ICSE Class 10 Mathematics (paper code 511) is the highest-stakes subject in the Indian Certificate of Secondary Education examination — both because of its heavy weightage in cumulative aggregate calculations and because it remains the single most-feared paper in the ICSE timetable. The paper carries 80 marks for theory and a further 20 marks for internal assessment (project work), totalling 100 marks. CISCE accepts three prescribed textbooks as equivalent references: Selina Concise Mathematics for ICSE Class 10, ML Aggarwal Understanding ICSE Mathematics, and RS Aggarwal Mathematics for Class 10. The CISCE syllabus is identical across all three; the choice between books is a stylistic one.
This page is the official icseboard.org Class 10 Maths hub. You will find the complete Selina Concise chapter library, every CISCE-released board paper from 2017 through 2026, pre-board and specimen papers, the marking scheme, the formula sheet you must memorise, and an empirically-validated study plan. Every PDF download is hosted on icseboard.org and verified against the original CISCE release.
How the ICSE Class 10 Maths Curriculum Is Structured
The 2026-27 syllabus is organised across six major thematic blocks: Commercial Mathematics, Algebra, Coordinate Geometry, Geometry, Mensuration & Trigonometry, and Statistics & Probability. The chapter ordering in Selina Concise differs slightly from ML Aggarwal — Selina front-loads commercial maths (GST, banking, shares), then algebra, before moving to geometry and statistics; ML Aggarwal interleaves algebra and geometry. We recommend studying in thematic order rather than chapter order, because intra-theme practice compounds far more efficiently than chronological page-flipping.
Chapter-wise Selina Concise Mathematics PDFs
The Selina Concise Mathematics textbook covers 25–27 chapters depending on the edition. Below we have grouped the chapter PDFs into the six thematic blocks above, so you can study by topic rather than chapter number.
Commercial Mathematics (Chapters 1–3)
The opening block applies arithmetic to real-world finance. Chapter 1 covers the Goods and Services Tax (GST), introduced in the 2023 syllabus revision to replace Value Added Tax. The CGST + SGST split for intra-state sales versus IGST for inter-state is the standard 4-mark numerical:
\mathrm{Total\ GST} = \mathrm{CGST} + \mathrm{SGST} = 2 \times \left( \frac{r}{2} \times P \right) = r \times P
where r is the GST rate and P the taxable value. Chapter 2 introduces Banking — specifically Recurring Deposit Accounts. The interest-on-RD formula is:
I = P \times \frac{n(n+1)}{2 \times 12} \times \frac{r}{100}
Chapter 3 covers Shares and Dividends — face value, market value, dividend percent, yield, and the difference between a “premium” and a “discount” share. Download the Banking chapter PDF for worked RD interest problems.
Algebra (Chapters 4–11)
The longest block in the syllabus and the highest-weighted in board papers — typically 22–26 of the 80 theory marks. Chapter 4 (Linear Inequations) tests solution sets on the number line and in roster/set-builder notation. Chapter 5 introduces Quadratic Equations — the standard form, the discriminant, and the quadratic formula:
x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}, \qquad D = b^2 – 4ac
Download the Quadratic Equations chapter PDF. Chapter 6 (Problems on Quadratic Equations) applies the formula to word problems on age, speed–distance, mensuration, and number-theoretic puzzles — typically a 6-mark question in Section B.
Chapter 7 (Ratio and Proportion) covers compound ratio, duplicate ratio, sub-duplicate ratio, and the four properties of proportion (invertendo, alternendo, componendo, dividendo). Chapter 8 (Remainder and Factor Theorems) handles polynomial factorisation using p(a) = 0 ⇒ (x − a) is a factor.
Chapter 9 (Matrices) introduces matrix operations limited to 2×2 — addition, scalar multiplication, and matrix multiplication. Inverse and determinant are NOT in the Class 10 syllabus. Chapter 10 (Arithmetic Progression) tests the nth-term and sum formulas:
T_n = a + (n-1)d, \qquad S_n = \frac{n}{2}\left2a + (n-1)d\right
Chapter 11 (Geometric Progression) does the same for GP with the common ratio r:
T_n = a r^{n-1}, \qquad S_n = \frac{a(r^n – 1)}{r – 1} \ \text{(for } r \ne 1)
Coordinate Geometry (Chapters 12–14)
Chapter 12 (Reflection) covers reflection in the x-axis, y-axis, origin, and the lines y = a, x = a. The transformation rules (x, y) → (x, −y) for x-axis reflection are 1-mark Section A definitions. Chapter 13 — Section & Mid-Point Formula tests the internal and external division of a line segment and the centroid formula for a triangle. Chapter 14 (Equation of a Line) develops slope, slope-intercept, two-point, and point-slope forms. The slope formula between two points (x₁, y₁) and (x₂, y₂):
m = \frac{y_2 – y_1}{x_2 – x_1}
and the perpendicularity condition m₁ × m₂ = −1 appear in nearly every board paper.
