Hiroshima Entrance Science flashcards

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

Quadratic discriminant

For ax² + bx + c = 0, the value b² − 4ac. Positive means two distinct real roots, zero means one repeated real root, negative means no real roots.

Cosine rule

a² = b² + c² − 2bc·cos A. It finds a side from two sides and the included angle, or an angle from all three sides of a triangle.

Geometric series sum

For a geometric sequence with first term a₁ and ratio r ≠ 1, the sum of n terms is a₁(1 − rⁿ)/(1 − r).

Combination versus permutation

A permutation counts arrangements where order matters, n!/(n − r)!. A combination counts selections where order does not matter, n!/(r!(n − r)!).

Definite integral as area

The integral of f from a to b gives the signed area between the curve and the x-axis. Regions below the axis contribute negative values.

Newton's second law

The net force on an object equals its mass times its acceleration, F = ma. Force and acceleration point in the same direction.

Momentum conservation

In any collision or explosion with no external net force, total momentum before equals total momentum after. Kinetic energy is conserved only in elastic collisions.

Ohm's law and power

Voltage equals current times resistance, V = IR. Electrical power is P = VI, equivalently I²R or V²/R.

Total internal reflection

Light travelling from a denser to a less dense medium is fully reflected when the incidence angle exceeds the critical angle, given by sin θc = n₂/n₁.

Wave equation

Wave speed equals frequency times wavelength, v = fλ. Frequency is set by the source; speed depends on the medium.

Ideal gas law

PV = nRT relates pressure, volume, amount and absolute temperature of a gas. Temperature must be in kelvin, never degrees Celsius.

Mole calculations

The amount in moles is n = m/M using molar mass. For gases at standard conditions, n = V/22.4 litres per mole.

pH definition

pH = −log₁₀[H⁺]. At 25 °C a neutral solution has pH 7, and pH plus pOH equals 14.

Oxidation and reduction

Oxidation is loss of electrons and an increase in oxidation number. Reduction is gain of electrons and a decrease in oxidation number.

Le Chatelier's principle

When a system at equilibrium is disturbed, it shifts in the direction that opposes the change. Raising pressure favours the side with fewer gas moles.

Periodic trend across a period

Moving left to right across a period, atomic radius decreases while ionisation energy and electronegativity increase, because nuclear charge grows with electrons added to the same shell.

Central dogma

Genetic information flows from DNA to mRNA by transcription in the nucleus, then to protein by translation at ribosomes, with each codon specifying one amino acid.

Photosynthesis equation

6CO₂ + 6H₂O → C₆H₁₂O₆ + 6O₂. Light energy absorbed by chlorophyll drives the conversion of carbon dioxide and water into glucose and oxygen.

Cellular respiration equation

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy. Glycolysis occurs in the cytoplasm; most ATP is produced in the mitochondria.

Law of segregation

The two alleles of a gene separate during gamete formation, so each gamete carries only one. A cross of two heterozygotes gives a 3:1 phenotype ratio.

Enzyme denaturation

Above an optimum temperature, an enzyme's shape changes and its active site no longer fits the substrate, so activity falls sharply and the change is usually irreversible.

Negative feedback

A homeostatic mechanism in which a deviation from a set point triggers a response that opposes and reverses the deviation, restoring the internal condition.

DNA base pairing

In the double helix, adenine pairs with thymine by two hydrogen bonds and guanine pairs with cytosine by three, holding the two antiparallel strands together.

Seismic P and S waves

P waves are longitudinal and pass through solids and liquids. S waves are transverse and cannot pass through liquids, which reveals Earth's liquid outer core.

Plate boundary types

Divergent boundaries create new crust at ridges, convergent boundaries cause subduction and volcanism, and transform boundaries produce earthquakes from lateral sliding.

Earthquake magnitude scale

Magnitude is logarithmic, so each whole-number increase corresponds to roughly 31.6 times more energy released and about ten times greater ground amplitude.

Rock cycle

Igneous rock forms from cooling magma, sedimentary rock from compacted and cemented deposits, and metamorphic rock from existing rock altered by heat and pressure.

Greenhouse effect

Atmospheric gases such as carbon dioxide, methane and water vapour absorb outgoing infrared radiation, warming the surface above the temperature it would otherwise have.

Independent and dependent variables

The independent variable is deliberately changed by the experimenter; the dependent variable is measured in response; controlled variables are kept constant for a fair test.

Accuracy versus precision

Accuracy is closeness to the true value. Precision is closeness of repeated measurements to each other, so results can be precise yet systematically wrong.

Correlation and causation

Two variables changing together does not prove one causes the other. A confounding variable may influence both, or the association may be coincidental.

Significant figures rule

For multiplication and division, keep the smallest number of significant figures among the inputs. For addition and subtraction, keep the fewest decimal places.

Falsifiable hypothesis

A scientific hypothesis must generate a prediction that an experiment could show to be false. Statements that cannot fail are not testable.