MCAT cheat sheet

Ideal gas law: PV = nRT; at constant T and n, P₁V₁ = P₂V₂ (Boyle), and at constant P, V₁/T₁ = V₂/T₂ (Charles).

Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]); a buffer resists pH change best within ±1 unit of its pKa, and pH = pKa at half-equivalence.

Michaelis–Menten: v = Vmax[S]/(Km + [S]); Km equals the substrate concentration at half-maximal velocity and is inversely related to enzyme affinity.

Gibbs free energy: ΔG = ΔH − TΔS; ΔG < 0 is spontaneous, and ΔG° = −RT ln Keq, so Keq > 1 implies ΔG° < 0.

Mendelian ratios: monohybrid Aa × Aa gives 3:1 phenotype and 1:2:1 genotype; dihybrid AaBb × AaBb gives 9:3:3:1 with independent assortment.

SN1 vs SN2: SN2 is one-step, backside attack, inversion of configuration, favored by methyl/primary substrates and strong nucleophiles; SN1 proceeds via carbocation, favored by tertiary substrates and polar protic solvents.

Le Chatelier: adding reactant shifts right; increasing pressure shifts toward fewer gas moles; raising temperature shifts toward the endothermic direction; a catalyst changes rate only, not Keq.

Fluid and circuit analogs: Q = Av (continuity), P + ½ρv² + ρgh = constant (Bernoulli), V = IR, and power P = IV = I²R; resistors in series add, in parallel add reciprocally.

Classical conditioning (Pavlov): a neutral conditioned stimulus paired with an unconditioned stimulus acquires the ability to elicit a conditioned response; extinction weakens but does not erase the association.

Operant conditioning (Skinner): reinforcement increases behavior, punishment decreases it; positive adds a stimulus, negative removes one.

Piaget's stages: sensorimotor (0–2, object permanence), preoperational (2–7, egocentrism, no conservation), concrete operational (7–11, conservation), formal operational (11+, abstract reasoning).

Erikson's psychosocial stages pair each life period with a crisis; success yields a virtue (e.g., trust vs mistrust in infancy, identity vs role confusion in adolescence).

Weber's ideal bureaucracy: division of labor, hierarchy of authority, written rules, impersonal relations, and merit-based employment.

Durkheim's suicide typology: egoistic (low integration), altruistic (excess integration), anomic (normlessness), fatalistic (excess regulation).

Fundamental attribution error: overestimating dispositional and underestimating situational causes for others' behavior; the self-serving bias credits successes internally and blames failures externally.

Demographic transition: Stage 1 high birth/high death, Stage 2 high birth/falling death (rapid growth), Stage 3 falling birth, Stage 4 low birth/low death (stable population).

Independent variable is manipulated by the researcher; dependent variable is measured; confounding variables co-vary with the independent variable and threaten internal validity.

Internal validity concerns causal inference within the study; external validity concerns generalizability; random assignment supports internal validity, random sampling supports external validity.

Sensitivity = TP/(TP + FN); specificity = TN/(TN + FP); positive predictive value depends on prevalence, so a highly specific test still yields false positives when prevalence is low.

Standard error of the mean = s/√n; larger n narrows the sampling distribution, but a 95% CI overlapping between groups implies the difference may not be statistically significant.

A p-value is the probability of data at least as extreme assuming the null hypothesis is true; it is not the probability that the null is true.

Correlation does not establish causation; a third variable or reverse causation can produce an observed association, so only controlled or randomized designs support causal claims.

Scientific reasoning forms: deductive reasoning moves from general premises to specific conclusions (validity concerns form), inductive reasoning moves from specific observations to general claims (strength is probabilistic).

Confirmation bias favors information consistent with existing beliefs; control groups, blinding, and preregistration reduce bias and demand characteristics.

Ideal gas law: PV = nRT; at constant T and n, P₁V₁ = P₂V₂ (Boyle), and at constant P, V₁/T₁ = V₂/T₂ (Charles).

Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]); a buffer resists pH change best within ±1 unit of its pKa, and pH = pKa at half-equivalence.

Michaelis–Menten: v = Vmax[S]/(Km + [S]); Km equals the substrate concentration at half-maximal velocity and is inversely related to enzyme affinity.

Gibbs free energy: ΔG = ΔH − TΔS; ΔG < 0 is spontaneous, and ΔG° = −RT ln Keq, so Keq > 1 implies ΔG° < 0.

Mendelian ratios: monohybrid Aa × Aa gives 3:1 phenotype and 1:2:1 genotype; dihybrid AaBb × AaBb gives 9:3:3:1 with independent assortment.

SN1 vs SN2: SN2 is one-step, backside attack, inversion of configuration, favored by methyl/primary substrates and strong nucleophiles; SN1 proceeds via carbocation, favored by tertiary substrates and polar protic solvents.

Le Chatelier: adding reactant shifts right; increasing pressure shifts toward fewer gas moles; raising temperature shifts toward the endothermic direction; a catalyst changes rate only, not Keq.

