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By Ankit Gupta
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Updated on 20 Jul 2026, 14:25 IST
These CBSE Class 10 Maths Notes 2026–27 provide concise, chapter-wise revision material for all 14 chapters in the current Class 10 Mathematics Syllabus. Students can use the notes to review concepts, formulas, worked methods, common mistakes and competency-based applications before practising NCERT Solutions, sample papers and previous-year questions.
The official course structure covers seven units and carries 80 marks in the written examination, with 20 marks assigned to internal assessment. These notes support Mathematics Standard, subject code 041, and Mathematics Basic, subject code 241; practice questions should be selected according to the paper a student has chosen.
Also Check: CBSE Class 10 2027 Exam Pattern
Students can read each chapter online or use the chapter-wise PDF links below for offline revision.
| Chapter | Download PDF |
| 1. Real Numbers | Real Numbers Class 10 notes PDF |
| 2. Polynomials | Polynomials Class 10 notes PDF |
| 3. Pair of Linear Equations in Two Variables | Pair of Linear Equations notes PDF |
| 4. Quadratic Equations | Quadratic Equations Class 10 notes PDF |
| 5. Arithmetic Progressions | Arithmetic Progressions notes PDF |
| 6. Triangles | Triangles Class 10 notes PDF |
| 7. Coordinate Geometry | Coordinate Geometry notes PDF |
| 8. Introduction to Trigonometry | Introduction to Trigonometry notes PDF |
| 9. Applications of Trigonometry | Applications of Trigonometry notes PDF |
| 10. Circles | Circles Class 10 notes PDF |
| 11. Areas Related to Circles | Areas Related to Circles notes PDF |
| 12. Surface Areas and Volumes | Surface Areas and Volumes notes PDF |
| 13. Statistics | Statistics Class 10 notes PDF |
| 14. Probability | Probability Class 10 notes PDF |
The 2026–27 Class 10 Mathematics course is organized into seven units worth 80 theory marks, but CBSE Board does not prescribe guaranteed marks for individual chapters.
| Unit | Marks |
| Number Systems | 6 |
| Algebra | 20 |
| Coordinate Geometry | 6 |
| Geometry | 15 |
| Trigonometry | 12 |
| Mensuration | 10 |
| Statistics and Probability | 11 |
| Theory total | 80 |
| Internal assessment | 20 |
The unit table can guide revision time, but it should not be presented as a chapter-wise prediction. A board paper may distribute questions differently among the chapters within a unit.
Each chapter should be checked against the following primary materials before publication:
Historical or enrichment topics must be labeled separately. Topics such as Constructions, Euclid’s Division Lemma, frustums and ogives should not be described as prescribed 2026–27 content unless the current official documents expressly include them.
Mathematics Basic and Mathematics Standard share core Class 10 concepts, but students should practise with the question level and official sample paper for their chosen subject code.
| Feature | Mathematics Basic | Mathematics Standard |
| Subject code | 241 | 041 |
| Main purpose | Assess foundational mathematical understanding and application | Assess mathematical understanding through broader and potentially more demanding applications |
| Notes | Shared chapter concepts and formulas | Shared chapter concepts and formulas |
| Practice | Basic-labeled examples and official Basic papers | Standard-labeled examples and official Standard papers |
| Best source for exam format | Official Basic sample paper and marking scheme | Official Standard sample paper and marking scheme |
Students should not assume that Basic preparation requires only memorising formulas. Both papers can test whether a student can interpret information, select a method and apply a concept in an unfamiliar context.
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The following chapter summaries identify the concepts and formulas students should review before solving textbook and exam-style questions.
Real Numbers focuses on prime factorisation, the Fundamental Theorem of Arithmetic and proofs involving irrational numbers.
Fundamental Theorem of Arithmetic: Every composite number can be expressed as a product of primes, and this factorisation is unique apart from the order of the prime factors.
Prime-factor method: Express each number as a product of prime powers before identifying the HCF or LCM.
Irrationality proof: A standard proof assumes that a number such as √2 is rational, writes it in lowest terms and derives a contradiction.
Common mistake: Do not treat a decimal approximation as proof that a number is rational or irrational.
Polynomials covers zeroes and the relationship between the zeroes and coefficients of a quadratic polynomial.
For p(x) = ax² + bx + c, where a ≠ 0, and zeroes α and β:
Sum of zeroes:
α + β = -b/a
Product of zeroes:
α × β = c/a
Zero of a polynomial: A value x = k is a zero when p(k) = 0.
Common mistake: Include the negative sign in -b/a when calculating the sum of the zeroes.
Example: For 2x² - 5x + 2, the sum of zeroes is 5/2, while their product is 1.
A pair of linear equations can have one solution, no solution or infinitely many solutions, depending on the relationship between the two lines.
The general pair of equations is:
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
| Condition | Result |
| a₁/a₂ ≠ b₁/b₂ | One solution |
| a₁/a₂ = b₁/b₂, but b₁/b₂ ≠ c₁/c₂ | No solution |
| a₁/a₂ = b₁/b₂ = c₁/c₂ | Infinitely many solutions |
Substitution: Best when one variable is already isolated or has coefficient 1.
