In short: This guide lists every formula from all 15 CBSE Class 10 Maths chapters, organized chapter-wise for quick revision. From Real Numbers and Polynomials to Statistics and Probability, bookmark this page and use it as your go-to reference before the 2027 board exam.
Your One-Stop Formula Reference
Formulas are the backbone of Class 10 Mathematics. You can understand concepts, you can practice problems, but if you forget a formula during the exam, you are stuck. This chapter-wise formula list covers every formula from all 15 CBSE Class 10 Maths chapters. Bookmark this page and use it as your quick-revision companion before the 2027 board exam.
Chapter 1: Real Numbers
Euclid's Division Lemma: a = bq + r, where 0 is less than or equal to r, which is less than b.
Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product of primes, and this factorization is unique (apart from the order of factors).
HCF and LCM relationship: HCF(a, b) x LCM(a, b) = a x b
For three numbers: LCM(a, b, c) = (a x b x c x HCF(a,b,c)) / (HCF(a,b) x HCF(b,c) x HCF(a,c))
Rational number p/q has a terminating decimal expansion if and only if the prime factorization of q is of the form 2^n x 5^m, where n and m are non-negative integers.
Chapter 2: Polynomials
For a quadratic polynomial ax^2 + bx + c with zeroes alpha and beta: Sum of zeroes: alpha + beta = -b/a Product of zeroes: alpha x beta = c/a
If alpha and beta are given, the polynomial is: k[x^2 - (alpha + beta)x + alpha x beta], where k is any non-zero constant.
Division Algorithm for Polynomials: p(x) = g(x) x q(x) + r(x), where degree of r(x) is less than degree of g(x).
Chapter 3: Pair of Linear Equations in Two Variables
General form: a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0
Condition for unique solution (intersecting lines): a1/a2 is not equal to b1/b2
Condition for no solution (parallel lines): a1/a2 = b1/b2, but not equal to c1/c2
Condition for infinitely many solutions (coincident lines): a1/a2 = b1/b2 = c1/c2
Methods of solving: Graphical, Substitution, Elimination, Cross-multiplication.
Cross-multiplication formula: x / (b1c2 - b2c1) = y / (c1a2 - c2a1) = 1 / (a1b2 - a2b1)
Chapter 4: Quadratic Equations
Standard form: ax^2 + bx + c = 0, where a is not equal to 0.
Quadratic formula: x = [-b plus or minus the square root of (b^2 - 4ac)] / 2a
Discriminant: D = b^2 - 4ac
If D is greater than 0: Two distinct real roots If D = 0: Two equal real roots (x = -b/2a) If D is less than 0: No real roots
Sum of roots: -b/a Product of roots: c/a
Chapter 5: Arithmetic Progressions
nth term: an = a + (n - 1)d, where a = first term, d = common difference.
Sum of first n terms: Sn = n/2 [2a + (n - 1)d] or equivalently Sn = n/2 [a + l], where l = last term.
Common difference: d = a2 - a1
nth term from the sum: an = Sn - S(n-1)
If a, b, c are in AP, then 2b = a + c (b is the arithmetic mean of a and c).
Chapter 6: Triangles
Basic Proportionality Theorem (Thales' theorem): If a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides those sides proportionally.
If DE is parallel to BC in triangle ABC: AD/DB = AE/EC
Criteria for Similarity of Triangles: AAA (Angle-Angle-Angle) AA (Angle-Angle) SSS (Side-Side-Side) SAS (Side-Angle-Side)
If triangles ABC and DEF are similar: AB/DE = BC/EF = CA/FD
Ratio of areas of similar triangles = ratio of squares of corresponding sides: Area of ABC / Area of DEF = (AB/DE)^2 = (BC/EF)^2 = (CA/FD)^2
Pythagoras Theorem: In a right triangle, the square of the hypotenuse = sum of squares of the other two sides. Hypotenuse^2 = Base^2 + Perpendicular^2
Converse: If the square of one side = sum of squares of the other two sides, the triangle is right-angled.