Fluid and circuit analogs: Q = Av (continuity), P + ½ρv² + ρgh = constant (Bernoulli), V = IR, and power P = IV = I²R; resistors in series add, in parallel add reciprocally.

Classical conditioning (Pavlov): a neutral conditioned stimulus paired with an unconditioned stimulus acquires the ability to elicit a conditioned response; extinction weakens but does not erase the association.

Operant conditioning (Skinner): reinforcement increases behavior, punishment decreases it; positive adds a stimulus, negative removes one.

Piaget's stages: sensorimotor (0–2, object permanence), preoperational (2–7, egocentrism, no conservation), concrete operational (7–11, conservation), formal operational (11+, abstract reasoning).

Erikson's psychosocial stages pair each life period with a crisis; success yields a virtue (e.g., trust vs mistrust in infancy, identity vs role confusion in adolescence).

Weber's ideal bureaucracy: division of labor, hierarchy of authority, written rules, impersonal relations, and merit-based employment.

Durkheim's suicide typology: egoistic (low integration), altruistic (excess integration), anomic (normlessness), fatalistic (excess regulation).

Fundamental attribution error: overestimating dispositional and underestimating situational causes for others' behavior; the self-serving bias credits successes internally and blames failures externally.

Demographic transition: Stage 1 high birth/high death, Stage 2 high birth/falling death (rapid growth), Stage 3 falling birth, Stage 4 low birth/low death (stable population).

Independent variable is manipulated by the researcher; dependent variable is measured; confounding variables co-vary with the independent variable and threaten internal validity.

Internal validity concerns causal inference within the study; external validity concerns generalizability; random assignment supports internal validity, random sampling supports external validity.

Sensitivity = TP/(TP + FN); specificity = TN/(TN + FP); positive predictive value depends on prevalence, so a highly specific test still yields false positives when prevalence is low.

Standard error of the mean = s/√n; larger n narrows the sampling distribution, but a 95% CI overlapping between groups implies the difference may not be statistically significant.

A p-value is the probability of data at least as extreme assuming the null hypothesis is true; it is not the probability that the null is true.

Correlation does not establish causation; a third variable or reverse causation can produce an observed association, so only controlled or randomized designs support causal claims.

Scientific reasoning forms: deductive reasoning moves from general premises to specific conclusions (validity concerns form), inductive reasoning moves from specific observations to general claims (strength is probabilistic).

Confirmation bias favors information consistent with existing beliefs; control groups, blinding, and preregistration reduce bias and demand characteristics.

Ideal gas law: PV = nRT; at constant T and n, P₁V₁ = P₂V₂ (Boyle), and at constant P, V₁/T₁ = V₂/T₂ (Charles).

Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]); a buffer resists pH change best within ±1 unit of its pKa, and pH = pKa at half-equivalence.

Michaelis–Menten: v = Vmax[S]/(Km + [S]); Km equals the substrate concentration at half-maximal velocity and is inversely related to enzyme affinity.

Gibbs free energy: ΔG = ΔH − TΔS; ΔG < 0 is spontaneous, and ΔG° = −RT ln Keq, so Keq > 1 implies ΔG° < 0.

Mendelian ratios: monohybrid Aa × Aa gives 3:1 phenotype and 1:2:1 genotype; dihybrid AaBb × AaBb gives 9:3:3:1 with independent assortment.

SN1 vs SN2: SN2 is one-step, backside attack, inversion of configuration, favored by methyl/primary substrates and strong nucleophiles; SN1 proceeds via carbocation, favored by tertiary substrates and polar protic solvents.

Le Chatelier: adding reactant shifts right; increasing pressure shifts toward fewer gas moles; raising temperature shifts toward the endothermic direction; a catalyst changes rate only, not Keq.

Fluid and circuit analogs: Q = Av (continuity), P + ½ρv² + ρgh = constant (Bernoulli), V = IR, and power P = IV = I²R; resistors in series add, in parallel add reciprocally.

Classical conditioning (Pavlov): a neutral conditioned stimulus paired with an unconditioned stimulus acquires the ability to elicit a conditioned response; extinction weakens but does not erase the association.

Operant conditioning (Skinner): reinforcement increases behavior, punishment decreases it; positive adds a stimulus, negative removes one.

Piaget's stages: sensorimotor (0–2, object permanence), preoperational (2–7, egocentrism, no conservation), concrete operational (7–11, conservation), formal operational (11+, abstract reasoning).

Erikson's psychosocial stages pair each life period with a crisis; success yields a virtue (e.g., trust vs mistrust in infancy, identity vs role confusion in adolescence).

Weber's ideal bureaucracy: division of labor, hierarchy of authority, written rules, impersonal relations, and merit-based employment.

Durkheim's suicide typology: egoistic (low integration), altruistic (excess integration), anomic (normlessness), fatalistic (excess regulation).

Fundamental attribution error: overestimating dispositional and underestimating situational causes for others' behavior; the self-serving bias credits successes internally and blames failures externally.

