MCAT Physics and Math Review
Aberration—Visual alterations as the result of an imperfect optical device; may be chromatic or spherical.
Absolute pressure—The actual pressure at a given depth in a fluid, including both ambient pressure at the surface and the pressure associated with increased depth in the fluid; also called hydrostatic pressure.
Absolute zero—The theoretically coldest temperature at which all atomic movements would halt (0 K).
Acceleration—The rate of change in the velocity of an object; related to force through mass and measured in .
Accuracy—The tendency for data to represent the true answer; also known as validity.
Adhesion—The intermolecular force between molecules of a liquid and molecules of another substance.
Adiabatic—A thermodynamic process that occurs with no heat exchange.
Algebraic system—A method for determining the values of variables that are the same in two or more equations by relating them to each other.
α-particle—A helium nucleus .
Amplitude—The maximum displacement from the equilibrium point during wave or oscillatory motion.
Antinode—A point of zero displacement in a standing wave.
Archimedes’ principle—States that a body immersed in a volume of fluid experiences a buoyant force equal to the weight of the displaced fluid.
Atomic number—The number of protons in the nucleus of a given element.
Attenuation—The loss of energy of a propagating wave as a result of nonconservative forces; also known as damping.
Autonomy—The ethical principle that states that individuals have the right to make decisions about their own healthcare.
Beneficence—The ethical principle that states that practitioners should always act in their patients’ best interests; in research ethics, also states that a research project should create a net positive change for both the study population and general population.
β-particle—An electron emitted during β– decay, or a positron emitted during β+ decay.
Bernoulli’s equation—An equation that relates static and dynamic pressure for a fluid to the pressure exerted on the walls of a tube and the speed of the fluid.
Blinding—Withholding information about a research subject’s group assignment from the subject or evaluator to remove some potential bias from the results.
Boiling point—The temperature at which the vapor pressure of a liquid equals the ambient (incident) pressure, usually atmospheric pressure; the temperature at which the liquid boils.
Boundary layer—A region of laminar flow in an otherwise turbulent system that occurs at the very edges of the vessel.
Box-and-whisker plot—A visual representation of the range of data, quartiles, and the interquartile range; may contain outliers as separate points.
Buoyancy—The upward force that results from immersion in a fluid; described by Archimedes’ principle.
Capacitance—A measure of the ability of a capacitor to store charge; the magnitude of the charge on one plate divided by the potential difference between the plates; measured in farads (F).
Capacitor—Two conducting surfaces that store charges of equal magnitude but opposite sign when connected to a voltage source.
Center of gravity—A point such that the entire force of gravity acting on an object can be thought of as acting at that point.
Center of mass—The point that acts as if the entire mass of an object was concentrated at that point.
Centripetal acceleration—The acceleration of an object that travels in a circle; it is always directed toward the center of the circle if the object is in uniform circular motion.
Centripetal force—The force responsible for centripetal acceleration; usually a result of gravity, tension, or a normal force.
Charges—Entities that can influence the environment through electrostatic forces or be influenced by electrostatic forces, measured in coulombs (C).
Cohesion—The intermolecular forces experienced between the molecules of a liquid.
Concave—A surface that has a similar curvature to the interior of a sphere.
Condensation—The phase transition from a gas to a liquid.
Conductor—A material that allows the free movement of electrical charge; one with very low or zero resistance.
Confidence—A statistical indicator of the likelihood that acquired results did not occur by random chance; equal to 1 – α.
Confounding—An error that results when a causal variable is associated with two other variables in a study but is not accounted for; may falsely indicate that the two variables are associated.
Conservative force—A force that does not cause energy to be dissipated from a system, such as gravity, electrostatic forces, and springs (approximately conservative); pathway independent and associated with a potential energy function.
Control—A set of experimental conditions meant to ensure that the results of the experimental group are a result of the intervention.
Convection—Heat transfer as a result of bulk flow of a fluid over an object.
Converging—The tendency to move parallel light rays toward one another; concave mirrors and convex lenses converge parallel light to a focal point.
Convex—A surface that has a similar curvature to the exterior of a sphere.
Coulomb’s law—Relates the electrostatic force between two charged particles to their charges and the distance between them.
Critical angle—The angle above which any incident light will undergo total internal reflection; occurs when light is moving from a material with a higher refractive index to one with a lower refractive index.