Chapter 7: Coordinate Geometry
Distance formula: d = square root of [(x2 - x1)^2 + (y2 - y1)^2]
Section formula (internal division): Point dividing the join of (x1, y1) and (x2, y2) in ratio m:n is [(mx2 + nx1)/(m + n), (my2 + ny1)/(m + n)]
Midpoint formula: [(x1 + x2)/2, (y1 + y2)/2]
Area of a triangle with vertices (x1, y1), (x2, y2), (x3, y3): Area = 1/2 |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Condition for collinearity: Area of triangle = 0
Chapter 8: Introduction to Trigonometry
Basic ratios for angle theta in a right triangle: sin theta = Opposite/Hypotenuse cos theta = Adjacent/Hypotenuse tan theta = Opposite/Adjacent cosec theta = 1/sin theta = Hypotenuse/Opposite sec theta = 1/cos theta = Hypotenuse/Adjacent cot theta = 1/tan theta = Adjacent/Opposite
Standard angle values:
sin 0 = 0, sin 30 = 1/2, sin 45 = 1/root 2, sin 60 = root 3/2, sin 90 = 1 cos 0 = 1, cos 30 = root 3/2, cos 45 = 1/root 2, cos 60 = 1/2, cos 90 = 0 tan 0 = 0, tan 30 = 1/root 3, tan 45 = 1, tan 60 = root 3, tan 90 = undefined
Fundamental identities: sin^2 theta + cos^2 theta = 1 1 + tan^2 theta = sec^2 theta 1 + cot^2 theta = cosec^2 theta
Complementary angle relationships: sin(90 - theta) = cos theta cos(90 - theta) = sin theta tan(90 - theta) = cot theta
Chapter 9: Some Applications of Trigonometry
Angle of Elevation: The angle between the horizontal line of sight and the line of sight to an object above.
Angle of Depression: The angle between the horizontal line of sight and the line of sight to an object below.
Height and Distance problems use: tan theta = Perpendicular / Base (most common in these problems) sin theta = Perpendicular / Hypotenuse cos theta = Base / Hypotenuse
For problems with two angles of elevation from two points at distance d apart: Height h = d / (cot alpha - cot beta), where alpha and beta are the two angles.
Chapter 10: Circles
Tangent to a circle is perpendicular to the radius at the point of contact.
The lengths of tangents drawn from an external point to a circle are equal. If PA and PB are tangents from point P, then PA = PB.
The angle between a tangent and the radius through the point of contact is 90 degrees.
The perpendicular from the center to a chord bisects the chord.
Chapter 11: Areas Related to Circles
Area of a circle = pi r^2 Circumference = 2 pi r Area of a semicircle = pi r^2 / 2
Area of a sector = (theta / 360) x pi r^2, where theta is the angle in degrees. Length of an arc = (theta / 360) x 2 pi r
Area of a segment = Area of sector - Area of triangle For the triangle in a sector: Area = 1/2 x r^2 x sin theta
Chapter 12: Surface Areas and Volumes
Cuboid: TSA = 2(lb + bh + hl), Volume = lbh, Diagonal = root(l^2 + b^2 + h^2)
Cube: TSA = 6a^2, Volume = a^3, Diagonal = a x root 3
Cylinder: CSA = 2 pi r h, TSA = 2 pi r(r + h), Volume = pi r^2 h
Cone: CSA = pi r l, TSA = pi r(l + r), Volume = 1/3 pi r^2 h Slant height: l = root(r^2 + h^2)
Sphere: SA = 4 pi r^2, Volume = 4/3 pi r^3
Hemisphere: CSA = 2 pi r^2, TSA = 3 pi r^2, Volume = 2/3 pi r^3
Frustum of a cone: CSA = pi(r1 + r2)l, where l = root[h^2 + (r1 - r2)^2] TSA = pi(r1 + r2)l + pi r1^2 + pi r2^2 Volume = 1/3 pi h (r1^2 + r2^2 + r1 x r2)
When a solid is converted into another shape, volume remains the same. Use this principle for combination problems.
