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GED Oman Scientific Stream Core Formulas and Principles

Essential theorems, equations, and foundational formulas across Pure Mathematics, Physics, and Chemistry for the Oman General Education Diploma.

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Fundamental Theorem of Calculus (Part 1 and 2)
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1
Fundamental Theorem of Calculus (Part 1 and 2)
Part 1: If f is continuous on [a, b], then d/dx [integral from a to x of f(t) dt] = f(x). Part 2: integral from a to b of f(x) dx = F(b) - F(a), where F'(x) = f(x).
2
Derivatives of Primary Trigonometric Functions
d/dx [sin(x)] = cos(x); d/dx [cos(x)] = -sin(x); d/dx [tan(x)] = sec^2(x).
3
Chain Rule for Composite Functions
d/dx [f(g(x))] = f'(g(x)) g'(x); in differential notation: dy/dx = (dy/du) (du/dx).
4
Product and Quotient Rules of Differentiation
Product: (u v)' = u' v + u v'. Quotient: (u / v)' = (u' v - u * v') / v^2.
5
Integration by Parts Formula
integral of u dv = u * v - integral of v du, derived from the product rule of differentiation.
6
Area Between Two Continuous Curves y = f(x) and y = g(x)
Area = integral from a to b of [f(x) - g(x)] dx, where f(x) >= g(x) across the closed interval [a, b].
7
Volume of Revolution (Disk Method)
V = pi * integral from a to b of [f(x)]^2 dx for rotation around the x-axis.
8
Standard Equation of a Circle with Center (h, k)
(x - h)^2 + (y - k)^2 = r^2, where r is the radius and (h, k) is the coordinate of the center.
9
Newton's Second Law of Motion
Sigma F = m * a = dp/dt; net external force equals mass times acceleration or time rate of change of linear momentum.
10
Work-Energy Theorem
W_net = Delta KE = 0.5 m v_f^2 - 0.5 m v_i^2; net work done on an object equals its change in kinetic energy.
11
Law of Conservation of Linear Momentum
In an isolated system with no external net force: Sigma p_initial = Sigma p_final (m1v1i + m2v2i = m1v1f + m2v2f).
12
Coulomb's Law of Electrostatic Force
F = k_e |q1 q2| / r^2, where k_e = 8.99 10^9 Nm^2/C^2 and r is the center-to-center separation distance.
13
Ohm's Law and Electrical Power Equations
Potential difference V = I R; Electrical Power P = V I = I^2 * R = V^2 / R.
14
Equivalent Resistance in Series vs Parallel Circuits
Series: R_eq = R1 + R2 + ... + Rn. Parallel: 1 / R_eq = 1 / R1 + 1 / R2 + ... + 1 / Rn.
15
Faraday's Law of Electromagnetic Induction
emf = -N * (Delta Phi_B / Delta t); induced electromotive force equals the negative time rate of change of magnetic flux through N loops.
16
Lenz's Law Principle
The polarity of an induced electromotive force always produces an electric current whose magnetic field opposes the change in magnetic flux that induced it.
17
Snell's Law of Wave Refraction
n1 sin(theta1) = n2 sin(theta2); critical angle for total internal reflection: sin(theta_c) = n2 / n1 (when n1 > n2).
18
Photoelectric Effect Equation (Einstein)
E = h f = Phi + KE_max, where h is Planck's constant (6.626 10^-34 Js), Phi is the work function, and KE_max = q V_stop.
19
Ideal Gas Law Equation of State
P V = n R T, where R = 0.0821 Latm/(molK) or 8.314 J/(molK), with absolute temperature in Kelvin.
20
Le Chatelier's Principle in Chemical Equilibrium
If a dynamic equilibrium is disturbed by changing concentration, pressure, or temperature, the position of equilibrium moves to counteract the change.
21
Arrhenius Equation for Reaction Kinetics
k = A e^(-E_a / (R T)), relating the rate constant k to activation energy E_a, gas constant R, and absolute temperature T.
22
pH, pOH, and Ion-Product Constant of Water (K_w)
pH = -log10[H+]; pOH = -log10[OH-]; pH + pOH = 14 at 25 degrees Celsius (where K_w = [H+][OH-] = 1.0 * 10^-14).
23
Henderson-Hasselbalch Equation for Buffer Solutions
pH = pKa + log10([A-] / [HA]), where [A-] is the conjugate base concentration and [HA] is the weak acid concentration.
24
Standard Cell Potential and Gibbs Free Energy Relation
Delta G_standard = -n F E_cell_standard, where n is moles of electrons transferred and F is Faraday's constant (96,485 C/mol).
25
Standard Molar Volume of an Ideal Gas at STP
One mole of any ideal gas occupies 22.4 liters at Standard Temperature and Pressure (0 degrees Celsius and 1 atm).

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