Critical speed—The speed above which flow of a fluid will be turbulent.
Current—The orderly movement of charge, often in a circuit; measured by convention as the direction that positive charge would flow within the circuit, and measured in ampères (A).
Decay constant—The proportionality constant between the rate at which radioactive nuclei decay and the number of radioactive nuclei remaining.
Density—A measure of mass per unit volume; useful for buoyancy calculations and usually measured in , , or .
Dependent variable—The measured or observed variable in an experiment that is affected by manipulations of the independent variable.
Detection bias—An error in data collection that results from the tendency to look more carefully for certain outcomes because a known association with that outcome exists.
Dielectric material—An insulating material used to increase capacitance.
Diffraction—The spreading or bending of light rays.
Dispersion—The separation of light into its component wavelengths when passing through a medium, such as a prism.
Displacement—The vector representing the straight-line distance and direction from an initial point; not necessarily equal to total distance traveled, and measured in meters.
Diverging—The tendency to move parallel light rays away from one another; convex mirrors and concave lenses diverge parallel light rays from a focal point.
Doppler effect—Quantifies the perceived change in frequency of sound due to relative movement between the source and detector (observer).
Electric dipole—A separation of equal and opposite charge by a small distance; can be seen in polar molecules.
Electric field—A region generated by an electric charge or multiple charges that can exert a force on another charge brought into the field; measured in .
Electric meters—Devices used to measure circuit quantities like current, potential difference, or resistance.
Electrical potential—A measure of electrical potential energy per unit charge, given in volts (V); differences in electrical potential (voltage) also drive current as the electromotive force in a circuit.
Electromagnetic radiation—A form of energy composed of oscillating electric and magnetic fields perpendicular to each other and perpendicular to the direction of propagation; includes visible light and other types of transverse waves, and can travel through a vacuum.
Electromotive force—The difference in electrical potential (voltage) that drives current in a circuit or battery.
Energy—The capacity to do work or transfer heat, measured in joules (J).
Entropy—A statistical measure of the distribution of unusable energy or heat; randomness introduced to a system, measured in .
Equilibrium—The state at which the net torque or net force is equal to zero, such that there is no acceleration.
Equipoise—The state of not knowing whether there is a difference between two interventions; ethically necessary for comparative study of the interventions.
Equipotential lines—Regions within an electric field with equal electrical potential; movement from one point on these lines to another causes no change in the energy of the system.
Excited state—Describes an atom in which an electron occupies an energy state above the minimum energy (ground) state.
External validity—The ability to apply findings of a research study to other populations; also called generalizability.
Field line—A visual representation of the electric field; points to the direction a force would be exerted on a positive test charge in the electric field.
FINER method—A way to determine the usefulness of a research question on the basis of feasibility, interest, novelty, ethics, and relevance.
Fission—The splitting of a large nucleus into smaller nuclei with the release of energy.
Fluid—A material that conforms to the shape of its container and that can flow.
Fluorescence—A process in which the electrons of certain substances are excited to higher energy levels by high-frequency photons, and then emit visible light as the energy is released in two or more steps back to the ground state.
Focal length—The distance from a mirror or lens to the focal point.
Focal point—The point at which rays of light parallel to the axis of a mirror or lens converge, or from which they appear to diverge when reflected by a mirror or refracted by a lens.
Force—A push or a pull, measured in newtons (N).
Free fall—A system in which the only force is gravity.
Freezing—The phase transition from liquid to solid; also called solidification.
Frequency—The rate at which a recurring event occurs; usually measured in hertz (Hz).
Friction—A nonconservative force that arises from the interactions between two surfaces in contact.
Fundamental frequency—The first harmonic of a pipe, string, or other standing wave.
Fusion—The merging of small nuclei into a larger nucleus with the release of energy.
γ-rays—High-energy photons released during radioactive decay; part of the electromagnetic spectrum.
Gauge pressure—Pressure above and beyond atmospheric pressure.
Gravity—An attractive force between two objects that depends on their masses and the distance between them.
Ground state—The lowest energy state of an atom.
Half-life—The amount of time it takes for one-half of a sample of radioactive nuclei to decay.
Harmonic series—The set of frequencies that can create standing waves in a given pipe or string.
Hawthorne effect—The tendency for research participants to change their behavior because they know they are being observed.
