The Council for the
Indian School Certificate Examinations (abbreviated as CISCE) popularly known
as ICSE, is one of the best educational boards of India. Students of ICSE
board should know their syllabus of each subject as it is quite in-depth than
any other board of India. To score good marks in class 10 board examination, students
should study according to the syllabus. Students can download the pdf of the syllabus of mathematics class 9
and 10 from the link given in the bottom of this page.

**ICSE Mathematics Class
10 Syllabus**

There will be **one **paper of **two and a half
**hours duration carrying 80 marks and Internal Assessment of 20 marks.

The paper will be divided into **two **sections,
Section I (40 marks), Section II (40 marks).

**Section I: **Will consist of
compulsory short answer questions.

**Section II: **Candidates will be
required to answer **four **out of **seven **questions.

**1.
Commercial Mathematics**

** ****(i)
Compound Interest**

(a) Compound
interest as a repeated Simple Interest computation with a growing Principal.
Use of this in computing Amount over a period of 2 or 3-years.

(b) Use of formula A = P(1+ r/100)^{n}.
Finding CI from the relation CI = A – P.

Interest
compounded half-yearly included.

Using the formula to find one quantity
given different combinations of A, P, r, n, CI and SI; difference between CI
and SI type included.

Rate of growth and depreciation.

**Note:
**Paying
back in equal installments, being given rate of interest and installment
amount, **not included**.

**(ii) Sales Tax and Value Added Tax **

Computation of tax including problems involving discounts, list-price, profit, loss, basic/cost price including inverse cases.

**(iii)
Banking**

(a)
Savings Bank Accounts.

Types of accounts. Idea of savings Bank Account, computation of interest for a series of months.

(b)
Recurring Deposit Accounts:
computation of interest using the formula:

SI = P × n(n + 1)/(2 × 12) × r/100

**(iv) Shares and Dividends **

(a) Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium.

(b) Formulae

Income
= number of shares × rate of
dividend × FV.

Return = (Income / Investment) ×100.

**Note: **Brokerage and
fractional shares **not included **

**2.
Algebra **

**(i) Linear Inequations**

Linear Inequations in one unknown for x Ïµ N, W, Z, R. Solving

Algebraically
and writing the solution in set notation form.

Representation
of solution on the number line.

**(ii)
Quadratic Equations **

(a) Quadratic
equations in one unknown. Solving by:

Factorisation.

Formula.

(b) Nature of roots,

Two distinct real roots if b^{2} – 4ac >
0

Two equal real roots if b^{2} – 4ac = 0

No real roots if b^{2} – 4ac < 0

(c) Solving problems.

**(iii)
Reflection **

(a) Reflection of a point in a line:

x=0, y =0, x= a, y=a, the origin.

(b) Reflection of a point in the origin.

(c) Invariant points.

**(iv) Ratio and Proportion **

(a) Duplicate, triplicate, sub-duplicate, sub-triplicate, compounded ratios.

(b) Continued
proportion, mean proportion

(c) Componendo and
dividendo, alternendo and invertendo properties.

(d) Direct applications.

**(v) Factorisation **

(a) Factor Theorem.

(b) Remainder
Theorem.

(c) Factorising a polynomial completely after
obtaining one factor by factor theorem.

**Note:
**f (x)
not to exceed degree 3.

**(vi)
Matrices **

(a) Order of a
matrix. Row and column matrices.

(b) Compatibility
for addition and multiplication.

(c) Null and
Identity matrices.

(d) Addition and
subtraction of 2×2 matrices.

(e) Multiplication of a 2×2 matrix by

a
non-zero rational number

a matrix.

**(vii) Co-ordinate Geometry **

Co-ordinates expressed as (x, y) Distance between two points, section, and Midpoint formula, Concept of slope, equation of a line, Various forms of straight lines.

(a) Distance
formula.

(b) Section and
Mid-point formula (Internal section only, co-ordinates of the centroid of a
triangle included).

(c) Equation of a
line:

Slope
–intercept form y = mx + c

Two- point form _{1}) = m(x-x_{1})

Geometric understanding of ‘m’ as slope/ gradient/ tan Î¸ where Î¸ is the angle the line makes with the positive direction of the x axis.

Geometric understanding of c as the y-intercept/the
ordinate of the point where the line intercepts the y axis/ the point on the
line where x=0.

Conditions
for two lines to be parallel or perpendicular. Simple applications of all of
the above.

** **

**3. Geometry **

**(i)
Symmetry **

(a) Lines of
symmetry of an isosceles triangle, equilateral triangle, rhombus, square,
rectangle, pentagon, hexagon, octagon (all regular) and diamond-shaped figure.

(b) Being given a
figure, to draw its lines of symmetry. Being given part of one of the figures
listed above to draw the rest of the figure based on the given lines of
symmetry (neat recognizable free hand sketches acceptable).

**(ii) Similarity **

Axioms of similarity of triangles. Basic theorem of proportionality.

(a) Areas of similar
triangles are proportional to the squares on corresponding sides.