Geometry — Similarity, Loci, Circles (Chapters 15–19)
The geometry block accounts for 16–20 marks per paper. Chapter 15 (Similarity) covers SAS, AAA similarity criteria and the basic proportionality theorem with map and model applications. Chapter 16 (Loci) handles geometric locus constructions with compass and ruler — angle bisector, perpendicular bisector, and parallel locus.
Chapter 17 (Circles) develops the central-angle theorem, the inscribed-angle theorem, and cyclic quadrilateral properties. Chapter 18 (Tangents and Intersecting Chords) closes the circles unit with the tangent-from-external-point theorem and the intersecting-chord power formula. Chapter 19 covers the geometric constructions involving circles and tangents — a 4-mark Section A construction question is standard.
Mensuration & Trigonometry (Chapters 20–22)
Chapter 20 (Cylinder, Cone and Sphere) tests surface area and volume formulas for the three solids, including conversion problems (a sphere melted to form cones, etc.). The four formulas to memorise:
V_{\text{cyl}} = \pi r^2 h, \quad V_{\text{cone}} = \frac{1}{3}\pi r^2 h, \quad V_{\text{sphere}} = \frac{4}{3}\pi r^3, \quad V_{\text{hemi}} = \frac{2}{3}\pi r^3
Chapter 21 (Trigonometrical Identities) tests the three Pythagorean identities — derived once, memorised once, applied repeatedly:
\sin^2\theta + \cos^2\theta = 1, \quad 1 + \tan^2\theta = \sec^2\theta, \quad 1 + \cot^2\theta = \csc^2\theta
Chapter 22 (Heights and Distances) applies trigonometry to angle-of-elevation and angle-of-depression problems with a single observer or two observers on opposite sides of an object. A 6-mark Section B question is the standard.
Statistics & Probability (Chapters 23–25)
Chapter 23 (Graphical Representation) covers histograms and ogives (cumulative frequency curves), including reading mean, median, mode, and quartiles from the graph. Chapter 24 (Measures of Central Tendency) computes mean (direct + step-deviation methods), median, mode, and the empirical relation:
\text{Mode} = 3 \times \text{Median} – 2 \times \text{Mean}
Chapter 25 (Probability) closes the syllabus with classical probability — events, sample space, mutually exclusive vs independent events, and complementary probability. Conditional probability is NOT in the Class 10 syllabus.
ICSE Class 10 Maths Marking Scheme & Paper Pattern
The Maths theory paper runs for two and a half hours — 30 minutes longer than the Science papers — plus the standard 15-minute reading time. The 80-mark allocation:
| Section | Question type | Compulsory? | Marks |
|---|---|---|---|
| A | Short answer — 4 questions, 10 marks each (sub-parts of 3+3+4) | All compulsory | 40 |
| B | Long answer — answer any 4 of 7 questions, 10 marks each | Internal choice | 40 |
| Internal Assessment | Project work | School-assessed, year-round | 20 |
| Total | 100 | ||
Step marking is generous: every correct intermediate step is awarded marks even when the final answer is wrong due to arithmetic slip. The single biggest source of avoidable marks lost is the missing or incorrect method label — write “By section formula:” or “By Pythagoras’ theorem:” before applying any formula, and CISCE rewards the labelling itself.
Past Papers, Pre-board & Specimen Practice
Specimen papers
Pre-board papers
- Pre-Board Maths Paper — January 2026 (latest)
- Pre-Board Maths Paper — Mid-January 2026
- Pre-Board Maths Paper — 2025
- Pre-Board Maths Paper — 2023
Solved board papers — 2017 to 2026
- Maths Board Paper — 2026
- Maths Board Paper — 2025
- Maths Board Paper — 2024
- Maths Board Paper — 2023
- Maths Board Paper — 2020
- Maths Board Paper — 2019
- Maths Board Paper — 2018
- Maths Board Paper — 2017
Term-test papers — between-chapter practice
Three-Month Study Plan for ICSE Class 10 Maths
| Weeks | Focus | Output target |
|---|---|---|
| 1 | Commercial Maths (GST, Banking, Shares) — Ch 1–3 | 30 worked numericals |
| 2–4 | Algebra block (Quadratics, AP/GP, Matrices, Inequations, Polynomials) — Ch 4–11 | 50 numericals; reproduce 10 standard derivations from memory |
| 5 | Coordinate geometry — Ch 12–14 | 20 problems mixing slope, midpoint, section formula |
| 6–7 | Geometry — Similarity, Loci, Circles, Tangents — Ch 15–19 | 15 ruler-compass constructions practised under time |
| 8 | Mensuration + Trigonometry — Ch 20–22 | Formula sheet completed; 20 mensuration conversion problems |
| 9 | Statistics + Probability — Ch 23–25 | Hand-drawn histogram + ogive for one provided dataset |
| 10 | First specimen + first pre-board under 2.5-hour timed conditions | Self-mark; list 3 weakest topics |
| 11–12 | Remaining pre-boards + 3 most recent board papers + targeted revision | Average 65+/80 on the last three papers |
Common Mistakes Class 10 ICSE Students Make in Maths
- Skipping the method label — failing to write “By section formula:” or “By componendo and dividendo:” before applying the formula costs ½–1 mark per question. Always state the method.