Heat—The transfer of thermal energy; measured in joules (J), calories (cal), or kilocalories (kcal or Cal).
Heat of transformation—The amount of heat necessary to cause a phase transition of a unit mass of a substance at the characteristic temperature and pressure of that phase transition.
Hill’s criteria—A systematized way of evaluating evidence for causality; only temporality is absolutely necessary to demonstrate causality.
Histogram—A visual representation for numerical data; related to a bar chart.
Hydraulic system—A simple machine that exerts mechanical advantage using an incompressible fluid; based on Pascal’s principle and conservation of energy.
Hydrostatics—The study of fluid systems at rest.
Hyperopia—Farsightedness, or the ability to see distant objects while nearby objects are unfocused or blurry.
Hypothesis testing—A statistical method used to compare results between groups or to a theoretical value with a given level of confidence.
Image—The region where light rays converge or appear to converge after being reflected from a mirror or passing through a lens.
Independent variable—The manipulated variable in an experiment that affects measurements or observations of the dependent variable.
Index of refraction—A ratio of the speed of light in a vacuum to the speed of light in a given medium.
Inertia—An object’s resistance to a change in its motion when a force is applied.
Informed consent—An ethical requirement for treatments or research, which requires that the patient or participant is able to understand the procedure and its consequences and alternatives; related to autonomy.
Infrared—A region of the electromagnetic spectrum that is not visible; may be perceived as heat.
Infrasonic—Sound that has a frequency that is lower than the range of human hearing.
Insulator—A material that resists the movement of charge because the electrons are tightly associated with their nuclei.
Intensity—The average rate of energy expenditure (power) per unit area, measured in ; in waves, intensity is related to the amplitude of the wave.
Interference—Interactions between waves traveling in the same space; may be constructive (waves adding together), destructive (waves cancelling each other), partially constructive, or partially destructive.
Internal validity—The ability to infer causality from a study or to replicate its results under the same conditions.
Interquartile range—A measure of distribution of a sample; outliers lie at least 1.5 interquartile ranges below Q1 or above Q3.
Inverted—Describes an image that is upside down relative to the object; in single-mirror or single-lens systems, inverted images are always real.
Irreversible—A thermodynamic process that is extraordinarily unfavorable in reverse, usually as a result of changes in entropy.
Isobaric—A thermodynamic process that occurs under constant pressure.
Isothermal—A thermodynamic process that occurs under constant temperature.
Isotopes—Atoms of a given element with different numbers of neutrons and therefore different mass numbers.
Isovolumetric—A thermodynamic process that occurs under constant volume; also called isochoric.
Justice—The ethical principle that states that practitioners should fairly distribute healthcare resources, and which requires that differences in treatment choices between individuals are only due to morally relevant differences.
Kinetic energy—The energy of movement, which depends on both mass and speed; measured in joules (J).
Kirchhoff’s laws—Rules that describe the conservation of charge and conservation of energy within an electric circuit; includes the junction rule and loop rule.
Laminar flow—Smooth flow within a fluid; characterized by streamlines that do not cross each other and an absence of backwards movement.
Lenses—Devices that act to create an image by refracting light; usually have spherical surfaces.
Logarithm—The inverse function of exponentiation; logarithmic scales are often used to mask large absolute differences between quantities by presenting them as small scale differences.
Longitudinal wave—A wave in which the oscillation of the material is parallel to the direction of propagation; sound is a classic example.
Loudness—Perceived intensity of a sound, which correlates with sound level; measured in decibels (dB).
Magnification—Apparent increase or decrease in size of an image as a result of forming the image with a converging or diverging system.
Mass—A measure of inertia or of the amount of “stuff” in an object; measured in kilograms.
Mass defect—The difference between the sum of the masses of unbound nucleons forming a nucleus and the mass of that nucleus in the bound state.
Mass number—The sum of the number of protons and neutrons in an atom; also called the atomic mass.
Mean—The average of a group of data; specifically, the arithmetic mean.
Mechanical advantage—The reduction in input force required to accomplish a desired amount of output work using a simple machine.
Median—The central value of a data set.
Melting—The phase transition from solid to liquid; also known as fusion.
Metric system—A system of measurements based on the powers of ten; most commonly used in scientific disciplines.
Microwaves—Long-wavelength electromagnetic radiation capable of inducing vibration in bonds.
