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30 cardsSaudi Secondary School Certificate

Secondary Certificate: Maths, Science and Computing Facts

Thirty cards covering calculus, matrices, modern physics, chemistry and computer science for the Saudi secondary certificate.

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Derivative of a power

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Derivative of a power

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

Product rule

(uv)^{'} = u^{'} v + u v^{'}

Chain rule

\frac{d y}{d x} = \frac{d y}{d u} \cdot \frac{d u}{d x}

Stationary points

Solve

f^{'} (x) = 0

; a sign change from positive to negative gives a maximum.

Definite integral

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

Area between curves

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

where

f \geq g

Logarithm laws

lo g (ab) = lo g a + lo g b

;

lo g (a / b) = lo g a - lo g b

Double angle

sin 2 θ = 2 sin θ cos θ

Discriminant

b^{2} - 4 a c

: positive gives two real roots; zero one; negative none.

Arithmetic series

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

Infinite geometric series

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

for

∣ r ∣ < 1

Determinant of 2 x 2

a d - b c

Inverse of a 2 x 2 matrix

\frac{1}{a d - b c} (d - c - b a)

Dot product

Sum of products of components; zero for perpendicular vectors.

Capacitor energy

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

Induced e.m.f.

ε = B Lv

Photoelectric effect

E_{k} = h f - ϕ

Half-life

After n half-lives the fraction left is

(1/2)^{n}

Equilibrium constant

Products over reactants, each raised to its coefficient.

Standard cell potential

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

Binary to decimal

Add the place values (128, 64, 32 ...) of the 1 bits.

Number of values with n bits

2^{n}

Usable hosts in a /n network

2^{32 - n} - 2

Binary search

Needs at most

⌊ lo g_{2} n ⌋ + 1

comparisons on a sorted list.

Stack and queue

Stack: last in, first out. Queue: first in, first out.

Python slicing

s[a:b] includes index a and excludes index b.

Floor division and modulus

7 // 2 = 3 and 7 % 2 = 1.

SQL basics

SELECT reads rows; WHERE filters; INSERT adds; UPDATE changes; DELETE removes.

Hashing passwords

A hash is a one-way function that stores a fixed-length value instead of the password.

Phishing

A message that imitates a trusted organisation to steal information.

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