📖NCTB Curriculum Aligned Mathematical Reference Sheets

Complete Board Exam Formula Sheet

All essential equations, scientific constants, and problem-solving rules for Physics, Chemistry, Higher Math, General Math, ICT, and Biology. Copy plain text or LaTeX codes with one click, verify steps in live calculators, or print a concise exam cheat sheet.

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Dedicated Subject Formula Sheets

6 Subjects Covered

General Mathematicsসাধারণ গণিত

📐59 Formulas

Higher Mathematicsউচ্চতর গণিত

💻12 Formulas

Information & Communication Technology (ICT)তথ্য ও যোগাযোগ প্রযুক্তি

🧬14 Formulas

Biologyজীববিজ্ঞান

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Showing 218 of 218 formulas

HSCChapter 3

De Morgan's First Law

ডি মরগানের প্রথম সূত্র • Number Systems & Digital Devices

\overline{A + B} = \overline{A} \cdot \overline{B}

NOT(A + B) = NOT(A) * NOT(B)

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HSCChapter 3

De Morgan's Second Law

ডি মরগানের দ্বিতীয় সূত্র • Number Systems & Digital Devices

\overline{A \cdot B} = \overline{A} + \overline{B}

NOT(A * B) = NOT(A) + NOT(B)

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HSCChapter 3

Half Adder Sum

হাফ অ্যাডার যোগফল (Sum) • Number Systems & Digital Devices

S = A \oplus B = \overline{A}B + A\overline{B}

S = A XOR B = NOT(A)B + ANOT(B)

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HSCChapter 3

Half Adder Carry

হাফ অ্যাডার ক্যারি (Carry) • Number Systems & Digital Devices

C = A \cdot B

C = A * B

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HSCChapter 3

Full Adder Sum

ফুল অ্যাডার যোগফল (Sum) • Number Systems & Digital Devices

S = A \oplus B \oplus C_{in}

S = A XOR B XOR C_in

💡 Condition: Sum output bit when adding three binary inputs (A, B, Cin) in a Full Adder circuit.

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HSCChapter 3

Full Adder Carry-out

ফুল অ্যাডার ক্যারি (Carry-out) • Number Systems & Digital Devices

C_{out} = AB + BC_{in} + C_{in}A = AB + C_{in}(A \oplus B)

C_out = AB + BC_in + C_inA = AB + C_in(A XOR B)

💡 Condition: Carry output generated to higher bit positions in Full Adder addition.

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HSCChapter 3

Positional Number System Expansion

স্থানিক সংখ্যা পদ্ধতির সাধারণ বিস্তার • Number Systems & Digital Devices

N = \sum_{i=-m}^{n-1} d_i \cdot r^i = d_{n-1}r^{n-1} + \dots + d_0 r^0 + d_{-1}r^{-1} + \dots + d_{-m}r^{-m}

N = Σ_i=-m^n-1 d_i * r^i = d_n-1r^n-1 + dots + d_0 r^0 + d_-1r^-1 + dots + d_-mr^-m

💡 Condition: General base-r polynomial expansion formula to compute the decimal equivalent value.

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HSCChapter 3

n-bit Two's Complement Range

২-এর পরিপূরকে n-বিট সংখ্যার সীমা • Number Systems & Digital Devices

\text{Range} = -2^{n-1} \text{ to } +(2^{n-1} - 1)

Range = -2^n-1 to +(2^n-1 - 1)

💡 Condition: Represents the range of signed integers representable in n bits (e.g., -128 to +127 for 8-bit registers).

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HSCChapter 3

Boolean Absorption Laws

বুলিয়ান শোষণ উপপাদ্য • Number Systems & Digital Devices

A + AB = A, \quad A(A + B) = A, \quad A + \overline{A}B = A + B

A + AB = A, A(A + B) = A, A + NOT(A)B = A + B

💡 Condition: Reduces logic expression complexity by eliminating redundant literals.

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HSCChapter 3

Consensus Theorem

কনসেনসাস উপপাদ্য • Number Systems & Digital Devices

AB + \overline{A}C + BC = AB + \overline{A}C

AB + NOT(A)C + BC = AB + NOT(A)C

💡 Condition: Eliminates redundant terms in SOP logic expressions where the BC term is redundant.

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HSCChapter 3

Encoder and Decoder Line Relations

এনকোডার ও ডিকোডার লাইন সম্পর্ক • Number Systems & Digital Devices

\text{Encoder: } 2^n \to n, \quad \text{Decoder: } n \to 2^n

Encoder: 2^n to n, Decoder: n to 2^n

💡 Condition: Input-to-output channel ratios for standard binary Encoders and Decoders.

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HSCChapter 3

Multiplexer Select Line Formula

মাল্টিপ্লেক্সার নির্বাচন লাইন সূত্র • Number Systems & Digital Devices

2^n \text{ Data Inputs} \implies n \text{ Select Lines} \to 1 \text{ Output}

2^n Data Inputs implies n Select Lines to 1 Output

💡 Condition: Determines the number of select lines needed to route 2^n input data channels to 1 output.

