- Powerhouse of the cell?
- The mitochondria — site of aerobic respiration, producing most of the cell's ATP.
- Site of protein synthesis?
- The ribosomes — they translate mRNA into polypeptide chains.
- Function of the nucleus?
- Stores the cell's DNA and controls gene expression and cell activity.
- Role of the Golgi apparatus?
- Modifies, packages, and ships proteins and lipids in vesicles.
- Rough vs smooth ER?
- Rough ER (with ribosomes) processes proteins; smooth ER makes lipids and detoxifies.
- Function of lysosomes?
- Digestion — they contain hydrolytic enzymes that break down waste and worn organelles.
- Prokaryote vs eukaryote?
- Prokaryotes (bacteria) lack a membrane-bound nucleus and organelles; eukaryotes have both.
- Three stages of aerobic respiration?
- Glycolysis (cytoplasm) → Krebs/citric acid cycle (matrix) → electron transport chain (inner membrane).
- Net ATP from glycolysis?
- 2 ATP and 2 NADH per glucose; no oxygen required.
- Final electron acceptor in the ETC?
- Oxygen — it combines with electrons and H⁺ to form water.
- Total ATP per glucose (aerobic)?
- About 30–32 ATP, most made by the electron transport chain via oxidative phosphorylation.
- Where does photosynthesis occur?
- In chloroplasts — light reactions in the thylakoid membranes, the Calvin cycle in the stroma.
- Mitosis vs meiosis?
- Mitosis → 2 identical diploid cells (growth/repair); meiosis → 4 unique haploid gametes (reproduction).
- Phases of mitosis (in order)?
- Prophase → metaphase → anaphase → telophase (PMAT), then cytokinesis.
- What is crossing over?
- Exchange of genetic material between homologous chromosomes in meiosis I — creates genetic variation.
- Central dogma of molecular biology?
- DNA → RNA → protein (replication, transcription, translation).
- Complementary DNA base pairs?
- Adenine–Thymine and Guanine–Cytosine (A–T, G–C).
- In RNA, what replaces thymine?
- Uracil (U) pairs with adenine instead of thymine.
- Mendel's law of segregation?
- Each parent's two alleles separate so each gamete carries one allele for a trait.
- Genotype ratio of a Bb × Bb cross?
- 1 BB : 2 Bb : 1 bb (1:2:1); phenotype ratio is 3 dominant : 1 recessive.
- Hardy-Weinberg equations?
- p + q = 1 and p² + 2pq + q² = 1, where 2pq is the heterozygote frequency.
- Five Hardy-Weinberg conditions?
- No mutation, no migration, no selection, random mating, and a large population.
- Enzyme function?
- A biological catalyst that lowers a reaction's activation energy without being consumed.
- What is the active site?
- The region of an enzyme where the substrate binds and the reaction occurs.
- Cardiac blood-flow pattern?
- Vein → atrium → valve → ventricle → valve → artery (right side deoxygenated, left side oxygenated).
- Tricuspid vs bicuspid valve?
- Right side = tricuspid (3 cusps); left side = bicuspid/mitral (2 cusps). LAB RAT mnemonic.
- Strongest heart chamber?
- The left ventricle — it pumps oxygenated blood to the entire body.
- Which vessel carries deoxygenated blood?
- The pulmonary artery (the famous exception — arteries usually carry oxygenated blood).
- Functional unit of the kidney?
- The nephron — it filters blood and forms urine.
- Functional unit of the nervous system?
- The neuron — dendrites receive signals, the axon transmits the impulse.
- What is a resting membrane potential?
- About −70 mV; maintained by the Na⁺/K⁺ pump moving 3 Na⁺ out and 2 K⁺ in.
- Six kingdoms of life?
- Archaebacteria, Eubacteria, Protista, Fungi, Plantae, Animalia.
- Are viruses alive?
- No — they lack cells and metabolism and must hijack a host cell to replicate.
- Difference between artery and vein?
- Arteries carry blood away from the heart (thick, muscular); veins carry blood toward the heart (have valves).
- What is natural selection?
- Differential survival and reproduction of individuals with favorable heritable traits.
- Producers vs consumers?
