ≤ 10% of population (independence).

AP Statistics Practice Questions

🎯 Drill by Topic

Investigative Task (Question 6)

What It Is

The Investigative Task

Question 6 is a multi-part, open-ended problem worth more points than any other FRQ. It often introduces a new concept or variant you haven't seen before — that's intentional. You're being tested on statistical reasoning, not just recall.

Strategy

Score Points Even When Lost

The investigative task is designed to be hard. Most students don't complete it fully. Focus on parts (a) and (b) first — they're usually more accessible. Partial credit adds up: a 5 out of 6 is excellent.

Strategy

Always Write a Conclusion

Every inference question needs a conclusion sentence. State: reject/fail to reject H₀, what that means in context, and acknowledge what could go wrong (Type I/II error). This earns "E" (essentially correct) vs. "P" (partially correct).

Common Trap

Conditions Must Be Verified

Simply saying "the conditions are met" is worth zero. You must show the work: "The sample is random (given). n=50 ≥ 30, so CLT applies. 50 < 10% of all students (independence condition met)."


✍️ Practice FRQs
FRQ 5 — Inference: One-Sample t-Test
Typical point value: 4 pts | Calculator permitted
Context

A teacher claims the average exam score for her class is 80 points. A random sample of 25 students from this class has a mean of 77 points with a standard deviation of 10 points.

Part (a) — 4 pts

Conduct a one-sample t-test at α = 0.05 to determine if there is convincing evidence that the true mean is less than 80. Include all four steps.

Step 1 — Hypotheses (1 pt): H₀: μ = 80 points; Hₐ: μ < 80 points. Use population parameter μ (not x̄).
Step 2 — Conditions (1 pt): (1) Random sample ✓ (stated); (2) n = 25 < 10% of class population (independence); (3) n = 25 < 30, but assume approximately normal distribution. Conditions met — proceed with t-test.
Step 3 — Test statistic & p-value (1 pt): t = (x̄ − μ₀)/(s/√n) = (77 − 80)/(10/√25) = −3/2 = −1.5. df = 24. p-value = P(t < −1.5 | df=24) ≈ 0.073.
Step 4 — Conclusion (1 pt): Since p = 0.073 > α = 0.05, we fail to reject H₀. There is NOT convincing evidence that the true mean exam score is less than 80 points. Must use "fail to reject" (not "accept") and state conclusion in context.
Investigative Task — Sampling and Inference
Typical point value: 6 pts | Extended response
Context

A school district wants to estimate the proportion of students who regularly eat breakfast. They survey 120 randomly selected students and find that 78 reported eating breakfast that morning. A researcher claims the true proportion is 0.70.

Part (a) — 2 pts

Construct a 95% confidence interval for the true proportion of students who eat breakfast. Interpret the interval in context.

Full credit (2 pts): p̂ = 78/120 = 0.65. Conditions: random sample ✓; np̂ = 78 ≥ 10, n(1−p̂) = 42 ≥ 10 ✓; n < 10% population ✓. SE = √(p̂(1−p̂)/n) = √(0.65×0.35/120) = √0.001896 ≈ 0.0435. 95% CI: 0.65 ± 1.96(0.0435) = 0.65 ± 0.085 = (0.565, 0.735). Interpretation: "We are 95% confident the true proportion of students in this district who eat breakfast is between 0.565 and 0.735."
Part (b) — 2 pts

Using your interval from part (a), does the interval provide convincing evidence against the researcher's claim that p = 0.70? Explain.

Full credit (2 pts): No, the interval does NOT provide convincing evidence against p = 0.70. Since 0.70 is within the interval (0.565, 0.735), the claimed value is plausible. At the 95% confidence level, we cannot rule out p = 0.70. A value is "plausible" if it falls inside the confidence interval (1 pt), and must state that 0.70 is inside the interval (1 pt).
Part (c) — 2 pts

A classmate suggests that if the sample size were increased to 480 students, the interval would be more useful. Explain what would happen to the interval and why.

Full credit (2 pts): With n = 480 (4× larger), the standard error = √(p̂(1−p̂)/n) is halved (SE ∝ 1/√n). The margin of error = 1.96 × SE is also halved, making the interval narrower. A narrower interval gives a more precise estimate of the true proportion, making it more useful for decision-making. Must mention: SE decreases (1 pt); interval becomes narrower / more precise (1 pt).

AP Statistics Prep Checklist

Describing distributions (shape, center, spread, outliers)Unit 1
Normal distribution and z-scoresUnit 1
LSRL, residuals, r², and lurking variablesUnit 2
Sampling methods and sources of biasUnit 3
Experimental design: randomization, control, replicationUnit 3
Probability rules, binomial, and geometric distributionsUnit 4
Central Limit Theorem and sampling distributionsUnit 5
One-prop z-test and interval, two-prop z-testUnit 6
One-sample t-test and interval, two-sample t-testUnit 7
Chi-square goodness-of-fit and independence testsUnit 6
Practiced writing full inference procedures with contextExam Skill

AP Statistics — My Progress

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