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General Mathematics Formulas

সাধারণ গণিত

Essential SSC General Math formula reference including algebraic expansions, arithmetic & geometric series, trigonometry, and statistics.

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HSC (Paper 1) - Chapter 5: Permutations & Combinations

2 Formulas
HSCChapter 5 (Paper 1)

Permutation Formula

বিন্যাস সূত্র • Permutations & Combinations

nPr=n!(n−r)!^nP_r = \frac{n!}{(n-r)!}
^nP_r = (n!)/((n-r)!)
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HSCChapter 5 (Paper 1)

Combination Formula

সমাবেশ সূত্র • Permutations & Combinations

nCr=n!r!(n−r)!^nC_r = \frac{n!}{r!(n-r)!}
^nC_r = (n!)/(r!(n-r)!)
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HSC (Paper 2) - Chapter 10: Probability Theory

2 Formulas
HSCChapter 10 (Paper 2)

Probability Definition

মৌলিক সম্ভাবনা • Probability Theory

P(A)=n(A)n(S)P(A) = \frac{n(A)}{n(S)}
P(A) = (n(A))/(n(S))
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HSCChapter 10 (Paper 2)

Addition Rule

সম্ভাবনার যোগসূত্র • Probability Theory

P(A∪B)=P(A)+P(B)−P(A∩B)P(A \cup B) = P(A) + P(B) - P(A \cap B)
P(A cup B) = P(A) + P(B) - P(A cap B)
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SSC - Chapter 3: Algebraic Expressions

5 Formulas
SSCChapter 3

Square Expansions & Identities

বর্গের মৌলিক সূত্র ও অনুসিদ্ধান্ত • Algebraic Expressions

(a±b)2=a2±2ab+b2,a2+b2=(a+b)2−2ab=(a−b)2+2ab(a \pm b)^2 = a^2 \pm 2ab + b^2, \quad a^2 + b^2 = (a+b)^2 - 2ab = (a-b)^2 + 2ab
(a ± b)^2 = a^2 ± 2ab + b^2, a^2 + b^2 = (a+b)^2 - 2ab = (a-b)^2 + 2ab

💡 Condition: Fundamental binomial square expansions and algebraic corollaries.

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SSCChapter 3

Difference of Squares & 4ab Formula

বর্গের বিয়োগফল ও ৪ab সূত্র • Algebraic Expressions

a2−b2=(a+b)(a−b),4ab=(a+b)2−(a−b)2,ab=(a+b2)2−(a−b2)2a^2 - b^2 = (a+b)(a-b), \quad 4ab = (a+b)^2 - (a-b)^2, \quad ab = \left(\frac{a+b}{2}\right)^2 - \left(\frac{a-b}{2}\right)^2
a^2 - b^2 = (a+b)(a-b), 4ab = (a+b)^2 - (a-b)^2, ab = ((a+b)/(2))^2 - ((a-b)/(2))^2

💡 Condition: Difference of squares factorization and expression of product ab as difference of two squares.

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SSCChapter 3

Three-Term Square Expansion

তিন পদের বর্গের সূত্র • Algebraic Expressions

(a+b+c)2=a2+b2+c2+2(ab+bc+ca)(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)
(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)

💡 Condition: Trinomial square expansion identity relating individual squares to pairwise products.

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SSCChapter 3

Cube Expansions & Corollaries

ঘনফল ও ঘনের অনুসিদ্ধান্ত • Algebraic Expressions

(a±b)3=a3±3a2b+3ab2±b3=a3±b3±3ab(a±b)(a \pm b)^3 = a^3 \pm 3a^2 b + 3ab^2 \pm b^3 = a^3 \pm b^3 \pm 3ab(a \pm b)
(a ± b)^3 = a^3 ± 3a^2 b + 3ab^2 ± b^3 = a^3 ± b^3 ± 3ab(a ± b)

💡 Condition: Binomial cube expansions and calculation corollaries.

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SSCChapter 3

Sum & Difference of Cubes Factorization

দুটি ঘনের যোগফল ও বিয়োগফল (উৎপাদক) • Algebraic Expressions

a3±b3=(a±b)(a2∓ab+b2)a^3 \pm b^3 = (a \pm b)(a^2 \mp ab + b^2)
a^3 ± b^3 = (a ± b)(a^2 ∓ ab + b^2)

💡 Condition: Factorization identities for the sum and difference of two cubic terms.