- Producers (autotrophs) make their own food; consumers (heterotrophs) eat other organisms.
- What is a trophic level?
- A position in a food chain; only ~10% of energy passes to the next level.
- Homeostasis?
- The maintenance of a stable internal environment despite external changes.
- Diffusion vs osmosis?
- Diffusion = movement of solute down its gradient; osmosis = movement of water across a membrane.
- Hypertonic vs hypotonic solution?
- A cell shrinks in hypertonic (more solute outside) and swells in hypotonic (less solute outside).
- What is the function of the cell membrane?
- A selectively permeable phospholipid bilayer that controls what enters and leaves the cell.
- Active vs passive transport?
- Active transport requires ATP and moves substances against the gradient; passive transport does not.
- Anaerobic respiration product (humans)?
- Lactic acid (lactate) fermentation, regenerating NAD⁺ so glycolysis can continue without oxygen.
- Where does the Krebs cycle occur?
- In the mitochondrial matrix; it releases CO₂ and produces NADH, FADH₂, and a little ATP.
- What is gene expression?
- Transcription of DNA to mRNA followed by translation of mRNA into a protein.
- What is a codon?
- A sequence of three mRNA nucleotides that codes for one amino acid (or a stop signal).
- Dominant vs recessive allele?
- A dominant allele shows in the phenotype with one copy; a recessive needs two copies to show.
- Genotype vs phenotype?
- Genotype is the genetic makeup (alleles); phenotype is the observable trait.
- Homozygous vs heterozygous?
- Homozygous = two identical alleles (BB or bb); heterozygous = two different alleles (Bb).
- What does a Punnett square predict?
- The probability of offspring genotypes and phenotypes from a given cross.
- Innate vs adaptive immunity?
- Innate is fast, nonspecific (skin, phagocytes); adaptive is slower, specific, and has memory (lymphocytes).
- Endocrine vs nervous system signaling?
- Endocrine uses hormones in blood (slow, widespread); nervous uses electrical impulses (fast, targeted).
- What is feedback inhibition?
- A pathway's end product inhibits an earlier enzyme, regulating its own production (negative feedback).
- Plant vs animal cell differences?
- Plant cells have a cell wall, chloroplasts, and a large central vacuole; animal cells have centrioles.
- The ideal gas law?
- PV = nRT, with R = 0.0821 L·atm/mol·K; always use absolute temperature in kelvin.
- Boyle's law?
- At constant temperature, P ∝ 1/V — pressure and volume are inversely related (P₁V₁ = P₂V₂).
- Charles's law?
- At constant pressure, V ∝ T — volume is directly proportional to absolute temperature.
- The pH formula?
- pH = −log[H⁺]; the scale runs 0–14, and pH + pOH = 14 at 25 °C.
- Acidic, neutral, and basic pH?
- Below 7 is acidic, exactly 7 is neutral, above 7 is basic.
- Brønsted-Lowry acid vs base?
- An acid donates a proton (H⁺); a base accepts a proton.
- What is oxidation? (redox)
- Loss of electrons (oxidation number increases). OIL RIG: Oxidation Is Loss.
- What is reduction? (redox)
- Gain of electrons (oxidation number decreases). OIL RIG: Reduction Is Gain.
- Le Chatelier's principle?
- A system at equilibrium shifts to partly offset any disturbance (concentration, pressure, temperature).
- What is stoichiometry?
- Using mole ratios from a balanced equation to relate amounts of reactants and products.
- Avogadro's number?
- 6.022 × 10²³ particles per mole.
- What is the limiting reactant?
- The reactant that runs out first and therefore caps how much product can form.
- Define molarity.
- Moles of solute per liter of solution (mol/L).
- Endothermic vs exothermic?
- Endothermic absorbs heat (ΔH > 0); exothermic releases heat (ΔH < 0).
- Second law of thermodynamics?
- The entropy (disorder) of an isolated system tends to increase over time.
- Gibbs free energy and spontaneity?
- ΔG = ΔH − TΔS; a reaction is spontaneous when ΔG < 0.
- Periodic trend: atomic radius?
- Increases down a group and decreases across a period (left to right).
- Periodic trend: ionization energy?
