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Tawjihi Scientific Stream Core Formulas and Rules

Essential formulas and key rules across Mathematics, Physics, Chemistry, and English for Jordan's Tawjihi Scientific Stream.

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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 sin(kx) and cos(kx)
d/dx [sin(kx)] = k cos(kx); d/dx [cos(kx)] = -k sin(kx).
5
Pythagorean Trigonometric Identity
sin^2(x) + cos^2(x) = 1; 1 + tan^2(x) = sec^2(x); 1 + cot^2(x) = csc^2(x).
6
Double Angle Formulas for sin(2x) and cos(2x)
sin(2x) = 2 sin(x) cos(x); cos(2x) = cos^2(x) - sin^2(x) = 2 cos^2(x) - 1 = 1 - 2 sin^2(x).
7
Fundamental Theorem of Calculus (Definite Integral)
integral from a to b of f(x) dx = F(b) - F(a), where F'(x) = f(x).
8
Newton's Second Law of Motion
Sigma F = m * a = dp/dt, where force equals mass times acceleration or rate of change of linear momentum.
9
Law of Conservation of Linear Momentum
In a closed, isolated system with no external net forces: Sigma p_initial = Sigma p_final.
10
Work-Energy Theorem
W_net = Delta KE = 0.5 m v_f^2 - 0.5 m v_i^2.
11
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.
12
Ohm's Law and Electrical Power Relations
V = I R; Power P = V I = I^2 * R = V^2 / R.
13
Magnetic Force on a Moving Charge (Lorentz Force)
F_B = q (v x B); magnitude |F_B| = |q| v B sin(theta).
14
Faraday's Law of Electromagnetic Induction
EMF = -N * (d Phi_B / dt), where the negative sign denotes Lenz's Law of opposing induced current.
15
Ideal Gas Law Equation of State
P V = n R T, where R = 0.0821 Latm/(molK) or 8.314 J/(molK).
16
Molarity (M) Definition and Dilution Equation
M = moles of solute / liters of solution; Dilution formula: M1 V1 = M2 V2.
17
pH and pOH Definitions in Aqueous Solutions
pH = -log10[H3O+]; pOH = -log10[OH-]; at 25 °C, pH + pOH = 14.00.
18
Buffer Solution Henderson-Hasselbalch Equation
pH = pKa + log10([Conjugate Base A-] / [Weak Acid HA]).
19
Gibbs Free Energy Equation and Spontaneity Criterion
Delta G = Delta H - T * Delta S; spontaneous when Delta G < 0 at constant temperature and pressure.
20
First-Order Reaction Integrated Rate Law and Half-Life
ln[A]_t = -k * t + ln[A]_0; Half-life t_(1/2) = ln(2) / k approx 0.693 / k.
21
Tawjihi English: Third Conditional Form and Function
If + past perfect (had + V3), would have + V3. Expresses an unreal past condition and its hypothetical past result.
22
Tawjihi English: Reported Speech Tense Backshift Rules
Present Simple -> Past Simple; Present Perfect -> Past Perfect; Past Simple -> Past Perfect; will -> would; can -> could.
23
Tawjihi English: Cleft Sentences for Emphasis
'The person who... was [Name]' or 'It was [Subject] that/who [action]...' to focus emphasis on a specific clause element.
24
Tawjihi English: Passive Voice Construction Formula
Object + appropriate tense form of auxiliary 'to be' + Past Participle (V3) (+ by agent).
25
Tawjihi English: Defining vs Non-Defining Relative Clauses
Defining: essential information, no commas, can use 'that'. Non-defining: extra incidental info, separated by commas, cannot use 'that'.

Tawjihi (General Secondary) in Jordan

In Jordan, Tawjihi (General Secondary) is part of: Secondary school.

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