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SSC - Chapter 9: Trigonometric Ratios & Distances

2 Formulas
SSCChapter 9

Fundamental Identity

মৌলিক অভেদ • Trigonometric Ratios & Distances

sin⁡2θ+cos⁡2θ=1,1+tan⁡2θ=sec⁡2θ\sin^2\theta + \cos^2\theta = 1, \quad 1 + \tan^2\theta = \sec^2\theta
sin^2θ + cos^2θ = 1, 1 + tan^2θ = sec^2θ
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SSCChapter 9

Height Equation

উচ্চতা সূত্র • Trigonometric Ratios & Distances

h=d⋅tan⁡θh = d \cdot \tan\theta
h = d * tanθ
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SSC - Chapter 16: Mensuration (2D & 3D Solids)

5 Formulas
SSCChapter 16

Heron's Formula

হ্যারনের ক্ষেত্রফল সূত্র • Mensuration (2D & 3D Solids)

Area=s(s−a)(s−b)(s−c)\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}
Area = sqrt(s(s-a)(s-b)(s-c))
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SSCChapter 16

Cylinder Volume

সিলিন্ডারের আয়তন • Mensuration (2D & 3D Solids)

V=πr2hV = \pi r^2 h
V = π r^2 h
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SSCChapter 16

Heron's Formula for Triangle Area

বিষমবাহু ত্রিভুজ ও হেরনের সূত্র • Mensuration (2D & 3D Solids)

A=s(s−a)(s−b)(s−c),s=a+b+c2A = \sqrt{s(s-a)(s-b)(s-c)}, \quad s = \frac{a+b+c}{2}
A = sqrt(s(s-a)(s-b)(s-c)), s = (a+b+c)/(2)

💡 Condition: Heron's formula to find triangle area given three side lengths and semi-perimeter s.

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SSCChapter 16

Equilateral & Isosceles Triangle Area

সমবাহু ও সমদ্বিবাহু ত্রিভুজের ক্ষেত্রফল • Mensuration (2D & 3D Solids)

সমবাহু: A=34a2,সমদ্বিবাহু: A=b44a2−b2\text{সমবাহু: } A = \frac{\sqrt{3}}{4}a^2, \quad \text{সমদ্বিবাহু: } A = \frac{b}{4}\sqrt{4a^2 - b^2}
সমবাহু: A = fracsqrt(3)4a^2, সমদ্বিবাহু: A = (b)/(4)sqrt(4a^2 - b^2)

💡 Condition: Dedicated area formulas for equilateral and isosceles triangles.

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SSCChapter 16

Cylinder & Sphere Volume and Surface Area

বেলন ও গোলকের আয়তন ও ক্ষেত্রফল • Mensuration (2D & 3D Solids)

বেলন: V=πr2h,  A=2πr(r+h);গোলক: V=43πr3,  A=4πr2\text{বেলন: } V = \pi r^2 h, \; A = 2\pi r(r+h); \quad \text{গোলক: } V = \frac{4}{3}\pi r^3, \; A = 4\pi r^2
বেলন: V = π r^2 h, ; A = 2π r(r+h); গোলক: V = (4)/(3)π r^3, ; A = 4π r^2

💡 Condition: Volume and total surface area formulas for cylinders and spherical solids.

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SSC - Chapter 17: Statistics (Mean, Median & Mode)

3 Formulas
SSCChapter 17

Step-Deviation Mean

সংক্ষিপ্ত গড় • Statistics (Mean, Median & Mode)

xˉ=a+(∑fiuin)×h\bar{x} = a + \left( \frac{\sum f_i u_i}{n} \right) \times h
barx = a + ( (Σ f_i u_i)/(n) ) * h
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SSCChapter 17

Grouped Median

মধ্যক সূত্র • Statistics (Mean, Median & Mode)

Median=L+(n2−Fcfm)×h\text{Median} = L + \left( \frac{\frac{n}{2} - F_c}{f_m} \right) \times h
Median = L + ( (fracn)/(2) - F_cf_m ) * h
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SSCChapter 17

Grouped Mode

প্রচুরক সূত্র • Statistics (Mean, Median & Mode)

Mode=L+(f1f1+f2)×h\text{Mode} = L + \left( \frac{f_1}{f_1 + f_2} \right) \times h
Mode = L + ( (f_1)/(f_1 + f_2) ) * h
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SSC - Chapter 4: Exponents and Logarithms

2 Formulas
SSCChapter 4

Laws of Indices / Exponents

সূচকের মৌলিক সূত্রাবলী • Exponents and Logarithms

am⋅an=am+n,aman=am−n,(am)n=amn,a0=1,a−n=1ana^m \cdot a^n = a^{m+n}, \quad \frac{a^m}{a^n} = a^{m-n}, \quad (a^m)^n = a^{mn}, \quad a^0 = 1, \quad a^{-n} = \frac{1}{a^n}
a^m * a^n = a^m+n, (a^m)/(a^n) = a^m-n, (a^m)^n = a^mn, a^0 = 1, a^-n = (1)/(a^n)

💡 Condition: Fundamental laws of powers and integer/fractional exponents.