- Decreases down a group and increases across a period.
- Periodic trend: electronegativity?
- Decreases down a group and increases across a period; fluorine is highest.
- What is an isotope?
- Atoms of the same element with the same protons but a different number of neutrons.
- Define electronegativity.
- An atom's tendency to attract shared electrons in a bond.
- Ionic vs covalent bond?
- Ionic = transfer of electrons (metal + nonmetal); covalent = sharing of electrons (nonmetals).
- What is a mole?
- The amount of substance containing 6.022 × 10²³ entities; equals the molar mass in grams.
- Arrhenius acid?
- A substance that increases H⁺ (H₃O⁺) concentration in water.
- How does a catalyst work?
- It lowers the activation energy, speeding a reaction without being consumed.
- What is half-life?
- The time for half of a radioactive sample (or reactant) to decay or react.
- Alpha vs beta decay?
- Alpha emits a helium nucleus (₂⁴He); beta emits an electron and converts a neutron to a proton.
- STP conditions and molar volume?
- 0 °C and 1 atm; one mole of ideal gas occupies 22.4 L.
- Conjugate acid-base pair?
- Two species differing by one proton (H⁺), e.g. HCl and Cl⁻.
- Strong vs weak acid?
- A strong acid fully dissociates (HCl); a weak acid only partly dissociates (acetic acid).
- What is a buffer?
- A solution of a weak acid and its conjugate base that resists changes in pH.
- Henderson-Hasselbalch idea?
- pH = pKa + log([base]/[acid]); pH equals pKa when acid and conjugate base are equal.
- Exothermic reaction and equilibrium?
- Raising temperature shifts an exothermic equilibrium toward reactants (heat is a product).
- Effect of a catalyst on equilibrium?
- It speeds up both directions equally — it changes the rate, not the position of equilibrium.
- Define electrolyte.
- A substance that dissociates into ions in solution and conducts electricity.
- Bond energy and stability?
- Stronger (higher-energy) bonds are harder to break; bond breaking absorbs energy, bond forming releases it.
- What is electronegativity difference and bond type?
- Large difference → ionic; small/moderate → polar covalent; near zero → nonpolar covalent.
- VSEPR theory predicts?
- Molecular geometry, by arranging electron pairs around a central atom to minimize repulsion.
- Geometry: 4 bonding pairs, no lone pairs?
- Tetrahedral, with bond angles of about 109.5°.
- What is a dipole moment?
- A measure of bond/molecular polarity from unequal sharing of electrons.
- Hydrogen bonding requires?
- H bonded to N, O, or F interacting with a lone pair on another N, O, or F.
- First law of thermodynamics (chem)?
- Energy is conserved: ΔU = Q − W; the internal energy of an isolated system is constant.
- Rate-determining step?
- The slowest step in a reaction mechanism; it sets the overall reaction rate.
- Catalyst vs intermediate?
- A catalyst is consumed early and regenerated; an intermediate is formed then used up later.
- Define oxidation number of an element in its free state.
- Zero (e.g., O₂, Na metal, H₂ all have oxidation number 0).
- Common strong acids to memorize?
- HCl, HBr, HI, HNO₃, H₂SO₄, HClO₄ (fully dissociate in water).
- What is molality?
- Moles of solute per kilogram of solvent (mol/kg) — used for colligative properties.
- Boiling-point elevation depends on?
- The number of dissolved particles (a colligative property), not their identity.
- SN1 vs SN2 — number of steps?
- SN1 is two steps (via a carbocation); SN2 is one concerted step.
- SN1 vs SN2 — best substrate?
- SN1 favors tertiary (3°) carbons; SN2 favors primary (1°)/methyl carbons.
- SN1 vs SN2 — stereochemistry?
- SN1 gives racemization; SN2 inverts the stereocenter (backside attack).
- SN1 vs SN2 — rate law?
- SN1 is first order (rate = k[substrate]); SN2 is second order (rate = k[substrate][nucleophile]).
- E1 vs E2 elimination?
- E1 is stepwise via a carbocation; E2 is concerted and needs a strong base (anti-periplanar).
- What is a chiral center?
