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BCS Science, ICT & Mathematical Reasoning

Essential scientific laws, computer networking concepts, database terms, and quantitative formulas for BCS Preliminary.

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SI Unit of Electric Capacitance and Symbol

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SI Unit of Electric Capacitance and Symbol

Farad (F), defined as one coulomb of electric charge stored per one volt potential difference (1 F = 1 C/V).

SI Unit of Magnetic Flux and Magnetic Flux Density

Magnetic flux is measured in Weber (Wb); Magnetic flux density (magnetic field B) is measured in Tesla (T) (1 T = 1 Wb/m^2).

Difference Between Plant Cell Wall and Fungal Cell Wall Composition

Plant cell walls are made predominantly of cellulose, while fungal cell walls are made of chitin.

Universal Blood Donor and Universal Blood Recipient

O negative (O-) is the universal red cell donor; AB positive (AB+) is the universal red cell recipient.

Atmospheric Layer Where Weather Occurs vs Where Ozone Layer Resides

Weather occurs in the Troposphere (lowest layer, 0-12 km); the protective ozone layer is in the Stratosphere (15-35 km).

Boyle's Law vs Charles's Law Gas Relationships

Boyle's Law: Pressure is inversely proportional to volume at constant temperature (

P_{1} V_{1} = P_{2} V_{2}

). Charles's Law: Volume is directly proportional to absolute temperature at constant pressure (

V_{1} / T_{1} = V_{2} / T_{2}

Number of IPv4 Address Bits vs IPv6 Address Bits

IPv4 uses 32 bits (4 octets, 4.3 billion addresses); IPv6 uses 128 bits (hexadecimal notation, 3.4 x 10^38 addresses).

OSI 7-Layer Reference Model (Top to Bottom)

Layer 7: Application, Layer 6: Presentation, Layer 5: Session, Layer 4: Transport, Layer 3: Network, Layer 2: Data Link, Layer 1: Physical.

Primary Function of Transport Layer Protocols TCP vs UDP

TCP (Transmission Control Protocol) is connection-oriented, reliable, and ordered. UDP (User Datagram Protocol) is connectionless, lightweight, and unordered.

ACID Properties of Database Management Systems

Atomicity (all-or-nothing), Consistency (valid state preservation), Isolation (concurrent transaction independence), Durability (committed data survival).

Symmetric Key vs Asymmetric Key Cryptography

Symmetric: Single shared secret key for encryption and decryption (AES, DES). Asymmetric: Public key for encryption, private key for decryption (RSA, ECC).

Volatile vs Non-Volatile Primary Memory

RAM (Random Access Memory) is volatile (loses data on power loss); ROM (Read Only Memory) and flash memory are non-volatile.

Formula for the Sum of an Arithmetic Series

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

w h er e

a$ is the first term, $d$ is common difference, and $l$ is the last term.

Formula for the Sum of an Infinite Geometric Series (

∣ r ∣ < 1

)

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

w h er e

a$ is the first term and $r$ is the common ratio.

Quadratic Equation Roots Formula and Discriminant

For

a x^{2} + b x + c = 0

, roots are

x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

. Discriminant

D = b^{2} - 4 a c

: if

D > 0

two distinct real roots; if

D = 0

one repeated real root; if

D < 0

two complex conjugate roots.

Relationship Between HCF and LCM of Two Numbers

a

and

b

HCF (a, b) \times LCM (a, b) = a \times b

Formula for Permutations vs Combinations

^{n} P_{r} = \frac{n !}{( n - r )!}

$ (order matters); $

^{n} C_{r} = \frac{n !}{r ! ( n - r )!}

$ (order does not matter).

Compound Interest Formula

A = P (1 + \frac{r}{n})^{n t}

w h er e

A$ is final amount, $P

i s p r in c i p a l,

r$ is annual interest rate, $n$ is compounding frequency per year, and $t$ is time in years.

Area of Equilateral Triangle with Side Length

a

Area = \frac{3}{4} a^{2}

$ and height $h = \frac{\sqrt{3}}{2} a$.

Logarithm Change of Base Formula and Product Rule

lo g_{b} (a) = \frac{l o g _{c} ( a )}{l o g _{c} ( b )}

an d

lo g_{b} (x y) = lo g_{b} (x) + lo g_{b} (y)

;

lo g_{b} (x / y) = lo g_{b} (x) - lo g_{b} (y)

Pythagorean Theorem and Common Integer Triples

a^{2} + b^{2} = c^{2}

$ in right triangles. Common triples: $(3, 4, 5)

,

(5, 12, 13)

,

(7, 24, 25)

,

(8, 15, 17)

,

(9, 40, 41)$.

Probability Addition Rule for Any Two Events

A

and

B

P (A \cup B) = P (A) + P (B) - P (A \cap B)

$. If mutually exclusive, $P(A \cap B) = 0$.

Complement Rule and Law of Independent Events

P (A^{'}) = 1 - P (A)

. E v e n t s

an d

B$ are independent if and only if $

P (A \cap B) = P (A) \times P (B)

Mean, Median, and Mode Relationship in Moderately Skewed Distributions

Mode \approx 3 \times Median - 2 \times Mean

$ (Karl Pearson empirical relationship).

Sum of Interior Angles of an

n

-sided Convex Polygon

Sum = (n - 2) \times 18 0^{\circ}

$. Each interior angle in a regular $n

- g o ni s

\frac{( n - 2 ) \times 18 0 ^{\circ}}{n}

Number of Diagonals in an

n

-sided Polygon

Diagonals = \frac{n ( n - 3 )}{2}

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