Elimination: Best when matching or easily matched coefficients allow one variable to be removed.
Graphical method: Shows the solution as the intersection of two lines.
Common mistake: When multiplying an equation, multiply every term on both sides.
A quadratic equation has the form ax² + bx + c = 0, where a ≠ 0, and its real roots can be found through factorisation or the quadratic formula.
Quadratic formula:
x = (-b ± √(b² - 4ac))/(2a)
Discriminant:
D = b² - 4ac
| Value of D | Nature of real roots |
| D > 0 | Two distinct real roots |
| D = 0 | Two equal real roots |
| D < 0 | No real roots |
Factorisation: Use it when the quadratic splits into convenient linear factors.
Quadratic formula: Use it when factors are not apparent or when the question asks about the nature of the roots.
Common mistake: The denominator is 2a, not merely 2.
An arithmetic progression is a sequence in which the difference between consecutive terms is constant.
For first term a, common difference d and term number n:
nth term:
aₙ = a + (n - 1)d
Sum of the first n terms:
Sₙ = n/2 × [2a + (n - 1)d
If the last term l is known:
Sₙ = n/2 × (a + l)
Common mistake: Use n - 1, not n, when finding the nth term.
Example: In 3, 7, 11, ..., a = 3 and d = 4, so the 10th term is:
a₁₀ = 3 + (10 - 1) × 4
a₁₀ = 3 + 36
a₁₀ = 39
Triangles focuses on similarity, proportional sides and theorem-based reasoning.
Basic Proportionality Theorem: A line drawn parallel to one side of a triangle divides the other two sides in the same ratio.
Similarity: Similar triangles have equal corresponding angles and proportional corresponding sides.
Common mistake: Write corresponding vertices in the same order before forming ratios. If triangle ABC is similar to triangle DEF, then A corresponds to D, B corresponds to E and C corresponds to F.
A proof should identify the theorem used, show that its conditions are satisfied and maintain the correct correspondence throughout.
Coordinate Geometry uses algebraic formulas to calculate distances and divide line segments on the coordinate plane.
For A(x₁, y₁) and B(x₂, y₂):
Distance formula:
AB = √[(x₂ - x₁)² + (y₂ - y₁)²
A point dividing AB internally in the ratio m:n is:
[(mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)
Common mistake: Match m with the coordinates of the second point and n with those of the first point in the standard section formula.
Reasonableness check: An internally dividing point should lie between the two endpoints.
Trigonometry relates the angles of a right triangle to ratios of its sides.
For an acute angle θ:
Sine:
sin θ = Opposite side/Hypotenuse
Cosine:
cos θ = Adjacent side/Hypotenuse
Tangent:
tan θ = Opposite side/Adjacent side
Important identities include:
sin² θ + cos² θ = 1
1 + tan² θ = sec² θ
1 + cot² θ = cosec² θ
Common mistake: Opposite and adjacent sides change when the reference angle changes; the hypotenuse does not.
Applications of Trigonometry uses right triangles and trigonometric ratios to calculate unknown heights and distances.
Angle of elevation: The angle measured upward from the horizontal line of sight.
Angle of depression: The angle measured downward from the horizontal line of sight.
Use this process:
Common mistake: Add the observer’s height when the angle is measured from eye level rather than ground level.
The Circles chapter focuses on tangents and their relationship with the radius at the point of contact.
Tangent-radius theorem: A tangent to a circle is perpendicular to the radius through the point of contact.
Equal tangents theorem: Tangent segments drawn from the same external point to a circle have equal lengths.
If PA and PB are tangents from external point P, then:
PA = PB
A theorem-based solution should clearly identify the centre, point of contact, tangent and relevant right angle.
Areas Related to Circles covers arc length, sector area and composite figures.
For central angle θ and radius r:
Arc length:
Arc length = (θ/360°) × 2πr
Sector area:
Sector area = (θ/360°) × πr²
| Quantity | Measurement |
| Arc | Length |
| Sector | Area enclosed by two radii and an arc |
| Segment | Area between a chord and its corresponding arc |
Common mistake: Convert diameter to radius before using a formula containing r.
Surface Areas and Volumes calculates the exposed area or enclosed space of three-dimensional solids.
| Solid | Curved or lateral area | Total surface area | Volume |
| Cylinder | 2πrh | 2πr(r + h) | πr²h |
| Cone | πrl | πr(l + r) | (1/3)πr²h |
| Sphere | 4πr² | 4πr² | (4/3)πr³ |
| Hemisphere | 2πr² | 3πr² | (2/3)πr³ |
Here:
Surface area: Measures the exposed covering of a solid in square units.
Volume: Measures the space occupied by a solid in cubic units.
Common mistake: Do not count a joined circular face as exposed when two solids are attached along that face.
Statistics summarizes grouped data through the mean, median and mode.