Demographic transition: Stage 1 high birth/high death, Stage 2 high birth/falling death (rapid growth), Stage 3 falling birth, Stage 4 low birth/low death (stable population).

Independent variable is manipulated by the researcher; dependent variable is measured; confounding variables co-vary with the independent variable and threaten internal validity.

Internal validity concerns causal inference within the study; external validity concerns generalizability; random assignment supports internal validity, random sampling supports external validity.

Sensitivity = TP/(TP + FN); specificity = TN/(TN + FP); positive predictive value depends on prevalence, so a highly specific test still yields false positives when prevalence is low.

Standard error of the mean = s/√n; larger n narrows the sampling distribution, but a 95% CI overlapping between groups implies the difference may not be statistically significant.

A p-value is the probability of data at least as extreme assuming the null hypothesis is true; it is not the probability that the null is true.

Correlation does not establish causation; a third variable or reverse causation can produce an observed association, so only controlled or randomized designs support causal claims.

Scientific reasoning forms: deductive reasoning moves from general premises to specific conclusions (validity concerns form), inductive reasoning moves from specific observations to general claims (strength is probabilistic).

Confirmation bias favors information consistent with existing beliefs; control groups, blinding, and preregistration reduce bias and demand characteristics.

Ideal gas law: PV = nRT; at constant T and n, P₁V₁ = P₂V₂ (Boyle), and at constant P, V₁/T₁ = V₂/T₂ (Charles).

Henderson–Hasselbalch: pH = pKa + log([A⁻]/[HA]); a buffer resists pH change best within ±1 unit of its pKa, and pH = pKa at half-equivalence.

Michaelis–Menten: v = Vmax[S]/(Km + [S]); Km equals the substrate concentration at half-maximal velocity and is inversely related to enzyme affinity.

Gibbs free energy: ΔG = ΔH − TΔS; ΔG < 0 is spontaneous, and ΔG° = −RT ln Keq, so Keq > 1 implies ΔG° < 0.

Mendelian ratios: monohybrid Aa × Aa gives 3:1 phenotype and 1:2:1 genotype; dihybrid AaBb × AaBb gives 9:3:3:1 with independent assortment.

SN1 vs SN2: SN2 is one-step, backside attack, inversion of configuration, favored by methyl/primary substrates and strong nucleophiles; SN1 proceeds via carbocation, favored by tertiary substrates and polar protic solvents.

Le Chatelier: adding reactant shifts right; increasing pressure shifts toward fewer gas moles; raising temperature shifts toward the endothermic direction; a catalyst changes rate only, not Keq.

Fluid and circuit analogs: Q = Av (continuity), P + ½ρv² + ρgh = constant (Bernoulli), V = IR, and power P = IV = I²R; resistors in series add, in parallel add reciprocally.

Classical conditioning (Pavlov): a neutral conditioned stimulus paired with an unconditioned stimulus acquires the ability to elicit a conditioned response; extinction weakens but does not erase the association.

Operant conditioning (Skinner): reinforcement increases behavior, punishment decreases it; positive adds a stimulus, negative removes one.

Piaget's stages: sensorimotor (0–2, object permanence), preoperational (2–7, egocentrism, no conservation), concrete operational (7–11, conservation), formal operational (11+, abstract reasoning).

Erikson's psychosocial stages pair each life period with a crisis; success yields a virtue (e.g., trust vs mistrust in infancy, identity vs role confusion in adolescence).

Weber's ideal bureaucracy: division of labor, hierarchy of authority, written rules, impersonal relations, and merit-based employment.

Durkheim's suicide typology: egoistic (low integration), altruistic (excess integration), anomic (normlessness), fatalistic (excess regulation).

Fundamental attribution error: overestimating dispositional and underestimating situational causes for others' behavior; the self-serving bias credits successes internally and blames failures externally.

Demographic transition: Stage 1 high birth/high death, Stage 2 high birth/falling death (rapid growth), Stage 3 falling birth, Stage 4 low birth/low death (stable population).

Independent variable is manipulated by the researcher; dependent variable is measured; confounding variables co-vary with the independent variable and threaten internal validity.

Internal validity concerns causal inference within the study; external validity concerns generalizability; random assignment supports internal validity, random sampling supports external validity.

Sensitivity = TP/(TP + FN); specificity = TN/(TN + FP); positive predictive value depends on prevalence, so a highly specific test still yields false positives when prevalence is low.

Standard error of the mean = s/√n; larger n narrows the sampling distribution, but a 95% CI overlapping between groups implies the difference may not be statistically significant.

A p-value is the probability of data at least as extreme assuming the null hypothesis is true; it is not the probability that the null is true.

Correlation does not establish causation; a third variable or reverse causation can produce an observed association, so only controlled or randomized designs support causal claims.

Scientific reasoning forms: deductive reasoning moves from general premises to specific conclusions (validity concerns form), inductive reasoning moves from specific observations to general claims (strength is probabilistic).

Confirmation bias favors information consistent with existing beliefs; control groups, blinding, and preregistration reduce bias and demand characteristics.