Mode—The most common data point in a data set.
Monochromatic—Electromagnetic radiation wherein the wavelength is the same for all incident photons.
Mutually exclusive—Describes outcomes that cannot occur simultaneously.
Myopia—Nearsightedness, or the ability to see nearby objects while distant objects are unfocused or blurry.
Natural frequency—The frequency at which a system resonates; also called the resonant frequency.
Node—A point of maximum displacement of a standing wave.
Nonconservative force—A force that causes energy to be dissipated from a system, such as friction, air resistance, and viscous drag; pathway dependent.
Nonmaleficence—The ethical principle that states that practitioners have an obligation to avoid treatments or interventions in which the potential for harm is greater than the potential for good.
Normal—A line perpendicular to the surface of interest.
Normal force—The force that two surfaces in contact exert on each other that is perpendicular to the plane of contact.
Nucleon—A proton or neutron.
Null hypothesis—The hypothesis of no difference; given enough statistical evidence, the null hypothesis may be rejected.
Ohm’s law—Relates voltage, current, and resistance for a given circuit element.
Outlier—A data point that deviates significantly from the perceived pattern of distribution; depending on the context, an outlier may be disregarded, analyzed normally, or given disproportionate weight when calculating statistics.
Parallel—An arrangement of circuit elements in which the current can go through one element or the other, but not through both.
Parameter—A measure of population data.
Pascal’s principle—States that pressure applied to a noncompressible fluid is distributed equally to all points within that fluid and the walls of the container.
Period—The amount of time it takes for a wave or oscillation to complete one cycle, measured in seconds; the inverse of frequency.
Pitch—A perception of sound that results from its frequency; as frequency increases, pitch gets higher.
Pitot tubes—Measurement devices for pressure or flow rate of a dynamic fluid system.
Plane mirrors—Reflecting surfaces with an infinite radius of curvature, which results in equal image and object distances.
Plane-polarized light—Electromagnetic radiation in which all of the electric field vectors are oriented parallel to one another.
Poiseuille’s law—Relates viscosity, tube dimensions, and pressure differentials to the rate of flow between two points in a system.
Population—The group of all individuals who have certain desired characteristics.
Positron—Antiparticle of an electron; it has the same mass as an electron and the opposite charge (e+ or β+).
Potential difference—The difference of electrical potential between two distinct points, measured in volts (V); also called voltage.
Potential energy—Energy associated with position, measured in joules (J); includes gravitational, elastic, chemical, and electrical forms.
Power—Rate at which work is accomplished, or energy expenditure per unit time; measured in watts (W).
Precision—The tendency of measurements to agree with one another; also called reliability.
Pressure—The ratio of force to the area over which it is applied; measured in pascals (Pa), millimeters of mercury (mmHg) or torr, or atmospheres (atm).
Process functions—Physical quantities that depend on the path taken to get from one state to another; include work and heat.
Quantum—A discrete bundle of energy such as the photon.
Quartiles—Values that separate data in ascending order into four evenly sized groups.
Radiation—A method of heat transfer that relies on electromagnetic waves; can occur in a vacuum.
Radio waves—Very long wavelength electromagnetic radiation.
Randomization—A method of reducing bias and confounding during research in which participants are assigned to a group by a random number generator or similar method; participants or researchers cannot choose the groups.
Range—The difference between the smallest number in a data set and the largest.
Ray diagram—Visual representation of a geometrical optics system.
Real—Describes an image on the same side of a lens or mirror as the refracted or reflected light that can be projected on a screen; in single-mirror or single-lens systems, real images are always inverted.
Reflection—The return of light rays from a medium at an angle equal to the incident angle.
Refraction—The bending of light rays as a result of a change in the index of refraction between media.
Resistance—A measure of the opposition to current flow through a material, measured in ohms (Ω); the inverse of conductance.
Resistivity—A measure of the intrinsic resistance of a material independent of its shape or size; resistivity generally increases with temperature.
Resonance—Oscillation at maximum amplitude as the result of a periodically applied force at the natural (resonant) frequency of an object.
Respect for persons—A principle of research ethics that encompasses autonomy and informed consent.
Resultant—The sum, difference, or product of vector mathematics; also refers to the sum or difference of two waves.
Right-hand rule—A method for determining the direction of a vector that is the product of two vectors.
