ICSE Class 10 Mathematics Syllabus 2017 - 2018

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) Value Added Tax

Computation of tax including problems involving discounts, list-price, profit, loss,

basic/cost price including inverse cases.

(ii) Banking

Recurring Deposit Accounts: computation of interest using the formula:

n(n  1) r
IP 
2  12 100

MV = P × n + I

(iii) 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

www.topperlearning.com
 Mathematics CBSE Class 10 Mathematics Syllabus 2017 - 2018

2. Algebra
(i) Linear Inequations

Linear Inequations in one unknown for x  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) Nature of roots,

 Two distinct real roots if b2 – 4ac > 0

 Two equal real roots if b2 – 4ac = 0
 No real roots if b2 – 4ac < 0

(b) Solving Quadratic equations by:

 Factorisation
 Using Formula

(c) Solving simple quadratic equation problems.

(iii) Ratio and Proportion

(a) Proportion, Continued proportion, mean proportion

(b) Componendo and dividendo, alternendo and invertendo properties and their
combinations.
(c) Direct simple applications on proportions only.

(iv) Factorization of polynomials

(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.

www.topperlearning.com 2
 Mathematics CBSE Class 10 Mathematics Syllabus 2017 - 2018

(v) 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.

(vi) Arithmetic and Geometric Progression

 Finding their General term.
 Finding Sum of their first ‘n’ terms.
 Simple Applications.

(vii) Co-ordinate Geometry

(a) Reflection

(i) Reflection of a point in a line: x=0, y =0, x= a, y=a, the origin.

(ii) Reflection of a point in the origin.
(iii) Invariant points.

(b) 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.

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

(ii) Equation of a line:

 Slope –intercept form y = mx + c

 Two- point form (y - y1) = m(x - x1)

www.topperlearning.com 3
 Mathematics CBSE Class 10 Mathematics Syllabus 2017 - 2018

Geometric understanding of ‘m’ as slope/ gradient/ tan  where  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
(a) Similarity
(i) As a size transformation.

(ii) Comparison with congruency, keyword being proportionality.

(iii) Three conditions: SSS, SAS, AA. Simple applications (proof not included).

(iv) Applications of Basic Proportionality Theorem.

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

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

(b) Loci
Loci: Definition, meaning, Theorems based on Loci.
(i) The locus of a point equidistant from a fixed point is a circle with the fixed point as

centre.

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

between the lines.

(iii) The locus of a point equidistant from two given points is the perpendicular bisector

of the line joining the points.

Proofs not required.

www.topperlearning.com 4
 Mathematics CBSE Class 10 Mathematics Syllabus 2017 - 2018

(c) Circles

(i) Angle 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.

(ii) 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).

(iii) Tangent and Secant 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 two chords intersect internally or externally then the product of the lengths of the
segments are equal.
 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.

www.topperlearning.com 5
 Mathematics CBSE Class 10 Mathematics Syllabus 2017 - 2018

(iv) 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.

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

sin2A + cos2 A = 1
1 + tan2A = sec2A
1+cot2A = cosec2A; 0 ≤ A ≤ 90

(b) 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.

www.topperlearning.com 6
 Mathematics CBSE Class 10 Mathematics Syllabus 2017 - 2018

6. Statistics

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

(a) 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:

 fx
Direct :
f
 fd
Short-cut : A+ where d = x – A
f
 ft xA
Step-deviation : A  i, where t =
f i

(b) Graphical Representation. Histograms and Less than ogive.

 Finding the mode from the histogram, the upper quartile, lower Quartile and median
etc. from the ogive.
 Calculation of inter Quartile range.

7. Probability

 Random experiments

 Sample space

 Events

 Definition of probability

 Simple problems on single events

www.topperlearning.com 7