CBSE Class 10 Maths: All Important Formulas (Chapter-Wise)
Having a solid grasp of all mathematical formulas is essential for scoring high in the CBSE Class 10 Board Exam. This comprehensive chapter-wise formula sheet covers all 15 chapters with approximately 80-100 key formulas you must memorize.
JITENDRA SIR'S CLASSES
CLASS 10 MATHS NCERT FORMULA SHEET
========================================CHAPTER 1: REAL NUMBERS
- Euclid Division Lemma: a = bq + r, where 0 <= r < b HCF x LCM:
- For two positive integers a and b: HCF(a,b) x LCM(a,b) = a x b
- If p is prime and p divides a^2, then p divides a.
- Decimal Expansion:
- Rational number p/q has terminating decimal if q = 2^m x 5^n Otherwise decimal is non-terminating repeating.
Chapter 2: Polynomials
For quadratic polynomial ax^2 + bx + c:
- Sum of zeroes = -b/a
- Product of zeroes = c/a
- Polynomial = k[x^2 - (alpha + beta)x + alpha beta]
- Sum of zeroes = -b/a
- Sum of product of zeroes two at a time = c/a
- Product of zeroes = -d/a
If zeroes are alpha and beta:
For cubic polynomial ax^3 + bx^2 + cx + d:
Chapter 3: Pair of Linear Equations in Two Variables
For equations a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0:
- Unique solution: a₁/a₂ ≠ b₁/b₂
- No solution: a₁/a₂ = b₁/b₂ ≠ c₁/c₂
- Infinite solutions: a₁/a₂ = b₁/b₂ = c₁/c₂
Chapter 4: Quadratic Equations
- Standard form: ax² + bx + c = 0
- Discriminant: D = b² − 4ac
- Roots formula: x = (−b ± √D) / 2a
- Nature of roots: D > 0 (real & distinct), D = 0 (equal), D < 0 (imaginary) If roots are alpha and beta:
- alpha + beta = -b/a
- alpha .beta = c/a
Chapter 5: Arithmetic Progressions (AP)
- nth term: aₙ = a + (n − 1)d
- Common difference: d = an - a(n-1)
- Sum of n terms: Sₙ = n/2 [2a + (n − 1)d]
- Also:Sn = n/2 (a + l)
- nth term from last:an = l - (n - 1)d
Chapter 6: Triangles
-
Basic Proportionality Theorem:
- If DE || BC, then AD/DB = AE/EC
- Pythagoras Theorem: Hypotenuse² = Base² + Height²
- Similarity criteria: AAA, AA, SAS, SSS
- Areas of similar triangles: Area of triangle 1 / Area of triangle 2 = (square of corresponding side 1) / (square of corresponding side 2)
- Area of triangle: (1/2) × base × height
Chapter 7: Coordinate Geometry
- Distance formula: √[(x₂−x₁)² + (y₂−y₁)²]
- Section formula: X = (mx₂ + nx₁)/(m+n), Y = (my₂ + ny₁)/(m+n)
- Mid-point formula:x = (x1 + x2)/2,y = (y1 + y2)/2
- Area of triangle: Area = 1/2 |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|
- Condition for collinear points:Area of triangle = 0
Chapter 8: Trigonometry
- sin θ = Perpendicular / Hypotenuse
- cos θ = Base / Hypotenuse
- tan θ = Perpendicular / Base
- cosec theta = Hypotenuse / Perpendicular = 1/sin theta
- sec theta = Hypotenuse / Base = 1/cos theta
- cot theta = Base / Perpendicular = 1/tan theta
- tan theta = sin theta / cos theta
- cot theta = cos theta / sin theta
- Key Identities: sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ, 1 + cot²θ = cosec²θ
Standard values:
| theta | 0 | 30 | 45 | 60 | 90 |
|---|---|---|---|---|---|
| sin | 0 | 1/2 | 1/sqrt2 | sqrt3/2 | 1 |
| cos | 1< /td> | sqrt3/2 | 1/sqrt2 | 1/2 | 0 |
| tan | 0 | 1/sqrt3 | 1 | sqrt3 | Not defined |
| cosec | Not defined | 2 | sqrt2 | 2/sqrt3 | 1 |
| sec | 1 | 2/sqrt3 | sqrt2 | 2 | Not defined |
| cot | Not defined | sqrt3 | 1 | 1/sqrt3 | 0 |
Chapter 9: Applications of Trigonometry
Height and Distance problems: tan θ = height / distance
Chapter 10: Circles
- Tangent: A tangent touches the circle at exactly one point.
