ICSE Class 10 Syllabus 2027 Mathematics

ICSE YEAR 2027

INDIAN CERTIFICATE OF
SECONDARY EDUCATION
EXAMINATION

MATHEMATICS
(51)

February 2025
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MISSION STATEMENT

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Examinations is committed to serving the nation's
children, through high quality educational
endeavours, empowering them to contribute towards
a humane, just and pluralistic society, promoting
introspective living, by creating exciting learning
opportunities, with a commitment to excellence.

ETHOS OF CISCE

Trust and fair play.
Minimum monitoring.
Allowing schools to evolve their own niche.
Catering to the needs of the children.
Giving freedom to experiment with new ideas
and practices.
Diversity and plurality - the basic strength for
evolution of ideas.
Schools to motivate pupils towards the
cultivation of:
Excellence - The Indian and Global
experience.
Values - Spiritual and cultural - to be the bedrock
of the educational experience.
Schools to have an 'Indian Ethos', strong roots in
the national psyche and be sensitive to national
aspirations.

CLASS X
There will be one paper of three hours duration • Algebraically and writing the
carrying 80 marks and Internal Assessment of 20 solution in set notation form.
marks.
• Representation of solution on the
Certain questions may require the use of number line.
Mathematical tables (Logarithmic and Trigonometric
tables). (ii) Quadratic Equations in one variable
(a) Nature of roots
1. Commercial Mathematics
• Two distinct real roots if b2 – 4ac >
(i) Goods and Services Tax (GST) 0
Computation of tax including problems • Two equal real roots if b2 – 4ac = 0
involving discounts, list-price, profit, loss,
basic/cost price including inverse cases. • No real roots if b2 – 4ac < 0
Candidates are also expected to find price (b) Solving Quadratic equations by:
paid by the consumer after paying State
Goods and Service Tax (SGST) and Central • Factorisation
Goods and Service Tax (CGST) - the • Using Formula.
different rates as in vogue on different types (c) Solving simple quadratic equation
of items will be provided. Problems based on problems.
corresponding inverse cases are also
included. (iii) Ratio and Proportion
(ii) Banking (a) Proportion, Continued proportion, mean
proportion
Recurring Deposit Accounts: computation of
interest and maturity value using the (b) Componendo, dividendo, alternendo,
formula: invertendo properties and their
combinations.
n(n + 1) r
I =P × (c) Direct simple applications on
2 ×12 100
proportions only.
MV = P x n + I
(iv) Factorisation of polynomials:
(iii) Shares and Dividends
(a) Factor Theorem.
(a) Face/Nominal Value, Market Value,
(b) Remainder Theorem.
Dividend, Rate of Dividend, Premium.
(b) Formulae (c) Factorising a polynomial completely
after obtaining one factor by factor
• Income = number of shares × rate of theorem.
dividend × FV.
Note: f (x) not to exceed degree 3.
• Return = (Income / Investment) × 100.
Note: Brokerage and fractional shares not (v) Matrices
included. (a) Order of a matrix. Row and column
2. Algebra matrices.
(i) Linear Inequations (b) Compatibility for addition and
multiplication.
Linear Inequations in one unknown for x ∈
N, W, Z, R. Solving: (c) Null and Identity matrices.
(d) Addition and subtraction of 2×2
matrices.

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(e) Multiplication of a 2×2 matrix by (ii) Comparison with congruency, keyword
being proportionality.
• a non-zero rational number
• a matrix. (iii) Three conditions: SSS, SAS, AA. Simple
applications (proof not included).
(vi) Arithmetic and Geometric Progression
(iv) Applications of Basic Proportionality
• Finding their General term. Theorem.
• Finding Sum of their first ‘n’ terms. (v) Areas of similar triangles are
• Simple Applications. proportional to the squares of
(vii) Co-ordinate Geometry corresponding sides.
(a) Reflection (vi) Direct applications based on the above
including applications to maps and
(i) Reflection of a point in a line:
models.
x=0, y =0, x= a, y=a, the origin.
(b) Loci
(ii) Reflection of a point in the origin.
Loci: Definition, meaning, Theorems and
(iii) Invariant points.
constructions based on Loci.
(b) Co-ordinates expressed as (x,y), Section
formula, Midpoint formula, Concept of (i) The locus of a point at a fixed distance
slope, equation of a line, Various forms from a fixed point is a circle with the
of straight lines. fixed point as centre and fixed distance
as radius.
(i) Section and Mid-point formula
(Internal section only, co-ordinates (ii) The locus of a point equidistant from two
of the centroid of a triangle intersecting lines is the bisector of the
included). angles between the lines.
(ii) Equation of a line: (iii) The locus of a point equidistant from two
given points is the perpendicular bisector
• Slope –intercept form y = mx + c
of the line joining the points.
• Two- point form (y-y 1 ) = m(x-x 1 )
Proofs not required.
• Geometric understanding of ‘m’
(c) Circles
as slope/ gradient/ tanθ where θ
is the angle the line makes with (i) Angle Properties
the positive direction of the x axis.
• The angle that an arc of a circle
• Geometric understanding of ‘c’ as subtends at the centre is double that
the y-intercept/the ordinate of the which it subtends at any point on the
point where the line intercepts the remaining part of the circle.
y axis/ the point on the line where
x=0. • Angles in the same segment of a
circle are equal (without proof).
• Conditions for two lines to be
parallel or perpendicular. • Angle in a semi-circle is a right
Simple applications of all the angle.
above. (ii) Cyclic Properties:
3. Geometry • Opposite angles of a cyclic
quadrilateral are supplementary.
(a) Similarity
• The exterior angle of a cyclic
Similarity, conditions of similar triangles. quadrilateral is equal to the opposite
(i) As a size transformation. interior angle (without proof).