Chapter 13: Statistics
Mean of grouped data:
Direct method: Mean = Sum of (fi x xi) / Sum of fi
Assumed mean method: Mean = a + [Sum of (fi x di) / Sum of fi], where di = xi - a
Step deviation method: Mean = a + [Sum of (fi x ui) / Sum of fi] x h, where ui = (xi - a)/h
Median of grouped data: Median = l + [(n/2 - cf) / f] x h where l = lower limit of median class, n = total frequency, cf = cumulative frequency of the class before median class, f = frequency of median class, h = class size.
Mode of grouped data: Mode = l + [(f1 - f0) / (2f1 - f0 - f2)] x h where l = lower limit of modal class, f1 = frequency of modal class, f0 = frequency of class before modal class, f2 = frequency of class after modal class, h = class size.
Empirical formula: 3 Median = Mode + 2 Mean
Chapter 14: Probability
Probability of an event: P(E) = Number of favorable outcomes / Total number of outcomes
Probability of a sure event = 1 Probability of an impossible event = 0 0 is less than or equal to P(E), which is less than or equal to 1
P(E) + P(not E) = 1, so P(not E) = 1 - P(E)
For a standard deck of 52 cards: 4 suits (hearts, diamonds, clubs, spades), each with 13 cards. Face cards = 12 (4 Jacks, 4 Queens, 4 Kings).
For two dice: Total outcomes = 36
How to Use This Formula List
Print this list or save it on your phone. During the last month before boards, review it every morning for 10 minutes. The repetition will embed these formulas in your long-term memory.
After you memorize the formulas, test yourself. Cover the right side and try to recall each formula from just the chapter name and topic. If you get stuck, mark it and focus extra attention on those formulas. To see which chapters carry the most marks, check our CBSE Class 10 Maths chapter-wise marks weightage guide.
For formulas you find hard to remember, create a story or visual association. For example, for the quadratic formula, think of "negative boy (-b) was unsure (plus or minus) if he could go to the radical party (square root), but the boy was too square (b^2) to miss 4 awesome chicks (4ac). The party was over at 2AM (2a)."
Frequently Asked Questions
How many formulas are there in CBSE Class 10 Maths?
There are approximately 80 to 100 formulas across all 15 chapters. The exact count depends on whether you count variations and derived formulas separately. The chapters with the most formulas are Trigonometry, Mensuration, and Statistics.
What is the best way to memorize Maths formulas for board exams?
Write each formula by hand at least 3 to 5 times, then practice problems using that formula. Revision through flashcards is highly effective. For tips on using flashcards, see our guide on why flashcards work for revision. Daily 10-minute revision of your formula sheet in the last month before exams helps transfer formulas to long-term memory.
Are the formulas the same for CBSE 2026 and 2027?
Yes. The CBSE Class 10 Maths syllabus and formulas have remained consistent. Unless CBSE announces a syllabus change for 2027, all formulas listed here are valid and current.
Which chapter has the most important formulas for the board exam?
Trigonometry (Chapter 8) and Statistics (Chapter 14) have the most formula-heavy questions on the board exam. Mensuration (Chapters 12-13) also relies heavily on formulas for surface area and volume calculations.
Can I carry a formula sheet into the CBSE board exam?
No. No reference material is allowed inside the exam hall. That is why memorization and regular practice are essential. However, keeping a formula sheet for daily revision during preparation is one of the most effective study habits.
Platforms like Padhaao can help you practice problems using these formulas interactively, so you do not just memorize them but actually use them in context. A formula you have used 20 times in practice is a formula you will remember in the exam hall.
One Final Tip
Knowing a formula is different from knowing when to use it. During practice, whenever you encounter a problem, first identify which formula applies before solving. This builds the connection between question types and formulas, which is exactly the skill the board exam tests. Memorize the formulas, practice their application, and walk into the exam confident that you have every tool you need. For chapter-wise important questions to test these formulas on, see our CBSE Class 10 Maths important questions guide. You can also explore science-backed study techniques to make your revision more effective.
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