Rotation—The turning of an extended body about an axis or center.
Sample—A subset of a population that is used to make generalizations about the population as a whole.
Scalar—A mathematical quantity that lacks directionality.
Scientific method—A systematized way of evaluating data and investigating new hypotheses.
Scientific notation—A mathematical representation of quantities as multiples of powers of ten.
Selection bias — Occurs when research participants differ from the general population in a meaningful way.
Series—An arrangement of circuit elements in which the current must go through all of the elements.
Shock wave—The buildup of wave fronts that occurs when the source is travelling at or above the speed of sound.
Significant figures—A tool for maintaining appropriate levels of precision when performing mathematical calculations.
Snell’s law—Relates the incident angle, refracted angle, and indices of refraction for two media.
Solid—A material with distinct boundaries and strong intermolecular forces capable of resisting shear forces.
Sound—The perception of longitudinal waves of pressure changes in air and other media.
Specific gravity—The ratio of an object’s density to the density of water; unitless.
Specific heat—The relationship between thermal energy and temperature change per unit mass of a substance, measured in .
Speed—The ratio of distance traveled to time; at any given point, instantaneous speed is the magnitude of instantaneous velocity; measured in .
Spherical mirror—A mirror that causes convergence or divergence of light rays incident upon its surface.
Standard deviation—A measure of distribution of data from the mean of a sample; outliers lie at least three standard deviations above or below the mean.
Standing waves—Waveforms with steady nodes and antinodes formed from the interference of incident and reflected waves at a boundary.
State functions—Physical quantities that can be determined based on the state of an object, such as pressure, density, temperature, volume, enthalpy, internal energy, Gibbs free energy, and entropy; pathway independent.
Statistic—A measure of sample data.
Streamlines—Visual representations of the movement of fluid during laminar flow.
Surface tension—The result of the cohesive forces in a liquid creating a barrier at the interface between a liquid and the environment.
Surroundings—Everything that is not being measured as part of a given system.
System—The observed and quantified region of the universe of interest to the experimenter.
Temperature—A measure of the average kinetic energy of particles in a substance; measured in degrees Fahrenheit (°F), degrees Celsius (°C), or kelvins (K).
Terminal velocity—The velocity at which air resistance is equal to gravitational force and no acceleration occurs for an object in free fall.
Thermal expansion—An increase in length or volume of a substance as a result of an increase in temperature.
Torque—The primary motivator for rotational movement that combines force, lever arm, and the angle between them; measured in N·m.
Traveling wave—A wave that propagates through a medium with changes in the locations of crests and troughs.
Translation—Motion through space without rotation.
Transverse wave—A wave that propagates in a direction perpendicular to the direction of oscillation.
Turbulent flow—Fluid movement that does not follow parallel streamlines; has backflow, eddies, and swirls.
Twin study—A research design used heavily in psychology to differentiate between genetic and environmental effects.
Ultrasonic—Above the frequencies that humans can hear.
Ultrasound—A treatment and diagnostic modality using ultrasonic waves for medical purposes.
Ultraviolet—A region of the electromagnetic spectrum that is not visible; primarily responsible for the damaging effects of sunlight on skin.
Upright—Describes an image that is the same orientation as the object; in single-mirror or single-lens systems, upright images are always virtual.
Vaporization—The phase transition from solid to gas; also called boiling or evaporation.
Vector—A mathematical quantity that has both magnitude and direction.
Velocity—The rate of change in the displacement of an object; measured in .
Venturi effect—Describes the relationship between the continuity equation and Bernoulli’s equation; as cross-sectional area of a tube decreases, the speed of the fluid increases, and the pressure exerted on the walls of the tube decreases.
Virtual—Describes an image on the opposite side of a lens or mirror as the refracted or reflected light; in single-mirror or single-lens systems, virtual images are always upright.
Viscosity—A measure of the resistance to flow in a fluid.
Wavelength—The distance between two corresponding points of successive cycles in a waveform, measured in meters.
Weight—The force of gravity acting on an object.
Work—A function of the applied force and the distance through which it is applied or the pressure and volume changes in a gas system; work is the use of energy to accomplish something and is measured in joules (J).
Work—energy theorem—States that net work is equal to the change in energy (usually kinetic energy) of an object.
X-rays—A type of electromagnetic radiation; primarily used for medical imaging.