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(iii) Tangent and Secant Properties: 5. Trigonometry
• The tangent at any point of a circle (a) Using Identities to solve/prove simple
and the radius through the point are algebraic trigonometric expressions
perpendicular to each other. sin2 A + cos2 A = 1
• If two circles touch, the point of 1 + tan2 A = sec2A
contact lies on the straight line
1+cot2A = cosec2A; 0 ≤ A ≤ 90°
joining their centres.
(b) Heights and distances: Solving 2-D problems
• From any point outside a circle, two involving angles of elevation and depression
tangents can be drawn, and they are using trigonometric tables.
equal in length.
Note: Cases involving more than two right
• If two chords intersect internally or angled triangles excluded.
externally then the product of the
lengths of the segments are equal. 6. Statistics
• If a chord and a tangent intersect Statistics – basic concepts, Mean, Median, Mode.
externally, then the product of the Histograms and Ogive.
lengths of segments of the chord is
equal to the square of the length of (a) Computation of:
the tangent from the point of contact • Measures of Central Tendency: Mean,
to the point of intersection. median, mode for raw and arrayed data.
Mean*, median class and modal class for
• If a line touches a circle and from the
grouped data. (both continuous and
point of contact, a chord is drawn,
discontinuous).
the angles between the tangent and
the chord are respectively equal to * Mean by all 3 methods included:
the angles in the corresponding
Direct : Σfx
alternate segments. Σf
Note: Proofs of the theorems given above
Σfd
are to be taught unless specified otherwise. Short-cut : A+ where d = x − A
Σf
(iv) Constructions
Step-deviation: A + Σft × i where t = x − A
(a) Construction of tangents to a circle Σf i
from an external point.
(b) Graphical Representation. Histograms and
(b) Circumscribing and inscribing a Less than Ogive.
circle on a triangle and a
regular hexagon. • Finding the mode from the histogram,
the upper quartile, lower Quartile and
4. Mensuration median etc. from the ogive.
• Calculation of inter Quartile range.
Area and volume of solids – Cylinder, Cone and
Sphere.
7. Probability
Three-dimensional solids - right circular Random experiments, Sample space, Events,
cylinder, right circular cone and sphere: Area definition of probability, Simple problems on
(total surface and curved surface) and Volume. single events.
Direct application problems including cost, Inner
and Outer volume and melting and recasting
method to find the volume or surface area of a
new solid. Combination of solids included.
Note: Problems on Frustum are not included.

ICSE Examination Year 2027 7

SI UNITS, SIGNS, SYMBOLS AND INTERNAL ASSESSMENT
ABBREVIATIONS
The minimum number of assignments: Two
(1) Agreed conventions assignments as prescribed by the teacher.
(a) Units may be written in full or using the Suggested Assignments
agreed symbols, but no other abbreviation
may be used. • Comparative newspaper coverage of different
items.
(b) The letter ‘s’ is never added to symbols to
indicate the plural form. • Survey of various types of Bank accounts,
(c) A full stop is not written after symbols for rates of interest offered.
units unless it occurs at the end of a sentence. • Planning a home budget.
(d) When unit symbols are combined as a • Conduct a survey in your locality to study the
quotient, e.g., metre per second, it is mode of conveyance / Price of various
recommended that it should be written as essential commodities / favourite sports.
m/s, or as m s-1. Represent the data using a bar graph /
(e) Three decimal signs are in common histogram and estimate the mode.
international use: the full point, the mid-point
and the comma. Since the full point is
• To use a newspaper to study and report on
shares and dividends.
sometimes used for multiplication and the
comma for spacing digits in large numbers, it • Set up a dropper with ink in it vertical at a
is recommended that the mid-point be used height say 20 cm above a horizontally placed
for decimals. sheet of plain paper. Release one ink drop;
(2) Names and symbols observe the pattern, if any, on the paper.
Vary the vertical distance and repeat.
In general Discover any pattern of relationship between
Implies that ⇒ is logically equivalent to ⇔ the vertical height and the ink drop observed.
Identically equal to ≡ is approximately equal to >>
• You are provided (or you construct a model
In set language
Belongs to ∈ does not belong to ∉ as shown) - three vertical sticks (size of a
is equivalent to ↔ is not equivalent to ↔ pencil) stuck to a horizontal board. You
union ∪ intersection ∩ should also have discs of varying sizes with
universal set ξ is contained in ⊂
natural (counting) Ν the empty set
holes (like a doughnut). Start with one disc;
ø
numbers whole numbers W
place it on (in) stick A. Transfer it to another
integers Ζ real numbers R stick (B or C); this is one move (m). Now try
In measures with two discs placed in A such that the large
Kilometre km Metre m disc is below, and the smaller disc is above
Centimetre cm Millimetre mm (number of discs = n=2 now). Now transfer
Kilogram kg Gram g
Litre L Centilitre cL them one at a time in B or C to obtain similar
square kilometre km2 Square meter m2 situation (larger disc below). How many
square centimetre cm2 Hectare ha moves? Try with more discs (n = 1, 2, 3,
cubic metre m3 Cubic centimetre cm3
etc.) and generalise.
kilometres per hour km/h Metres per second m/s

