MAP The Section at a Glance
- 59 questions, 95 min. ~10 passages (4 Q each) + ~15 discrete questions.
- Content mix (approx.): Gen Chem ~30%, Physics ~25%, Biochem ~25%, Organic ~15%, intro Bio ~5% — all in a biological context.
- Tests applied reasoning on experiments and data, not plug-and-chug. No calculator — arithmetic is kept clean; know how to estimate.
Exam-day math: use scientific notation, round aggressively, and track units — dimensional analysis alone answers many questions. Log rules: log(10ⁿ)=n; a 10× change = ±1 log unit.
Estimation: to find log(x·10ⁿ): answer ≈ n + (decimal from x, where log2≈0.3, log3≈0.48, log5≈0.7).
REF Constants & Conversions
| Symbol | Value |
|---|---|
| g (gravity) | 9.8 m/s² (≈10) |
| G (gravitation) | 6.67×10⁻¹¹ N·m²/kg² |
| k (Coulomb) | 8.99×10⁹ N·m²/C² (≈9×10⁹) |
| c (light) | 3.0×10⁸ m/s |
| h (Planck) | 6.63×10⁻³⁴ J·s |
| N_A (Avogadro) | 6.022×10²³ /mol |
| R (gas) | 8.314 J/mol·K = 0.0821 L·atm/mol·K |
| e (charge) | 1.6×10⁻¹⁹ C |
| ε₀ (permittivity) | 8.85×10⁻¹² C²/N·m² |
| K_w | 1.0×10⁻¹⁴ (25 °C) |
| Quantity | Equivalent |
|---|---|
| 1 atm | 760 mmHg = 760 torr = 101 kPa |
| STP | 0 °C, 1 atm → 22.4 L/mol (ideal) |
| Temperature | K = °C + 273 |
| 1 cal | 4.18 J |
| 1 mole gas (STP) | 22.4 L |
| 1 eV | 1.6×10⁻¹⁹ J |
Water: density 1 g/mL (1000 kg/m³); specific heat 4.18 J/g·°C; L_fusion 334 J/g; L_vapor 2260 J/g.
PHYS Physics — Complete Equation Sheet
Kinematics (constant a)
v = v₀ + a·Δt
Δx = v₀Δt + ½a·Δt²
v² = v₀² + 2a·Δx
v̄ = (v₀ + v)/2
Projectile: x and y are independent. Horizontal a=0 (v_x constant); vertical a=−g. At peak, v_y=0. Range max at 45° (level ground).
Forces & Dynamics
ΣF = m·a
Weight W = m·g
Friction f = μN (kinetic); f ≤ μ_sN (static)
Gravity F = G·m₁m₂/r²
Incline: F∥ = mg·sinθ, F⊥ = mg·cosθ
μ_s > μ_k. Normal force N is not always mg (changes on inclines, in elevators, with applied angles).
Work, Energy, Power
W = F·d·cosθ
KE = ½mv²
PE_grav = mgh
PE_spring = ½kx²; F = −kx
P = W/t = F·v
W_net = ΔKE (work–energy theorem)
Conservative forces (gravity, spring): W path-independent, define PE. Total mechanical E conserved if no friction. Efficiency = useful out / total in.
Momentum & Collisions
p = m·v
Impulse J = F·Δt = Δp
Σp conserved in all collisions
| Collision | p | KE |
|---|---|---|
| Elastic | ✔ | ✔ conserved |
| Inelastic | ✔ | ✖ (lost) |
| Perfectly inelastic | ✔ | ✖ (stick together) |
Circular Motion & Rotation
Centripetal a_c = v²/r
F_c = mv²/r (net inward)
Torque τ = r·F·sinθ = I·α
Rotational KE = ½I·ω²
Angular momentum L = I·ω
Equilibrium: ΣF = 0 AND Στ = 0. Torque = force × lever arm (perpendicular distance).
