ICSE Class 9 Maths Syllabus & Exam Pattern: A Complete Guide

Units

Chapters

PDF’s

Unit 1

1. Rational And Irrational Numbers

2. Compound Interest

3. Expansions

4. Factorization

5. Linear Equations in Two Variables

6. Indices/Exponents

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Unit 2

7. Logarithms

8. Triangles

9. Mid Point And Intercept Theorem

10. Pythagoras Theorem

11. Rectilinear Fgures

12. Theorems on Areas of Parallelograms and Triangles

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Unit 3

13. Circles

14. Statistics

15. Mensuration

16. Trigonometry

17. Coordinate Geometry

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Particulars

Details

Total Marks

100 Marks

Theory Paper (External Exam)

80 Marks

Internal Assessment (Project Work)

20 Marks

Duration of Theory Paper

2.5 Hours

Passing Criteria

Generally 33% to 35% in aggregate (school-specific).

Section

Marks

Format & Focus

Preparation Strategy

Section A

40 Marks

Compulsory Short Answer Questions: Covers the entire syllabus. Often includes objective-type questions (MCQs, VSA, Fill-in-the-blanks) and short numerical problems.

Master fundamentals—ensure every topic is covered thoroughly as no choice is provided.

Section B

40 Marks

Descriptive/Long Answer Questions: Students are typically required to answer four questions out of seven offered (or a similar internal choice).

Strategic selection—identify and master strong chapters to attempt the chosen questions with maximum accuracy.

Unit

Major Topics & Subtopics

Key Focus Areas

1. Pure Arithmetic

Rational and Irrational Numbers: Real numbers, representation on a number line, Surds and Rationalisation of the denominator, proof of irrationality (e.g., $\sqrt{2},\sqrt{3}$).

Deep conceptual clarity on real numbers and operations with surds.

2. Commercial Mathematics

Compound Interest: Calculation of CI using the growing principal (Simple Interest method) and the formula $A=P{\left(1+\frac{R}{100}\right)}^n$. Interest compounded half-yearly, difference between CI and SI, Rate of growth and depreciation.

Numerical problem-solving involving the CI formula.

3. Algebra

Expansions (${\left(a\pm b\right)}^2,{\left(a\pm b\right)}^3,{\left(a\pm b\pm c\right)}^2$), Factorisation ($a^2-b^2,a^3\pm b^3$, splitting the middle term), Simultaneous Linear Equations (Elimination, Substitution, Cross-Multiplication), Indices/Exponents, and Logarithms (laws of logarithms, interchanging forms).

Proficiency in algebraic manipulations and logarithmic laws.

4. Geometry

The geometric shapes we will study will include triangles (congruency: SSS, SAS, AAS, RHS), properties of triangles (angles opposite equal sides, inequality theorems), the mid-point theorem and converses, the Pythagorean theorem (proof, application), rectilinear figures (parallelogram theorems, construction of polygons), and circles (chord and arc properties).

Proof-based questions and applications of theorems.

5. Statistics

Introduction to statistics, collection and presentation of data, Tabulation, Grouped Frequency Distributions (need for converting discontinuous intervals), Drawing a Histogram and Frequency Polygon, Mean and Median of ungrouped data.

Practical skills in drawing and interpreting statistical data.

6. Mensuration

Area & Perimeter of Triangles and Quadrilaterals (Square, Rhombus, Parallelogram, Trapezium), Area & Circumference of Circle, Surface Area & Volume of 3D solids (Cube and Cuboid), problems involving internal/external dimensions and cross-sections.

Application of formulae to complex 2D and 3D shapes.

7. Trigonometry

Trigonometric Ratios ($\sin ,\cos ,\tan ,\csc ,\sec ,\cot$), Ratios of Standard Angles ($0^{\circ },30^{\circ },45^{\circ },60^{\circ },90^{\circ }$), Simple 2-D problems involving one right-angled triangle, and Ratios of Complementary Angles.

Memorizing standard values and solving simple height and distance problems.

8. Co-ordinate Geometry

Cartesian System (plotting points), Graphical solution of Simultaneous Linear Equations, and Distance Formula between two points.

Accurate plotting and application of the distance formula.

Aspect

Details

Weightage

20 Marks (Added to 80 marks of Theory for a total of 100).

Modality

Subject teachers generally assign two to three projects/assignments during the academic year. Examples include: conducting surveys, models/charts on geometrical theorems, statistical data analysis, or detailed case studies on commercial maths applications (e.g., banking/investments).

Assessment Focus

Projects should demonstrate: Conceptual clarity, analytical ability, logical reasoning, and presentation skills (neatness, clarity, and quality of documentation).