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SSCChapter 4

Laws of Logarithms & Base Change

লগারিদমের মৌলিক সূত্র ও ভিত্তি পরিবর্তন • Exponents and Logarithms

log⁡a(MN)=log⁡aM+log⁡aN,log⁡a(MN)=log⁡aM−log⁡aN,log⁡a(Mp)=plog⁡aM,log⁡ab=log⁡cblog⁡ca\log_a(MN) = \log_a M + \log_a N, \quad \log_a\left(\frac{M}{N}\right) = \log_a M - \log_a N, \quad \log_a(M^p) = p\log_a M, \quad \log_a b = \frac{\log_c b}{\log_c a}
log_a(MN) = log_a M + log_a N, log_a((M)/(N)) = log_a M - log_a N, log_a(M^p) = plog_a M, log_a b = (log_c b)/(log_c a)

💡 Condition: Product, quotient, power rules of logarithms and the change of base formula.

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SSC - Chapter 13: Finite Series (Arithmetic & Geometric)

5 Formulas
SSCChapter 13

nth Term of Arithmetic Progression (AP)

সমান্তর ধারার n-তম পদ • Finite Series (Arithmetic & Geometric)

Tn=a+(n−1)dT_n = a + (n-1)d
T_n = a + (n-1)d

💡 Condition: Formula for the nth term of an arithmetic sequence with first term a and common difference d.

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SSCChapter 13

Sum of First n Terms of AP

সমান্তর ধারার n পদের সমষ্টি • Finite Series (Arithmetic & Geometric)

Sn=n2[2a+(n−1)d]=n2(a+l)S_n = \frac{n}{2}[2a + (n-1)d] = \frac{n}{2}(a + l)
S_n = (n)/(2)[2a + (n-1)d] = (n)/(2)(a + l)

💡 Condition: Total sum of first n terms of arithmetic series given difference d or last term l.

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SSCChapter 13

nth Term of Geometric Progression (GP)

গুণোত্তর ধারার n-তম পদ • Finite Series (Arithmetic & Geometric)

Tn=arn−1T_n = a r^{n-1}
T_n = a r^n-1

💡 Condition: Nth term formula for geometric sequence with common ratio r.

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SSCChapter 13

Sum of First n Terms of GP

গুণোত্তর ধারার n পদের সমষ্টি • Finite Series (Arithmetic & Geometric)

Sn=a(1−rn)1−r  (r<1)বাSn=a(rn−1)r−1  (r>1)S_n = \frac{a(1 - r^n)}{1 - r} \; (r < 1) \quad \text{বা} \quad S_n = \frac{a(r^n - 1)}{r - 1} \; (r > 1)
S_n = (a(1 - r^n))/(1 - r) ; (r < 1) বা S_n = (a(r^n - 1))/(r - 1) ; (r > 1)

💡 Condition: Sum of n terms of a geometric progression depending on whether ratio r is less than or greater than 1.

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SSCChapter 13

Sum of Natural Numbers, Squares & Cubes

স্বাভাবিক সংখ্যা, বর্গ ও ঘনের সমষ্টি • Finite Series (Arithmetic & Geometric)

∑i=1ni=n(n+1)2,∑i=1ni2=n(n+1)(2n+1)6,∑i=1ni3=[n(n+1)2]2\sum_{i=1}^n i = \frac{n(n+1)}{2}, \quad \sum_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}, \quad \sum_{i=1}^n i^3 = \left[\frac{n(n+1)}{2}\right]^2
Σ_i=1^n i = (n(n+1))/(2), Σ_i=1^n i^2 = (n(n+1)(2n+1))/(6), Σ_i=1^n i^3 = [(n(n+1))/(2)]^2

💡 Condition: Summation identities for the first n integers, their squares, and their cubes.

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❓ General Mathematics Board Examination FAQs

Common questions on formula application and exam problem-solving rules

Q1: What are the formulas for the nth term and sum of an arithmetic progression?

For an arithmetic progression with first term aa and common difference dd, the nn-th term is Tn=a+(n−1)dT_n = a + (n-1)d and the sum of first nn terms is Sn=n2[2a+(n−1)d]S_n = \frac{n}{2}[2a + (n-1)d].

Q2: What is the step-deviation method formula for calculating statistical mean?

The step-deviation formula is xˉ=a+∑fiuiN×h\bar{x} = a + \frac{\sum f_i u_i}{N} \times h, where aa is assumed mean, fif_i is class frequency, ui=xi−ahu_i = \frac{x_i - a}{h} is step deviation, NN is total frequency, and hh is class interval.

Q3: What are the three fundamental Pythagorean trigonometric identities?

The three fundamental identities are: (1) sin⁡2θ+cos⁡2θ=1\sin^2\theta + \cos^2\theta = 1, (2) sec⁡2θ−tan⁡2θ=1\sec^2\theta - \tan^2\theta = 1, and (3) csc⁡2θ−cot⁡2θ=1\csc^2\theta - \cot^2\theta = 1.

Q4: What are the formulas for circumference and area of a circle?

For a circle of radius rr, the circumference is C=2πrC = 2\pi r and the area is A=πr2A = \pi r^2. The area of a circular sector with angle θ\theta is A=θ360∘×πr2A = \frac{\theta}{360^\circ} \times \pi r^2.
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