- A carbon bonded to four different groups, making the molecule non-superimposable on its mirror image.
- What are enantiomers?
- Non-superimposable mirror-image molecules that rotate plane-polarized light in opposite directions.
- Enantiomers vs diastereomers?
- Enantiomers are mirror images; diastereomers are stereoisomers that are NOT mirror images.
- What is a functional group?
- A specific atom/group giving a molecule characteristic reactivity (−OH, C=O, −COOH, −NH₂).
- Functional group: alcohol?
- Hydroxyl group, −OH.
- Functional group: carboxylic acid?
- Carboxyl group, −COOH.
- Functional group: aldehyde vs ketone?
- Both have C=O; an aldehyde's carbonyl is at the chain end (−CHO), a ketone's is internal.
- Functional group: amine?
- Contains nitrogen, −NH₂ (or substituted).
- Hückel's rule (aromaticity)?
- A cyclic, planar, fully conjugated ring is aromatic if it has 4n + 2 π electrons.
- How many π electrons in benzene?
- Six delocalized π electrons (n = 1 in 4n + 2), making it aromatic and very stable.
- Markovnikov's rule?
- In HX addition to an alkene, H adds to the carbon with more hydrogens (gives the more stable carbocation).
- What does IR spectroscopy identify?
- Functional groups via bond vibrations (e.g., a broad −OH stretch, a sharp C=O near 1700 cm⁻¹).
- What does ¹H NMR reveal?
- The number, environment, and neighbors of hydrogen atoms — mapping the carbon-hydrogen skeleton.
- Constitutional (structural) isomers?
- Same molecular formula but different connectivity of atoms.
- cis vs trans isomers?
- Geometric isomers about a double bond/ring — cis = same side, trans = opposite sides.
- sp³, sp², sp hybridization geometry?
- sp³ = tetrahedral (109.5°), sp² = trigonal planar (120°), sp = linear (180°).
- Nucleophile vs electrophile?
- A nucleophile donates an electron pair (electron-rich); an electrophile accepts one (electron-poor).
- What is a carbocation stability order?
- 3° > 2° > 1° > methyl — more alkyl groups stabilize the positive charge.
- Saturated vs unsaturated?
- Saturated = only single C–C bonds (alkanes); unsaturated = has double/triple bonds.
- What is resonance?
- Delocalization of electrons over multiple structures; the real molecule is a hybrid, which adds stability.
- Common protecting reaction — oxidation of a 1° alcohol?
- Gives an aldehyde (mild oxidant) or a carboxylic acid (strong oxidant).
- Polar protic vs aprotic solvent?
- Protic solvents (water, alcohols) have O–H/N–H and favor SN1/E1; aprotic (acetone, DMSO) favor SN2/E2.
- Leaving group quality?
- Better leaving groups are weak bases — e.g., I⁻ > Br⁻ > Cl⁻; tosylate is excellent.
- Alkane, alkene, alkyne bonds?
- Alkanes have C–C single bonds, alkenes a C=C double bond, alkynes a C≡C triple bond.
- General formula of an alkane?
- CₙH₂ₙ₊₂.
- What is an electrophilic addition?
- Addition of an electrophile across a double bond, e.g. HBr or Br₂ adding to an alkene.
- Anti vs syn addition?
- Anti adds groups to opposite faces (e.g. Br₂); syn adds to the same face (e.g. hydrogenation).
- Optical activity?
- A chiral compound rotates plane-polarized light; a racemic 50:50 mix shows no net rotation.
- R vs S configuration?
- Assigned by Cahn-Ingold-Prelog priority: clockwise = R, counterclockwise = S (lowest priority pointing away).
- Conformational isomers?
- Different spatial arrangements from rotation about single bonds (e.g. chair vs boat cyclohexane).
- Most stable cyclohexane conformation?
- The chair conformation, with bulky groups in equatorial positions.
- Aromatic substitution vs addition?
- Aromatic rings undergo substitution (preserving aromaticity) rather than addition.
- What is a Grignard reagent?
- An organomagnesium compound (R–MgX) that acts as a strong nucleophile/carbon base.
- Carbonyl reactivity order?