Fluids
Density ρ = m/V
Pressure P = F/A
Hydrostatic P = ρgh (gauge); P_abs = P₀ + ρgh
Buoyancy F_b = ρ_fluid·V_disp·g
Continuity A₁v₁ = A₂v₂ (Q = Av)
Bernoulli P + ½ρv² + ρgy = const
Archimedes: floats if ρ_object < ρ_fluid; fraction submerged = ρ_object/ρ_fluid. Bernoulli: faster flow → lower pressure. Poiseuille: flow ∝ r⁴ (halving radius drops flow 16×).
Thermodynamics & Heat
1st law ΔU = Q − W (W by system)
Sensible heat Q = mcΔT
Phase change Q = mL (T constant)
Ideal gas PV = nRT
Expansion ΔL = αL·ΔT
Engine efficiency = 1 − Q_c/Q_h
Q>0 heat in; W>0 work by gas (expansion). ΔS_universe ≥ 0 (2nd law). Isothermal ΔU=0; adiabatic Q=0.
SHM & Waves
v = f·λ; T = 1/f
Pendulum T = 2π√(L/g)
Spring T = 2π√(m/k)
String wave v = √(T_tension/μ)
| System | f_n | n |
|---|---|---|
| String / open pipe | n·v/2L | 1,2,3… |
| Closed pipe (1 end) | n·v/4L | odd only |
Sound
Intensity I = P/A ∝ 1/r²
Level β = 10·log(I/I₀), I₀=10⁻¹² W/m²
Doppler f′ = f·(v ± v_o)/(v ∓ v_s)
Doppler: choose signs so approaching → higher f′. Each ×10 intensity = +10 dB. Beats freq = |f₁ − f₂|.
Geometric Optics
Index n = c/v
Snell n₁sinθ₁ = n₂sinθ₂
Critical angle sinθ_c = n₂/n₁
Lens/mirror 1/f = 1/o + 1/i
Magnif. m = −i/o = h_i/h_o
Power P = 1/f (diopters); mirror f = R/2
Sign rules: f>0 converging (convex lens / concave mirror). i>0 real/inverted (same side as outgoing light); i<0 virtual/upright. |m|>1 enlarged. Total internal reflection occurs only going to a lower-index medium (n₁>n₂) past θ_c.
Electrostatics
Coulomb F = k·q₁q₂/r²
Field E = F/q = kQ/r²; uniform E = V/d
Potential V = kQ/r; U = qV = kq₁q₂/r
Capacitance C = Q/V; C = ε₀A/d
Stored U = ½CV² = ½QV
Field points away from + charge. Potential is scalar. Work by field W = qΔV. Field inside a conductor = 0.
Circuits
Current I = Q/t
Ohm V = IR; R = ρL/A
Power P = IV = I²R = V²/R
Time constant τ = RC
| Resistors | Capacitors | |
|---|---|---|
| Series | R_eq=ΣR (same I) | 1/C_eq=Σ1/C |
| Parallel | 1/R_eq=Σ1/R (same V) | C_eq=ΣC |
Kirchhoff: Σ current in = out (node); ΣV around loop = 0.
Magnetism & Modern
On charge F = qvB·sinθ
On wire F = BIL·sinθ
Photon E = hf = hc/λ
Mass–energy E = mc²
Right-hand rule for direction. Nuclear decay: α (−2p,−2n), β⁻ (n→p+e⁻), β⁺ (p→n+e⁺), γ (energy). After n half-lives, fraction = (½)ⁿ.
Fig 1. Projectile motion. Horizontal velocity is constant (no horizontal force); vertical velocity decreases to zero at the apex, then increases downward. Speed at landing equals launch speed (level ground).
GC General Chemistry
Atomic Structure
- Quantum #s: n (shell), l (0–n−1: s,p,d,f), m_l (−l…+l), m_s (±½).
- Fill order: Aufbau (low E first), Hund (unpaired first), Pauli (no two same 4 #s).
- Orbitals: s(2), p(6), d(10), f(14) e⁻.