(b) Direct
applications based on the above including applications to maps and models.

**(iii) Loci **

Loci: Definition, meaning, Theorems based on Loci.

(a) The locus of a
point equidistant from a fixed point is a circle with the fixed point as
centre.

(b) The locus of a
point equidistant from two interacting lines is the bisector of the angles
between the lines.

(c) The locus of a point
equidistant from two given points is the perpendicular bisector of the line
joining the points.

**(iv)
Circles **

(a) Chord Properties:

A straight line drawn from the center of a circle to bisect a chord which is not a diameter is at right angles to the chord.

The perpendicular to a
chord from the center bisects the chord (without proof).

Equal chords are
equidistant from the center.

Chords equidistant from
the center are equal (without proof).

There is one and only
one circle that passes through three given points not in a straight line.

(b) Arc and chord properties:

The angle that an arc
of a circle subtends at the center is double that which it subtends at any
point on the remaining part of the circle.

Angles in the same
segment of a circle are equal (without proof).

Angle in a semi-circle
is a right angle.

If two arcs subtend
equal angles at the center, they are equal, and its converse.

If two chords are
equal, they cut off equal arcs, and its converse (without proof).

If two chords intersect
internally or externally then the product of the lengths of the segments are
equal.

(c) Cyclic Properties:

Opposite angles of a
cyclic quadrilateral are supplementary.

The exterior angle of a
cyclic quadrilateral is equal to the opposite interior angle (without proof).

(d) Tangent Properties:

The tangent at any point of a circle and the radius through the point
are perpendicular to each other.

If two circles touch, the point of contact lies on the straight line joining their centers.

From any point outside
a circle two tangents can be drawn and they are equal in length.

If a chord and a
tangent intersect externally, then the product of the lengths of segments of
the chord is equal to the square of the length of the tangent from the point of
contact to the point of intersection.

If a line touches a circle and from the point of contact, a chord is
drawn, the angles between the tangent and the chord are respectively equal to
the angles in the corresponding alternate segments.

**Note:
Proofs of the theorems given above are to be taught unless specified otherwise.
**

**(v)
Constructions **

(a)
Construction of tangents to a circle from an external point.

(b) Circumscribing and inscribing a circle on a triangle and a regular hexagon.

** **

**4.
Mensuration **

Area and circumference of circle, Area and volume of solids – cone, sphere.

(a) Circle: Area and Circumference.
Direct application problems including Inner and Outer area.

(b)
Three-dimensional solids - right circular cone and sphere: Area (total surface
and curved surface) and Volume. 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 two solids included.

**Note: **Frustum is
not included.

Areas of sectors of circles
other than quarter-circle and semicircle are not included.

** **

**5. Trigonometry **

(a)
Using Identities to solve/prove simple algebraic trigonometric expressions

sin^{2} A + cos^{2} A = 1

1 + tan^{2} A = sec^{2} A

1 + cot^{2} A = cosec^{2} A; 0 ≤ A ≤ 90˚

(b) Trigonometric ratios of complementary angles
and direct application:

sin A = cos(90 - A), cos A = sin(90 – A)

tan A = cot (90 – A), cot A = tan (90- A)

sec A = cosec (90 – A), cosec A = sec(90 – A)

(c) Heights and distances: Solving 2-D problems
involving angles of elevation and depression using trigonometric tables.

**Note:
**Cases
involving more than two right angled triangles excluded.

** **

**6.
Statistics **

Statistics – basic concepts, Histograms and Ogive, Mean, Median, Mode.

(a) Graphical
Representation. Histograms and ogives.

Finding
the mode from the histogram, the upper quartile, lower Quartile and median from
the ogive.

Calculation
of inter Quartile range.

(b) Computation of:

Measures of Central Tendency: Mean,
median, mode for raw and arrayed data. Mean*, median class and modal class for
grouped data. (both continuous and discontinuous).

* Mean by all 3 methods included:

**7.
Probability**

Random
experiments

Sample
space

Events

Definition of
probability

Simple problems on single events

(tossing of one or two
coins, throwing a die and selecting a student from a group)

**Note: SI
units, signs, symbols and abbreviations **

** **

**(1) Agreed
conventions **

(a) Units may be written in full or using the agreed symbols, but no other abbreviation may be used.

(b) The letter ‘s’ is never
added to symbols to indicate the plural form.

(c) A full stop is not
written after symbols for units unless it occurs at the end of a sentence.

(d) When unit symbols are
combined as a quotient, e.g. metre per second, it is recommended that they be
written as m/s, or as ms^{-1}.

(e) Three decimal signs are in common international use: the full
point, the mid-point and the comma. Since the full point is sometimes used for
multiplication and the comma for spacing digits in large numbers, it is
recommended that the mid-point be used for decimals.

**Download ICSE Mathematics Class
9 and 10 Syllabus**

Click on the following link to download the pdf of syllabus for ICSE mathematics class 9 and 10.

Download the Syllabus of ICSE Mathematics Class 9 and 10