- Aldehydes are more reactive than ketones toward nucleophilic addition (less steric/electronic hindrance).
- Esterification?
- A carboxylic acid plus an alcohol (acid-catalyzed) forms an ester and water.
- Degree of unsaturation meaning?
- Each ring or π bond counts as one; calculated from the molecular formula to deduce structure.
- Most acidic common functional group?
- Carboxylic acids (−COOH) — resonance stabilizes the carboxylate anion.
- Newton's first law?
- An object stays at rest or in uniform motion unless acted on by a net external force (inertia).
- Newton's second law?
- F = ma — net force equals mass times acceleration.
- Newton's third law?
- For every action there is an equal and opposite reaction.
- Scalar vs vector?
- A scalar has magnitude only (speed, mass); a vector has magnitude and direction (velocity, force).
- Speed vs velocity?
- Speed is a scalar (how fast); velocity is a vector (how fast and in what direction).
- Definition of acceleration?
- The rate of change of velocity: a = Δv/Δt (m/s²).
- Kinematics: v = ?
- v = v₀ + at (final velocity from initial velocity and acceleration).
- Kinematics: displacement?
- x = v₀t + ½at².
- Kinematics: v² formula?
- v² = v₀² + 2aΔx (no time needed).
- Acceleration due to gravity (g)?
- About 9.8 m/s² downward near Earth's surface.
- Projectile motion key idea?
- Horizontal and vertical motions are independent; horizontal velocity is constant, vertical accelerates at g.
- Horizontal range of a projectile?
- R = v₀²·sin(2θ)/g; maximum range occurs at a launch angle of 45°.
- Definition of momentum?
- p = mv — mass times velocity; it is conserved in an isolated system.
- Impulse-momentum theorem?
- Impulse = FΔt = Δp (the change in momentum).
- Kinetic energy formula?
- KE = ½mv².
- Gravitational potential energy?
- PE = mgh (mass × gravity × height).
- Conservation of energy?
- Energy is neither created nor destroyed; total mechanical energy is constant without friction.
- Work formula?
- W = F·d·cos θ (force times displacement times the cosine of the angle between them).
- Definition of power?
- The rate of doing work: P = W/t (watts).
- Hooke's law?
- F = −kx — a spring's restoring force is proportional to its displacement.
- Period of a simple pendulum?
- T = 2π·√(L/g) — depends on length and gravity, not mass or amplitude.
- Period of a mass on a spring?
- T = 2π·√(m/k).
- Wave speed equation?
- v = f·λ — speed equals frequency times wavelength.
- Frequency and period relation?
- f = 1/T — frequency is the inverse of the period.
- Ohm's law?
- V = IR — voltage equals current times resistance.
- Electrical power formulas?
- P = IV = I²R = V²/R (watts).
- Resistors in series vs parallel?
- Series: R_total = R₁ + R₂ + …; parallel: 1/R_total = 1/R₁ + 1/R₂ + ….
- Coulomb's law?
- F = k·q₁q₂/r² — the electrostatic force between two charges.
- Concave (converging) mirror image?
- Forms a real, inverted image when the object is beyond the focal point; virtual/upright when closer.
- Convex (diverging) mirror image?
- Always forms a virtual, upright, reduced image.
- Converging vs diverging lens?
- A converging (convex) lens has positive focal length; a diverging (concave) lens has negative focal length.
- Thin-lens / mirror equation?
- 1/f = 1/dₒ + 1/dᵢ (focal length from object and image distances).
- Law of reflection?
- The angle of incidence equals the angle of reflection (measured from the normal).
- Snell's law (refraction)?
- n₁·sin θ₁ = n₂·sin θ₂ — light bends toward the normal entering a denser medium.
- Index of refraction?
- n = c/v — the ratio of light's speed in vacuum to its speed in the medium (n ≥ 1).
- Density formula?
- ρ = m/V (mass per unit volume).
- Pressure in a fluid (with depth)?
- P = ρgh — pressure increases with depth, density, and gravity.
- Archimedes' principle?
- The buoyant force on a submerged object equals the weight of the fluid it displaces.
- First law of thermodynamics?
- ΔU = Q − W — change in internal energy equals heat added minus work done by the system.
