1st Year Math Formulas
All 1st Year Math formulas, chapter by chapter, with search and a printable layout.
Chapters are placed in 1st or 2nd Year following the usual Punjab and Federal board outline. Your board may order chapters differently, so check your own syllabus.
Chapters: Logarithms · Trigonometry · Sequences & Series · Complex Numbers · Matrices · Inverse Trig Identities · Partial Fractions · Trigonometric Equations · Set Theory
Logarithms (6)
| Formula | Expression |
|---|
| Product Rule | log(mn) = log m + log n |
| Quotient Rule | log(m/n) = log m - log n |
| Power Rule | log(mⁿ) = n log m |
| Change of Base | logₐ b = log b / log a |
| log base a of a | logₐa = 1 |
| log of 1 | logₐ1 = 0 |
Trigonometry (36)
| Formula | Expression |
|---|
| Pythagorean Identity | sin²θ + cos²θ = 1 |
| 1 + tan²θ | sec²θ |
| 1 + cot²θ | cosec²θ |
| sin(A ± B) | sinA cosB ± cosA sinB |
| cos(A ± B) | cosA cosB ∓ sinA sinB |
| tan(A ± B) | (tanA ± tanB) / (1 ∓ tanA tanB) |
| Double Angle sin2θ | 2 sinθ cosθ |
| Double Angle cos2θ | cos²θ - sin²θ = 2cos²θ - 1 |
| Law of Sines | a/sinA = b/sinB = c/sinC |
| Law of Cosines | c² = a² + b² - 2ab cosC |
| Half Angle sin(θ/2) | ±√((1-cosθ)/2) |
| Half Angle cos(θ/2) | ±√((1+cosθ)/2) |
| Product to Sum | sinA cosB = ½[sin(A+B)+sin(A-B)] |
| Sum to Product | sinA+sinB = 2 sin((A+B)/2) cos((A-B)/2) |
| cot θ | cotθ = cosθ/sinθ |
| sec θ | secθ = 1/cosθ |
| cosec θ | cosecθ = 1/sinθ |
| Triple Angle sin3θ | 3sinθ − 4sin³θ |
| Triple Angle cos3θ | 4cos³θ − 3cosθ |
| Half Angle tan(θ/2) | ±√((1−cosθ)/(1+cosθ)) |
| sinθ Definition | sinθ = Opposite/Hypotenuse |
| cosθ Definition | cosθ = Adjacent/Hypotenuse |
| tanθ Definition | tanθ = Opposite/Adjacent = sinθ/cosθ |
| Reciprocal Identity cosecθ | cosecθ = 1/sinθ |
| Reciprocal Identity secθ | secθ = 1/cosθ |
| Reciprocal Identity cotθ | cotθ = 1/tanθ |
| Angle of Elevation/Depression (concept) | angle from horizontal to line of sight |
| sin(A − B) | sinA cosB − cosA sinB |
| Sum to Product sinA+sinB | 2 sin((A+B)/2) cos((A−B)/2) |
| Sum to Product cosA+cosB | 2 cos((A+B)/2) cos((A−B)/2) |
| Product to Sum 2sinAcosB | sin(A+B) + sin(A−B) |
| Area of Triangle (Trig) | Area = ½ab sinC |
| Radian to Degree | θ(deg) = θ(rad) × 180/π |
| Arc Length | s = rθ |
| Area of Circular Sector | A = ½r²θ |
| Period of sin/cos | T = 2π/b for sin(bx) |
Sequences & Series (16)
| Formula | Expression |
|---|
| nth term of AP | aₙ = a₁ + (n-1)d |
| Sum of AP | Sₙ = n/2 × (2a₁ + (n-1)d) |
| nth term of GP | aₙ = a₁rⁿ⁻¹ |
| Sum of GP | Sₙ = a₁(1-rⁿ)/(1-r) |
| Infinite GP | S = a₁/(1-r), |r| < 1 |
| Sum of Squares (1 to n) | Σn² = n(n+1)(2n+1)/6 |
| Sum of Cubes (1 to n) | Σn³ = [n(n+1)/2]² |
| Harmonic Mean | HM = n/Σ(1/aᵢ) |
| Arithmetic-Geometric Mean Inequality | AM ≥ GM ≥ HM |
