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STEM Egypt Scientific Principles and Cognitive Logic

Essential physical laws, chemical reaction principles, cellular biology concepts, and logical deduction rules for the Egyptian STEM Admissions Assessment.

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Archimedes' Principle of Flotation
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1
Archimedes' Principle of Flotation
A floating object displaces a weight of fluid equal to its own total weight: rho_object / rho_fluid = V_submerged / V_total.
2
Newton's Second Law and Momentum Conservation
F_net = m a = dp / dt. In an isolated system with no external forces, total linear momentum is conserved (m1v1 + m2v2 = m_tot v_f).
3
Ohm's Law and Resistors in Parallel
V = I * R. In parallel: 1 / R_eq = 1/R1 + 1/R2 + ... Equivalent resistance is always smaller than the smallest branch resistor.
4
Work Done by a Constant Force
W = F d cos(theta), where theta is the angle between force and displacement vectors. Unit is Joule (N * m).
5
Kinetic and Gravitational Potential Energy
KE = (1/2) m v^2, and PE = m g h. In a frictionless system, total mechanical energy KE + PE is conserved.
6
Boyle's Law and Charles's Law (Gas Laws)
Boyle's: P1V1 = P2V2 (constant T). Charles's: V1/T1 = V2/T2 (constant P with T in Kelvin).
7
Molarity (M) Concentration Formula
M = moles of solute (mol) / volume of solution (liters) = (mass / molar mass) / V(L).
8
Electronegativity and Chemical Bond Types
Delta EN < 0.4: Nonpolar covalent; 0.4 - 1.7: Polar covalent; Delta EN > 1.7: Ionic bond.
9
Periodic Trends Across a Period (Left to Right)
Effective nuclear charge (Z_eff) increases: atomic radius decreases, ionization energy increases, and electronegativity increases.
10
Enzyme Active Site and Thermal Denaturation
Enzymes lower activation energy. High temperatures (> 50-60 C) break tertiary non-covalent bonds, permanently denaturing the active site.
11
Cellular Photosynthesis Net Balanced Equation
6 CO2 + 6 H2O + Light energy -> C6H12O6 + 6 O2, occurring in chloroplast thylakoids and stroma.
12
Glycolysis Net Energy Yield and Location
Takes place in cytoplasm without oxygen, yielding net 2 ATP and 2 NADH per glucose molecule.
13
DNA Base-Pairing Rules (Chargaff's Rules)
Adenine (A) pairs with Thymine (T) via 2 hydrogen bonds; Guanine (G) pairs with Cytosine (C) via 3 hydrogen bonds. Antiparallel 5' to 3'.
14
Mendelian Monohybrid Cross Phenotypic Ratio
Crossing two heterozygotes (Tt x Tt) yields a 3 : 1 phenotypic ratio (3 tall : 1 dwarf) and a 1 : 2 : 1 genotypic ratio (1 TT : 2 Tt : 1 tt).
15
X-Linked Recessive Inheritance Characteristics
Affects males predominantly; affected father cannot pass trait to sons (gives Y), but all daughters become obligate carriers (X^C X^c).
16
Trophic Energy Efficiency (The 10% Rule)
Only approx 10% of energy is transferred from one trophic level to the next; 90% is lost as metabolic heat and respiration.
17
Harmonic Mean for Round-Trip Average Speed
V_avg = (2 v1 v2) / (v1 + v2) when traveling equal distances at two different constant speeds.
18
Pipes and Cisterns Work Rate Principle
If pipe A fills in t1 and pipe B in t2, combined rate is 1/t1 + 1/t2. Combined time is (t1 * t2) / (t1 + t2).
19
Clock Angle Formula at H hours and M minutes
Angle = |30H - 5.5M| degrees (since hour hand moves 0.5 deg/min and minute hand moves 6 deg/min).
20
Number of Handshakes Formula for n People
Total handshakes = n * (n - 1) / 2 = nC2.
21
Cube Painting Problem (Edge Cubes)
In an n x n x n painted cube cut into unit cubes: 3 faces painted = 8 (corners); 2 faces = 12(n-2) (edges); 1 face = 6(n-2)^2; 0 faces = (n-2)^3.
22
Plane Mirror Clock Time Reflection
Actual time + Mirror image time = 12:00 (or 11:60). If mirror shows 3:45, actual time is 11:60 - 3:45 = 8:15.
23
Independent vs Dependent Variables in Scientific Inquiry
Independent variable is manipulated by the experimenter; dependent variable is the measured effect; control variables are kept strictly constant.
24
Genetic Drift vs Natural Selection
Genetic drift changes allele frequencies due to random chance (strongest in small populations); natural selection favors traits that improve reproductive fitness.
25
Number of Diagonals in an n-gon
Number of diagonals = n * (n - 3) / 2.

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