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HSCChapter 2 (Paper 1)

Resultant Magnitude

লব্ধির মান • Vectors

R = \sqrt{P^2 + Q^2 + 2PQ\cos\alpha}

R = sqrt(P^2 + Q^2 + 2PQcosα)

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HSCChapter 2 (Paper 1)

Dot Product

স্কেলার গুণন • Vectors

\vec{A} \cdot \vec{B} = AB\cos\theta

A * B = ABcosθ

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HSCChapter 2 (Paper 1)

Cross Product

ভেক্টর গুণন • Vectors

|\vec{A} \times \vec{B}| = AB\sin\theta

|A * B| = ABsinθ

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HSCChapter 3 (Paper 1)

Maximum Height

সর্বোচ্চ উচ্চতা • Dynamics & Projectile Motion

H = \frac{v_0^2 \sin^2\theta}{2g}

H = (v_0^2 sin^2θ)/(2g)

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HSCChapter 3 (Paper 1)

Time of Flight

বিচরণকাল • Dynamics & Projectile Motion

T = \frac{2v_0 \sin\theta}{g}

T = (2v_0 sinθ)/(g)

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HSCChapter 3 (Paper 1)

Horizontal Range

অনুভূমিক পাল্লা • Dynamics & Projectile Motion

R = \frac{v_0^2 \sin(2\theta)}{g}

R = (v_0^2 sin(2θ))/(g)

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HSCChapter 4 (Paper 1)

Road Banking Angle

ব্যাংকিং কোণ • Newtonian Mechanics

\tan\theta = \frac{v^2}{rg}

tanθ = (v^2)/(rg)

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HSCChapter 4 (Paper 1)

Moment of Inertia

জড়তার ভ্রামক • Newtonian Mechanics

I = \sum m_i r_i^2 = M K^2

I = Σ m_i r_i^2 = M K^2

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HSCChapter 8 (Paper 1)

Pendulum Period

দোলনকাল (সরল দোলক) • Periodic Motion

T = 2\pi \sqrt{\frac{L}{g}}

T = 2π sqrt((L)/(g))

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HSCChapter 8 (Paper 1)

Spring Period

দোলনকাল (স্প্রিং) • Periodic Motion

T = 2\pi \sqrt{\frac{m}{k}}

T = 2π sqrt((m)/(k))

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HSCChapter 6 (Paper 1)

Newton's Law of Gravitation

মহাকর্ষীয় বল সূত্র • Gravitation & Gravity

F = G \frac{m_1 m_2}{r^2}

F = G (m_1 m_2)/(r^2)

💡 Condition: Universal gravitational force between two point masses where G = 6.673 x 10^-11 N m^2 kg^-2.

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HSCChapter 6 (Paper 1)

Gravity at Altitude h

উচ্চতায় অভিকর্ষজ ত্বরণ • Gravitation & Gravity

g_h = g \left(1 - \frac{2h}{R}\right) = g \frac{R^2}{(R+h)^2}

g_h = g (1 - (2h)/(R)) = g (R^2)/((R+h)^2)

💡 Condition: Gravitational acceleration at altitude h above Earth surface.

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Three Golden Rules for Flawless Formula Application in Board Exams

Guaranteed best practices to score full marks in numerical creative questions

1. Standardize SI Units Before Substitution

Always convert given parameters into standard SI units (meters, seconds, kilograms, moles) before substituting into formulas. Substituting centimeters or kilometers directly leads to order-of-magnitude calculation errors.

2. Validate Boundary Conditions

Never apply equations outside their physical constraints. For example, $s = ut + \frac12at^2$ strictly requires constant acceleration; for uniform velocity, use $s = vt$.

3. Verify Roots with Scientific Calculator

After working through algebraic derivations on your paper, use the SOLVE and EQN modes on approved Casio fx-991EX or fx-991MS calculators to cross-check roots and eliminate arithmetic slip-ups.

Dedicated Subject Formula Sheets

De Morgan's First Law

De Morgan's Second Law

Half Adder Sum

Half Adder Carry

Full Adder Sum

Full Adder Carry-out

Positional Number System Expansion

n-bit Two's Complement Range

Boolean Absorption Laws

Consensus Theorem

Encoder and Decoder Line Relations

Multiplexer Select Line Formula

Resultant Magnitude

Dot Product

Cross Product

Maximum Height

Time of Flight

Horizontal Range

Road Banking Angle

Moment of Inertia

Pendulum Period

Spring Period

Newton's Law of Gravitation

Gravity at Altitude h

Three Golden Rules for Flawless Formula Application in Board Exams

1. Standardize SI Units Before Substitution

2. Validate Boundary Conditions

3. Verify Roots with Scientific Calculator

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