- Forgetting units in mensuration answers — volume in cm³, surface area in cm², height in cm. ½ mark deducted per missing unit.
- Calculation errors in Banking RD interest — the n(n+1)/2 term is the most-fumbled factor. Practise it on its own until automatic.
- Treating proportion properties as memorisation — componendo, dividendo, alternendo, invertendo are derivations, not mnemonics. Learn the algebraic derivation once.
- Not drawing rough sketches in coordinate geometry — even a freehand axis with rough point positions prevents sign errors in distance and section formulas.
- Forgetting to verify the discriminant before applying the quadratic formula — D < 0 means no real roots; missing this in Section A loses 1 mark.
- Mixing direct-method and step-deviation method in mean calculations — pick one method, label it, stick with it. Examiners deduct 1 mark for mixed working.
Related ICSE Resources
For chapter-by-chapter solved exercises, see the complete ICSE Class 10 Maths Selina Concise Solutions and the alternative ML Aggarwal Class 10 Solutions + RS Aggarwal Class 10 Solutions. For exam context: ICSE Class 10 syllabus 2026-27, all-subject previous year question papers, and the sister subjects Physics, Chemistry, Biology.
Frequently Asked Questions
Which textbook is best for ICSE Class 10 Maths 2026-27?
All three CISCE-recognised textbooks — Selina Concise Mathematics, ML Aggarwal Understanding ICSE Mathematics, and RS Aggarwal Mathematics — cover the identical syllabus. Selina is most concise and the closest in style to the actual board paper. ML Aggarwal has the broadest set of worked examples and is the strongest reference for the geometry block. RS Aggarwal has the largest number of exercise problems and is ideal for additional practice. The practical recommendation: study from Selina, drill from RS Aggarwal.
How long is the ICSE Class 10 Maths board exam?
The Maths theory paper is two and a half hours (150 minutes) long — half an hour longer than each of the Science papers — plus the standard 15-minute reading time at the start. The paper is worth 80 marks in writing and a further 20 marks come from school-assessed project work, totalling 100 marks.
Which chapter has the highest weightage in ICSE Class 10 Maths?
Empirically across 2017–2026 board papers, three chapters consistently lead in marks: Quadratic Equations + Problems on Quadratics (Ch 5–6) with 10–12 marks per paper, Circles + Tangents (Ch 17–18) with 8–10 marks, and Mensuration (Cylinder/Cone/Sphere, Ch 20) with 6–8 marks. Mastering these three blocks reliably secures 24–30 of the 80 theory marks before any other chapter is opened.
How do I score full marks on geometry constructions?
Four rules that recover most lost marks: (1) Always show rough construction lines lightly — examiners need to verify your method; do not erase them. (2) Label every constructed point with letters from the question — examiners cross-check labels against the question prompt. (3) Write the procedure in short steps next to the diagram. (4) Verify the construction with a measurement (radius, angle, length) and state it. The full procedure + diagram + verification together earn the full 4 marks; a clean diagram alone caps at 2–3.
Where can I download free ICSE Class 10 Maths past papers?
This page hosts CISCE-released board papers from 2017 through 2026 (paper code 511), specimen papers from 2023–2026, pre-board papers from 2023–2026, and term tests. All are free PDFs hosted on icseboard.org, organised in the past papers section above.
Does the ICSE Class 10 Maths exam allow calculators?
No. Non-programmable scientific calculators are not permitted in the Maths board exam. You will need to be fluent with manual arithmetic, including long multiplication, long division, square-root extraction by long method, and decimal-to-fraction conversion. The exam provides a four-place log table and a four-place natural-log table where needed (e.g., for the AP-sum-formula 100-term problem). Practise without a calculator from Week 1 of your preparation.
How is the 20-mark internal assessment evaluated?
The 20 IA marks are for a written project on a Maths topic of your choice, approved by your subject teacher. CISCE specifies that the project must demonstrate independent investigation: data collection or theoretical derivation, organised presentation with tables/diagrams, and a conclusion that ties back to the topic. The project is school-assessed by your Maths teacher against a CISCE-published rubric, with moderation by an external examiner. Start the project in Term 1 — leaving it to Term 2 is the most common reason students lose IA marks.