For observations xᵢ with frequencies fᵢ:
Mean:
Mean = Σ(fᵢ × xᵢ)/Σfᵢ
Median for grouped data:
Median = l + {[(N/2) - cf/f} × h
Mode for grouped data:
Mode = l + [(f₁ - f₀)/(2f₁ - f₀ - f₂) × h
| Symbol | Meaning |
| l | Lower boundary of the relevant class |
| N | Total frequency |
| cf | Cumulative frequency before the median class |
| f | Frequency of the median class |
| h | Class width |
| f₁ | Frequency of the modal class |
| f₀ | Frequency before the modal class |
| f₂ | Frequency after the modal class |
Common mistake: Identify the median class using cumulative frequency, not the highest individual frequency.
Probability measures how likely an event is when all outcomes are equally likely.
Probability of an event:
P(E) = Number of favourable outcomes/Total number of equally likely outcomes
Complementary event:
P(E) + P(not E) = 1
A probability must satisfy:
0 ≤ P(E) ≤ 1
Common mistake: Count the complete sample space before counting favourable outcomes.
Example: For one fair die, the probability of an even result is:
P(even number) = 3/6 = 1/2
The favourable outcomes are 2, 4 and 6.
A formula sheet is most useful when it states what each symbol means and when the formula applies.
| Topic | Formula | Use |
| Quadratic equation | x = (-b ± √(b² - 4ac))/(2a) | Find roots of ax² + bx + c = 0 |
| AP term | aₙ = a + (n - 1)d | Find a specified term |
| AP sum | Sₙ = n/2 × [2a + (n - 1)d | Add the first n terms |
| Distance | √[(x₂ - x₁)² + (y₂ - y₁)² | Distance between two coordinate points |
| Trigonometric identity | sin² θ + cos² θ = 1 | Simplify or verify expressions |
| Sector area | (θ/360°) × πr² | Area of a circular sector |
| Cylinder volume | πr²h | Space inside a cylinder |
| Probability | Favourable outcomes/Total outcomes | Equally likely outcomes |
Class 10 Maths notes work best as a revision and error-correction resource after a student has learned the concept and attempted relevant NCERT questions.
Also Check
Competency-based questions test whether students can interpret information and apply mathematics, not merely recall a formula.
Common formats include:
CBSE’s current curriculum emphasizes problem-solving, visualisation, mathematical modelling, logical reasoning and mathematical communication.
Use this four-step method:
Official CBSE Grade 10 competency booklets provide practice items designed around these skills.
Most avoidable errors come from incorrect signs, mismatched formulas, missing conditions or incomplete presentation.
| Mistake | How to prevent it |
| Losing a negative sign | Put substituted values in brackets |
| Using n instead of n - 1 in an AP | Write the formula before substitution |
| Mixing corresponding triangle sides | Write the similarity statement in order |
| Choosing the wrong trigonometric ratio | Label opposite, adjacent and hypotenuse first |
| Using diameter as radius | Write r = d/2 before applying the formula |
| Confusing surface area and volume | Check whether the answer needs square or cubic units |
| Selecting the wrong median class | Calculate cumulative frequency first |
| Omitting units | Add the correct unit to every measured result |
| Rounding too early | Keep exact values until the final step |
| Skipping working | Show the formula, substitution and result |
A mistake tracker should record the question, error type, correct method and retest date.
A balanced revision plan combines concept review, practice, timed papers and error analysis.
| Day | Focus |
| 1 | Real Numbers and Algebra foundations |
| 2 | Linear and Quadratic Equations |
| 3 | Arithmetic Progressions and Coordinate Geometry |
| 4 | Triangles and Circles |
| 5 | Trigonometry and its applications |
| 6 | Mensuration, Statistics and Probability |
| 7 | One timed paper followed by error correction |
This is an editorial study plan, not an official CBSE schedule. Students should give additional time to topics identified as weak through practice.
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CBSE Class 10 Maths Notes are short, organized summaries of each chapter from the Class 10 Mathematics syllabus. They include important formulas, definitions, theorems, and key points in a simplified format. These notes help students revise faster, understand concepts better, and perform well in board exams.
Yes, the Class 10 Maths revision notes are completely updated according to the CBSE Class 10 Maths 2025–26 syllabus. They are prepared in line with the topics and structure given in the NCERT textbook and follow all recent changes or reductions announced by CBSE.
Absolutely! The notes are available as Maths Notes Class 10 PDF Download. These PDFs make it easy for students to revise on the go using mobile phones, tablets, or computers. You can also print them if you prefer studying from paper.
These notes save time during revision by highlighting only the most important parts of each chapter. They include quick tips, solved examples, and formula sheets that improve understanding and speed. Using these notes regularly boosts confidence and helps in scoring high marks in the exam.
Yes, the CBSE Class 10 Maths Revision Notes are excellent for quick reference while solving sample papers or previous year papers. They help recall formulas, theorems, and methods easily, which is especially useful during timed practice.
Yes, the notes provide complete coverage of all 14 chapters, including challenging ones like Trigonometry, Statistics, and Surface Areas & Volumes. Each chapter has dedicated summaries, examples, and formulas in a structured format.
These notes are primarily designed for students, but parents can also use them to help their children revise. They are written in simple language, so anyone can understand and explain the concepts easily.