| General Term of Binomial Expansion | Tᵣ₊₁ = ⁿCᵣ xⁿ⁻ʳ yʳ |
| Sum of Infinite Series (1+x)ⁿ | 1 + nx + n(n−1)x²/2! + ... |
| nth Term of HP | aₙ = 1/(1/a₁ + (n−1)d) |
| nth Term from End of AP | l - (n-1)d |
| Sum of AP (Last Term Form) | Sn = n/2 (a1 + an) |
| Arithmetic Mean Insertion | A = (a+b)/2 between a and b |
| Geometric Mean Insertion | G = sqrt(ab) between a and b |
Complex Numbers (8)
| Formula | Expression |
|---|
| Modulus | |z| = √(a² + b²), z = a + bi |
| Euler's Formula | e^(iθ) = cosθ + i sinθ |
| De Moivre's Theorem | (cosθ + i sinθ)ⁿ = cos(nθ) + i sin(nθ) |
| Conjugate of Complex Number | z̄ = a − bi, for z = a+bi |
| Argument of Complex Number | θ = tan⁻¹(b/a) |
| Polar Form | z = r(cosθ + i sinθ) |
| Product of Complex Numbers (Polar) | r₁r₂[cos(θ₁+θ₂)+i sin(θ₁+θ₂)] |
| i Powers Cycle | i²=−1, i³=−i, i⁴=1 |
Matrices (9)
| Formula | Expression |
|---|
| Determinant 3×3 | |A| = a(ei−fh) − b(di−fg) + c(dh−eg) |
| Matrix Multiplication | (AB)ᵢⱼ = Σₖ AᵢₖBₖⱼ |
| Transpose Property | (AB)ᵀ = BᵀAᵀ |
| Adjoint | adj(A) = transpose of cofactor matrix |
| Inverse via Adjoint | A⁻¹ = adj(A)/|A| |
| Singular Matrix Condition | |A| = 0 |
| Symmetric Matrix (10th) | aᵢⱼ = aⱼᵢ |
| Skew-Symmetric Matrix | Aᵀ = −A |
| Inverse Matrix Property | AA⁻¹ = I |
Inverse Trig Identities (2)
| Formula | Expression |
|---|
| sin⁻¹x + cos⁻¹x | π/2 |
| tan⁻¹x + cot⁻¹x | π/2 |
Partial Fractions (3)
| Formula | Expression |
|---|
| Linear Factor | 1/((x-a)(x-b)) = A/(x-a) + B/(x-b) |
| Repeated Linear Factor | 1/(x−a)² = A/(x−a) + B/(x−a)² |
| Quadratic Factor | (Ax+B)/(x²+px+q) |
Trigonometric Equations (3)
| Formula | Expression |
|---|
| General Solution sin x = sin a | x = nπ + (-1)ⁿ a |
| General Solution cos x = cos a | x = 2nπ ± a |
| General Solution tan x = tan a | x = nπ + a |
Set Theory (2)
| Formula | Expression |
|---|
| Cardinality of Union (3 Sets) | |A∪B∪C| = |A|+|B|+|C|-|A∩B|-|A∩C|-|B∩C|+|A∩B∩C| |
| Symmetric Difference | A Δ B = (A-B) ∪ (B-A) |
More class-wise formulas
Formulas are for revision. Always follow the notation and rounding used in your own textbook and board papers.
FAQ
How many 1st Year Math formulas are on this page?
85 formulas in 9 chapters.
Can I print the 1st Year Math formulas?
Yes. Press Print / Save as PDF. The page switches to a clean black-on-white layout without menus.
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Type a word such as velocity, area or mole in the search box. Only matching formulas stay visible.
Do the formulas follow my board syllabus?
They follow the usual school and intermediate syllabus, but chapter lists differ between boards. Check your own syllabus for what is included in your exam.
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