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Tahsili Core Formulas and Scientific Principles

24 flashcards to revise the key facts for the Tahsili SAAT. Study material written for practice, not the official exam.

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Snell's Law of Refraction
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1
Snell's Law of Refraction
n1 sin(theta1) = n2 sin(theta2), describing the relationship between angles of incidence and refraction when light passes between two isotropic media.
2
Newton's Universal Law of Gravitation
F = G (m1 m2) / r^2, where G is the gravitational constant (6.674 x 10^-11 N m^2/kg^2).
3
Coulomb's Electrostatic Law
F = k |q1 q2| / r^2, where electrostatic constant k = 1 / (4 pi epsilon_0) approx 8.99 x 10^9 N m^2/C^2.
4
Photoelectric Effect Energy Equation
E_photon = h * f = W + K_max, where h is Planck's constant, W is work function, and K_max is maximum photoelectron kinetic energy.
5
Ideal Gas Law
P V = n R * T, relating pressure (P), volume (V), amount of substance (n), gas constant (R), and absolute temperature (T in Kelvin).
6
Le Chatelier's Principle
If an external stress (change in concentration, temperature, or pressure) is applied to a chemical system at equilibrium, the system shifts to counteract that stress.
7
Hess's Law of Constant Heat Summation
The total enthalpy change for a chemical reaction is independent of the pathway taken, equal to the sum of enthalpy changes for individual elementary steps.
8
Nernst Equation (Standard Conditions, 298 K)
E_cell = E_cell_std - (0.0592 / n) * log10(Q), relating cell potential to reaction quotient Q and electron transfer number n.
9
Markovnikov's Rule
In the electrophilic addition of HX to an unsymmetrical alkene, the hydrogen atom bonds to the carbon with more hydrogen substituents, forming the more stable carbocation.
10
Derivative of Exponential and Natural Log Functions
d/dx [e^(kx)] = k * e^(kx), and d/dx [ln(x)] = 1/x for x > 0.
11
Integration by Parts Formula
integral(u dv) = u * v - integral(v du), derived from the product rule of differential calculus.
12
Trigonometric Pythagorean Identities
sin^2(x) + cos^2(x) = 1; 1 + tan^2(x) = sec^2(x); 1 + cot^2(x) = csc^2(x).
13
Mendel's Law of Independent Assortment
Alleles of two or more different genes sort into gametes independently of one another during meiosis (applies to unlinked genes on non-homologous chromosomes).
14
Cellular Respiration ATP Yield
Complete aerobic oxidation of 1 molecule of glucose yields approximately 30 to 32 ATP through glycolysis, pyruvate decarboxylation, citric acid cycle, and oxidative phosphorylation.
15
Central Dogma of Molecular Biology
Genetic information flows from DNA replication to transcription into messenger RNA (mRNA), and translation into polypeptides (proteins).
16
Hardy-Weinberg Equilibrium Equations
p + q = 1 (allele frequencies) and p^2 + 2pq + q^2 = 1 (genotype frequencies), assuming no mutation, migration, selection, genetic drift, or non-random mating.
17
Doppler Effect Frequency Shift
f_observed = f_source * (v +/- v_detector) / (v -/+ v_source), where upper signs apply when detector and source move toward each other.
18
Ohm's Law and Electrical Power
V = I R, and Power P = V I = I^2 * R = V^2 / R.
19
Faraday's Law of Electromagnetic Induction
EMF = -N * (dPhi_B / dt), where induced electromotive force opposes the rate of change of magnetic flux (Lenz's law indicated by negative sign).
20
pH and pOH Relationship
pH = -log10[H3O+], pOH = -log10[OH-], and pH + pOH = 14.00 at 25 degrees Celsius (Kw = 1.0 x 10^-14).
21
Buffer Solution pH (Henderson-Hasselbalch Equation)
pH = pKa + log10([A-] / [HA]), where [A-] is conjugate base concentration and [HA] is weak acid concentration.
22
Centripetal Acceleration and Centripetal Force
a_c = v^2 / r = omega^2 r, and F_c = m v^2 / r, directed radially inward toward the center of curvature.
23
Work-Energy Theorem
W_net = Delta K = 1/2 m v_final^2 - 1/2 m v_initial^2; net work done on a particle equals the change in its kinetic energy.
24
Quadratic Formula and Discriminant Rules
x = (-b +/- sqrt(b^2 - 4ac)) / (2a); Delta = b^2 - 4ac: Delta > 0 gives two real roots, Delta = 0 gives one repeated real root, Delta < 0 gives two complex conjugate roots.

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