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Jubilee Admission Test STEM Sciences and Logic Core Concepts

Fundamental scientific laws, mathematical reasoning formulas, and logical deduction rules for the King Hussein Foundation Jubilee School Admission Test.

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Archimedes' Principle of Buoyancy
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1
Archimedes' Principle of Buoyancy
Any object wholly or partially immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced: F_buoyant = rho_fluid V_submerged g.
2
Snell's Law of Refraction and Critical Angle Formula
n1 sin(theta1) = n2 sin(theta2); Critical angle for total internal reflection: sin(theta_c) = n2 / n1 (where n1 > n2).
3
Kinematics Formula Relating Velocity, Acceleration, and Distance
v^2 = u^2 + 2 a s, where u is initial velocity, v is final velocity, a is constant acceleration, and s is displacement.
4
Le Chatelier's Principle for Chemical Equilibria
When a chemical system at dynamic equilibrium experiences a change in concentration, temperature, or pressure, it shifts in the direction that counteracts the change.
5
Electrochemical Cell Standard Potential Formula
E°_cell = E°_cathode (reduction) - E°_anode (oxidation). A positive E°_cell indicates a thermodynamically spontaneous reaction under standard conditions.
6
Period of a Simple Mass-Spring Harmonic Oscillator
T = 2 pi sqrt(m / k), where m is the oscillating mass and k is the spring stiffness constant.
7
Equivalent Resistance in Parallel vs Series
Series: R_eq = R1 + R2 + ... + Rn. Parallel: 1 / R_eq = 1 / R1 + 1 / R2 + ... + 1 / Rn.
8
Stages and Net ATP Yield of Cellular Respiration
Glycolysis (cytosol, 2 ATP), Krebs cycle (matrix, 2 ATP), Electron Transport Chain & Chemiosmosis (inner membrane, approx 26-28 ATP). Total: ~30-32 ATP per glucose.
9
Mendelian Monohybrid Cross Phenotypic and Genotypic Ratios
In a cross between two heterozygotes (Tt x Tt): Genotypic ratio is 1 TT : 2 Tt : 1 tt (1:2:1); Phenotypic ratio is 3 dominant : 1 recessive (3:1).
10
DNA to RNA Transcription Complementary Base-Pairing
Template DNA strand pairs with RNA: Adenine (A) -> Uracil (U), Thymine (T) -> Adenine (A), Cytosine (C) -> Guanine (G), Guanine (G) -> Cytosine (C).
11
Lindeman's 10% Ecological Trophic Efficiency Rule
Only approximately 10% of chemical energy stored as organic biomass in one trophic level is transferred to the next higher level; 90% is dissipated as metabolic heat.
12
Law of Cosines in Any Triangle
c^2 = a^2 + b^2 - 2 a b * cos(C), solving for unknown sides or angles in non-right triangles.
13
Sum of an Infinite Convergent Geometric Series
S_infinity = a / (1 - r), valid strictly when the common ratio satisfies |r| < 1.
14
Permutations vs Combinations Formulas
Order matters: P(n, r) = n! / (n - r)!. Order does NOT matter: C(n, r) = n! / [r! * (n - r)!].
15
Harmonic Mean for Round-Trip Average Speed
For equal distances traveled at speeds v1 and v2: v_average = (2 v1 v2) / (v1 + v2). It is lower than the simple arithmetic mean.
16
Interior and Exterior Angles of a Regular n-Sided Polygon
Each exterior angle = 360° / n; Each interior angle = 180° - (360° / n) = [(n - 2) * 180°] / n.
17
Logarithm Product and Power Rules
log_b(x y) = log_b(x) + log_b(y); log_b(x / y) = log_b(x) - log_b(y); log_b(x^k) = k log_b(x).
18
Work-Rate Combined Formula (Pipes and Workers)
If A finishes a task in t_A days and B in t_B days, combined daily rate = 1/t_A + 1/t_B; combined time = (t_A * t_B) / (t_A + t_B).
19
Formal Logic: Conditional, Converse, Inverse, Contrapositive
Conditional: P -> Q. Converse: Q -> P (not equivalent). Inverse: ~P -> ~Q (not equivalent). Contrapositive: ~Q -> ~P (strictly logically equivalent to P -> Q).
20
Letter Sequence Alpha-Numeric Position Strategy
Convert letters to 1-26 numerical positions (A=1, B=2 ... Z=26) and test for arithmetic differences, alternating steps, prime shifts, or rotational modulo 26 wraps.
21
Clock Face Angular Distance Calculation Formula
Minute hand advances 6° per minute. Hour hand advances 0.5° per minute (30° per hour). Angle = |30 H - 5.5 M|.
22
Painted Cube Slicing Rules (n x n x n)
Corner cubes (3 faces painted) = 8; Edge cubes (2 faces painted) = 12(n - 2); Face center cubes (1 face painted) = 6(n - 2)^2; Inner unpainted cubes = (n - 2)^3.
23
Principle of Inclusion-Exclusion for Two Sets
|A union B| = |A| + |B| - |A intersect B|; |A intersect B| = |A| + |B| - |A union B|.
24
Syllogistic Fallacy: Undistributed Middle
'All A are B. All C are B. Therefore all A are C' is invalid. The middle term (B) must be distributed in at least one premise to establish a valid link.
25
Classic Knights and Knaves (Truth-Teller vs Liar) Strategy
Test hypotheses by assuming a speaker tells the truth. If their statement creates a logical contradiction with other statements or conditions, the assumption is false.

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