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Thanaweya Qatar Scientific Stream Core Formulas and Principles

Essential formulas, theorems, and principles across Advanced Mathematics, Physics, and Chemistry for the Qatar Secondary School Certificate.

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Product Rule of Differentiation
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1
Product Rule of Differentiation
d/dx [f(x) g(x)] = f'(x) g(x) + f(x) * g'(x).
2
Quotient Rule of Differentiation
d/dx [f(x) / g(x)] = [f'(x) g(x) - f(x) g'(x)] / [g(x)]^2 for g(x) != 0.
3
Chain Rule for Composite Functions
d/dx [f(g(x))] = f'(g(x)) * g'(x).
4
Derivative of Natural Logarithm ln(u(x))
d/dx [ln(u(x))] = u'(x) / u(x) for u(x) > 0.
5
Derivative of Exponential Functions e^(kx) and a^x
d/dx [e^(kx)] = k e^(kx); d/dx [a^x] = a^x ln(a) for a > 0, a != 1.
6
Integration by Parts Formula
integral of u dv = u * v - integral of v du, where u and v are differentiable functions of x.
7
Area Between Two 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) on [a, b].
8
Volume of Solid of Revolution (Disk Method)
V = pi * integral from a to b of [R(x)]^2 dx for rotation about a horizontal line.
9
Newton's Second Law of Motion
Sigma F = m * a = dp/dt, where net force equals mass times acceleration or time rate of change of momentum.
10
Law of Conservation of Linear Momentum
In a closed, isolated system with no external net forces: Sigma p_initial = Sigma p_final.
11
Work-Energy Theorem
W_net = Delta KE = 0.5 m v_f^2 - 0.5 m v_i^2.
12
Coulomb's Law of Electrostatic Force
F = k_e |q1 q2| / r^2, where k_e = 1 / (4 pi epsilon_0) approx 8.99 10^9 Nm^2/C^2.
13
Ohm's Law and Electrical Power Equations
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 + ...; Parallel: 1 / R_eq = 1 / R1 + 1 / R2 + ...
15
Faraday's Law of Electromagnetic Induction
EMF = -N (dPhi_B / dt), where N is number of turns and Phi_B = B A * cos(theta).
16
Photoelectric Effect Energy Equation (Einstein)
KE_max = h * f - Phi, where h is Planck's constant, f is photon frequency, and Phi is work function.
17
Snell's Law of Refraction
n1 sin(theta1) = n2 sin(theta2), where n is refractive index and theta is angle to normal.
18
Ideal Gas Law Equation
P V = n R T, where R = 0.0821 Latm/(molK) or 8.314 J/(molK).
19
pH and pOH Definitions and Pure Water Equilibrium
pH = -log10[H3O+]; pOH = -log10[OH-]; pH + pOH = 14.00 at 25°C (Kw = 1.0 * 10^-14).
20
Henderson-Hasselbalch Equation for Acidic Buffers
pH = pKa + log10([Conjugate Base] / [Weak Acid]).
21
Gibbs Free Energy Equation and Spontaneity
Delta G = Delta H - T * Delta S; spontaneous when Delta G < 0; at equilibrium when Delta G = 0.
22
First Law of Thermodynamics
Delta U = Q - W (or Delta U = Q + W depending on work sign convention), where U is internal energy.
23
Arrhenius Equation for Reaction Rate Constant
k = A e^(-E_a / (R T)), where E_a is activation energy and A is frequency factor.
24
Standard Cell Potential and Free Energy Relationship
Delta G° = -n F E°_cell, where F is Faraday's constant (96,485 C/mol e-) and n is moles of electrons.
25
Le Chatelier's Principle
If a dynamic equilibrium system is disturbed by changing T, P, or concentration, the system shifts to counteract that change.

Qatar Senior Secondary Certificate (Thanaweya) in Qatar

In Qatar, Qatar Senior Secondary Certificate (Thanaweya) is part of: Secondary school.

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