- Tangent is perpendicular to radius at the point of contact
- Tangents from external point: PA = PB
Tangents drawn from an external point are equal in length
Chapter 12: Areas Related to Circles
- Area of semicircle:A = 1/2 pi r^2
- Perimeter of semicircle:P = pi r + 2r
- Perimeter of semicircle:P = pi r + 2r
- Area of segment: Area of segment = Area of sector - Area of triangle
- Area of ring:A = pi(R^2 - r^2)
- Area of circle: πr²
- Circumference: 2πr
- Sector area: (θ/360) × πr²
- Arc length: (θ/360) × 2πr
Chapter 13: Surface Areas & Volumes
-
Cuboid:
- TSA = 2(lb + bh + hl)
- LSA = 2h(l + b)
- Volume = lbh
- Diagonal = sqrt(l^2 + b^2 + h^2)
- Cube: SA = 6a², LSA = 4a^2,Diagonal = a sqrt3,Volume = a³
- Cylinder: CSA = 2πrh,TSA = 2 pi r(r + h), Volume = πr²h
- Sphere: SA = 4πr², Volume = (4/3)πr³
- Cone:Slant height l = sqrt(r^2 + h^2),CSA = pi rl,TSA = pi r(l + r), Volume = 1/3 pi r^2 h
- Hemisphere:CSA = 2 pi r^2,TSA = 3 pi r^2,Volume = 2/3 pi r^3
Chapter 14: Statistics
-
Mean of ungrouped data:
- Mean = Sum of observations / Number of observations
- Mean by direct method:Mean = Sum fixi / Sum fi
- Assumed mean method: Mean = a + Sum fidi / Sum fi where di = xi - a
- Mean (Direct): Σfx / Σf
- Median: l + [(n/2 − cf)/f] × h
- Mode: l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h
- Empirical relation:Mode = 3 Median - 2 Mean
Chapter 15: Probability
- P(E) = Favorable outcomes / Total outcomes
- Range: 0 ≤ P(E) ≤ 1
- Impossible event:P(E) = 0
- Sure event:P(E) = 1
- Complementary event:P(not E) = 1 - P(E)
- Also:P(E) + P(not E) = 1
FAQs – CBSE Class 10 Maths Formula Sheet 2026
I. What is a Class 10 Maths formula sheet?
A Maths formula sheet is a quick revision resource that includes all important formulas chapter-wise to help students revise efficiently before the board exam.
II. Is a formula sheet useful for CBSE Class 10 board exam preparation?
Yes, it helps in quick revision, improves accuracy, and saves time during exam preparation.
III. Which chapters are most important for Class 10 Maths formulas?
Important chapters include Algebra, Trigonometry, Coordinate Geometry, Mensuration, and Statistics.
IV. Can I revise the entire syllabus using a formula sheet?
A formula sheet is best for revision, but students should also practice questions to fully understand concepts.
V. How can I memorize Maths formulas easily?
Regular revision, solving problems, and writing formulas repeatedly are effective ways to memorize them.
VI. Is this formula sheet enough for scoring high marks?
It is very helpful for revision, but combining it with sample papers and previous year questions will give better results.
VII. Is the Class 10 Maths formula sheet available for free download?
Yes, you can download the complete PDF for free and start your preparation immediately.
VIII. Can this formula sheet help in last-minute revision?
Absolutely, it is designed for quick and effective last-minute revision before exams.