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30 cardsWazari Exam (Iraq Baccalaureate) - Scientific Branch

Wazari Scientific Branch: More Formulas and Key Facts

Thirty revision cards for the Iraqi scientific branch: calculus, vectors, circuits, modern physics, equilibrium and genetics.

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Derivative of

x^{n}

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Wazari Exam (Iraq Baccalaureate) - Scientific Branch mock tests →

Derivative of

x^{n}

\frac{d}{d x} x^{n} = n x^{n - 1}

; the derivative of a constant is 0.

Gradient of a tangent

The gradient of the tangent at

x = a

f^{'} (a)

Stationary points

Solve

f^{'} (x) = 0

; use the sign of

f^{'}

(or

f^{''}

) to find maxima and minima.

Integral of

x^{n}

\int x^{n} d x = \frac{x ^{n + 1}}{n + 1} + C

for

n \neq = - 1

Area between two curves

\int_{a}^{b} (f (x) - g (x)) d x

where

f \geq g

[a, b]

Modulus of a complex number

∣ a + bi ∣ = a^{2} + b^{2}

De Moivre's theorem

[r (cos θ + i sin θ)]^{n} = r^{n} (cos n θ + i sin n θ)

Determinant of a 2 x 2 matrix

det (a c b d) = a d - b c

;

det (k A) = k^{2} det A

Dot product

u \cdot v = u_{1} v_{1} + u_{2} v_{2} = ∣ u ∣∣ v ∣ cos θ

Sum of an arithmetic series

S_{n} = \frac{n}{2} (2 a + (n - 1) d)

Sum to infinity of a geometric series

S_{\infty} = \frac{a}{1 - r}

when

∣ r ∣ < 1

Binomial probability

P (X = k) = (k n) p^{k} (1 - p)^{n - k}

Ohm's law and power

V = I R

and

P = V I = I^{2} R = V^{2} / R

Resistors in series and parallel

Series:

R = R_{1} + R_{2}

. Parallel:

1/ R = 1/ R_{1} + 1/ R_{2}

Energy stored in a capacitor

E = \frac{1}{2} C V^{2}

;

Q = C V

Force on a current-carrying wire

F = B I L sin θ

Induced e.m.f. of a moving rod

ε = B Lv

for a rod moving at right angles to the field.

Impedance in a series RLC circuit

Z = R^{2} + (X_{L} - X_{C})^{2}

, with

X_{L} = 2 π f L

and

X_{C} = 1/ (2 π f C)

Lens equation

1/ f = 1/ u + 1/ v

Photoelectric equation

E_{k} = h f - ϕ

Half-life

After

n

half-lives the fraction left is

(1/2)^{n}

Moles

n = m / M

; concentration

c = n / V

p H = - lo g [H^{+}]

; at 25 °C

p H + pO H = 14

Equilibrium constant

For

a A + b B ⇌ c C + d D

K_{c} = \frac{[ C ] ^{c} [ D ] ^{d}}{[ A ] ^{a} [ B ] ^{b}}

Le Chatelier's principle

A system at equilibrium shifts to oppose any change in concentration, pressure or temperature.

Standard cell potential

E_{ce l l}^{\circ} = E_{c a t h o d e}^{\circ} - E_{an o d e}^{\circ}

Faraday's law

Charge needed

Q = n z F

, with

F = 96500

C/mol.

Chargaff's rule

In DNA, A = T and G = C.

Hardy-Weinberg equation

p^{2} + 2 pq + q^{2} = 1

and

p + q = 1

Ten percent rule

About 10 percent of the energy passes from one trophic level to the next.

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