- Specific heat equation?
- Q = mcΔT — heat equals mass × specific heat × temperature change.
- Centripetal acceleration?
- a_c = v²/r, directed toward the center of the circular path.
- Photon energy?
- E = hf = hc/λ — proportional to frequency (Planck's constant h).
- Torque?
- τ = r·F·sin θ — the rotational effect of a force about a pivot.
- Doppler effect?
- The observed frequency rises as a source approaches and falls as it recedes.
- Weight vs mass?
- Mass is the amount of matter (kg, constant); weight is the force of gravity on it (W = mg, varies).
- Static vs kinetic friction?
- Static friction resists starting motion (larger max); kinetic friction acts during sliding (usually smaller).
- Friction force formula?
- f = μN — coefficient of friction times the normal force.
- Normal force on a flat surface?
- Equal and opposite to the object's weight component perpendicular to the surface (N = mg on level ground).
- Elastic vs inelastic collision?
- Both conserve momentum; only an elastic collision also conserves kinetic energy.
- Conservation of momentum?
- In an isolated system, total momentum before a collision equals total momentum after.
- Frequency unit?
- The hertz (Hz) — one cycle per second.
- Wavelength definition?
- The distance between successive crests (or troughs) of a wave.
- Amplitude and energy of a wave?
- A wave's energy is proportional to the square of its amplitude.
- Transverse vs longitudinal wave?
- Transverse: oscillation ⊥ to travel (light); longitudinal: oscillation ∥ to travel (sound).
- Real vs virtual image?
- A real image forms where light actually converges (can be projected); a virtual image only appears to.
- Total internal reflection?
- Occurs when light hits a less-dense medium beyond the critical angle and fully reflects.
- Charge of an electron?
- −1.6 × 10⁻¹⁹ coulombs (the proton is +1.6 × 10⁻¹⁹ C).
- Current definition?
- The rate of flow of electric charge: I = Q/t (amperes).
- Capacitor function?
- Stores electric charge and energy in an electric field between two plates (Q = CV).
- Magnetic force on a moving charge?
- F = qvB·sin θ — maximum when velocity is perpendicular to the field.
- Series circuit current vs parallel?
- Series: current is the same everywhere; parallel: voltage is the same across each branch.
- Kelvin to Celsius?
- K = °C + 273.15 (absolute zero is 0 K = −273.15 °C).
- Heat of transformation (latent heat)?
- Q = mL — heat absorbed/released during a phase change at constant temperature.
- Terminal velocity?
- The constant speed reached when drag force equals gravity, so net force (and acceleration) is zero.
- How many passages on OAT Reading?
- Three passages on scientific topics, 50 items total in 60 minutes.
- Golden rule of OAT Reading?
- Answer ONLY from the text — no outside knowledge; bringing in your own facts is the #1 trap.
- Detail (explicit) question?
- Asks for a directly stated fact; locate the exact line — don't rely on memory.
- Main idea question?
- Asks the passage's overall point; pick the choice covering the WHOLE passage, not one detail.
- Inference question?
- Asks an unstated but supported conclusion; stay one short step from the text and reject added facts.
- Tone/purpose question?
- Asks the author's attitude or goal; most science passages are neutral and informational.
- Vocabulary-in-context question?
- Asks a word's meaning AS USED; use the sentence's clue, not the dictionary's first definition.
- What is passage mapping?
- Skim for structure and note where key facts live, then jump to the relevant lines for each question.
- Trap: detail dressed as main idea?
- A true detail is too narrow to be the main idea — the main idea must cover the entire passage.
- Extreme-language trap?
- Choices with 'always,' 'only,' or 'never' are usually wrong unless the passage states them outright.
- Search-and-locate strategy?
- Treat Reading as finding information, not memorizing it — confirm every detail answer against the text.
- Time per Reading item?
- About 72 seconds per item (50 items in 60 minutes) across three passages.
- Application question?
- Asks you to apply the passage's idea to a new situation; the logic must come from the text.
- Author's tone in science passages?
- Usually objective and informative — beware reading them as persuasive or emotional.
- How to handle 'EXCEPT' or 'NOT' questions?