Stable exceptions: half/fully-filled d (Cr = [Ar]4s¹3d⁵; Cu = 4s¹3d¹⁰).
Periodic Trends
| Trend | Across → (L→R) | Down ↓ |
|---|---|---|
| Atomic radius | ↓ | ↑ |
| Ionization energy | ↑ | ↓ |
| Electronegativity | ↑ | ↓ |
| Electron affinity | ↑ (more −) | ↓ |
Zeff rises L→R → electrons held tighter → smaller radius, higher IE/EN.
Bonding & Geometry (VSEPR)
| e⁻ domains | Shape (0 LP) | Angle |
|---|---|---|
| 2 | linear | 180° |
| 3 | trigonal planar | 120° |
| 4 | tetrahedral | 109.5° |
| 5 | trig. bipyramidal | 90/120° |
| 6 | octahedral | 90° |
Lone pairs bend shape (4 domains: 1 LP→trigonal pyramidal; 2 LP→bent). Hybridization: 2=sp, 3=sp², 4=sp³.
Intermolecular Forces (strength)
- Ion–ion > H-bond (N,O,F–H) > dipole–dipole > London (all; ↑ with size/polarizability).
- More IMF → ↑ boiling pt, ↑ viscosity, ↓ vapor pressure.
Stoichiometry & Gases
moles = mass/MW; N = n·N_A
PV = nRT; P₁V₁/T₁ = P₂V₂/T₂
Dalton: P_total = ΣP_i
Graham: rate ∝ 1/√MW
Limiting reagent → least product. % yield = actual/theoretical ×100. Real gases deviate at high P, low T (van der Waals).
Solutions & Colligative
Molarity M = mol solute / L soln
Dilution M₁V₁ = M₂V₂
ΔT_b = i·K_b·m; ΔT_f = i·K_f·m
Osmotic π = i·M·R·T
i = van't Hoff factor (particles per formula unit: NaCl=2). Colligative = depend on # particles, not identity.
Kinetics
- Rate = k[A]ˣ[B]ʸ; order = x+y (from data, not coefficients).
- Arrhenius k = A·e^(−Ea/RT): ↑T or catalyst (↓Ea) → ↑k.
- Rate-determining step = slowest step.
- Catalysts lower Ea, unchanged by reaction (not consumed), don't shift equilibrium.
Equilibrium
K = [products]/[reactants] (coeff = exponents)
- Q vs K: Q<K → forward; Q>K → reverse; Q=K → at eq.
- Le Châtelier: stress (add reactant, ↑P by ↓volume toward fewer gas moles, ΔT) shifts to relieve it. Adding an inert gas at constant volume does not shift equilibrium.
- Pure solids/liquids omitted from K.
Acids & Bases
pH = −log[H⁺]; pOH = −log[OH⁻]
pH + pOH = 14 (25 °C); K_w=[H⁺][OH⁻]=10⁻¹⁴
Henderson–Hasselbalch pH = pKa + log([A⁻]/[HA])
Strong acids/bases fully dissociate. Buffer resists ΔpH near pH≈pKa (best when [A⁻]=[HA]). At titration equivalence: moles acid = moles base (½-eq point: pH = pKa).
Thermochemistry
ΔG = ΔH − TΔS
ΔG = −RT·lnK = −nFE°
Hess: ΔH_rxn = ΣΔH_f(prod) − ΣΔH_f(react)
| ΔH | ΔS | Spontaneity |
|---|---|---|
| − | + | always (ΔG<0) |
| + | − | never |
| − | − | low T |
| + | + | high T |
Electrochemistry
- Redox: OIL RIG — Oxidation Is Loss, Reduction Is Gain (of e⁻).
- AN OX / RED CAT: oxidation at anode, reduction at cathode (both cells).
- Galvanic (voltaic): spontaneous, E°cell>0, ΔG<0. Electrolytic: driven, E°<0.
- E°cell = E°cathode − E°anode.
