ICSE Class 9 Syllabus 2027 Mathematics

ICSE YEAR 2027

INDIAN CERTIFICATE OF
SECONDARY EDUCATION
EXAMINATION

MATHEMATICS
(51)

February 2025
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endeavours, empowering them to contribute towards
a humane, just and pluralistic society, promoting
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Minimum monitoring.
Allowing schools to evolve their own niche.
Catering to the needs of the children.
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and practices.
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aspirations.

MATHEMATICS (51)

Aims:
1. To acquire knowledge and understanding of the 4. To develop the necessary skills to work with
terms, symbols, concepts, principles, processes, modern technological devices such as calculators
proofs, etc. of mathematics. and computers in real life situations.
2. To develop an understanding of mathematical 5. To develop drawing skills, skills of reading
concepts and their application to further studies tables, charts and graphs.
in mathematics and science. 6. To develop an interest in mathematics.
3. To develop skills to apply mathematical
knowledge to solve real life problems.

CLASS IX
There will be one paper of three hours duration • Using the formula to find one quantity
carrying 80 marks and Internal Assessment of 20 given different combinations of A, P, r, n,
marks. CI and SI; difference between CI and SI
Certain questions may require the use of type included. Rate of growth and
Mathematical tables (Logarithmic and Trigonometric depreciation.
tables). Note: Paying back in equal installments, being
The solution of a question may require the knowledge given rate of interest and installment
of more than one branch of the syllabus. amount, not included.

1. Pure Arithmetic 3. Algebra
Rational and Irrational Numbers (i) Expansions
Rational, irrational numbers as real numbers, Recall of concepts learned in earlier classes.
their place in the number system. Surds and (a ± b)2
rationalization of surds. Simplifying an
expression by rationalizing the denominator. (a ± b)3
Representation of rational and irrational (x ± a) (x ± b)
numbers on the number line.
(a ± b ± c)2
Proofs of irrationality of
(ii) Factorisation
2. Commercial Mathematics a 2 – b2
Compound Interest a3 ± b3
(a) Compound interest as a repeated Simple ax2 + bx + c, by splitting the middle term.
Interest computation with a growing
Principal. Use of this in computing Amount (iii) Simultaneous Linear Equations in two
over a period of 2 or 3 years. variables. (With numerical coefficients only)
(b) Use of formula n
. Finding CI • Solving algebraically by:
from the relation CI = A – P. - Elimination
• Interest compounded half-yearly included. - Substitution and

ICSE Examination Year 2027 1

- Cross Multiplication method (i) Proof and simple applications of mid-
point theorem and its converse.
• Solving simple problems by framing
appropriate equations. (ii) Equal intercept theorem: proof and
simple application.
(iv) Indices/ Exponents
(d) Pythagoras Theorem
Handling positive, fractional, negative and
“zero” indices. Area based proof and simple applications
of Pythagoras Theorem and its converse.
Simplification of expressions involving
various exponents (ii) Rectilinear Figures
(a) Proof and use of theorems on
etc. Use of laws of exponents. parallelogram.

(v) Logarithms • Both pairs of opposite sides equal
(without proof).
(a) Logarithmic form vis-à-vis exponential
form: interchanging. • Both pairs of opposite angles equal.
(b) Laws of Logarithms and their uses. • One pair of opposite sides equal and
Expansion of expression with the help of parallel (without proof).
laws of logarithms • Diagonals bisect each other and
4 2 bisect the parallelogram.
a ×b
e.g. y = • Rhombus as a special parallelogram
c3
whose diagonals meet at right angles.
log y = 4 log a + 2 log b – 3 log c etc.
• In a rectangle, diagonals are equal,
4. Geometry in a square they are equal and meet
at right angles.
(i) Triangles
(b) Constructions of Polygons
(a) Congruency: four cases: SSS, SAS,
Construction of quadrilaterals (including
AAS, and RHS. Illustration through
parallelograms and rhombus) and
cutouts. Simple applications.
regular hexagon using ruler and
(b) Problems based on: compasses only.
• Angles opposite equal sides are (c) Proof and use of Area theorems on
equal and converse. parallelograms:
• If two sides of a triangle are • Parallelograms on the same base
unequal, then the greater angle is and between the same parallels are
opposite the greater side and equal in area.
converse. • The area of a triangle is half that of
• Sum of any two sides of a triangle is a parallelogram on the same base
greater than the third side. and between the same parallels.
• Of all straight lines that can be • Triangles between the same base and
drawn to a given line from a point between the same parallels are equal
outside it, the perpendicular is the in area (without proof).
shortest. • Triangles with equal areas on the
Proofs not required. same bases have equal corresponding
(c) Mid-Point Theorem and its converse, altitudes.
equal intercept theorem