A B C

ICSE Examination Year 2027 8

• The board has some holes to hold marbles, red on • Find by construction the centre of a circle, using
one side and blue on the other. Start with one only a 60-30 setsquare and a pencil.
pair. Interchange the positions by making one
move at a time. A marble can jump over another • Various types of “cryptarithm”.
to fill the hole behind. The move (m) equal 3.
Try with 2 (n=2) and more. Find the relationship EVALUATION
between n and m. The assignments/project work are to be evaluated by
the subject teacher and by an External Examiner.
(The External Examiner may be a teacher nominated
by the Head of the school, who could be from the
faculty, but not teaching the subject in the
Red Blue
section/class. For example, a teacher of Mathematics
of Class VIII may be deputed to be an External
• Take a square sheet of paper of side 10 cm. Four Examiner for Class X, Mathematics projects.)
small squares are to be cut from the corners of
The Internal Examiner and the External Examiner
the square sheet and then the paper folded at the
will assess the assignments independently.
cuts to form an open box. What should be the
size of the squares cut so that the volume of the Award of Marks (20 Marks)
open box is maximum?
Subject Teacher (Internal Examiner) 10 marks
• Take an open box, four sets of marbles (ensuring External Examiner 10 marks
that marbles in each set are of the same size) and
some water. By placing the marbles and water The total marks obtained out of 20 are to be sent to
in the box, attempt to answer the question: do CISCE by the Head of the school.
larger marbles or smaller marbles occupy more The Head of the school will be responsible for the
volume in a given space? online entry of marks on CISCE’s CAREERS portal
• An eccentric artist says that the best paintings by the due date.
have the same area as their perimeter
(numerically). Let us not argue whether such
sizes increase the viewer’s appreciation, but only
try and find what sides (in integers only) a
rectangle must have if its area and perimeter are
to be equal (Note: there are only two such
rectangles).

ICSE Examination Year 2027 9

INTERNAL ASSESSMENT IN MATHEMATICS - GUIDELINES FOR MARKING WITH GRADES
Criteria Preparation Concepts Computation Presentation Understanding Marks

Grade I Exhibits and Admirable use of Careful and Presents well stated Shows strong personal 4 marks for
selects a well- mathematical concepts accurate work with conclusions; uses contribution; each
defined problem. and methods and appropriate effective mathematical demonstrate knowledge criterion
Appropriate use exhibits competency in computation, language, symbols, and understanding of
of techniques. using extensive range of construction and conventions, tables, assignment and can
mathematical measurement with diagrams, graphs, etc. apply the same in
techniques. correct units. different situations.
Grade II Exhibits and Appropriate use of Commits negligible Some statements of Neat with average 3 marks for
selects routine mathematical concepts errors in conclusions; uses amount of help; each
approach. and methods and shows computation, appropriate math assignment shows criterion
Fairly good adequate competency in construction and language, learning of mathematics
techniques. using limited range of measurement. symbols, conventions, with a limited ability to
techniques. tables, diagrams, use it.
graphs, etc.
Grade III Exhibits and Uses appropriate Commits a few Assignment is Lack of ability to 2 marks for
selects trivial mathematical concepts errors in presentable though it is conclude without help; each
problems. and shows competency computation, disorganized in some shows some learning of criterion
Satisfactory in using limited range construction and places. mathematics with a
techniques. of techniques. measurement. limited ability to use it.

Grade IV Exhibits and Uses inappropriate Commits many Presentation made is Lack of ability to 1 mark for
selects an mathematical concepts mistakes in somewhat disorganized conclude even with each
insignificant for the assignment. computation, and untidy. considerable help; criterion
problem. construction and assignment contributes
Uses some measurement. to mathematical learning
unsuitable to a certain extent.
techniques.
Grade V Exhibits and Not able to use Inaccurate Presentation made is Assignment does not 0 mark
selects a mathematical concepts. computation, completely contribute to
completely construction and disorganized, untidy mathematical learning
irrelevant measurement. and poor. and lacks practical
problem. applicability.
Uses unsuitable
techniques.

ICSE Examination Year 2027
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