Lebanese Baccalaureate - General Sciences (GS) 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, the roots are x=(−b±√(b²−4ac))/(2a); the discriminant b²−4ac determines whether roots are real and distinct, equal, or complex.

Derivative of a product

The product rule states (uv)′=u′v+uv′, where u and v are differentiable functions of the same variable.

Chain rule

For a composite function, (f∘g)′(x)=f′(g(x))·g(x); differentiate the outer function and multiply by the derivative of the inner function.

Geometric sequence sum

For first term u₁ and common ratio q≠1, the sum of n terms is Sₙ=u₁(1−qⁿ)/(1−q).

Conditional probability

P(A|B)=P(A∩B)/P(B) for P(B)>0; it gives the probability of A given that B has occurred.

Complex number modulus

For z=a+bi, the modulus is |z|=√(a²+b²), the distance from the origin in the complex plane; z·z̄=|z|².

Dot product of vectors

u·v=|u||v|cos θ, where θ is the angle between them; the vectors are perpendicular exactly when the dot product is zero.

Newton's second law

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

Constant-acceleration kinematics

With initial velocity u and acceleration a, velocity is v=u+at and displacement is s=ut+½at².

Conservation of mechanical energy

Without friction or other non-conservative forces, the sum of kinetic and potential energy stays constant during motion.

Ohm's law and power

For a resistor, U=RI; electrical power dissipated is P=UI=RI²=U²/R.

Half-life

The time for half the radioactive nuclei in a sample to decay; it equals ln2/λ, where λ is the decay constant.

Centripetal acceleration

An object moving in a circle of radius r at speed v has acceleration v²/r directed toward the center of the circle.

Wave equation

For any wave, speed equals frequency times wavelength, v=fλ; frequency is set by the source and wavelength by the medium.

Mole and molar mass

The number of moles is n=m/M, where m is mass in grams and M is molar mass in g/mol; one mole contains Avogadro's number of particles.

pH definition

pH=−log[H₃O⁺]; at 25 °C, pH+pOH=14, so pH below 7 indicates an acidic solution.

Dilution relation

When a solution is diluted with solvent, C₁V₁=C₂V₂ because the number of moles of solute stays constant.

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 by a change in concentration, pressure, or temperature, it shifts to oppose that change.

Alkane general formula

Saturated hydrocarbons containing only single carbon–carbon bonds have the formula CₙH₂ₙ₊₂, such as methane CH₄ and ethane C₂H₆.

Faraday and electrolysis

One mole of electrons carries about 96500 coulombs; the charge passed is Q=I·t and determines the amount of substance deposited.

DNA base pairing

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

Transcription and translation

Transcription copies DNA into mRNA in the nucleus; translation reads mRNA codons at ribosomes to assemble a polypeptide chain.

Mitosis versus meiosis

Mitosis yields two identical diploid cells for growth; meiosis yields four haploid gametes and increases genetic variation.

Monohybrid cross ratio

Crossing two heterozygotes Aa×Aa gives offspring genotypes in a 1:2:1 ratio and phenotypes in a 3:1 ratio.

Enzyme active site

The region of an enzyme where substrate binds; its shape is specific, and high temperature or extreme pH can denature it.

Cellular respiration equation

C₆H₁₂O₆+6O₂→6CO₂+6H₂O+energy stored in ATP; it occurs partly in the cytoplasm and mainly in mitochondria.

SI unit conversion rule

Before substituting into formulas, convert mass to kilograms, length to metres, time to seconds, and temperature to kelvin.

Area under a velocity-time graph

On a velocity–time graph, the area between the curve and the time axis equals the distance travelled.

Relative error

Relative error equals |measured−accepted| divided by accepted, multiplied by 100 to give a percentage.

Testable hypothesis

A hypothesis must predict a relationship between an independent and a dependent variable and be falsifiable by experiment.

Peer review purpose

Independent experts check a manuscript's originality, methods, and clarity before publication; it reduces but does not eliminate errors.