- Find the choice that is FALSE or unsupported; the other three are stated or implied.
- Should you read the questions first?
- Many high scorers preview questions or map the passage first, then locate answers — pick a consistent method.
- How to verify a detail answer?
- Return to the exact line in the passage; never answer a detail question from memory.
- Why is outside knowledge dangerous on OAT Reading?
- The test only credits what THIS passage says — a true real-world fact can still be the wrong answer.
- Pacing across three passages?
- Budget about 20 minutes per passage; don't let one hard passage eat another's time.
- Spotting the main idea quickly?
- Check the first and last sentences of paragraphs and the overall structure of the passage.
- Percent change formula?
- (new − old) ÷ old × 100; always divide by the ORIGINAL value.
- Solving a proportion?
- Cross-multiply: a/b = c/d means ad = bc.
- Quadratic formula?
- x = (−b ± √(b² − 4ac)) ÷ 2a, for ax² + bx + c = 0.
- Pythagorean theorem?
- a² + b² = c² for a right triangle (c is the hypotenuse).
- Area and circumference of a circle?
- Area = πr²; circumference = 2πr.
- SOH-CAH-TOA?
- sin = opp/hyp, cos = adj/hyp, tan = opp/adj.
- 30-60-90 triangle side ratio?
- 1 : √3 : 2 (opposite the 30°, 60°, 90° angles).
- 45-45-90 triangle side ratio?
- 1 : 1 : √2.
- Simple probability?
- Favorable outcomes ÷ total outcomes (a value from 0 to 1).
- Probability: AND vs OR?
- Independent AND → multiply; mutually exclusive OR → add.
- Mean, median, mode?
- Mean = average; median = middle value; mode = most frequent value.
- Slope of a line?
- m = (y₂ − y₁) ÷ (x₂ − x₁) — rise over run.
- Slope-intercept form?
- y = mx + b, where m is the slope and b is the y-intercept.
- Exponent rule: xᵃ · xᵇ?
- xᵃ⁺ᵇ — add exponents when multiplying like bases.
- Exponent rule: (xᵃ)ᵇ?
- (xᵃ)ᵇ = xᵃᵇ — multiply the exponents.
- Negative exponent meaning?
- x⁻ⁿ = 1/xⁿ.
- Volume of a cylinder?
- V = πr²h.
- Volume of a rectangular box?
- V = length × width × height.
- Distance-rate-time relation?
- distance = rate × time (d = rt).
- Average of n numbers?
- Sum of the values ÷ n (the count of values).
- Order of operations?
- PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction (left to right).
- Converting a percent to a decimal?
- Divide by 100 (move the decimal two places left): 25% = 0.25.
- Area of a triangle?
- A = ½ × base × height.
- Sum of interior angles of a triangle?
- 180°; for an n-sided polygon it is (n − 2) × 180°.
- Surface area vs volume scaling?
- If a length scales by k, area scales by k² and volume by k³.
- Combination vs permutation?
- Permutations count ordered arrangements; combinations count unordered selections (order doesn't matter).
- Factorial notation?
- n! = n × (n−1) × … × 1; for example 4! = 24.
- Solving a system of equations?
- Use substitution or elimination to find the values that satisfy both equations.
- Absolute value meaning?
- |x| is the distance from zero, always nonnegative: |−3| = 3.
- Direct vs inverse variation?
- Direct: y = kx (rise together); inverse: y = k/x (one rises as the other falls).
- Ratio simplification?
- Divide both terms by their greatest common factor: 8:12 → 2:3.
- Mean vs median when data is skewed?
- The median resists outliers; the mean is pulled toward extreme values.
- Range of a data set?
- The largest value minus the smallest value.
- Compound interest idea?
- Interest is earned on principal plus accumulated interest: A = P(1 + r)ᵗ.
- Probability of the complement?
- P(not A) = 1 − P(A).
- Converting a fraction to a percent?
- Divide and multiply by 100: 3/4 = 0.75 = 75%.
- Standard deviation in one line?
- A measure of how spread out data values are around the mean.
- Solving an inequality — sign flip rule?
- Reverse the inequality sign when multiplying or dividing both sides by a negative number.
