Kagawa Entrance Science flashcards

32 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, D=b²−4ac. D>0 gives two distinct real roots, D=0 gives one repeated root, D<0 gives complex conjugate roots.

Geometric series sum

The sum of the first n terms of a geometric sequence with first term a and ratio r is Sₙ=a(1−rⁿ)/(1−r), valid when r≠1.

Dot product perpendicularity

For vectors a and b, a·b=|a||b|cosθ. The vectors are perpendicular exactly when their dot product equals zero.

Conditional probability formula

P(A|B)=P(A∩B)/P(B), the probability of A given B. Events are independent when P(A∩B)=P(A)P(B).

De Moivre's theorem

For a complex number in polar form, (cosθ+isinθ)ⁿ=cos nθ+isin nθ, useful for powers and roots of complex numbers.

Constant acceleration kinematics

With constant acceleration a: v=v₀+at, displacement x=v₀t+½at², and v²=v₀²+2ax. These relate velocity, time, and displacement without calculus.

Conservation of momentum

In an isolated system with no external net force, total momentum p=mv is conserved. In elastic collisions kinetic energy is also conserved.

Centripetal acceleration

An object moving in a circle of radius r at speed v has centripetal acceleration a=v²/r directed toward the center, requiring a net inward force.

Snell's law

For light crossing a boundary, n₁sinθ₁=n₂sinθ₂, where n is the refractive index and θ is the angle from the normal.

Photon energy

A photon's energy is E=hf=hc/λ, where h is Planck's constant. The photoelectric effect occurs when hf exceeds the work function.

Molar volume at STP

One mole of any ideal gas occupies about 22.4 liters at standard temperature and pressure (0°C, 1 atm), enabling mole-volume conversions.

pH definition

pH=−log[H⁺], so a tenfold increase in hydrogen ion concentration lowers pH by one unit. Neutral water at 25°C has pH 7.

Le Chatelier's principle

When a system at equilibrium is disturbed by changes in concentration, pressure, or temperature, it shifts to counteract the change and restore equilibrium.

Standard cell potential

E°cell=E°cathode−E°anode. A positive value indicates a spontaneous galvanic reaction; oxidation occurs at the anode, reduction at the cathode.

Esterification

A carboxylic acid reacts with an alcohol in the presence of an acid catalyst to form an ester and water, an equilibrium-limited condensation reaction.

Mendel's law of segregation

During gamete formation, the two alleles of a gene separate so each gamete carries only one allele, restoring pairs at fertilization.

Photosynthesis overall equation

6CO₂+6H₂O→C₆H₁₂O₆+6O₂, driven by light in chloroplasts. Light reactions make ATP and NADPH; the Calvin cycle fixes carbon.

Enzyme function

Enzymes are biological catalysts that lower activation energy. Their activity is sensitive to temperature and pH, denaturing at extremes.

Meiosis purpose

Meiosis halves chromosome number to produce haploid gametes. Crossing over and independent assortment generate genetic variation among offspring.

Seismic S-waves

S-waves are transverse seismic waves that cannot travel through liquids. Their absence beyond the outer core reveals that it is liquid.

Plate boundary types

Divergent boundaries create new crust, convergent boundaries cause subduction and volcanism, and transform boundaries produce strike-slip earthquakes.

Law of superposition

In undisturbed sedimentary sequences, older layers lie below younger ones, a principle of relative dating of rock strata.

Richter scale

A logarithmic scale of earthquake magnitude; each whole-number increase represents roughly a thirtyfold increase in released seismic energy.

Kepler's third law

The square of an orbital period is proportional to the cube of the semi-major axis: T²∝a³, relating distance and orbital time.

Third conditional form

If + past perfect, then would have + past participle (e.g., 'If I had studied, I would have passed'), describing unreal past situations.

Subject-verb agreement

Singular subjects take singular verbs and plural subjects take plural verbs. Indefinite pronouns such as 'everyone' and 'each' are grammatically singular.

Non-restrictive relative clause

A clause set off by commas that adds extra information about a noun. Use 'which' or 'who', not 'that', in non-restrictive clauses.

Japanese topic particle は

The particle は marks the topic of a sentence, pronounced 'wa'. It contrasts with が, which marks the grammatical subject.

Japanese conditional forms

と expresses natural consequence, ば a hypothetical, たら 'if/when', and なら 'given that'. Each carries distinct nuance in conditional sentences.

Keigo categories

Japanese honorific language has 尊敬語 (respectful, elevating others), 謙譲語 (humble, lowering oneself), and 丁寧語 (polite です/ます forms).

Independent vs dependent variable

The independent variable is manipulated by the experimenter; the dependent variable is measured in response. Controlled variables are held constant.

Systematic vs random error

Systematic error shifts all measurements in one direction and persists; random error scatters readings and can be reduced by repeating trials and averaging.