ICSE Examination Year 2027 2

(iii) Circle: 6. Mensuration
(a) Chord properties Area and perimeter of a triangle and a
quadrilateral. Area and circumference of circle.
• A straight line drawn from the centre Surface area and volume of Cube and Cuboids.
of a circle to bisect a chord which is
not a diameter is at right angles to (a) Area and perimeter of triangle (including
the chord. Heron’s formula), all types of
Quadrilaterals.
• The perpendicular to a chord from
the centre bisects the chord (without (b) Circle: Area and Circumference. Direct
proof). application problems including Inner and
Outer area.
• Equal chords are equidistant from
Areas of sectors of circles other than
the centre.
quarter-circle and semicircle are not
• Chords equidistant from the centre included.
are equal (without proof). (c) Surface area and volume of 3-D solids: cube
• There is one and only one circle that and cuboid including problems of type
passes through three given points not involving:
in a straight line. • Different internal and external
(b) Arc and chord properties: dimensions of the solid.

• If two arcs subtend equal angles at • Cost.
the centre, they are equal, and its • Concept of volume being equal to area of
converse. cross-section x height.
• If two chords are equal, they cut off • Open/closed cubes/cuboids.
equal arcs, and its converse (without
proof). 7. Trigonometry
Note: Proofs of the theorems given above (a) Trigonometric Ratios: sine, cosine, tangent
are to be taught unless specified otherwise. of an angle and their reciprocals.
(b) Trigonometric ratios of standard angles - 0,
5. Statistics 30, 45, 60, 90 degrees. Evaluation of an
Introduction, collection of data, presentation of expression involving these ratios.
data, Graphical representation of data, Mean, (c) Simple 2-D problems involving one
Median of ungrouped data. right-angled triangle.
(i) Understanding and recognition of raw, (d) Concept of trigonometric ratios of
arrayed and grouped data. complementary angles and their direct
(ii) Tabulation of raw data using tally-marks. application:
(iii) Understanding and recognition of discrete sin A = cos (90 - A), cos A = sin (90 – A)
and continuous variables.
tan A = cot (90 – A), cot A = tan (90- A)
(iv) Mean, median of ungrouped data.
sec A = cosec (90 – A), cosec A=sec (90 – A)
(v) Class intervals, class boundaries and limits,
frequency, frequency table, class size for 8. Coordinate Geometry
grouped data.
Cartesian System, plotting of points in the plane
(vi) Grouped frequency distributions: the need to
for given coordinates, solving simultaneous
and how to convert discontinuous intervals to
linear equations in 2 variables graphically and
continuous intervals.
finding the distance between two points using
(vii)Drawing a frequency polygon. distance formula.

ICSE Examination Year 2027 3

(a) Dependent and independent variables. • Running a tuck shop/canteen.
(b) Ordered pairs, coordinates of points and • Study ways of raising a loan to buy a car or
plotting them in the Cartesian plane. house, e.g. bank loan or purchase a refrigerator or
(c) Solution of Simultaneous Linear Equations a television set through hire purchase.
graphically. • Cutting a circle into equal sections of a small
(d) Distance formula. central angle to find the area of a circle by using
the formula A = πr2.
INTERNAL ASSESSMENT • To use flat cutouts to form cube, cuboids and
pyramids to obtain formulae for volume and total
A minimum of two assignments are to be done during
surface area.
the year as prescribed by the teacher.
Suggested Assignments • Draw a circle of radius r on a ½ cm graph paper,
and then on a 2 mm graph paper. Estimate the
• Conduct a survey of a group of students and area enclosed in each case by actually counting
represent it graphically - height, weight, number the squares. Now try out with circles of different
of family members, pocket money, etc. radii. Establish the pattern, if any, between the
• Planning delivery routes for a postman/milkman. two observed values and the theoretical value
(area = π r2). Any modifications?

ICSE Examination Year 2027 4