CBSE Class 10 Maths (2026) has 14 chapters in 7 units, and about 60 formulas cover the entire 80-mark paper — far fewer than seniors think. The biggest scoring blocks are Algebra (20 marks) and Trigonometry (12), followed by Geometry (15) and Mensuration (10). Every chapter's formulas are listed below, with what each one is actually used for.
- Unit weightage 2026
- 1. Real Numbers · 2. Polynomials · 3. Linear Equations · 4. Quadratic Equations · 5. Arithmetic Progressions
- 6. Triangles · 7. Coordinate Geometry
- 8. Trigonometry · 9. Heights & Distances
- 10. Circles · 11. Areas Related to Circles · 12. Surface Areas & Volumes
- 13. Statistics · 14. Probability
- Tricks to remember them · FAQs
Where the 80 marks come from
| Unit (chapters) | Marks |
|---|---|
| Algebra (Ch 2–5) | 20 |
| Geometry (Ch 6, 10) | 15 |
| Trigonometry (Ch 8–9) | 12 |
| Statistics & Probability (Ch 13–14) | 11 |
| Mensuration (Ch 11–12) | 10 |
| Coordinate Geometry (Ch 7) | 6 |
| Number Systems (Ch 1) | 6 |
Theory 80 + internal assessment 20 = 100. Algebra and Trigonometry together are 32 marks — nearly half the paper from six chapters.
Ch 1 — Real Numbers 6 marks
| Formula | Used for |
|---|---|
| HCF × LCM = product of the two numbers | Works for two numbers only — the most common mistake in this chapter |
| Fundamental Theorem of Arithmetic | Every number = a unique product of primes; HCF/LCM by prime factorisation |
Ch 2 — Polynomials 20-mark unit
| Formula | Used for |
|---|---|
| Quadratic: α + β = −b/a; αβ = c/a | Sum and product of zeroes — a near-certain question |
| Polynomial from zeroes: x² − (α + β)x + αβ | Building the polynomial backwards |
| Cubic: α+β+γ = −b/a; αβ+βγ+γα = c/a; αβγ = −d/a | Cubic relations (signs alternate: −, +, −) |
Ch 3 — Pair of Linear Equations 20-mark unit
| Condition | What it means |
|---|---|
| a1/a2 ≠ b1/b2 | Unique solution — lines intersect (consistent) |
| a1/a2 = b1/b2 = c1/c2 | Infinitely many solutions — same line (dependent) |
| a1/a2 = b1/b2 ≠ c1/c2 | No solution — parallel lines (inconsistent) |
Ch 4 — Quadratic Equations 20-mark unit
| Formula | Used for |
|---|---|
| x = (−b ± √(b² − 4ac))/2a | The quadratic formula — works when factorisation fails |
| D = b² − 4ac | Discriminant: D > 0 two distinct real roots, D = 0 two equal roots, D < 0 no real roots |
Ch 5 — Arithmetic Progressions 20-mark unit
| Formula | Used for |
|---|---|
| an = a + (n − 1)d | nth term of an AP |
| Sn = (n/2)[2a + (n − 1)d] | Sum of n terms — use when d is known |
| Sn = (n/2)(a + l) | Sum when the last term l is known — much faster |
| an = Sn − Sn−1 | Finding a term from the sum formula |
Ch 6 — Triangles 15-mark unit
| Theorem | Used for |
|---|---|
| BPT (Thales): DE ∥ BC ⇒ AD/DB = AE/EC | The chapter's most-asked proof |
| Similarity: AAA, SSS, SAS criteria | Proving two triangles similar |
| Area ratio = (ratio of corresponding sides)² | Areas of similar triangles — the square is what students forget |
| Pythagoras: AC² = AB² + BC² | Right triangles; converse proves a triangle is right-angled |
Ch 7 — Coordinate Geometry 6 marks
| Formula | Used for |
|---|---|
| d = √((x2 − x1)² + (y2 − y1)²) | Distance between two points |
| P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) | Section formula — dividing a line in ratio m : n |
| Midpoint = ((x1 + x2)/2, (y1 + y2)/2) | Section formula with m = n = 1 |
Note: the area-of-triangle formula is not in the current rationalized syllabus for this chapter.
