Iwate Entrance Science flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Quadratic formula

For ax² + bx + c = 0 with a ≠ 0, the solutions are x = (-b ± √(b² - 4ac)) / 2a. The discriminant b² - 4ac determines whether there are two, one, or no real roots.

Chain rule

When a function is composed of an outer and inner function, its derivative is the outer derivative evaluated at the inner function multiplied by the inner derivative: dy/dx = dy/du · du/dx.

Sum of geometric series

A finite geometric series with first term a and ratio r sums to a(1 - rⁿ)/(1 - r) for r ≠ 1. As n grows, it converges to a/(1 - r) only when |r| < 1.

Sine rule

In any triangle, the ratio of each side to the sine of its opposite angle is constant: a/sin A = b/sin B = c/sin C. It applies to non-right triangles where the cosine rule is also useful.

Newton's second law

The net force on an object equals its mass times acceleration, F = ma. Acceleration points in the direction of the net force and is inversely proportional to mass for a fixed force.

Conservation of energy

In an isolated system, total energy is constant; it changes form but is neither created nor destroyed. For a falling body without friction, ½mv² + mgh stays constant.

Snell's law

When light crosses a boundary between media, n₁ sin θ₁ = n₂ sin θ₂, where n is the refractive index and angles are measured from the normal. Higher index means slower light.

Ohm's law

For an ohmic conductor at constant temperature, current is proportional to voltage: V = IR. Resistance R is measured in ohms, current in amperes, and potential difference in volts.

First law of thermodynamics

The change in internal energy of a system equals heat added minus work done by the system: ΔU = Q - W. For an adiabatic process Q = 0, so ΔU = -W.

Resonance on a string

A string fixed at both ends supports standing waves only at wavelengths λ = 2L/n, where L is length and n is a positive integer. The corresponding frequencies are f = nv/(2L).

Ionic versus covalent bonding

Ionic bonds transfer electrons from a metal to a nonmetal, creating oppositely charged ions held by electrostatic attraction. Covalent bonds share electron pairs, typically between nonmetals with similar electronegativity.

Mole and molar mass

One mole contains 6.02 × 10²³ particles. The number of moles equals mass divided by molar mass, n = m/M, allowing conversion between grams and particle counts in reactions.

Le Chatelier's principle

When a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, it shifts in the direction that partially opposes the change. Catalysts do not shift equilibrium position.

Oxidation and reduction

Oxidation is loss of electrons and reduction is gain. In a redox reaction the oxidizing agent is reduced while the reducing agent is oxidized; the two half-reactions must balance in electrons.

pH definition

pH is the negative base-10 logarithm of hydrogen ion concentration, pH = -log[H⁺]. A decrease of one pH unit corresponds to a tenfold increase in hydrogen ion concentration.

Limiting reactant

The reactant that is fully consumed first limits how much product can form. Comparing the mole ratio actually available with the stoichiometric ratio in the balanced equation identifies it.

Mitosis versus meiosis

Mitosis produces two genetically identical diploid cells for growth and repair. Meiosis produces four haploid gametes and includes crossing over and independent assortment, generating genetic variation.

Mendel's law of segregation

Each organism carries two alleles for a gene; these separate during gamete formation so each gamete receives only one. Random fertilization then restores pairs in offspring, producing predictable phenotypic ratios.

DNA base pairing

In double-stranded DNA, adenine pairs with thymine by two hydrogen bonds and guanine pairs with cytosine by three. This complementary pairing underlies semi-conservative replication and transcription.

Natural selection

Heritable variation among individuals, combined with differential survival and reproduction, changes allele frequencies across generations. Traits that improve reproductive success become more common in the population over time.

Trophic energy transfer

Energy enters ecosystems through producers and passes to consumers, but only about ten percent transfers between trophic levels. The rest is lost mainly as heat through respiration, limiting food chain length.

Enzyme function

Enzymes are proteins that lower activation energy by binding substrates at an active site. They are not consumed, are sensitive to temperature and pH, and can be inhibited competitively or non-competitively.

Correlation versus causation

Two variables can move together without one causing the other, because a third variable or coincidence may explain the association. Causal claims require controlled experiments or strong mechanistic evidence.

Accuracy versus precision

Accuracy is closeness of a measurement to the true value; precision is closeness of repeated measurements to each other. A measurement can be precise but inaccurate due to systematic error.

Significant figures rule

For multiplication and division, round the result to the fewest significant figures among the inputs. For addition and subtraction, round to the fewest decimal places among the inputs.

Percent error

Percent error compares a measured value with an accepted value: |measured - accepted| / accepted × 100%. It quantifies overall deviation but does not distinguish random from systematic error.

Interpreting a linear graph

In y = mx + b, the slope m is the rate of change of y per unit x and the intercept b is the value of y when x is zero. Units of slope are units of y divided by units of x.

Independent and dependent variables

The independent variable is deliberately changed by the experimenter; the dependent variable is measured as a response. Controlled variables are held constant so they do not confound the comparison.

Control group purpose

A control group receives no treatment or a standard treatment, providing a baseline for comparison. Without it, observed changes cannot be attributed confidently to the manipulated variable rather than other factors.

Reading a meniscus

For most liquids in glass, the meniscus curves downward; read the lowest point at eye level. Record one estimated digit beyond the smallest graduation to reflect measurement uncertainty.

Diluting concentrated acid

Add concentrated acid slowly to water while stirring, never water to acid. The dilution releases substantial heat, and adding water to concentrated acid can cause violent boiling and spattering.

Titration endpoint

The endpoint is the point where the indicator changes color, ideally matching the equivalence point where moles of acid and base are stoichiometrically equal. Consistent swirling and dropwise addition improve accuracy.