Analytical / Lab
- Separations: distillation (bp), extraction (polarity/solubility), chromatography (polar stationary phase → polar compounds retained longer), electrophoresis (charge/size).
- IR: O–H broad ~3300, C=O sharp ~1700, N–H ~3300.
- ¹H NMR: shift=environment, splitting=n+1 neighbors, integration=# H.
- UV-Vis: conjugation; Beer's law A = εbc (absorbance ∝ concentration). Mass spec: m/z, molecular ion.
Fig 2. Weak-acid/strong-base titration. The flat buffer region centers on the half-equivalence point, where pH = pKa. The equivalence point lands above pH 7 because the conjugate base remains. A strong-acid titration would cross at exactly pH 7.
Fig 3. Converging lens, object beyond 2F. A parallel ray refracts through the far focus; a ray through the center is undeviated. They meet to form a real, inverted, reduced image (i>0, m<0). Move the object inside F and the image becomes virtual, upright, magnified (a magnifier).
ORG Organic Chemistry
Functional Groups
| Group | Structure |
|---|---|
| Carboxylic acid | –COOH |
| Ester | –COOR |
| Amide | –CONH₂ |
| Aldehyde | –CHO (terminal) |
| Ketone | C=O (internal) |
| Alcohol | –OH |
| Amine | –NH₂ |
Carbon oxidation state rises: alcohol → aldehyde → carboxylic acid.
Isomers
- Structural (constitutional): different connectivity.
- Stereoisomers: same connectivity, different 3-D arrangement.
- Enantiomers: nonsuperimposable mirror images (opposite at every stereocenter); identical physical properties except they rotate plane-polarized light oppositely and behave differently in chiral environments.
- Diastereomers: differ at some but not all stereocenters; different physical properties (includes cis/trans).
- Meso: has stereocenters but an internal mirror plane → achiral overall.
- n stereocenters → up to 2ⁿ stereoisomers.
Chirality & R/S
- Chiral (stereo)center = carbon with 4 different groups.
- Assign R/S: rank groups by atomic number (Cahn–Ingold–Prelog), point lowest priority away, then 1→2→3 clockwise = R, counterclockwise = S.
- Racemic mixture = 50/50 enantiomers → no net optical rotation.
Substitution & Elimination
| SN1 | SN2 | |
|---|---|---|
| Steps | 2 (carbocation) | 1 (concerted) |
| Rate law | [substrate] | [substrate][Nu] |
| Best substrate | 3° > 2° | 1° > 2° |
| Stereochem | racemization | inversion |
| Favored by | polar protic, weak Nu | polar aprotic, strong Nu |
Elimination mirrors these: E1 (∥ SN1) and E2 (strong/bulky base, anti-periplanar H) → alkenes; Zaitsev = more-substituted (major) product.
Carbonyl Chemistry
- Nucleophilic addition (aldehydes/ketones): + alcohol → hemiacetal/acetal; + amine → imine (Schiff base).
- Nucleophilic acyl substitution (acid derivatives): reactivity acyl chloride > anhydride > ester > amide.
- Keto–enol tautomerism; acidic α-carbon → aldol reaction.
- Aldehydes oxidize to carboxylic acids easily; ketones resist.
Acidity, Resonance & Redox
- Acidity ↑ when the conjugate base is more stable: resonance, higher electronegativity, more s-character, electron-withdrawing induction.
- Carboxylic acids are acidic (resonance-delocalized carboxylate).
- Reducing agents: NaBH₄ (mild: carbonyl → alcohol), LiAlH₄ (strong: also reduces acids/esters).
- Oxidizing agents: PCC (stops at aldehyde), strong (KMnO₄, CrO₃) → carboxylic acid.
Fig 4. SN2 mechanism. The nucleophile approaches from directly opposite the leaving group through a single concerted transition state, so the rate depends on both reactants and a chiral center undergoes inversion of configuration. Contrast SN1, which forms a planar carbocation and gives racemization.