Ch 8 — Introduction to Trigonometry 12-mark unit
| Formula | Used for |
|---|---|
| sin θ = P/H; cos θ = B/H; tan θ = P/B | The basic ratios (P = perpendicular, B = base, H = hypotenuse) |
| cosec θ = 1/sin θ; sec θ = 1/cos θ; cot θ = 1/tan θ | Reciprocal pairs — note sin pairs with cosec, not sec |
| tan θ = sin θ/cos θ; cot θ = cos θ/sin θ | Quotient relations |
| sin²θ + cos²θ = 1 | The three identities — nearly every proof question uses one of these |
| 1 + tan²θ = sec²θ | |
| 1 + cot²θ = cosec²θ | |
| sin(90° − θ) = cos θ; tan(90° − θ) = cot θ; sec(90° − θ) = cosec θ | Complementary angles — the pairs simply swap |
The value table you must know cold
| θ | 0° | 30° | 45° | 60° | 90° |
|---|---|---|---|---|---|
| sin θ | 0 | 1/2 | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | ∞ |
Ch 9 — Some Applications of Trigonometry 12-mark unit
| Concept | Used for |
|---|---|
| Angle of elevation — looking up from the horizontal | Heights and distances word problems; angles used are only 30°, 45°, 60° |
| Angle of depression — looking down from the horizontal | |
| tan θ = height/distance | The workhorse ratio — most questions reduce to this one line |
Ch 10 — Circles 15-mark unit
| Theorem | Used for |
|---|---|
| Tangent ⊥ radius at the point of contact | The foundation of every circle question |
| Tangents from an external point are equal | The second most-used theorem; both are proof questions |
Ch 11 — Areas Related to Circles 10-mark unit
| Formula | Used for |
|---|---|
| Area = πr²; Circumference = 2πr | Full circle |
| Arc length = (θ/360°) × 2πr | Sector arc |
| Area of sector = (θ/360°) × πr² | Sector area — the chapter's main formula |
| Area of segment = area of sector − area of triangle | Segments (minor/major) |
Ch 12 — Surface Areas & Volumes 10-mark unit
| Solid | Formulas |
|---|---|
| Cube | V = a³; TSA = 6a² |
| Cuboid | V = lbh; TSA = 2(lb + bh + hl) |
| Cylinder | V = πr²h; CSA = 2πrh; TSA = 2πr(r + h) |
| Cone | V = ⅓πr²h; CSA = πrl; TSA = πr(l + r); l = √(r² + h²) |
| Sphere | V = (4/3)πr³; SA = 4πr² |
| Hemisphere | V = (2/3)πr³; CSA = 2πr²; TSA = 3πr² |
Ch 13 — Statistics 11-mark unit
| Formula | Used for |
|---|---|
| Mean = Σfixi/Σfi | Direct method |
| Mean = a + Σfidi/Σfi | Assumed mean method — faster with big numbers |
| Median = l + [(n/2 − cf)/f] × h | Median of grouped data |
| Mode = l + [(f1 − f0)/(2f1 − f0 − f2)] × h | Mode of grouped data |
Note: the empirical relation (3 Median = Mode + 2 Mean) and step-deviation method are not part of the current rationalized syllabus.
Ch 14 — Probability 11-mark unit
| Formula | Used for |
|---|---|
| P(E) = favourable outcomes / total outcomes | The only formula in the chapter |
| P(E) + P(not E) = 1 | Complement rule; 0 ≤ P(E) ≤ 1 always |
Tricks to remember them
Trigonometry's value table in one hand. For sin, write 0, 1, 2, 3, 4 under 0°–90°, divide each by 4, then take the square root: you get 0, 1/2, 1/√2, √3/2, 1. For cos, read the same row backwards. tan = sin ÷ cos. One 10-second trick replaces the whole table.
Cone, cylinder, sphere are one family. A cone's volume is exactly ⅓ of a cylinder with the same base and height. A sphere is (4/3)πr³ and a hemisphere is half of it. Learn the cylinder, then derive the rest instead of memorising six volumes.
The "l" in a cone is not the height. Slant height l = √(r² + h²) — this single confusion costs more marks in Ch 12 than any other error. Whenever you see CSA = πrl, check whether the question gave you h or l.
Similar triangles: the square rule. Sides in ratio 2 : 3 means areas in ratio 4 : 9. Students apply the ratio directly and lose the mark. Sides ratio → square it for areas.
Write, don't read. Once a week, write every chapter's formulas on a blank page from memory, then check against this list and rewrite only the ones you missed. Three weeks of this and the whole chart is in your head — because in the exam your hand writes, your eyes don't read.
The complete handwritten Class 10 Maths formula chart
This page is your online quick-check. The handwritten sheet is what goes on your study wall:
- Full 2026-27 syllabus — all 14 chapters, compact and exam-focused
- Colour-coded formula boxes with diagrams for fast recall
- Real handwritten notes by toppers — IITians, NITians and district toppers
- Instant PDF or printed book (COD available, all-India delivery)
- Available in English and Hindi medium
FAQs
How many formulas are there in Class 10 Maths?
About 60 core formulas across the 14 chapters — far fewer than most students expect. Surface Areas & Volumes and Trigonometry contribute the largest share.
Which chapter has the highest weightage in Class 10 Maths 2026?
Algebra (Polynomials, Linear Equations, Quadratic Equations, Arithmetic Progressions) carries 20 of the 80 marks, followed by Geometry at 15 and Trigonometry at 12.
How can I remember the trigonometry table easily?
Write 0, 1, 2, 3, 4 under 0° to 90°, divide each by 4, then take the square root — that gives the sin row. Read it backwards for cos, and divide sin by cos for tan.
What is the difference between slant height and height in a cone?
Height h is the vertical distance from base to tip; slant height l runs along the surface, and l = √(r² + h²). Curved surface area uses l, while volume uses h.
Are Class 10 Maths formulas enough to score full marks?
Formulas plus three habits: matching units before substituting, writing every step so step marks are visible, and practising previous-year questions so you recognise which formula a question wants.
Is the empirical relation between mean, median and mode in the syllabus?
No. The empirical relation and the step-deviation method are not part of the current rationalized Class 10 Statistics syllabus.
Which Class 10 formulas are used again in Class 11?
Trigonometric identities, arithmetic progressions, quadratic equations and coordinate geometry all reappear in Class 11 in deeper form — Class 10 is the foundation layer, not a one-year syllabus.
Is there a Class 10 Maths formula sheet in Hindi?
Yes — the handwritten notes linked above are available in both English and Hindi medium versions, with the same formulas and diagrams.