Chiba 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 the number of real roots.

Arithmetic sequence sum

For an arithmetic sequence with first term a and nth term l, the sum of the first n terms is Sₙ = n(a + l)/2. Equivalently Sₙ = n[2a + (n − 1)d]/2.

Sine rule

In any triangle, a/sin A = b/sin B = c/sin C = 2R, where R is the circumradius. Use it when you know a side and its opposite angle.

Dot product

For vectors a and b, a·b = |a||b|cos θ = a₁b₁ + a₂b₂. The dot product is zero exactly when the two vectors are perpendicular.

Combination formula

The number of ways to choose r items from n without regard to order is nCr = n!/(r!(n − r)!). Order matters for permutations, not for combinations.

Newton's second law

The net force on an object equals its mass times its acceleration, F = ma. Acceleration points in the direction of the net force and is zero when forces balance.

Momentum conservation

In an isolated system with no external net force, total momentum before a collision equals total momentum after. This holds for both elastic and inelastic collisions.

Wave equation

Wave speed equals frequency times wavelength, v = fλ. Increasing frequency at fixed speed shortens the wavelength, as when a sound rises in pitch.

Ohm's law

For a conductor at constant temperature, voltage equals current times resistance, V = IR. Resistance in series adds directly; in parallel, reciprocals add.

Snell's law

At a boundary between media, n₁sin θ₁ = n₂sin θ₂, where n is the refractive index and angles are measured from the normal. Light bends toward the normal entering a denser medium.

Centripetal force

An object moving in a circle of radius r at speed v accelerates toward the center with a = v²/r, requiring a net inward force F = mv²/r.

Mole concept

One mole contains Avogadro's number (about 6.02 × 10²³) of particles and has a mass in grams equal to the molar mass. Moles n = mass/M.

Molarity

Molar concentration is moles of solute divided by liters of solution, c = n/V. On dilution the moles stay constant, so c₁V₁ = c₂V₂.

pH definition

pH = −log₁₀[H⁺], where [H⁺] is hydrogen-ion concentration in mol/L. A decrease of one pH unit means ten times greater acidity.

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 partly counteracts the change.

Oxidation and reduction

Oxidation is loss of electrons and an increase in oxidation number; reduction is gain of electrons. Both always occur together in a redox reaction.

Ideal gas law

PV = nRT relates pressure, volume, moles, and absolute temperature; R ≈ 8.31 J/(mol·K). Temperature must be in kelvin, and volume must match the units of R.

Periodic table trends

Across a period, atomic radius decreases while ionization energy and electronegativity increase. Down a group, radius increases and ionization energy decreases.

Photosynthesis equation

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

Cellular respiration

C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O + energy. Glycolysis occurs in the cytoplasm; the Krebs cycle and electron transport chain occur in mitochondria.

DNA base pairing

In double-stranded DNA, adenine pairs with thymine by two hydrogen bonds and guanine pairs with cytosine by three. The two strands run antiparallel.

Mendelian monohybrid ratio

Crossing two heterozygotes (Aa × Aa) gives a 3:1 phenotype ratio and a 1:2:1 genotype ratio when one allele is completely dominant.

Prokaryote versus eukaryote

Prokaryotes lack a membrane-bound nucleus and organelles; eukaryotes have a nucleus, mitochondria, and in plants chloroplasts and a cellulose wall.

Trophic energy transfer

Only about 10% of energy at one trophic level passes to the next; the rest is lost as heat and through respiration, limiting food chains to a few levels.

Plate boundary types

Divergent boundaries create new crust at ridges; convergent boundaries produce subduction, trenches, and volcanoes; transform boundaries cause strike-slip earthquakes.

Earthquake magnitude scale

The Richter scale is logarithmic: each whole-number increase corresponds to about 31.6 times more energy released and about ten times greater wave amplitude.

Seasons cause

Seasons result from Earth's 23.4° axial tilt as it orbits the Sun, not from distance to the Sun. The tilted hemisphere receiving more direct sunlight has summer.

Rock cycle

Igneous rock forms from cooling magma, sedimentary from compacted deposits, and metamorphic from heat and pressure. Any type can transform into another.

Greenhouse effect

Atmospheric gases such as CO₂, water vapor, and methane absorb outgoing infrared radiation and re-emit it, warming the surface. More CO₂ raises average temperature.

Subject-verb agreement

A verb must match its subject in number. Phrases between them do not change this: "The list of items is long" keeps the singular verb.

Comma splice

Joining two independent clauses with only a comma is an error. Use a period, semicolon, or a comma plus a coordinating conjunction instead.

Dangling modifier

An introductory participial phrase must describe the subject of the main clause. "Walking home, she saw rain" is correct; "Walking home, the rain fell" is not.